From 0639dda9142d1cf047b07e61fb557e8877aba4d8 Mon Sep 17 00:00:00 2001 From: Enrico Tassi Date: Mon, 15 Jun 2009 09:36:46 +0000 Subject: [PATCH] tacticals are really tactics now, they have an AST at the same level of tactics. Parser/engine fixed accordingly. This allowed a better TPTP exportation --- helm/software/components/grafite/.depend.opt | 2 + .../software/components/grafite/grafiteAst.ml | 16 +++- .../components/grafite/grafiteAstPp.ml | 20 +++-- .../grafite_parser/grafiteParser.ml | 51 +++++++++-- .../components/tptp_grafite/tptp2grafite.ml | 33 +++---- .../matita/contribs/ng_TPTP/ALG005-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/ALG006-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/ALG007-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/BOO001-1.ma | 34 +++---- .../matita/contribs/ng_TPTP/BOO002-1.ma | 34 +++---- .../matita/contribs/ng_TPTP/BOO002-2.ma | 36 ++++---- .../matita/contribs/ng_TPTP/BOO003-2.ma | 54 +++++------ .../matita/contribs/ng_TPTP/BOO003-4.ma | 42 ++++----- .../matita/contribs/ng_TPTP/BOO004-2.ma | 54 +++++------ .../matita/contribs/ng_TPTP/BOO004-4.ma | 42 ++++----- .../matita/contribs/ng_TPTP/BOO005-2.ma | 54 +++++------ .../matita/contribs/ng_TPTP/BOO005-4.ma | 42 ++++----- .../matita/contribs/ng_TPTP/BOO006-2.ma | 54 +++++------ .../matita/contribs/ng_TPTP/BOO006-4.ma | 42 ++++----- .../matita/contribs/ng_TPTP/BOO007-2.ma | 58 ++++++------ .../matita/contribs/ng_TPTP/BOO007-4.ma | 46 +++++----- .../matita/contribs/ng_TPTP/BOO008-2.ma | 58 ++++++------ .../matita/contribs/ng_TPTP/BOO008-4.ma | 46 +++++----- .../matita/contribs/ng_TPTP/BOO009-2.ma | 56 ++++++------ .../matita/contribs/ng_TPTP/BOO009-4.ma | 44 ++++----- .../matita/contribs/ng_TPTP/BOO010-2.ma | 56 ++++++------ .../matita/contribs/ng_TPTP/BOO010-4.ma | 44 ++++----- .../matita/contribs/ng_TPTP/BOO011-2.ma | 52 +++++------ .../matita/contribs/ng_TPTP/BOO011-4.ma | 40 ++++----- .../matita/contribs/ng_TPTP/BOO012-2.ma | 54 +++++------ .../matita/contribs/ng_TPTP/BOO012-4.ma | 42 ++++----- .../matita/contribs/ng_TPTP/BOO013-2.ma | 66 +++++++------- .../matita/contribs/ng_TPTP/BOO013-4.ma | 48 +++++----- .../matita/contribs/ng_TPTP/BOO014-2.ma | 64 ++++++------- .../matita/contribs/ng_TPTP/BOO014-4.ma | 44 ++++----- .../matita/contribs/ng_TPTP/BOO015-2.ma | 64 ++++++------- .../matita/contribs/ng_TPTP/BOO015-4.ma | 44 ++++----- .../matita/contribs/ng_TPTP/BOO016-2.ma | 60 ++++++------- .../matita/contribs/ng_TPTP/BOO017-2.ma | 60 ++++++------- .../matita/contribs/ng_TPTP/BOO018-4.ma | 40 ++++----- .../matita/contribs/ng_TPTP/BOO019-1.ma | 34 +++---- .../matita/contribs/ng_TPTP/BOO021-1.ma | 40 ++++----- .../matita/contribs/ng_TPTP/BOO022-1.ma | 42 ++++----- .../matita/contribs/ng_TPTP/BOO023-1.ma | 44 ++++----- .../matita/contribs/ng_TPTP/BOO024-1.ma | 42 ++++----- .../matita/contribs/ng_TPTP/BOO025-1.ma | 42 ++++----- .../matita/contribs/ng_TPTP/BOO026-1.ma | 48 +++++----- .../matita/contribs/ng_TPTP/BOO027-1.ma | 34 +++---- .../matita/contribs/ng_TPTP/BOO028-1.ma | 46 +++++----- .../matita/contribs/ng_TPTP/BOO029-1.ma | 44 ++++----- .../matita/contribs/ng_TPTP/BOO030-1.ma | 34 +++---- .../matita/contribs/ng_TPTP/BOO031-1.ma | 52 +++++------ .../matita/contribs/ng_TPTP/BOO032-1.ma | 46 +++++----- .../matita/contribs/ng_TPTP/BOO033-1.ma | 36 ++++---- .../matita/contribs/ng_TPTP/BOO034-1.ma | 46 +++++----- .../matita/contribs/ng_TPTP/BOO067-1.ma | 38 ++++---- .../matita/contribs/ng_TPTP/BOO068-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/BOO069-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/BOO070-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/BOO071-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/BOO072-1.ma | 26 +++--- .../matita/contribs/ng_TPTP/BOO073-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/BOO074-1.ma | 26 +++--- .../matita/contribs/ng_TPTP/BOO075-1.ma | 22 ++--- .../matita/contribs/ng_TPTP/BOO076-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/BOO077-1.ma | 22 ++--- .../matita/contribs/ng_TPTP/BOO078-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/BOO079-1.ma | 22 ++--- .../matita/contribs/ng_TPTP/BOO080-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/BOO081-1.ma | 22 ++--- .../matita/contribs/ng_TPTP/BOO082-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/BOO083-1.ma | 22 ++--- .../matita/contribs/ng_TPTP/BOO084-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/BOO085-1.ma | 22 ++--- .../matita/contribs/ng_TPTP/BOO086-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/BOO087-1.ma | 22 ++--- .../matita/contribs/ng_TPTP/BOO088-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/BOO089-1.ma | 22 ++--- .../matita/contribs/ng_TPTP/BOO090-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/BOO091-1.ma | 22 ++--- .../matita/contribs/ng_TPTP/BOO092-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/BOO093-1.ma | 22 ++--- .../matita/contribs/ng_TPTP/BOO094-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/BOO095-1.ma | 22 ++--- .../matita/contribs/ng_TPTP/BOO096-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/BOO097-1.ma | 22 ++--- .../matita/contribs/ng_TPTP/BOO098-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/BOO099-1.ma | 22 ++--- .../matita/contribs/ng_TPTP/BOO100-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/BOO101-1.ma | 22 ++--- .../matita/contribs/ng_TPTP/BOO102-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/BOO103-1.ma | 22 ++--- .../matita/contribs/ng_TPTP/BOO104-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/BOO105-1.ma | 22 ++--- .../matita/contribs/ng_TPTP/BOO106-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/BOO107-1.ma | 22 ++--- .../matita/contribs/ng_TPTP/BOO108-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/COL001-1.ma | 33 ++++--- .../matita/contribs/ng_TPTP/COL001-2.ma | 45 +++++----- .../matita/contribs/ng_TPTP/COL002-1.ma | 41 +++++---- .../matita/contribs/ng_TPTP/COL002-4.ma | 38 ++++---- .../matita/contribs/ng_TPTP/COL002-5.ma | 38 ++++---- .../matita/contribs/ng_TPTP/COL003-1.ma | 33 ++++--- .../matita/contribs/ng_TPTP/COL003-2.ma | 32 +++---- .../matita/contribs/ng_TPTP/COL004-1.ma | 35 ++++---- .../matita/contribs/ng_TPTP/COL004-3.ma | 28 +++--- .../matita/contribs/ng_TPTP/COL005-1.ma | 33 ++++--- .../matita/contribs/ng_TPTP/COL006-1.ma | 33 ++++--- .../matita/contribs/ng_TPTP/COL006-5.ma | 30 +++---- .../matita/contribs/ng_TPTP/COL006-6.ma | 30 +++---- .../matita/contribs/ng_TPTP/COL006-7.ma | 30 +++---- .../matita/contribs/ng_TPTP/COL007-1.ma | 27 +++--- .../matita/contribs/ng_TPTP/COL008-1.ma | 33 ++++--- .../matita/contribs/ng_TPTP/COL009-1.ma | 33 ++++--- .../matita/contribs/ng_TPTP/COL010-1.ma | 33 ++++--- .../matita/contribs/ng_TPTP/COL011-1.ma | 33 ++++--- .../matita/contribs/ng_TPTP/COL012-1.ma | 27 +++--- .../matita/contribs/ng_TPTP/COL013-1.ma | 33 ++++--- .../matita/contribs/ng_TPTP/COL014-1.ma | 31 ++++--- .../matita/contribs/ng_TPTP/COL015-1.ma | 33 ++++--- .../matita/contribs/ng_TPTP/COL016-1.ma | 37 ++++---- .../matita/contribs/ng_TPTP/COL017-1.ma | 37 ++++---- .../matita/contribs/ng_TPTP/COL018-1.ma | 37 ++++---- .../matita/contribs/ng_TPTP/COL019-1.ma | 37 ++++---- .../matita/contribs/ng_TPTP/COL020-1.ma | 37 ++++---- .../matita/contribs/ng_TPTP/COL021-1.ma | 37 ++++---- .../matita/contribs/ng_TPTP/COL022-1.ma | 37 ++++---- .../matita/contribs/ng_TPTP/COL023-1.ma | 33 ++++--- .../matita/contribs/ng_TPTP/COL024-1.ma | 37 ++++---- .../matita/contribs/ng_TPTP/COL025-1.ma | 33 ++++--- .../matita/contribs/ng_TPTP/COL026-1.ma | 33 ++++--- .../matita/contribs/ng_TPTP/COL027-1.ma | 33 ++++--- .../matita/contribs/ng_TPTP/COL029-1.ma | 27 +++--- .../matita/contribs/ng_TPTP/COL030-1.ma | 33 ++++--- .../matita/contribs/ng_TPTP/COL031-1.ma | 31 ++++--- .../matita/contribs/ng_TPTP/COL032-1.ma | 33 ++++--- .../matita/contribs/ng_TPTP/COL033-1.ma | 37 ++++---- .../matita/contribs/ng_TPTP/COL034-1.ma | 37 ++++---- .../matita/contribs/ng_TPTP/COL035-1.ma | 37 ++++---- .../matita/contribs/ng_TPTP/COL036-1.ma | 37 ++++---- .../matita/contribs/ng_TPTP/COL037-1.ma | 37 ++++---- .../matita/contribs/ng_TPTP/COL038-1.ma | 37 ++++---- .../matita/contribs/ng_TPTP/COL039-1.ma | 37 ++++---- .../matita/contribs/ng_TPTP/COL041-1.ma | 37 ++++---- .../matita/contribs/ng_TPTP/COL042-1.ma | 33 ++++--- .../matita/contribs/ng_TPTP/COL042-6.ma | 30 +++---- .../matita/contribs/ng_TPTP/COL042-7.ma | 30 +++---- .../matita/contribs/ng_TPTP/COL042-8.ma | 30 +++---- .../matita/contribs/ng_TPTP/COL042-9.ma | 30 +++---- .../matita/contribs/ng_TPTP/COL043-1.ma | 33 ++++--- .../matita/contribs/ng_TPTP/COL043-3.ma | 30 +++---- .../matita/contribs/ng_TPTP/COL044-1.ma | 33 ++++--- .../matita/contribs/ng_TPTP/COL044-6.ma | 30 +++---- .../matita/contribs/ng_TPTP/COL044-7.ma | 30 +++---- .../matita/contribs/ng_TPTP/COL044-8.ma | 30 +++---- .../matita/contribs/ng_TPTP/COL044-9.ma | 30 +++---- .../matita/contribs/ng_TPTP/COL045-1.ma | 37 ++++---- .../matita/contribs/ng_TPTP/COL046-1.ma | 37 ++++---- .../matita/contribs/ng_TPTP/COL047-1.ma | 33 ++++--- .../matita/contribs/ng_TPTP/COL048-1.ma | 37 ++++---- .../matita/contribs/ng_TPTP/COL049-1.ma | 37 ++++---- .../matita/contribs/ng_TPTP/COL050-1.ma | 33 ++++--- .../matita/contribs/ng_TPTP/COL051-1.ma | 31 ++++--- .../matita/contribs/ng_TPTP/COL052-1.ma | 39 ++++---- .../matita/contribs/ng_TPTP/COL053-1.ma | 37 ++++---- .../matita/contribs/ng_TPTP/COL056-1.ma | 46 +++++----- .../matita/contribs/ng_TPTP/COL057-1.ma | 41 +++++---- .../matita/contribs/ng_TPTP/COL058-1.ma | 27 +++--- .../matita/contribs/ng_TPTP/COL058-2.ma | 18 ++-- .../matita/contribs/ng_TPTP/COL058-3.ma | 18 ++-- .../matita/contribs/ng_TPTP/COL060-1.ma | 37 ++++---- .../matita/contribs/ng_TPTP/COL060-2.ma | 30 +++---- .../matita/contribs/ng_TPTP/COL060-3.ma | 30 +++---- .../matita/contribs/ng_TPTP/COL061-1.ma | 37 ++++---- .../matita/contribs/ng_TPTP/COL061-2.ma | 30 +++---- .../matita/contribs/ng_TPTP/COL061-3.ma | 30 +++---- .../matita/contribs/ng_TPTP/COL062-1.ma | 37 ++++---- .../matita/contribs/ng_TPTP/COL062-2.ma | 30 +++---- .../matita/contribs/ng_TPTP/COL062-3.ma | 30 +++---- .../matita/contribs/ng_TPTP/COL063-1.ma | 37 ++++---- .../matita/contribs/ng_TPTP/COL063-2.ma | 30 +++---- .../matita/contribs/ng_TPTP/COL063-3.ma | 30 +++---- .../matita/contribs/ng_TPTP/COL063-4.ma | 30 +++---- .../matita/contribs/ng_TPTP/COL063-5.ma | 30 +++---- .../matita/contribs/ng_TPTP/COL063-6.ma | 30 +++---- .../matita/contribs/ng_TPTP/COL064-1.ma | 37 ++++---- .../matita/contribs/ng_TPTP/COL064-2.ma | 30 +++---- .../matita/contribs/ng_TPTP/COL064-3.ma | 30 +++---- .../matita/contribs/ng_TPTP/COL064-4.ma | 30 +++---- .../matita/contribs/ng_TPTP/COL064-5.ma | 30 +++---- .../matita/contribs/ng_TPTP/COL064-6.ma | 30 +++---- .../matita/contribs/ng_TPTP/COL064-7.ma | 30 +++---- .../matita/contribs/ng_TPTP/COL064-8.ma | 30 +++---- .../matita/contribs/ng_TPTP/COL064-9.ma | 30 +++---- .../matita/contribs/ng_TPTP/COL065-1.ma | 39 ++++---- .../matita/contribs/ng_TPTP/COL066-1.ma | 41 +++++---- .../matita/contribs/ng_TPTP/COL066-2.ma | 34 +++---- .../matita/contribs/ng_TPTP/COL066-3.ma | 34 +++---- .../matita/contribs/ng_TPTP/COL067-1.ma | 33 ++++--- .../matita/contribs/ng_TPTP/COL068-1.ma | 33 ++++--- .../matita/contribs/ng_TPTP/COL069-1.ma | 33 ++++--- .../matita/contribs/ng_TPTP/COL070-1.ma | 33 ++++--- .../matita/contribs/ng_TPTP/COL071-1.ma | 33 ++++--- .../matita/contribs/ng_TPTP/COL073-1.ma | 33 ++++--- .../matita/contribs/ng_TPTP/COL075-2.ma | 35 ++++---- .../matita/contribs/ng_TPTP/COL083-1.ma | 40 ++++----- .../matita/contribs/ng_TPTP/COL084-1.ma | 40 ++++----- .../matita/contribs/ng_TPTP/COL085-1.ma | 34 ++++--- .../matita/contribs/ng_TPTP/COL086-1.ma | 34 ++++--- .../matita/contribs/ng_TPTP/COL087-1.ma | 33 ++++--- .../matita/contribs/ng_TPTP/GRP001-2.ma | 40 ++++----- .../matita/contribs/ng_TPTP/GRP001-4.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP002-2.ma | 56 ++++++------ .../matita/contribs/ng_TPTP/GRP002-3.ma | 36 ++++---- .../matita/contribs/ng_TPTP/GRP002-4.ma | 40 ++++----- .../matita/contribs/ng_TPTP/GRP010-4.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP011-4.ma | 34 +++---- .../matita/contribs/ng_TPTP/GRP012-4.ma | 34 +++---- .../matita/contribs/ng_TPTP/GRP014-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP022-2.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP023-2.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP024-5.ma | 38 ++++---- .../matita/contribs/ng_TPTP/GRP114-1.ma | 70 +++++++-------- .../matita/contribs/ng_TPTP/GRP115-1.ma | 22 ++--- .../matita/contribs/ng_TPTP/GRP116-1.ma | 22 ++--- .../matita/contribs/ng_TPTP/GRP117-1.ma | 22 ++--- .../matita/contribs/ng_TPTP/GRP118-1.ma | 26 +++--- .../matita/contribs/ng_TPTP/GRP119-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/GRP120-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/GRP121-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/GRP122-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP136-1.ma | 62 ++++++------- .../matita/contribs/ng_TPTP/GRP137-1.ma | 62 ++++++------- .../matita/contribs/ng_TPTP/GRP138-1.ma | 64 ++++++------- .../matita/contribs/ng_TPTP/GRP139-1.ma | 64 ++++++------- .../matita/contribs/ng_TPTP/GRP140-1.ma | 64 ++++++------- .../matita/contribs/ng_TPTP/GRP141-1.ma | 64 ++++++------- .../matita/contribs/ng_TPTP/GRP142-1.ma | 58 ++++++------ .../matita/contribs/ng_TPTP/GRP143-1.ma | 58 ++++++------ .../matita/contribs/ng_TPTP/GRP144-1.ma | 58 ++++++------ .../matita/contribs/ng_TPTP/GRP145-1.ma | 58 ++++++------ .../matita/contribs/ng_TPTP/GRP146-1.ma | 64 ++++++------- .../matita/contribs/ng_TPTP/GRP147-1.ma | 64 ++++++------- .../matita/contribs/ng_TPTP/GRP148-1.ma | 64 ++++++------- .../matita/contribs/ng_TPTP/GRP149-1.ma | 64 ++++++------- .../matita/contribs/ng_TPTP/GRP150-1.ma | 58 ++++++------ .../matita/contribs/ng_TPTP/GRP151-1.ma | 58 ++++++------ .../matita/contribs/ng_TPTP/GRP152-1.ma | 58 ++++++------ .../matita/contribs/ng_TPTP/GRP153-1.ma | 58 ++++++------ .../matita/contribs/ng_TPTP/GRP154-1.ma | 62 ++++++------- .../matita/contribs/ng_TPTP/GRP155-1.ma | 62 ++++++------- .../matita/contribs/ng_TPTP/GRP156-1.ma | 62 ++++++------- .../matita/contribs/ng_TPTP/GRP157-1.ma | 62 ++++++------- .../matita/contribs/ng_TPTP/GRP158-1.ma | 62 ++++++------- .../matita/contribs/ng_TPTP/GRP159-1.ma | 62 ++++++------- .../matita/contribs/ng_TPTP/GRP160-1.ma | 56 ++++++------ .../matita/contribs/ng_TPTP/GRP161-1.ma | 56 ++++++------ .../matita/contribs/ng_TPTP/GRP162-1.ma | 64 ++++++------- .../matita/contribs/ng_TPTP/GRP163-1.ma | 64 ++++++------- .../matita/contribs/ng_TPTP/GRP164-1.ma | 60 ++++++------- .../matita/contribs/ng_TPTP/GRP164-2.ma | 60 ++++++------- .../matita/contribs/ng_TPTP/GRP165-1.ma | 58 ++++++------ .../matita/contribs/ng_TPTP/GRP165-2.ma | 58 ++++++------ .../matita/contribs/ng_TPTP/GRP166-1.ma | 62 ++++++------- .../matita/contribs/ng_TPTP/GRP166-2.ma | 62 ++++++------- .../matita/contribs/ng_TPTP/GRP166-3.ma | 62 ++++++------- .../matita/contribs/ng_TPTP/GRP166-4.ma | 62 ++++++------- .../matita/contribs/ng_TPTP/GRP167-1.ma | 68 +++++++------- .../matita/contribs/ng_TPTP/GRP167-2.ma | 74 +++++++-------- .../matita/contribs/ng_TPTP/GRP167-3.ma | 56 ++++++------ .../matita/contribs/ng_TPTP/GRP167-4.ma | 62 ++++++------- .../matita/contribs/ng_TPTP/GRP167-5.ma | 74 +++++++-------- .../matita/contribs/ng_TPTP/GRP168-1.ma | 62 ++++++------- .../matita/contribs/ng_TPTP/GRP168-2.ma | 62 ++++++------- .../matita/contribs/ng_TPTP/GRP169-1.ma | 60 ++++++------- .../matita/contribs/ng_TPTP/GRP169-2.ma | 60 ++++++------- .../matita/contribs/ng_TPTP/GRP170-1.ma | 66 +++++++------- .../matita/contribs/ng_TPTP/GRP170-2.ma | 66 +++++++------- .../matita/contribs/ng_TPTP/GRP170-3.ma | 66 +++++++------- .../matita/contribs/ng_TPTP/GRP170-4.ma | 66 +++++++------- .../matita/contribs/ng_TPTP/GRP171-1.ma | 62 ++++++------- .../matita/contribs/ng_TPTP/GRP171-2.ma | 62 ++++++------- .../matita/contribs/ng_TPTP/GRP172-1.ma | 62 ++++++------- .../matita/contribs/ng_TPTP/GRP172-2.ma | 62 ++++++------- .../matita/contribs/ng_TPTP/GRP173-1.ma | 60 ++++++------- .../matita/contribs/ng_TPTP/GRP174-1.ma | 60 ++++++------- .../matita/contribs/ng_TPTP/GRP175-1.ma | 60 ++++++------- .../matita/contribs/ng_TPTP/GRP175-2.ma | 60 ++++++------- .../matita/contribs/ng_TPTP/GRP175-3.ma | 60 ++++++------- .../matita/contribs/ng_TPTP/GRP175-4.ma | 60 ++++++------- .../matita/contribs/ng_TPTP/GRP176-1.ma | 62 ++++++------- .../matita/contribs/ng_TPTP/GRP176-2.ma | 64 ++++++------- .../matita/contribs/ng_TPTP/GRP177-1.ma | 66 +++++++------- .../matita/contribs/ng_TPTP/GRP177-2.ma | 66 +++++++------- .../matita/contribs/ng_TPTP/GRP178-1.ma | 68 +++++++------- .../matita/contribs/ng_TPTP/GRP178-2.ma | 68 +++++++------- .../matita/contribs/ng_TPTP/GRP179-1.ma | 58 ++++++------ .../matita/contribs/ng_TPTP/GRP179-2.ma | 56 ++++++------ .../matita/contribs/ng_TPTP/GRP179-3.ma | 62 ++++++------- .../matita/contribs/ng_TPTP/GRP180-1.ma | 58 ++++++------ .../matita/contribs/ng_TPTP/GRP180-2.ma | 64 ++++++------- .../matita/contribs/ng_TPTP/GRP181-1.ma | 64 ++++++------- .../matita/contribs/ng_TPTP/GRP181-2.ma | 70 +++++++-------- .../matita/contribs/ng_TPTP/GRP181-3.ma | 68 +++++++------- .../matita/contribs/ng_TPTP/GRP181-4.ma | 74 +++++++-------- .../matita/contribs/ng_TPTP/GRP182-1.ma | 56 ++++++------ .../matita/contribs/ng_TPTP/GRP182-2.ma | 62 ++++++------- .../matita/contribs/ng_TPTP/GRP182-3.ma | 56 ++++++------ .../matita/contribs/ng_TPTP/GRP182-4.ma | 62 ++++++------- .../matita/contribs/ng_TPTP/GRP183-1.ma | 56 ++++++------ .../matita/contribs/ng_TPTP/GRP183-2.ma | 62 ++++++------- .../matita/contribs/ng_TPTP/GRP183-3.ma | 56 ++++++------ .../matita/contribs/ng_TPTP/GRP183-4.ma | 62 ++++++------- .../matita/contribs/ng_TPTP/GRP184-1.ma | 56 ++++++------ .../matita/contribs/ng_TPTP/GRP184-2.ma | 62 ++++++------- .../matita/contribs/ng_TPTP/GRP184-3.ma | 56 ++++++------ .../matita/contribs/ng_TPTP/GRP184-4.ma | 66 +++++++------- .../matita/contribs/ng_TPTP/GRP185-1.ma | 58 ++++++------ .../matita/contribs/ng_TPTP/GRP185-2.ma | 64 ++++++------- .../matita/contribs/ng_TPTP/GRP185-3.ma | 58 ++++++------ .../matita/contribs/ng_TPTP/GRP185-4.ma | 64 ++++++------- .../matita/contribs/ng_TPTP/GRP186-1.ma | 58 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.../matita/contribs/ng_TPTP/GRP200-1.ma | 50 +++++------ .../matita/contribs/ng_TPTP/GRP201-1.ma | 50 +++++------ .../matita/contribs/ng_TPTP/GRP202-1.ma | 50 +++++------ .../matita/contribs/ng_TPTP/GRP203-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP204-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP205-1.ma | 50 +++++------ .../matita/contribs/ng_TPTP/GRP206-1.ma | 50 +++++------ .../matita/contribs/ng_TPTP/GRP207-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP403-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/GRP404-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/GRP405-1.ma | 26 +++--- .../matita/contribs/ng_TPTP/GRP406-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/GRP407-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/GRP408-1.ma | 26 +++--- .../matita/contribs/ng_TPTP/GRP409-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/GRP410-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/GRP411-1.ma | 26 +++--- .../matita/contribs/ng_TPTP/GRP412-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/GRP413-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/GRP414-1.ma | 26 +++--- .../matita/contribs/ng_TPTP/GRP415-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/GRP416-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/GRP417-1.ma | 26 +++--- .../matita/contribs/ng_TPTP/GRP418-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/GRP419-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/GRP420-1.ma | 26 +++--- .../matita/contribs/ng_TPTP/GRP421-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/GRP422-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/GRP423-1.ma | 26 +++--- .../matita/contribs/ng_TPTP/GRP424-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/GRP425-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/GRP426-1.ma | 26 +++--- .../matita/contribs/ng_TPTP/GRP427-1.ma | 26 +++--- .../matita/contribs/ng_TPTP/GRP428-1.ma | 26 +++--- .../matita/contribs/ng_TPTP/GRP429-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP430-1.ma | 26 +++--- .../matita/contribs/ng_TPTP/GRP431-1.ma | 26 +++--- .../matita/contribs/ng_TPTP/GRP432-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP433-1.ma | 26 +++--- .../matita/contribs/ng_TPTP/GRP434-1.ma | 26 +++--- .../matita/contribs/ng_TPTP/GRP435-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP436-1.ma | 26 +++--- .../matita/contribs/ng_TPTP/GRP437-1.ma | 26 +++--- .../matita/contribs/ng_TPTP/GRP438-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP439-1.ma | 26 +++--- .../matita/contribs/ng_TPTP/GRP440-1.ma | 26 +++--- .../matita/contribs/ng_TPTP/GRP441-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP442-1.ma | 26 +++--- .../matita/contribs/ng_TPTP/GRP443-1.ma | 26 +++--- .../matita/contribs/ng_TPTP/GRP444-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP445-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP446-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP447-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP448-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP449-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP450-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP451-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP452-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP453-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP454-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP455-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP456-1.ma | 36 ++++---- .../matita/contribs/ng_TPTP/GRP457-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP458-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP459-1.ma | 36 ++++---- .../matita/contribs/ng_TPTP/GRP460-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP461-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP462-1.ma | 36 ++++---- .../matita/contribs/ng_TPTP/GRP463-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP464-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP465-1.ma | 36 ++++---- .../matita/contribs/ng_TPTP/GRP466-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP467-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP468-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP469-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP470-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP471-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP472-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP473-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP474-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP475-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP476-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP477-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP478-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP479-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP480-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP481-1.ma | 34 +++---- .../matita/contribs/ng_TPTP/GRP482-1.ma | 34 +++---- .../matita/contribs/ng_TPTP/GRP483-1.ma | 38 ++++---- .../matita/contribs/ng_TPTP/GRP484-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP485-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP486-1.ma | 36 ++++---- .../matita/contribs/ng_TPTP/GRP487-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP488-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP489-1.ma | 36 ++++---- .../matita/contribs/ng_TPTP/GRP490-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP491-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP492-1.ma | 36 ++++---- .../matita/contribs/ng_TPTP/GRP493-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP494-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP495-1.ma | 36 ++++---- .../matita/contribs/ng_TPTP/GRP496-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP497-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP498-1.ma | 36 ++++---- .../matita/contribs/ng_TPTP/GRP499-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP500-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP501-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP502-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP503-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP504-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP505-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP506-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP507-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP508-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP509-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/GRP510-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/GRP511-1.ma | 26 +++--- .../matita/contribs/ng_TPTP/GRP512-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/GRP513-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/GRP514-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/GRP515-1.ma | 26 +++--- .../matita/contribs/ng_TPTP/GRP516-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/GRP517-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/GRP518-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/GRP519-1.ma | 26 +++--- .../matita/contribs/ng_TPTP/GRP520-1.ma | 24 ++--- .../matita/contribs/ng_TPTP/GRP521-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP522-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP523-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP524-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP525-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP526-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP527-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP528-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP529-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP530-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP531-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP532-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP533-1.ma | 34 +++---- .../matita/contribs/ng_TPTP/GRP534-1.ma | 34 +++---- .../matita/contribs/ng_TPTP/GRP535-1.ma | 36 ++++---- .../matita/contribs/ng_TPTP/GRP536-1.ma | 34 +++---- .../matita/contribs/ng_TPTP/GRP537-1.ma | 34 +++---- .../matita/contribs/ng_TPTP/GRP538-1.ma | 34 +++---- .../matita/contribs/ng_TPTP/GRP539-1.ma | 36 ++++---- .../matita/contribs/ng_TPTP/GRP540-1.ma | 34 +++---- .../matita/contribs/ng_TPTP/GRP541-1.ma | 34 +++---- .../matita/contribs/ng_TPTP/GRP542-1.ma | 34 +++---- .../matita/contribs/ng_TPTP/GRP543-1.ma | 36 ++++---- .../matita/contribs/ng_TPTP/GRP544-1.ma | 34 +++---- .../matita/contribs/ng_TPTP/GRP545-1.ma | 34 +++---- .../matita/contribs/ng_TPTP/GRP546-1.ma | 34 +++---- .../matita/contribs/ng_TPTP/GRP547-1.ma | 36 ++++---- .../matita/contribs/ng_TPTP/GRP548-1.ma | 34 +++---- .../matita/contribs/ng_TPTP/GRP549-1.ma | 34 +++---- .../matita/contribs/ng_TPTP/GRP550-1.ma | 34 +++---- .../matita/contribs/ng_TPTP/GRP551-1.ma | 36 ++++---- .../matita/contribs/ng_TPTP/GRP552-1.ma | 34 +++---- .../matita/contribs/ng_TPTP/GRP553-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP554-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP555-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP556-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP557-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP558-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP559-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP560-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP561-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP562-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP563-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP564-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP565-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP566-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP567-1.ma | 36 ++++---- .../matita/contribs/ng_TPTP/GRP568-1.ma | 34 +++---- .../matita/contribs/ng_TPTP/GRP569-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP570-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP571-1.ma | 36 ++++---- .../matita/contribs/ng_TPTP/GRP572-1.ma | 34 +++---- .../matita/contribs/ng_TPTP/GRP573-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP574-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP575-1.ma | 36 ++++---- .../matita/contribs/ng_TPTP/GRP576-1.ma | 34 +++---- .../matita/contribs/ng_TPTP/GRP577-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP578-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP579-1.ma | 36 ++++---- .../matita/contribs/ng_TPTP/GRP580-1.ma | 34 +++---- .../matita/contribs/ng_TPTP/GRP581-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP582-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/GRP583-1.ma | 36 ++++---- .../matita/contribs/ng_TPTP/GRP584-1.ma | 34 +++---- .../matita/contribs/ng_TPTP/GRP585-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP586-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP587-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP588-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP589-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP590-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP591-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP592-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP593-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP594-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP595-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP596-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP597-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP598-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP599-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP600-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP601-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP602-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP603-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP604-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP605-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP606-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP607-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP608-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP609-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP610-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP611-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP612-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP613-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP614-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/GRP615-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/GRP616-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/LAT006-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/LAT007-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/LAT008-1.ma | 26 +++--- .../matita/contribs/ng_TPTP/LAT009-1.ma | 42 ++++----- .../matita/contribs/ng_TPTP/LAT010-1.ma | 50 +++++------ .../matita/contribs/ng_TPTP/LAT011-1.ma | 50 +++++------ .../matita/contribs/ng_TPTP/LAT012-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/LAT013-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/LAT014-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/LAT016-1.ma | 48 +++++----- .../matita/contribs/ng_TPTP/LAT017-1.ma | 48 +++++----- .../matita/contribs/ng_TPTP/LAT018-1.ma | 48 +++++----- .../matita/contribs/ng_TPTP/LAT019-1.ma | 42 ++++----- .../matita/contribs/ng_TPTP/LAT020-1.ma | 42 ++++----- .../matita/contribs/ng_TPTP/LAT021-1.ma | 42 ++++----- .../matita/contribs/ng_TPTP/LAT022-1.ma | 42 ++++----- .../matita/contribs/ng_TPTP/LAT023-1.ma | 42 ++++----- .../matita/contribs/ng_TPTP/LAT024-1.ma | 50 +++++------ .../matita/contribs/ng_TPTP/LAT025-1.ma | 52 +++++------ .../matita/contribs/ng_TPTP/LAT026-1.ma | 38 ++++---- .../matita/contribs/ng_TPTP/LAT027-1.ma | 38 ++++---- .../matita/contribs/ng_TPTP/LAT028-1.ma | 44 ++++----- 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| 60 ++++++------- .../matita/contribs/ng_TPTP/RNG025-7.ma | 74 +++++++-------- .../matita/contribs/ng_TPTP/RNG025-8.ma | 70 +++++++-------- .../matita/contribs/ng_TPTP/RNG025-9.ma | 84 ++++++++--------- .../matita/contribs/ng_TPTP/RNG026-6.ma | 64 ++++++------- .../matita/contribs/ng_TPTP/RNG026-7.ma | 78 ++++++++-------- .../matita/contribs/ng_TPTP/RNG027-5.ma | 62 ++++++------- .../matita/contribs/ng_TPTP/RNG027-7.ma | 76 ++++++++-------- .../matita/contribs/ng_TPTP/RNG027-8.ma | 62 ++++++------- .../matita/contribs/ng_TPTP/RNG027-9.ma | 76 ++++++++-------- .../matita/contribs/ng_TPTP/RNG028-5.ma | 62 ++++++------- .../matita/contribs/ng_TPTP/RNG028-7.ma | 76 ++++++++-------- .../matita/contribs/ng_TPTP/RNG028-8.ma | 62 ++++++------- .../matita/contribs/ng_TPTP/RNG028-9.ma | 76 ++++++++-------- .../matita/contribs/ng_TPTP/RNG029-5.ma | 62 ++++++------- .../matita/contribs/ng_TPTP/RNG029-6.ma | 62 ++++++------- .../matita/contribs/ng_TPTP/RNG029-7.ma | 76 ++++++++-------- .../matita/contribs/ng_TPTP/RNG030-6.ma | 58 ++++++------ .../matita/contribs/ng_TPTP/RNG030-7.ma | 72 +++++++-------- .../matita/contribs/ng_TPTP/RNG031-6.ma | 58 ++++++------ .../matita/contribs/ng_TPTP/RNG031-7.ma | 72 +++++++-------- .../matita/contribs/ng_TPTP/RNG032-6.ma | 58 ++++++------ .../matita/contribs/ng_TPTP/RNG032-7.ma | 72 +++++++-------- .../matita/contribs/ng_TPTP/RNG033-6.ma | 64 ++++++------- .../matita/contribs/ng_TPTP/RNG033-7.ma | 78 ++++++++-------- .../matita/contribs/ng_TPTP/RNG033-8.ma | 66 +++++++------- .../matita/contribs/ng_TPTP/RNG033-9.ma | 80 ++++++++--------- .../matita/contribs/ng_TPTP/RNG035-7.ma | 50 +++++------ .../matita/contribs/ng_TPTP/RNG036-7.ma | 50 +++++------ .../matita/contribs/ng_TPTP/ROB001-1.ma | 28 +++--- .../matita/contribs/ng_TPTP/ROB002-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/ROB003-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/ROB004-1.ma | 38 ++++---- .../matita/contribs/ng_TPTP/ROB005-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/ROB006-1.ma | 34 +++---- .../matita/contribs/ng_TPTP/ROB006-2.ma | 37 ++++---- .../matita/contribs/ng_TPTP/ROB007-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/ROB007-2.ma | 37 ++++---- .../matita/contribs/ng_TPTP/ROB008-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/ROB009-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/ROB010-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/ROB013-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/ROB020-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/ROB020-2.ma | 37 ++++---- .../matita/contribs/ng_TPTP/ROB022-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/ROB023-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/ROB024-1.ma | 30 +++---- .../matita/contribs/ng_TPTP/ROB026-1.ma | 34 +++---- .../matita/contribs/ng_TPTP/ROB027-1.ma | 32 +++---- .../matita/contribs/ng_TPTP/ROB030-1.ma | 48 +++++----- .../matita/contribs/ng_TPTP/ROB031-1.ma | 42 +++++---- .../matita/contribs/ng_TPTP/ROB032-1.ma | 42 +++++---- .../matita/contribs/ng_TPTP/SYN080-1.ma | 22 ++--- .../matita/contribs/ng_TPTP/SYN083-1.ma | 26 +++--- .../matita/contribs/ng_TPTP/SYN305-1.ma | 27 +++--- 833 files changed, 16937 insertions(+), 16966 deletions(-) diff --git a/helm/software/components/grafite/.depend.opt b/helm/software/components/grafite/.depend.opt index 0f64ba789..e01d5bbfa 100644 --- a/helm/software/components/grafite/.depend.opt +++ b/helm/software/components/grafite/.depend.opt @@ -1,5 +1,7 @@ grafiteAstPp.cmi: grafiteAst.cmx grafiteMarshal.cmi: grafiteAst.cmx +grafiteAst.cmo: +grafiteAst.cmx: grafiteAstPp.cmo: grafiteAst.cmx grafiteAstPp.cmi grafiteAstPp.cmx: grafiteAst.cmx grafiteAstPp.cmi grafiteMarshal.cmo: grafiteAstPp.cmi grafiteAst.cmx grafiteMarshal.cmi diff --git a/helm/software/components/grafite/grafiteAst.ml b/helm/software/components/grafite/grafiteAst.ml index e86cb082f..27afd3904 100644 --- a/helm/software/components/grafite/grafiteAst.ml +++ b/helm/software/components/grafite/grafiteAst.ml @@ -63,6 +63,16 @@ type ntactic = | NReduce of loc * [ `Normalize of bool | `Whd of bool ] * npattern | NRewrite of loc * direction * CicNotationPt.term * npattern | NAuto of loc * CicNotationPt.term auto_params + | NDot of loc + | NSemicolon of loc + | NBranch of loc + | NShift of loc + | NPos of loc * int list + | NWildcard of loc + | NMerge of loc + | NSkip of loc + | NFocus of loc * int list + | NUnfocus of loc type ('term, 'lazy_term, 'reduction, 'ident) tactic = (* Higher order tactics (i.e. tacticals) *) @@ -176,7 +186,7 @@ type ('term,'lazy_term) macro = (** To be increased each time the command type below changes, used for "safe" * marshalling *) -let magic = 22 +let magic = 23 type ('term,'obj) command = | Index of loc * 'term option (* key *) * UriManager.uri (* value *) @@ -217,13 +227,11 @@ type non_punctuation_tactical = type ('term, 'lazy_term, 'reduction, 'obj, 'ident) code = | Command of loc * ('term, 'obj) command | Macro of loc * ('term,'lazy_term) macro - | NTactic of loc * ntactic * punctuation_tactical + | NTactic of loc * ntactic list | Tactic of loc * ('term, 'lazy_term, 'reduction, 'ident) tactic option * punctuation_tactical | NonPunctuationTactical of loc * non_punctuation_tactical * punctuation_tactical - | NNonPunctuationTactical of loc * non_punctuation_tactical - * punctuation_tactical type ('term, 'lazy_term, 'reduction, 'obj, 'ident) comment = | Note of loc * string diff --git a/helm/software/components/grafite/grafiteAstPp.ml b/helm/software/components/grafite/grafiteAstPp.ml index ba9f87abd..98d33464b 100644 --- a/helm/software/components/grafite/grafiteAstPp.ml +++ b/helm/software/components/grafite/grafiteAstPp.ml @@ -107,6 +107,18 @@ let pp_ntactic ~map_unicode_to_tex = function (String.concat "," (List.map CicNotationPp.pp_term l))) else "") ^ String.concat " " (List.map (fun a,b -> a ^ "=" ^ b) flgs) | NReduce _ | NGeneralize _ | NLetIn _ | NAssert _ -> assert false + | NDot _ -> "##." + | NSemicolon _ -> "##;" + | NBranch _ -> "##[" + | NShift _ -> "##|" + | NPos (_, l) -> "##" ^String.concat "," (List.map string_of_int l)^ ":" + | NWildcard _ -> "##*:" + | NMerge _ -> "##]" + | NFocus (_,l) -> + Printf.sprintf "##focus %s" + (String.concat " " (List.map string_of_int l)) + | NUnfocus _ -> "##unfocus" + | NSkip _ -> "##skip" ;; let rec pp_tactic ~map_unicode_to_tex ~term_pp ~lazy_term_pp = @@ -398,15 +410,11 @@ let pp_executable ~map_unicode_to_tex ~term_pp ~lazy_term_pp ~obj_pp = ^ pp_punctuation_tactical punct | Tactic (_, None, punct) -> pp_punctuation_tactical punct - | NTactic (_,tac, punct) -> - pp_ntactic ~map_unicode_to_tex tac - ^ pp_punctuation_tactical punct + | NTactic (_,tacl) -> + String.concat " " (List.map (pp_ntactic ~map_unicode_to_tex) tacl) | NonPunctuationTactical (_, tac, punct) -> pp_non_punctuation_tactical tac ^ pp_punctuation_tactical punct - | NNonPunctuationTactical (_, tac, punct) -> - pp_non_punctuation_tactical tac - ^ pp_punctuation_tactical punct | Command (_, cmd) -> pp_command ~term_pp ~obj_pp cmd ^ "." let pp_comment ~map_unicode_to_tex ~term_pp ~lazy_term_pp ~obj_pp = diff --git a/helm/software/components/grafite_parser/grafiteParser.ml b/helm/software/components/grafite_parser/grafiteParser.ml index 3b8435331..214a2d10e 100644 --- a/helm/software/components/grafite_parser/grafiteParser.ml +++ b/helm/software/components/grafite_parser/grafiteParser.ml @@ -100,6 +100,30 @@ let mk_rec_corec ng ind_kind defs loc = G.Obj (loc, N.Theorem(flavour, name, ty, Some (N.LetRec (ind_kind, defs, body)))) +let npunct_of_punct = function + | G.Branch loc -> G.NBranch loc + | G.Shift loc -> G.NShift loc + | G.Pos (loc, i) -> G.NPos (loc, i) + | G.Wildcard loc -> G.NWildcard loc + | G.Merge loc -> G.NMerge loc + | G.Semicolon loc -> G.NSemicolon loc + | G.Dot loc -> G.NDot loc +;; +let nnon_punct_of_punct = function + | G.Skip loc -> G.NSkip loc + | G.Unfocus loc -> G.NUnfocus loc + | G.Focus (loc,l) -> G.NFocus (loc,l) +;; +let npunct_of_punct = function + | G.Branch loc -> G.NBranch loc + | G.Shift loc -> G.NShift loc + | G.Pos (loc, i) -> G.NPos (loc, i) + | G.Wildcard loc -> G.NWildcard loc + | G.Merge loc -> G.NMerge loc + | G.Semicolon loc -> G.NSemicolon loc + | G.Dot loc -> G.NDot loc +;; + type by_continuation = BYC_done | BYC_weproved of N.term * string option * N.term option @@ -522,6 +546,17 @@ EXTEND | tac = tactic -> tac ] ]; + npunctuation_tactical: + [ + [ SYMBOL "[" -> G.NBranch loc + | SYMBOL "|" -> G.NShift loc + | i = LIST1 int SEP SYMBOL ","; SYMBOL ":" -> G.NPos (loc, i) + | SYMBOL "*"; SYMBOL ":" -> G.NWildcard loc + | SYMBOL "]" -> G.NMerge loc + | SYMBOL ";" -> G.NSemicolon loc + | SYMBOL "." -> G.NDot loc + ] + ]; punctuation_tactical: [ [ SYMBOL "[" -> G.Branch loc @@ -866,14 +901,20 @@ EXTEND | tac = atomic_tactical LEVEL "loops"; punct = punctuation_tactical -> G.Tactic (loc, Some tac, punct) | punct = punctuation_tactical -> G.Tactic (loc, None, punct) + | tac = ntactic; SYMBOL "#" ; SYMBOL "#" ; punct = punctuation_tactical -> + G.NTactic (loc, [tac; npunct_of_punct punct]) | tac = ntactic; punct = punctuation_tactical -> - G.NTactic (loc, tac, punct) - | SYMBOL "#" ; SYMBOL "#" ; punct = punctuation_tactical -> - G.NTactic (loc, G.NId loc, punct) + G.NTactic (loc, [tac; npunct_of_punct punct]) + | SYMBOL "#" ; SYMBOL "#" ; punct = npunctuation_tactical -> + G.NTactic (loc, [punct]) | tac = non_punctuation_tactical; punct = punctuation_tactical -> G.NonPunctuationTactical (loc, tac, punct) - | SYMBOL "#" ; SYMBOL "#" ; tac = non_punctuation_tactical; punct = punctuation_tactical -> - G.NNonPunctuationTactical (loc, tac, punct) + | SYMBOL "#" ; SYMBOL "#" ; tac = non_punctuation_tactical; + SYMBOL "#" ; SYMBOL "#" ; punct = punctuation_tactical -> + G.NTactic (loc, [nnon_punct_of_punct tac; npunct_of_punct punct]) + | SYMBOL "#" ; SYMBOL "#" ; tac = non_punctuation_tactical; + punct = punctuation_tactical -> + G.NTactic (loc, [nnon_punct_of_punct tac; npunct_of_punct punct]) | mac = macro; SYMBOL "." -> G.Macro (loc, mac) ] ]; diff --git a/helm/software/components/tptp_grafite/tptp2grafite.ml b/helm/software/components/tptp_grafite/tptp2grafite.ml index b4675066f..7950ca15d 100644 --- a/helm/software/components/tptp_grafite/tptp2grafite.ml +++ b/helm/software/components/tptp_grafite/tptp2grafite.ml @@ -216,18 +216,18 @@ let rec check_if_formula_is_negative = function let ng_generate_tactics fv ueq_case context arities = [ GA.Executable(floc,GA.NTactic(floc, - (GA.NIntro (floc,"Univ")),GA.Dot(floc))) ] + [GA.NIntro (floc,"Univ") ; GA.NDot(floc)])) ] @ (HExtlib.list_mapi (fun (name,_) _-> GA.Executable(floc,GA.NTactic(floc, - (GA.NIntro (floc,name)),GA.Dot(floc)))) + [GA.NIntro (floc,name);GA.NDot(floc)]))) arities) @ (HExtlib.list_mapi (fun _ i-> GA.Executable(floc,GA.NTactic(floc, - (GA.NIntro (floc,"H"^string_of_int i)),GA.Dot(floc)))) + [GA.NIntro (floc,"H"^string_of_int i);GA.NDot(floc)]))) context) @ (if fv <> [] then @@ -235,12 +235,14 @@ let ng_generate_tactics fv ueq_case context arities = (List.map (fun _ -> [GA.Executable(floc,GA.NTactic(floc, - (GA.NApply (floc,mk_ident "ex_intro")),GA.Branch floc)); - GA.Executable(floc,GA.NTactic(floc, GA.NId floc , - (GA.Pos (floc,[2]))))]) + [GA.NApply (floc, + PT.Appl [mk_ident "ex_intro";PT.Implicit;PT.Implicit; + PT.Implicit;PT.Implicit]);GA.NBranch floc])); + GA.Executable(floc,GA.NTactic(floc, + [GA.NPos (floc,[2])]))]) fv)) else [])@ - [GA.Executable(floc,GA.NTactic(floc, ( + [GA.Executable(floc,GA.NTactic(floc, [ if (*ueq_case*) true then GA.NAuto (floc,( HExtlib.list_mapi @@ -255,8 +257,8 @@ let ng_generate_tactics fv ueq_case context arities = "size",string_of_int 20; "timeout",string_of_int 10; ])) - ), - GA.Semicolon(floc))); + ; + GA.NSemicolon(floc)])); (* GA.Executable(floc,GA.NTactic(floc, Some (GA.Try(floc, GA.Assumption floc)), GA.Dot(floc))) @@ -266,9 +268,8 @@ let ng_generate_tactics fv ueq_case context arities = (List.flatten (List.map (fun _ -> - [GA.Executable(floc,GA.NTactic(floc, GA.NId floc, GA.Shift floc)); - GA.Executable(floc,GA.NNonPunctuationTactical(floc, GA.Skip floc, - (GA.Merge floc)))]) + [GA.Executable(floc,GA.NTactic(floc, [GA.NShift floc; + GA.NSkip floc; GA.NMerge floc]))]) fv)) else [])@ [GA.Executable(floc,GA.Command(floc, GA.NQed(floc)))] @@ -412,21 +413,21 @@ let tptp2grafite ?(timeout=600) ?(def_depth=10) ?raw_preamble ~tptppath ~filenam * which will show up using the following command line: * ./tptp2grafite -tptppath ~tassi/TPTP-v3.1.1 GRP170-1 *) let width = max_int in - let term_pp content_term = + let term_pp prec content_term = let pres_term = TermContentPres.pp_ast content_term in let lookup_uri = fun _ -> None in - let markup = CicNotationPres.render ~lookup_uri pres_term in + let markup = CicNotationPres.render ~lookup_uri ~prec pres_term in let s = BoxPp.render_to_string List.hd width markup ~map_unicode_to_tex:false in Pcre.substitute ~rex:(Pcre.regexp ~flags:[`UTF8] "∀[Ha-z][a-z0-9_]*") ~subst:(fun x -> "\n" ^ x) s in - CicNotationPp.set_pp_term term_pp; + CicNotationPp.set_pp_term (term_pp 90); let lazy_term_pp = fun x -> assert false in let obj_pp = CicNotationPp.pp_obj CicNotationPp.pp_term in Pcre.replace ~pat:"theorem" ~templ:"ntheorem" (GrafiteAstPp.pp_statement - ~map_unicode_to_tex:false ~term_pp ~lazy_term_pp ~obj_pp t) + ~map_unicode_to_tex:false ~term_pp:(term_pp 19) ~lazy_term_pp ~obj_pp t) in let buri = Pcre.replace ~pat:"\\.p$" ("cic:/matita/TPTP/" ^ filename) in let extra_statements_start = [ diff --git a/helm/software/matita/contribs/ng_TPTP/ALG005-1.ma b/helm/software/matita/contribs/ng_TPTP/ALG005-1.ma index a3209c30d..9837b4417 100644 --- a/helm/software/matita/contribs/ng_TPTP/ALG005-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/ALG005-1.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----Denial of associativity: *) ntheorem prove_associativity_of_multiply: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -63,22 +63,22 @@ ntheorem prove_associativity_of_multiply: ∀H0:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (difference X (difference X Y)). ∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (difference (difference X Y) Z) (difference (difference X Z) (difference Y Z)). ∀H2:∀X:Univ.∀Y:Univ.eq Univ (difference X (difference X Y)) (difference Y (difference Y X)). -∀H3:∀X:Univ.∀Y:Univ.eq Univ (difference X (difference Y X)) X.eq Univ (multiply (multiply a b) c) (multiply a (multiply b c)) +∀H3:∀X:Univ.∀Y:Univ.eq Univ (difference X (difference Y X)) X.eq Univ (multiply (multiply a b) c) (multiply a (multiply b c))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#difference. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#difference ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/ALG006-1.ma b/helm/software/matita/contribs/ng_TPTP/ALG006-1.ma index 991232454..c20bc0e4d 100644 --- a/helm/software/matita/contribs/ng_TPTP/ALG006-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/ALG006-1.ma @@ -50,27 +50,27 @@ include "logic/equality.ma". (* ----Denial of simplified third axiom: *) ntheorem prove_set_difference_3_simplified: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀difference:∀_:Univ.∀_:Univ.Univ. ∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (difference (difference X Y) Z) (difference (difference X Z) (difference Y Z)). ∀H1:∀X:Univ.∀Y:Univ.eq Univ (difference X (difference X Y)) (difference Y (difference Y X)). -∀H2:∀X:Univ.∀Y:Univ.eq Univ (difference X (difference Y X)) X.eq Univ (difference (difference a c) b) (difference (difference a b) c) +∀H2:∀X:Univ.∀Y:Univ.eq Univ (difference X (difference Y X)) X.eq Univ (difference (difference a c) b) (difference (difference a b) c)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#difference. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#difference ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/ALG007-1.ma b/helm/software/matita/contribs/ng_TPTP/ALG007-1.ma index 23b7a85d9..4fd49f617 100644 --- a/helm/software/matita/contribs/ng_TPTP/ALG007-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/ALG007-1.ma @@ -52,27 +52,27 @@ include "logic/equality.ma". (* ----Denial of original third axiom: *) ntheorem prove_set_difference_3: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀difference:∀_:Univ.∀_:Univ.Univ. ∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (difference (difference X Y) Z) (difference (difference X Z) Y). ∀H1:∀X:Univ.∀Y:Univ.eq Univ (difference X (difference X Y)) (difference Y (difference Y X)). -∀H2:∀X:Univ.∀Y:Univ.eq Univ (difference X (difference Y X)) X.eq Univ (difference (difference a b) c) (difference (difference a c) (difference b c)) +∀H2:∀X:Univ.∀Y:Univ.eq Univ (difference X (difference Y X)) X.eq Univ (difference (difference a b) c) (difference (difference a c) (difference b c))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#difference. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#difference ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO001-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO001-1.ma index 265fa9fa1..6ea0eaa9f 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO001-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO001-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_inverse_is_self_cancelling: - ∀Univ:Type.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.∀_:Univ.Univ. @@ -102,23 +102,23 @@ ntheorem prove_inverse_is_self_cancelling: ∀H1:∀X:Univ.∀Y:Univ.eq Univ (multiply (inverse Y) Y X) X. ∀H2:∀X:Univ.∀Y:Univ.eq Univ (multiply X X Y) X. ∀H3:∀X:Univ.∀Y:Univ.eq Univ (multiply Y X X) X. -∀H4:∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply V W X) Y (multiply V W Z)) (multiply V W (multiply X Y Z)).eq Univ (inverse (inverse a)) a +∀H4:∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply V W X) Y (multiply V W Z)) (multiply V W (multiply X Y Z)).eq Univ (inverse (inverse a)) a) . -#Univ. -#V. -#W. -#X. -#Y. -#Z. -#a. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -nauto by H0,H1,H2,H3,H4; +#Univ ##. +#V ##. +#W ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +nauto by H0,H1,H2,H3,H4 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO002-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO002-1.ma index a2114731c..f53f13e34 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO002-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO002-1.ma @@ -68,7 +68,7 @@ include "logic/equality.ma". (* [++equal(multiply(X,Y,inverse(Y)),X)]). *) ntheorem prove_equation: - ∀Univ:Type.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀inverse:∀_:Univ.Univ. @@ -76,23 +76,23 @@ ntheorem prove_equation: ∀H0:∀X:Univ.∀Y:Univ.eq Univ (multiply (inverse Y) Y X) X. ∀H1:∀X:Univ.∀Y:Univ.eq Univ (multiply X X Y) X. ∀H2:∀X:Univ.∀Y:Univ.eq Univ (multiply Y X X) X. -∀H3:∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply V W X) Y (multiply V W Z)) (multiply V W (multiply X Y Z)).eq Univ (multiply a (inverse a) b) b +∀H3:∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply V W X) Y (multiply V W Z)) (multiply V W (multiply X Y Z)).eq Univ (multiply a (inverse a) b) b) . -#Univ. -#V. -#W. -#X. -#Y. -#Z. -#a. -#b. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#V ##. +#W ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO002-2.ma b/helm/software/matita/contribs/ng_TPTP/BOO002-2.ma index 095229a2a..5e0f29312 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO002-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO002-2.ma @@ -56,7 +56,7 @@ include "logic/equality.ma". (* [++equal(multiply(X,Y,inverse(Y)),X)]). *) ntheorem prove_equation: - ∀Univ:Type.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀inverse:∀_:Univ.Univ. @@ -65,24 +65,24 @@ ntheorem prove_equation: ∀H1:∀X:Univ.∀Y:Univ.eq Univ (multiply (inverse Y) Y X) X. ∀H2:∀X:Univ.∀Y:Univ.eq Univ (multiply X X Y) X. ∀H3:∀X:Univ.∀Y:Univ.eq Univ (multiply Y X X) X. -∀H4:∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply V W X) Y (multiply V W Z)) (multiply V W (multiply X Y Z)).eq Univ (multiply a (inverse a) b) b +∀H4:∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply V W X) Y (multiply V W Z)) (multiply V W (multiply X Y Z)).eq Univ (multiply a (inverse a) b) b) . -#Univ. -#V. -#W. -#X. -#Y. -#Z. -#a. -#b. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -nauto by H0,H1,H2,H3,H4; +#Univ ##. +#V ##. +#W ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +nauto by H0,H1,H2,H3,H4 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO003-2.ma b/helm/software/matita/contribs/ng_TPTP/BOO003-2.ma index 7a827f432..a6f459648 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO003-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO003-2.ma @@ -88,7 +88,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_a_times_a_is_a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -108,33 +108,33 @@ ntheorem prove_a_times_a_is_a: ∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)). ∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (multiply X Y) Z) (multiply (add X Z) (add Y Z)). ∀H12:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X). -∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply a a) a +∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply a a) a) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#inverse. -#multiplicative_identity. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#inverse ##. +#multiplicative_identity ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO003-4.ma b/helm/software/matita/contribs/ng_TPTP/BOO003-4.ma index bf8893a5e..7d3e04b78 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO003-4.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO003-4.ma @@ -88,7 +88,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_a_times_a_is_a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -102,27 +102,27 @@ ntheorem prove_a_times_a_is_a: ∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)). ∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)). ∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X). -∀H7:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply a a) a +∀H7:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply a a) a) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#inverse. -#multiplicative_identity. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -nauto by H0,H1,H2,H3,H4,H5,H6,H7; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#inverse ##. +#multiplicative_identity ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO004-2.ma b/helm/software/matita/contribs/ng_TPTP/BOO004-2.ma index 7e6174330..e92554e89 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO004-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO004-2.ma @@ -88,7 +88,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_a_plus_a_is_a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -108,33 +108,33 @@ ntheorem prove_a_plus_a_is_a: ∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)). ∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (multiply X Y) Z) (multiply (add X Z) (add Y Z)). ∀H12:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X). -∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add a a) a +∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add a a) a) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#inverse. -#multiplicative_identity. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#inverse ##. +#multiplicative_identity ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO004-4.ma b/helm/software/matita/contribs/ng_TPTP/BOO004-4.ma index 58e659cd7..c62197502 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO004-4.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO004-4.ma @@ -88,7 +88,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_a_plus_a_is_a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -102,27 +102,27 @@ ntheorem prove_a_plus_a_is_a: ∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)). ∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)). ∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X). -∀H7:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add a a) a +∀H7:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add a a) a) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#inverse. -#multiplicative_identity. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -nauto by H0,H1,H2,H3,H4,H5,H6,H7; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#inverse ##. +#multiplicative_identity ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO005-2.ma b/helm/software/matita/contribs/ng_TPTP/BOO005-2.ma index c6178048a..6c5a5252d 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO005-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO005-2.ma @@ -90,7 +90,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_a_plus_1_is_a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -110,33 +110,33 @@ ntheorem prove_a_plus_1_is_a: ∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)). ∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (multiply X Y) Z) (multiply (add X Z) (add Y Z)). ∀H12:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X). -∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add a multiplicative_identity) multiplicative_identity +∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add a multiplicative_identity) multiplicative_identity) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#inverse. -#multiplicative_identity. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#inverse ##. +#multiplicative_identity ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO005-4.ma b/helm/software/matita/contribs/ng_TPTP/BOO005-4.ma index 5617ad0f8..45c440301 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO005-4.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO005-4.ma @@ -90,7 +90,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_a_plus_1_is_a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -104,27 +104,27 @@ ntheorem prove_a_plus_1_is_a: ∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)). ∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)). ∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X). -∀H7:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add a multiplicative_identity) multiplicative_identity +∀H7:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add a multiplicative_identity) multiplicative_identity) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#inverse. -#multiplicative_identity. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -nauto by H0,H1,H2,H3,H4,H5,H6,H7; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#inverse ##. +#multiplicative_identity ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO006-2.ma b/helm/software/matita/contribs/ng_TPTP/BOO006-2.ma index 73227bf42..4b5814d3e 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO006-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO006-2.ma @@ -88,7 +88,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_right_identity: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -108,33 +108,33 @@ ntheorem prove_right_identity: ∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)). ∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (multiply X Y) Z) (multiply (add X Z) (add Y Z)). ∀H12:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X). -∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply a additive_identity) additive_identity +∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply a additive_identity) additive_identity) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#inverse. -#multiplicative_identity. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#inverse ##. +#multiplicative_identity ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO006-4.ma b/helm/software/matita/contribs/ng_TPTP/BOO006-4.ma index 769b0071d..e2647ce1f 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO006-4.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO006-4.ma @@ -88,7 +88,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_right_identity: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -102,27 +102,27 @@ ntheorem prove_right_identity: ∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)). ∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)). ∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X). -∀H7:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply a additive_identity) additive_identity +∀H7:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply a additive_identity) additive_identity) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#inverse. -#multiplicative_identity. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -nauto by H0,H1,H2,H3,H4,H5,H6,H7; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#inverse ##. +#multiplicative_identity ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO007-2.ma b/helm/software/matita/contribs/ng_TPTP/BOO007-2.ma index 79c965651..686437c2c 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO007-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO007-2.ma @@ -88,7 +88,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_associativity: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -110,35 +110,35 @@ ntheorem prove_associativity: ∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)). ∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (multiply X Y) Z) (multiply (add X Z) (add Y Z)). ∀H12:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X). -∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply a (multiply b c)) (multiply (multiply a b) c) +∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply a (multiply b c)) (multiply (multiply a b) c)) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#b. -#c. -#inverse. -#multiplicative_identity. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#b ##. +#c ##. +#inverse ##. +#multiplicative_identity ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO007-4.ma b/helm/software/matita/contribs/ng_TPTP/BOO007-4.ma index 6f1a354ec..fb0fc3146 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO007-4.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO007-4.ma @@ -88,7 +88,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_associativity: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -104,29 +104,29 @@ ntheorem prove_associativity: ∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)). ∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)). ∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X). -∀H7:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply a (multiply b c)) (multiply (multiply a b) c) +∀H7:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply a (multiply b c)) (multiply (multiply a b) c)) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#b. -#c. -#inverse. -#multiplicative_identity. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -nauto by H0,H1,H2,H3,H4,H5,H6,H7; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#b ##. +#c ##. +#inverse ##. +#multiplicative_identity ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO008-2.ma b/helm/software/matita/contribs/ng_TPTP/BOO008-2.ma index 02080b8c8..7b0d442a5 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO008-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO008-2.ma @@ -98,7 +98,7 @@ include "logic/equality.ma". (* [++equal(multiply(X,X),X)]). *) ntheorem prove_associativity: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -120,35 +120,35 @@ ntheorem prove_associativity: ∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)). ∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (multiply X Y) Z) (multiply (add X Z) (add Y Z)). ∀H12:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X). -∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add a (add b c)) (add (add a b) c) +∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add a (add b c)) (add (add a b) c)) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#b. -#c. -#inverse. -#multiplicative_identity. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#b ##. +#c ##. +#inverse ##. +#multiplicative_identity ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO008-4.ma b/helm/software/matita/contribs/ng_TPTP/BOO008-4.ma index 73f5b9d26..1d42f4c01 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO008-4.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO008-4.ma @@ -88,7 +88,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_associativity: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -104,29 +104,29 @@ ntheorem prove_associativity: ∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)). ∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)). ∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X). -∀H7:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add a (add b c)) (add (add a b) c) +∀H7:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add a (add b c)) (add (add a b) c)) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#b. -#c. -#inverse. -#multiplicative_identity. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -nauto by H0,H1,H2,H3,H4,H5,H6,H7; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#b ##. +#c ##. +#inverse ##. +#multiplicative_identity ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO009-2.ma b/helm/software/matita/contribs/ng_TPTP/BOO009-2.ma index bee8bd8e0..870013660 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO009-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO009-2.ma @@ -88,7 +88,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_operation: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -109,34 +109,34 @@ ntheorem prove_operation: ∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)). ∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (multiply X Y) Z) (multiply (add X Z) (add Y Z)). ∀H12:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X). -∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply a (add a b)) a +∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply a (add a b)) a) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#b. -#inverse. -#multiplicative_identity. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#b ##. +#inverse ##. +#multiplicative_identity ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO009-4.ma b/helm/software/matita/contribs/ng_TPTP/BOO009-4.ma index 3b4ed24b9..2a96f2cf6 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO009-4.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO009-4.ma @@ -88,7 +88,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_operation: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -103,28 +103,28 @@ ntheorem prove_operation: ∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)). ∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)). ∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X). -∀H7:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply a (add a b)) a +∀H7:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply a (add a b)) a) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#b. -#inverse. -#multiplicative_identity. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -nauto by H0,H1,H2,H3,H4,H5,H6,H7; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#b ##. +#inverse ##. +#multiplicative_identity ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO010-2.ma b/helm/software/matita/contribs/ng_TPTP/BOO010-2.ma index 09d6378cc..87e92d1fb 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO010-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO010-2.ma @@ -88,7 +88,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_a_plus_ab_is_a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -109,34 +109,34 @@ ntheorem prove_a_plus_ab_is_a: ∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)). ∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (multiply X Y) Z) (multiply (add X Z) (add Y Z)). ∀H12:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X). -∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add a (multiply a b)) a +∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add a (multiply a b)) a) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#b. -#inverse. -#multiplicative_identity. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#b ##. +#inverse ##. +#multiplicative_identity ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO010-4.ma b/helm/software/matita/contribs/ng_TPTP/BOO010-4.ma index 3007e0679..392b74929 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO010-4.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO010-4.ma @@ -88,7 +88,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_a_plus_ab_is_a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -103,28 +103,28 @@ ntheorem prove_a_plus_ab_is_a: ∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)). ∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)). ∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X). -∀H7:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add a (multiply a b)) a +∀H7:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add a (multiply a b)) a) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#b. -#inverse. -#multiplicative_identity. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -nauto by H0,H1,H2,H3,H4,H5,H6,H7; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#b ##. +#inverse ##. +#multiplicative_identity ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO011-2.ma b/helm/software/matita/contribs/ng_TPTP/BOO011-2.ma index bb782f271..114c2b43d 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO011-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO011-2.ma @@ -92,7 +92,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_inverse_of_1_is_0: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀inverse:∀_:Univ.Univ. @@ -111,32 +111,32 @@ ntheorem prove_inverse_of_1_is_0: ∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)). ∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (multiply X Y) Z) (multiply (add X Z) (add Y Z)). ∀H12:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X). -∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (inverse additive_identity) multiplicative_identity +∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (inverse additive_identity) multiplicative_identity) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#inverse. -#multiplicative_identity. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#inverse ##. +#multiplicative_identity ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO011-4.ma b/helm/software/matita/contribs/ng_TPTP/BOO011-4.ma index bb25d309f..dbe470c82 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO011-4.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO011-4.ma @@ -90,7 +90,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_inverse_of_1_is_0: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀inverse:∀_:Univ.Univ. @@ -103,26 +103,26 @@ ntheorem prove_inverse_of_1_is_0: ∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)). ∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)). ∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X). -∀H7:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (inverse additive_identity) multiplicative_identity +∀H7:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (inverse additive_identity) multiplicative_identity) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#inverse. -#multiplicative_identity. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -nauto by H0,H1,H2,H3,H4,H5,H6,H7; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#inverse ##. +#multiplicative_identity ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO012-2.ma b/helm/software/matita/contribs/ng_TPTP/BOO012-2.ma index 8a5f8e95c..04cd28fbf 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO012-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO012-2.ma @@ -88,7 +88,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_inverse_is_an_involution: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀inverse:∀_:Univ.Univ. @@ -108,33 +108,33 @@ ntheorem prove_inverse_is_an_involution: ∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)). ∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (multiply X Y) Z) (multiply (add X Z) (add Y Z)). ∀H12:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X). -∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (inverse (inverse x)) x +∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (inverse (inverse x)) x) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#inverse. -#multiplicative_identity. -#multiply. -#x. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#inverse ##. +#multiplicative_identity ##. +#multiply ##. +#x ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO012-4.ma b/helm/software/matita/contribs/ng_TPTP/BOO012-4.ma index 43812ba77..c664f2645 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO012-4.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO012-4.ma @@ -88,7 +88,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_inverse_is_an_involution: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀inverse:∀_:Univ.Univ. @@ -102,27 +102,27 @@ ntheorem prove_inverse_is_an_involution: ∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)). ∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)). ∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X). -∀H7:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (inverse (inverse x)) x +∀H7:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (inverse (inverse x)) x) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#inverse. -#multiplicative_identity. -#multiply. -#x. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -nauto by H0,H1,H2,H3,H4,H5,H6,H7; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#inverse ##. +#multiplicative_identity ##. +#multiply ##. +#x ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO013-2.ma b/helm/software/matita/contribs/ng_TPTP/BOO013-2.ma index 2904dc72d..5e5a2006e 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO013-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO013-2.ma @@ -92,7 +92,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_b_is_a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -118,39 +118,39 @@ ntheorem prove_b_is_a: ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)). ∀H15:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (multiply X Y) Z) (multiply (add X Z) (add Y Z)). ∀H16:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X). -∀H17:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ b c +∀H17:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ b c) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#b. -#c. -#inverse. -#multiplicative_identity. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#b ##. +#c ##. +#inverse ##. +#multiplicative_identity ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO013-4.ma b/helm/software/matita/contribs/ng_TPTP/BOO013-4.ma index e8d4883d4..5cd7d7c61 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO013-4.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO013-4.ma @@ -88,7 +88,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_a_inverse_is_b: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -105,30 +105,30 @@ ntheorem prove_a_inverse_is_b: ∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)). ∀H7:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)). ∀H8:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X). -∀H9:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ b (inverse a) +∀H9:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ b (inverse a)) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#b. -#inverse. -#multiplicative_identity. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#b ##. +#inverse ##. +#multiplicative_identity ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO014-2.ma b/helm/software/matita/contribs/ng_TPTP/BOO014-2.ma index d0b8bbf23..ef1cca70c 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO014-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO014-2.ma @@ -88,7 +88,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_c_inverse_is_d: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -113,38 +113,38 @@ ntheorem prove_c_inverse_is_d: ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)). ∀H13:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (multiply X Y) Z) (multiply (add X Z) (add Y Z)). ∀H14:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X). -∀H15:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (inverse c) d +∀H15:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (inverse c) d) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#b. -#c. -#d. -#inverse. -#multiplicative_identity. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#b ##. +#c ##. +#d ##. +#inverse ##. +#multiplicative_identity ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO014-4.ma b/helm/software/matita/contribs/ng_TPTP/BOO014-4.ma index fa147bb4c..310b75649 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO014-4.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO014-4.ma @@ -88,7 +88,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_c_inverse_is_d: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -103,28 +103,28 @@ ntheorem prove_c_inverse_is_d: ∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)). ∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)). ∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X). -∀H7:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (inverse (add a b)) (multiply (inverse a) (inverse b)) +∀H7:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (inverse (add a b)) (multiply (inverse a) (inverse b))) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#b. -#inverse. -#multiplicative_identity. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -nauto by H0,H1,H2,H3,H4,H5,H6,H7; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#b ##. +#inverse ##. +#multiplicative_identity ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO015-2.ma b/helm/software/matita/contribs/ng_TPTP/BOO015-2.ma index f22296e98..9d0ef62f4 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO015-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO015-2.ma @@ -90,7 +90,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_c_inverse_is_d: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -115,38 +115,38 @@ ntheorem prove_c_inverse_is_d: ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)). ∀H13:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (multiply X Y) Z) (multiply (add X Z) (add Y Z)). ∀H14:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X). -∀H15:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (inverse c) d +∀H15:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (inverse c) d) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#b. -#c. -#d. -#inverse. -#multiplicative_identity. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#b ##. +#c ##. +#d ##. +#inverse ##. +#multiplicative_identity ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO015-4.ma b/helm/software/matita/contribs/ng_TPTP/BOO015-4.ma index 6688f1c79..6492c9c9a 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO015-4.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO015-4.ma @@ -88,7 +88,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_c_inverse_is_d: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -103,28 +103,28 @@ ntheorem prove_c_inverse_is_d: ∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)). ∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)). ∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X). -∀H7:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (inverse (multiply a b)) (add (inverse a) (inverse b)) +∀H7:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (inverse (multiply a b)) (add (inverse a) (inverse b))) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#b. -#inverse. -#multiplicative_identity. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -nauto by H0,H1,H2,H3,H4,H5,H6,H7; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#b ##. +#inverse ##. +#multiplicative_identity ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO016-2.ma b/helm/software/matita/contribs/ng_TPTP/BOO016-2.ma index d82ef6aba..31b8ea983 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO016-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO016-2.ma @@ -88,7 +88,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_sum: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀inverse:∀_:Univ.Univ. @@ -111,36 +111,36 @@ ntheorem prove_sum: ∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)). ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (multiply X Y) Z) (multiply (add X Z) (add Y Z)). ∀H13:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X). -∀H14:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add x z) x +∀H14:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add x z) x) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#inverse. -#multiplicative_identity. -#multiply. -#x. -#y. -#z. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#inverse ##. +#multiplicative_identity ##. +#multiply ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO017-2.ma b/helm/software/matita/contribs/ng_TPTP/BOO017-2.ma index fde29bc5e..82a270eb6 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO017-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO017-2.ma @@ -88,7 +88,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_sum: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀inverse:∀_:Univ.Univ. @@ -111,36 +111,36 @@ ntheorem prove_sum: ∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)). ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (multiply X Y) Z) (multiply (add X Z) (add Y Z)). ∀H13:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X). -∀H14:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply x z) x +∀H14:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply x z) x) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#inverse. -#multiplicative_identity. -#multiply. -#x. -#y. -#z. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#inverse ##. +#multiplicative_identity ##. +#multiply ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO018-4.ma b/helm/software/matita/contribs/ng_TPTP/BOO018-4.ma index 9790abf56..cf91e2371 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO018-4.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO018-4.ma @@ -90,7 +90,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_inverse_of_1_is_0: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀inverse:∀_:Univ.Univ. @@ -103,26 +103,26 @@ ntheorem prove_inverse_of_1_is_0: ∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)). ∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)). ∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X). -∀H7:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (inverse multiplicative_identity) additive_identity +∀H7:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (inverse multiplicative_identity) additive_identity) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#inverse. -#multiplicative_identity. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -nauto by H0,H1,H2,H3,H4,H5,H6,H7; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#inverse ##. +#multiplicative_identity ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO019-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO019-1.ma index c8e61c4c4..42b6f8354 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO019-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO019-1.ma @@ -50,7 +50,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_ternary_multiply_1_independant: - ∀Univ:Type.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.∀_:Univ.Univ. ∀x:Univ. @@ -58,23 +58,23 @@ ntheorem prove_ternary_multiply_1_independant: ∀H0:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y (inverse Y)) X. ∀H1:∀X:Univ.∀Y:Univ.eq Univ (multiply (inverse Y) Y X) X. ∀H2:∀X:Univ.∀Y:Univ.eq Univ (multiply X X Y) X. -∀H3:∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply V W X) Y (multiply V W Z)) (multiply V W (multiply X Y Z)).eq Univ (multiply y x x) x +∀H3:∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply V W X) Y (multiply V W Z)) (multiply V W (multiply X Y Z)).eq Univ (multiply y x x) x) . -#Univ. -#V. -#W. -#X. -#Y. -#Z. -#inverse. -#multiply. -#x. -#y. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#V ##. +#W ##. +#X ##. +#Y ##. +#Z ##. +#inverse ##. +#multiply ##. +#x ##. +#y ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO021-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO021-1.ma index a85d8cad7..b7511fd98 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO021-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO021-1.ma @@ -50,7 +50,7 @@ include "logic/equality.ma". (* ----Denial of conclusion: *) ntheorem prove_commutativity_of_multiply: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. @@ -63,26 +63,26 @@ ntheorem prove_commutativity_of_multiply: ∀H2:∀X:Univ.∀Y:Univ.eq Univ (add (multiply X Y) Y) Y. ∀H3:∀X:Univ.eq Univ (add X (inverse X)) n1. ∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply Y X) (multiply Z X)). -∀H5:∀X:Univ.∀Y:Univ.eq Univ (multiply (add X Y) Y) Y.eq Univ (multiply b a) (multiply a b) +∀H5:∀X:Univ.∀Y:Univ.eq Univ (multiply (add X Y) Y) Y.eq Univ (multiply b a) (multiply a b)) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#b. -#inverse. -#multiply. -#n0. -#n1. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -nauto by H0,H1,H2,H3,H4,H5; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#b ##. +#inverse ##. +#multiply ##. +#n0 ##. +#n1 ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +nauto by H0,H1,H2,H3,H4,H5 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO022-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO022-1.ma index 857f3440f..16fe8e3f6 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO022-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO022-1.ma @@ -50,7 +50,7 @@ include "logic/equality.ma". (* ----Denial of conclusion: *) ntheorem prove_associativity_of_multiply: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. @@ -64,27 +64,27 @@ ntheorem prove_associativity_of_multiply: ∀H2:∀X:Univ.∀Y:Univ.eq Univ (add (multiply X Y) Y) Y. ∀H3:∀X:Univ.eq Univ (add X (inverse X)) n1. ∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply Y X) (multiply Z X)). -∀H5:∀X:Univ.∀Y:Univ.eq Univ (multiply (add X Y) Y) Y.eq Univ (multiply (multiply a b) c) (multiply a (multiply b c)) +∀H5:∀X:Univ.∀Y:Univ.eq Univ (multiply (add X Y) Y) Y.eq Univ (multiply (multiply a b) c) (multiply a (multiply b c))) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#b. -#c. -#inverse. -#multiply. -#n0. -#n1. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -nauto by H0,H1,H2,H3,H4,H5; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#b ##. +#c ##. +#inverse ##. +#multiply ##. +#n0 ##. +#n1 ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +nauto by H0,H1,H2,H3,H4,H5 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO023-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO023-1.ma index ce6b2c997..b80deb137 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO023-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO023-1.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----Denial of conclusion: *) ntheorem prove_add_multiply_property: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. @@ -69,28 +69,28 @@ ntheorem prove_add_multiply_property: ∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (pixley X Y Z) (add (multiply X (inverse Y)) (add (multiply X Z) (multiply (inverse Y) Z))). ∀H4:∀X:Univ.eq Univ (add X (inverse X)) n1. ∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply Y X) (multiply Z X)). -∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply (add X Y) Y) Y.eq Univ (add a (multiply b c)) (multiply (add a b) (add a c)) +∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply (add X Y) Y) Y.eq Univ (add a (multiply b c)) (multiply (add a b) (add a c))) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#b. -#c. -#inverse. -#multiply. -#n1. -#pixley. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -nauto by H0,H1,H2,H3,H4,H5,H6; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#b ##. +#c ##. +#inverse ##. +#multiply ##. +#n1 ##. +#pixley ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +nauto by H0,H1,H2,H3,H4,H5,H6 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO024-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO024-1.ma index a4c6440e0..797a7c9f8 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO024-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO024-1.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----Denial of conclusion: *) ntheorem prove_add_multiply: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. @@ -68,27 +68,27 @@ ntheorem prove_add_multiply: ∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (pixley X Y Z) (add (multiply X (inverse Y)) (add (multiply X Z) (multiply (inverse Y) Z))). ∀H4:∀X:Univ.eq Univ (add X (inverse X)) n1. ∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply Y X) (multiply Z X)). -∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply (add X Y) Y) Y.eq Univ (add (multiply a b) b) b +∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply (add X Y) Y) Y.eq Univ (add (multiply a b) b) b) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#b. -#inverse. -#multiply. -#n1. -#pixley. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -nauto by H0,H1,H2,H3,H4,H5,H6; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#b ##. +#inverse ##. +#multiply ##. +#n1 ##. +#pixley ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +nauto by H0,H1,H2,H3,H4,H5,H6 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO025-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO025-1.ma index a502cb58f..379d219c1 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO025-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO025-1.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----Denial of conclusion: *) ntheorem prove_equal_identity: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. @@ -68,27 +68,27 @@ ntheorem prove_equal_identity: ∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (pixley X Y Z) (add (multiply X (inverse Y)) (add (multiply X Z) (multiply (inverse Y) Z))). ∀H4:∀X:Univ.eq Univ (add X (inverse X)) n1. ∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply Y X) (multiply Z X)). -∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply (add X Y) Y) Y.eq Univ (multiply b (inverse b)) (multiply a (inverse a)) +∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply (add X Y) Y) Y.eq Univ (multiply b (inverse b)) (multiply a (inverse a))) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#b. -#inverse. -#multiply. -#n1. -#pixley. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -nauto by H0,H1,H2,H3,H4,H5,H6; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#b ##. +#inverse ##. +#multiply ##. +#n1 ##. +#pixley ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +nauto by H0,H1,H2,H3,H4,H5,H6 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO026-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO026-1.ma index fb8eafa37..e40c2aec5 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO026-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO026-1.ma @@ -62,7 +62,7 @@ include "logic/equality.ma". (* ----Denial of the conclusion: *) ntheorem prove_multiply_add: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. @@ -79,30 +79,30 @@ ntheorem prove_multiply_add: ∀H6:∀X:Univ.eq Univ (multiply X (inverse X)) n0. ∀H7:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add Y X) (add Z X)). ∀H8:∀X:Univ.eq Univ (add X (inverse X)) n1. -∀H9:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply Y X) (multiply Z X)).eq Univ (multiply (add a b) b) b +∀H9:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply Y X) (multiply Z X)).eq Univ (multiply (add a b) b) b) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#b. -#inverse. -#multiply. -#n0. -#n1. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#b ##. +#inverse ##. +#multiply ##. +#n0 ##. +#n1 ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO027-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO027-1.ma index e494b6154..b11dc1215 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO027-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO027-1.ma @@ -52,7 +52,7 @@ include "logic/equality.ma". (* ----Denial of a property of Boolean Algebra: *) ntheorem prove_idempotence: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. @@ -62,23 +62,23 @@ ntheorem prove_idempotence: ∀H1:∀X:Univ.∀Y:Univ.eq Univ (add (multiply X (inverse Y)) (add (multiply X Y) (multiply (inverse Y) Y))) X. ∀H2:∀X:Univ.∀Y:Univ.eq Univ (add (multiply X (inverse X)) (add (multiply X Y) (multiply (inverse X) Y))) Y. ∀H3:∀X:Univ.eq Univ (add X (inverse X)) one. -∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply Y X) (multiply Z X)).eq Univ (add a a) a +∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply Y X) (multiply Z X)).eq Univ (add a a) a) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#inverse. -#multiply. -#one. -#H0. -#H1. -#H2. -#H3. -#H4. -nauto by H0,H1,H2,H3,H4; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#inverse ##. +#multiply ##. +#one ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +nauto by H0,H1,H2,H3,H4 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO028-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO028-1.ma index 346faaad0..b22ce789e 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO028-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO028-1.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----Denial of conclusion: *) ntheorem prove_multiply_add_property: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. @@ -70,29 +70,29 @@ ntheorem prove_multiply_add_property: ∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y (add X Z))) X. ∀H7:∀X:Univ.∀Y:Univ.eq Univ (multiply (add X Y) (add X (inverse Y))) X. ∀H8:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add (multiply X Y) (multiply Y Z)) Y) Y. -∀H9:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y (multiply X Z))) X.eq Univ (multiply a (add b c)) (add (multiply b a) (multiply c a)) +∀H9:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y (multiply X Z))) X.eq Univ (multiply a (add b c)) (add (multiply b a) (multiply c a))) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#b. -#c. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#b ##. +#c ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO029-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO029-1.ma index 0e04f92dc..a10f66d20 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO029-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO029-1.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----Denial of conclusion: *) ntheorem prove_equal_inverse: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. @@ -69,28 +69,28 @@ ntheorem prove_equal_inverse: ∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y (add X Z))) X. ∀H7:∀X:Univ.∀Y:Univ.eq Univ (multiply (add X Y) (add X (inverse Y))) X. ∀H8:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add (multiply X Y) (multiply Y Z)) Y) Y. -∀H9:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y (multiply X Z))) X.eq Univ (add b (inverse b)) (add a (inverse a)) +∀H9:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y (multiply X Z))) X.eq Univ (add b (inverse b)) (add a (inverse a))) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#b. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#b ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO030-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO030-1.ma index 3aee92bf9..915a56a71 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO030-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO030-1.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----Denial of a property of Boolean Algebra. *) ntheorem prove_inverse_involution: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. @@ -64,23 +64,23 @@ ntheorem prove_inverse_involution: ∀H2:∀X:Univ.∀Y:Univ.eq Univ (multiply (add (multiply X Y) X) (add X Y)) X. ∀H3:∀X:Univ.∀Y:Univ.eq Univ (multiply (add X Y) (add X (inverse Y))) X. ∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add (multiply X Y) (multiply Y Z)) Y) Y. -∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y (multiply X Z))) X.eq Univ (inverse (inverse a)) a +∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y (multiply X Z))) X.eq Univ (inverse (inverse a)) a) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -nauto by H0,H1,H2,H3,H4,H5; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +nauto by H0,H1,H2,H3,H4,H5 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO031-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO031-1.ma index 35f2d1d13..7051f0de7 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO031-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO031-1.ma @@ -56,7 +56,7 @@ include "logic/equality.ma". (* ----Denial of conclusion: *) ntheorem prove_multiply_add_property: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. @@ -75,32 +75,32 @@ ntheorem prove_multiply_add_property: ∀H7:∀X:Univ.∀Y:Univ.eq Univ (multiply (add X (inverse X)) Y) Y. ∀H8:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add (multiply X Y) (multiply Y Z)) Y) Y. ∀H9:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y (multiply X Z))) X. -∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (multiply X Y) (add (multiply Y Z) (multiply Z X))) (multiply (add X Y) (multiply (add Y Z) (add Z X))).eq Univ (multiply a (add b c)) (add (multiply b a) (multiply c a)) +∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (multiply X Y) (add (multiply Y Z) (multiply Z X))) (multiply (add X Y) (multiply (add Y Z) (add Z X))).eq Univ (multiply a (add b c)) (add (multiply b a) (multiply c a))) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#b. -#c. -#inverse. -#multiply. -#n0. -#n1. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#b ##. +#c ##. +#inverse ##. +#multiply ##. +#n0 ##. +#n1 ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO032-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO032-1.ma index c22d538ba..3d35fc877 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO032-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO032-1.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----A propery of Boolean Algebra fails to hold. *) ntheorem prove_inverse_involution: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. @@ -70,29 +70,29 @@ ntheorem prove_inverse_involution: ∀H8:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y (add X Z))) X. ∀H9:∀X:Univ.∀Y:Univ.eq Univ (multiply (add X (inverse X)) Y) Y. ∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add (multiply X Y) (multiply Y Z)) Y) Y. -∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y (multiply X Z))) X.eq Univ (inverse (inverse a)) a +∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y (multiply X Z))) X.eq Univ (inverse (inverse a)) a) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO033-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO033-1.ma index e73b92c6a..1a47749cc 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO033-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO033-1.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----A simple propery of Boolean Algebra fails to hold. *) ntheorem prove_inverse_involution: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. @@ -65,24 +65,24 @@ ntheorem prove_inverse_involution: ∀H3:∀X:Univ.∀Y:Univ.eq Univ (multiply (add X (inverse X)) Y) Y. ∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add (multiply X Y) (multiply Y Z)) Y) Y. ∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y (multiply X Z))) X. -∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (multiply X Y) (add (multiply Y Z) (multiply Z X))) (multiply (add X Y) (multiply (add Y Z) (add Z X))).eq Univ (inverse (inverse a)) a +∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (multiply X Y) (add (multiply Y Z) (multiply Z X))) (multiply (add X Y) (multiply (add Y Z) (add Z X))).eq Univ (inverse (inverse a)) a) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -nauto by H0,H1,H2,H3,H4,H5,H6; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +nauto by H0,H1,H2,H3,H4,H5,H6 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO034-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO034-1.ma index 6d6ee55b0..cfead0987 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO034-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO034-1.ma @@ -100,7 +100,7 @@ include "logic/equality.ma". (* ----Denial of single axiom: *) ntheorem prove_single_axiom: - ∀Univ:Type.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -114,29 +114,29 @@ ntheorem prove_single_axiom: ∀H1:∀X:Univ.∀Y:Univ.eq Univ (multiply (inverse Y) Y X) X. ∀H2:∀X:Univ.∀Y:Univ.eq Univ (multiply X X Y) X. ∀H3:∀X:Univ.∀Y:Univ.eq Univ (multiply Y X X) X. -∀H4:∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply V W X) Y (multiply V W Z)) (multiply V W (multiply X Y Z)).eq Univ (multiply (multiply a (inverse a) b) (inverse (multiply (multiply c d e) f (multiply c d g))) (multiply d (multiply g f e) c)) b +∀H4:∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply V W X) Y (multiply V W Z)) (multiply V W (multiply X Y Z)).eq Univ (multiply (multiply a (inverse a) b) (inverse (multiply (multiply c d e) f (multiply c d g))) (multiply d (multiply g f e) c)) b) . -#Univ. -#V. -#W. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#e. -#f. -#g. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -nauto by H0,H1,H2,H3,H4; +#Univ ##. +#V ##. +#W ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#e ##. +#f ##. +#g ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +nauto by H0,H1,H2,H3,H4 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO067-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO067-1.ma index 7ae2c5258..de472f612 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO067-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO067-1.ma @@ -44,7 +44,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_tba_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -52,25 +52,25 @@ ntheorem prove_tba_axioms_1: ∀e:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (multiply (multiply A (inverse A) B) (inverse (multiply (multiply C D E) F (multiply C D G))) (multiply D (multiply G F E) C)) B.eq Univ (multiply (multiply d e a) b (multiply d e c)) (multiply d e (multiply a b c)) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (multiply (multiply A (inverse A) B) (inverse (multiply (multiply C D E) F (multiply C D G))) (multiply D (multiply G F E) C)) B.eq Univ (multiply (multiply d e a) b (multiply d e c)) (multiply d e (multiply a b c))) . -#Univ. -#A. -#B. -#C. -#D. -#E. -#F. -#G. -#a. -#b. -#c. -#d. -#e. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#E ##. +#F ##. +#G ##. +#a ##. +#b ##. +#c ##. +#d ##. +#e ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO068-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO068-1.ma index 93894aa56..72278f3cc 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO068-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO068-1.ma @@ -44,27 +44,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_tba_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ. ∀a:Univ. ∀b:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (multiply (multiply A (inverse A) B) (inverse (multiply (multiply C D E) F (multiply C D G))) (multiply D (multiply G F E) C)) B.eq Univ (multiply b a a) a +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (multiply (multiply A (inverse A) B) (inverse (multiply (multiply C D E) F (multiply C D G))) (multiply D (multiply G F E) C)) B.eq Univ (multiply b a a) a) . -#Univ. -#A. -#B. -#C. -#D. -#E. -#F. -#G. -#a. -#b. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#E ##. +#F ##. +#G ##. +#a ##. +#b ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO069-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO069-1.ma index a59a37817..82259f1ce 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO069-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO069-1.ma @@ -44,27 +44,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_tba_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ. ∀a:Univ. ∀b:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (multiply (multiply A (inverse A) B) (inverse (multiply (multiply C D E) F (multiply C D G))) (multiply D (multiply G F E) C)) B.eq Univ (multiply a b (inverse b)) a +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (multiply (multiply A (inverse A) B) (inverse (multiply (multiply C D E) F (multiply C D G))) (multiply D (multiply G F E) C)) B.eq Univ (multiply a b (inverse b)) a) . -#Univ. -#A. -#B. -#C. -#D. -#E. -#F. -#G. -#a. -#b. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#E ##. +#F ##. +#G ##. +#a ##. +#b ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO070-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO070-1.ma index 14670fbe4..fef95ccaf 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO070-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO070-1.ma @@ -44,27 +44,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_tba_axioms_4: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ. ∀a:Univ. ∀b:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (multiply (multiply A (inverse A) B) (inverse (multiply (multiply C D E) F (multiply C D G))) (multiply D (multiply G F E) C)) B.eq Univ (multiply a a b) a +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (multiply (multiply A (inverse A) B) (inverse (multiply (multiply C D E) F (multiply C D G))) (multiply D (multiply G F E) C)) B.eq Univ (multiply a a b) a) . -#Univ. -#A. -#B. -#C. -#D. -#E. -#F. -#G. -#a. -#b. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#E ##. +#F ##. +#G ##. +#a ##. +#b ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO071-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO071-1.ma index 77dd1d11a..fe0c80b79 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO071-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO071-1.ma @@ -44,27 +44,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_tba_axioms_5: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ. ∀a:Univ. ∀b:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (multiply (multiply A (inverse A) B) (inverse (multiply (multiply C D E) F (multiply C D G))) (multiply D (multiply G F E) C)) B.eq Univ (multiply (inverse b) b a) a +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (multiply (multiply A (inverse A) B) (inverse (multiply (multiply C D E) F (multiply C D G))) (multiply D (multiply G F E) C)) B.eq Univ (multiply (inverse b) b a) a) . -#Univ. -#A. -#B. -#C. -#D. -#E. -#F. -#G. -#a. -#b. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#E ##. +#F ##. +#G ##. +#a ##. +#b ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO072-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO072-1.ma index 212ac81a1..a371aad9c 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO072-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO072-1.ma @@ -44,24 +44,24 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem huntinton_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀inverse:∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (add (inverse (add (inverse (add A B)) C)) (inverse (add A (inverse (add (inverse C) (inverse (add C D)))))))) C.eq Univ (add b a) (add a b) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (add (inverse (add (inverse (add A B)) C)) (inverse (add A (inverse (add (inverse C) (inverse (add C D)))))))) C.eq Univ (add b a) (add a b)) . -#Univ. -#A. -#B. -#C. -#D. -#a. -#add. -#b. -#inverse. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a ##. +#add ##. +#b ##. +#inverse ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO073-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO073-1.ma index d54152531..c5621febb 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO073-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO073-1.ma @@ -44,26 +44,26 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem huntinton_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀c:Univ. ∀inverse:∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (add (inverse (add (inverse (add A B)) C)) (inverse (add A (inverse (add (inverse C) (inverse (add C D)))))))) C.eq Univ (add (add a b) c) (add a (add b c)) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (add (inverse (add (inverse (add A B)) C)) (inverse (add A (inverse (add (inverse C) (inverse (add C D)))))))) C.eq Univ (add (add a b) c) (add a (add b c))) . -#Univ. -#A. -#B. -#C. -#D. -#a. -#add. -#b. -#c. -#inverse. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a ##. +#add ##. +#b ##. +#c ##. +#inverse ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO074-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO074-1.ma index 6cf23fada..97562a173 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO074-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO074-1.ma @@ -44,24 +44,24 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem huntinton_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀inverse:∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (add (inverse (add (inverse (add A B)) C)) (inverse (add A (inverse (add (inverse C) (inverse (add C D)))))))) C.eq Univ (add (inverse (add (inverse a) b)) (inverse (add (inverse a) (inverse b)))) a +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (add (inverse (add (inverse (add A B)) C)) (inverse (add A (inverse (add (inverse C) (inverse (add C D)))))))) C.eq Univ (add (inverse (add (inverse a) b)) (inverse (add (inverse a) (inverse b)))) a) . -#Univ. -#A. -#B. -#C. -#D. -#a. -#add. -#b. -#inverse. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a ##. +#add ##. +#b ##. +#inverse ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO075-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO075-1.ma index 2bbb7f81a..153b555c7 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO075-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO075-1.ma @@ -44,21 +44,21 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_meredith_2_basis_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀nand:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand (nand B A) A)) (nand B (nand C A))) B.eq Univ (nand (nand a a) (nand b a)) a +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand (nand B A) A)) (nand B (nand C A))) B.eq Univ (nand (nand a a) (nand b a)) a) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#nand. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#nand ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO076-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO076-1.ma index e4d3033cf..e65b1daa4 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO076-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO076-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_meredith_2_basis_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀nand:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand (nand B A) A)) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand (nand B A) A)) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#c. -#nand. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#c ##. +#nand ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO077-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO077-1.ma index a6e9c06ca..c9520a831 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO077-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO077-1.ma @@ -44,21 +44,21 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_meredith_2_basis_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀nand:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand (nand B A) A)) (nand B (nand A C))) B.eq Univ (nand (nand a a) (nand b a)) a +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand (nand B A) A)) (nand B (nand A C))) B.eq Univ (nand (nand a a) (nand b a)) a) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#nand. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#nand ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO078-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO078-1.ma index 87acc5b31..d2c89b560 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO078-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO078-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_meredith_2_basis_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀nand:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand (nand B A) A)) (nand B (nand A C))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand (nand B A) A)) (nand B (nand A C))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#c. -#nand. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#c ##. +#nand ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO079-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO079-1.ma index 705275054..96b16267f 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO079-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO079-1.ma @@ -44,21 +44,21 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_meredith_2_basis_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀nand:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand A (nand B A))) (nand B (nand C A))) B.eq Univ (nand (nand a a) (nand b a)) a +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand A (nand B A))) (nand B (nand C A))) B.eq Univ (nand (nand a a) (nand b a)) a) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#nand. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#nand ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO080-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO080-1.ma index f675e097e..a25e346a5 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO080-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO080-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_meredith_2_basis_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀nand:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand A (nand B A))) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand A (nand B A))) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#c. -#nand. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#c ##. +#nand ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO081-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO081-1.ma index 08da9f2bb..f23ca4c1d 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO081-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO081-1.ma @@ -44,21 +44,21 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_meredith_2_basis_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀nand:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand A (nand A B))) (nand B (nand C A))) B.eq Univ (nand (nand a a) (nand b a)) a +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand A (nand A B))) (nand B (nand C A))) B.eq Univ (nand (nand a a) (nand b a)) a) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#nand. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#nand ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO082-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO082-1.ma index 2709ed6ab..163cb0630 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO082-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO082-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_meredith_2_basis_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀nand:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand A (nand A B))) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand A (nand A B))) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#c. -#nand. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#c ##. +#nand ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO083-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO083-1.ma index f3ed9a3c1..71915d7ef 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO083-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO083-1.ma @@ -44,21 +44,21 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_meredith_2_basis_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀nand:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand A (nand A B))) (nand B (nand A C))) B.eq Univ (nand (nand a a) (nand b a)) a +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand A (nand A B))) (nand B (nand A C))) B.eq Univ (nand (nand a a) (nand b a)) a) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#nand. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#nand ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO084-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO084-1.ma index 23a75dc9b..c3987b636 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO084-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO084-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_meredith_2_basis_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀nand:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand A (nand A B))) (nand B (nand A C))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand A (nand A B))) (nand B (nand A C))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#c. -#nand. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#c ##. +#nand ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO085-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO085-1.ma index 7f374a5af..a77b032a0 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO085-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO085-1.ma @@ -44,21 +44,21 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_meredith_2_basis_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀nand:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand A (nand B C))) (nand B (nand C A))) B.eq Univ (nand (nand a a) (nand b a)) a +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand A (nand B C))) (nand B (nand C A))) B.eq Univ (nand (nand a a) (nand b a)) a) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#nand. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#nand ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO086-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO086-1.ma index 49533666d..8b23c1e3a 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO086-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO086-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_meredith_2_basis_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀nand:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand A (nand B C))) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand A (nand B C))) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#c. -#nand. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#c ##. +#nand ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO087-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO087-1.ma index f23a85f78..697128f67 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO087-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO087-1.ma @@ -44,21 +44,21 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_meredith_2_basis_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀nand:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand A (nand B C))) (nand C (nand A B))) C.eq Univ (nand (nand a a) (nand b a)) a +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand A (nand B C))) (nand C (nand A B))) C.eq Univ (nand (nand a a) (nand b a)) a) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#nand. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#nand ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO088-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO088-1.ma index d5557527d..a45c2295c 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO088-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO088-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_meredith_2_basis_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀nand:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand A (nand B C))) (nand C (nand A B))) C.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand A (nand B C))) (nand C (nand A B))) C.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#c. -#nand. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#c ##. +#nand ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO089-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO089-1.ma index 62b4c080b..541bda104 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO089-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO089-1.ma @@ -44,21 +44,21 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_meredith_2_basis_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀nand:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand A (nand B B))) (nand B (nand C A))) B.eq Univ (nand (nand a a) (nand b a)) a +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand A (nand B B))) (nand B (nand C A))) B.eq Univ (nand (nand a a) (nand b a)) a) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#nand. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#nand ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO090-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO090-1.ma index 3b548d3af..22368190e 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO090-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO090-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_meredith_2_basis_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀nand:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand A (nand B B))) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand A (nand B B))) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#c. -#nand. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#c ##. +#nand ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO091-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO091-1.ma index c761ae6d2..cddf64a8b 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO091-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO091-1.ma @@ -44,21 +44,21 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_meredith_2_basis_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀nand:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand A (nand A B)) A) (nand B (nand C A))) B.eq Univ (nand (nand a a) (nand b a)) a +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand A (nand A B)) A) (nand B (nand C A))) B.eq Univ (nand (nand a a) (nand b a)) a) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#nand. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#nand ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO092-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO092-1.ma index cf994c58c..cbd15c537 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO092-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO092-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_meredith_2_basis_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀nand:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand A (nand A B)) A) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand A (nand A B)) A) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#c. -#nand. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#c ##. +#nand ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO093-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO093-1.ma index e3a1aa472..c18bf7089 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO093-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO093-1.ma @@ -44,21 +44,21 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_meredith_2_basis_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀nand:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand A (nand B B)) A) (nand B (nand C A))) B.eq Univ (nand (nand a a) (nand b a)) a +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand A (nand B B)) A) (nand B (nand C A))) B.eq Univ (nand (nand a a) (nand b a)) a) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#nand. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#nand ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO094-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO094-1.ma index fda8d8a66..8afcc7130 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO094-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO094-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_meredith_2_basis_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀nand:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand A (nand B B)) A) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand A (nand B B)) A) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#c. -#nand. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#c ##. +#nand ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO095-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO095-1.ma index 5b078b616..aff12b42c 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO095-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO095-1.ma @@ -44,21 +44,21 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_meredith_2_basis_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀nand:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand A (nand B C)) A) (nand B (nand A C))) B.eq Univ (nand (nand a a) (nand b a)) a +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand A (nand B C)) A) (nand B (nand A C))) B.eq Univ (nand (nand a a) (nand b a)) a) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#nand. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#nand ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO096-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO096-1.ma index 7198792ce..e2acf34bc 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO096-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO096-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_meredith_2_basis_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀nand:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand A (nand B C)) A) (nand B (nand A C))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand A (nand B C)) A) (nand B (nand A C))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#c. -#nand. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#c ##. +#nand ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO097-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO097-1.ma index 228f90ad1..edcdfb6d3 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO097-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO097-1.ma @@ -44,21 +44,21 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_meredith_2_basis_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀nand:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand A (nand B C)) A) (nand C (nand A B))) C.eq Univ (nand (nand a a) (nand b a)) a +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand A (nand B C)) A) (nand C (nand A B))) C.eq Univ (nand (nand a a) (nand b a)) a) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#nand. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#nand ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO098-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO098-1.ma index 623992c0f..1f046448a 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO098-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO098-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_meredith_2_basis_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀nand:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand A (nand B C)) A) (nand C (nand A B))) C.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand A (nand B C)) A) (nand C (nand A B))) C.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#c. -#nand. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#c ##. +#nand ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO099-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO099-1.ma index 636055369..cbc5efc0d 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO099-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO099-1.ma @@ -44,21 +44,21 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_meredith_2_basis_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀nand:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand A (nand A B)) A) (nand B (nand A C))) B.eq Univ (nand (nand a a) (nand b a)) a +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand A (nand A B)) A) (nand B (nand A C))) B.eq Univ (nand (nand a a) (nand b a)) a) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#nand. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#nand ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO100-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO100-1.ma index cacf43c9c..32f73c445 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO100-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO100-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_meredith_2_basis_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀nand:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand A (nand A B)) A) (nand B (nand A C))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand A (nand A B)) A) (nand B (nand A C))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#c. -#nand. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#c ##. +#nand ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO101-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO101-1.ma index 22281b576..e3cfe66d7 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO101-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO101-1.ma @@ -44,21 +44,21 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_meredith_2_basis_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀nand:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand (nand A B) A) A) (nand B (nand C A))) B.eq Univ (nand (nand a a) (nand b a)) a +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand (nand A B) A) A) (nand B (nand C A))) B.eq Univ (nand (nand a a) (nand b a)) a) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#nand. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#nand ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO102-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO102-1.ma index fbfae7832..98b571e9f 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO102-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO102-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_meredith_2_basis_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀nand:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand (nand A B) A) A) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand (nand A B) A) A) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#c. -#nand. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#c ##. +#nand ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO103-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO103-1.ma index 460072e23..11c234008 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO103-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO103-1.ma @@ -44,21 +44,21 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_meredith_2_basis_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀nand:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand (nand A B) A) A) (nand B (nand A C))) B.eq Univ (nand (nand a a) (nand b a)) a +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand (nand A B) A) A) (nand B (nand A C))) B.eq Univ (nand (nand a a) (nand b a)) a) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#nand. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#nand ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO104-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO104-1.ma index bd9fc4da2..6787665b7 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO104-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO104-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_meredith_2_basis_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀nand:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand (nand A B) A) A) (nand B (nand A C))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand (nand A B) A) A) (nand B (nand A C))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#c. -#nand. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#c ##. +#nand ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO105-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO105-1.ma index fb523918a..36aad0897 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO105-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO105-1.ma @@ -44,21 +44,21 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_meredith_2_basis_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀nand:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand (nand A B) C) C) (nand B (nand A C))) B.eq Univ (nand (nand a a) (nand b a)) a +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand (nand A B) C) C) (nand B (nand A C))) B.eq Univ (nand (nand a a) (nand b a)) a) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#nand. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#nand ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO106-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO106-1.ma index 9a9b69baa..1339bd227 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO106-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO106-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_meredith_2_basis_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀nand:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand (nand A B) C) C) (nand B (nand A C))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand (nand A B) C) C) (nand B (nand A C))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#c. -#nand. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#c ##. +#nand ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO107-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO107-1.ma index 834a20509..777c17488 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO107-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO107-1.ma @@ -44,21 +44,21 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_meredith_2_basis_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀nand:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand (nand A B) C) C) (nand B (nand C A))) B.eq Univ (nand (nand a a) (nand b a)) a +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand (nand A B) C) C) (nand B (nand C A))) B.eq Univ (nand (nand a a) (nand b a)) a) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#nand. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#nand ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/BOO108-1.ma b/helm/software/matita/contribs/ng_TPTP/BOO108-1.ma index 19a5a055b..54c434c03 100644 --- a/helm/software/matita/contribs/ng_TPTP/BOO108-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/BOO108-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_meredith_2_basis_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀nand:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand (nand A B) C) C) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand (nand A B) C) C) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#c. -#nand. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#c ##. +#nand ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL001-1.ma b/helm/software/matita/contribs/ng_TPTP/COL001-1.ma index 26dc7e574..b8be44f85 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL001-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL001-1.ma @@ -50,29 +50,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀combinator:Univ. ∀k:Univ. ∀s:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply k X) Y) X. -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#combinator. -#k. -#s. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#combinator ##. +#k ##. +#s ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL001-2.ma b/helm/software/matita/contribs/ng_TPTP/COL001-2.ma index 949eed4f1..cd9253597 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL001-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL001-2.ma @@ -48,7 +48,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀combinator:Univ. @@ -60,29 +60,28 @@ ntheorem prove_fixed_point: ∀H1:∀X:Univ.eq Univ (apply i X) X. ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)). ∀H3:∀X:Univ.∀Y:Univ.eq Univ (apply (apply k X) Y) X. -∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y) +∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#combinator. -#i. -#k. -#s. -#x. -#H0. -#H1. -#H2. -#H3. -#H4. -napply ex_intro[ -nid2: -nauto by H0,H1,H2,H3,H4; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#combinator ##. +#i ##. +#k ##. +#s ##. +#x ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2,H3,H4 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL002-1.ma b/helm/software/matita/contribs/ng_TPTP/COL002-1.ma index 5c514573e..f985b86d4 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL002-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL002-1.ma @@ -46,7 +46,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀c:Univ. @@ -56,27 +56,26 @@ ntheorem prove_fixed_point: ∀H0:∀X:Univ.eq Univ (apply i X) X. ∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply c X) Y) Z) (apply (apply X Z) Y). ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)). -∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ Y (apply fixed_pt Y) +∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ Y (apply fixed_pt Y)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#c. -#fixed_pt. -#i. -#s. -#H0. -#H1. -#H2. -#H3. -napply ex_intro[ -nid2: -nauto by H0,H1,H2,H3; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#c ##. +#fixed_pt ##. +#i ##. +#s ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2,H3 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL002-4.ma b/helm/software/matita/contribs/ng_TPTP/COL002-4.ma index 18ce4366d..db2a10fb4 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL002-4.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL002-4.ma @@ -50,7 +50,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_weak_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀c:Univ. @@ -62,25 +62,25 @@ ntheorem prove_weak_fixed_point: ∀H1:∀X:Univ.eq Univ (apply i X) X. ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply c X) Y) Z) (apply (apply X Z) Y). ∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)). -∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).eq Univ (weak_fixed_point fixed_pt) (apply fixed_pt (weak_fixed_point fixed_pt)) +∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).eq Univ (weak_fixed_point fixed_pt) (apply fixed_pt (weak_fixed_point fixed_pt))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#c. -#fixed_pt. -#i. -#s. -#weak_fixed_point. -#H0. -#H1. -#H2. -#H3. -#H4. -nauto by H0,H1,H2,H3,H4; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#c ##. +#fixed_pt ##. +#i ##. +#s ##. +#weak_fixed_point ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +nauto by H0,H1,H2,H3,H4 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL002-5.ma b/helm/software/matita/contribs/ng_TPTP/COL002-5.ma index c026dd854..921e8fefd 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL002-5.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL002-5.ma @@ -50,7 +50,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_weak_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀c:Univ. @@ -62,25 +62,25 @@ ntheorem prove_weak_fixed_point: ∀H1:∀X:Univ.eq Univ (apply i X) X. ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply c X) Y) Z) (apply (apply X Z) Y). ∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)). -∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).eq Univ (weak_fixed_point fixed_pt) (apply fixed_pt (weak_fixed_point fixed_pt)) +∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).eq Univ (weak_fixed_point fixed_pt) (apply fixed_pt (weak_fixed_point fixed_pt))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#c. -#fixed_pt. -#i. -#s. -#weak_fixed_point. -#H0. -#H1. -#H2. -#H3. -#H4. -nauto by H0,H1,H2,H3,H4; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#c ##. +#fixed_pt ##. +#i ##. +#s ##. +#weak_fixed_point ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +nauto by H0,H1,H2,H3,H4 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL003-1.ma b/helm/software/matita/contribs/ng_TPTP/COL003-1.ma index 1de3e3087..e760015ee 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL003-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL003-1.ma @@ -82,29 +82,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_strong_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀f:∀_:Univ.Univ. ∀w:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y))) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y)))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#f. -#w. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#f ##. +#w ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL003-2.ma b/helm/software/matita/contribs/ng_TPTP/COL003-2.ma index a9031557b..f9f2ab29d 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL003-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL003-2.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_strong_fixed_point: - ∀Univ:Type.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀fixed_point:∀_:Univ.Prop. @@ -62,22 +62,22 @@ ntheorem prove_strong_fixed_point: ∀w:Univ. ∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point. ∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y). -∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply w w)) (apply (apply b w) (apply (apply b b) b))) +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply w w)) (apply (apply b w) (apply (apply b b) b)))) . -#Univ. -#Strong_fixed_point. -#X. -#Y. -#Z. -#apply. -#b. -#fixed_point. -#fixed_pt. -#w. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#Strong_fixed_point ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#fixed_point ##. +#fixed_pt ##. +#w ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL004-1.ma b/helm/software/matita/contribs/ng_TPTP/COL004-1.ma index 7a0bae2d0..9c85a79a7 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL004-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL004-1.ma @@ -46,31 +46,30 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_u_combinator: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀f:∀_:Univ.Univ. ∀g:∀_:Univ.Univ. ∀k:Univ. ∀s:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply k X) Y) X. -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Z:Univ.eq Univ (apply (apply Z (f Z)) (g Z)) (apply (g Z) (apply (apply (f Z) (f Z)) (g Z))) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Z:Univ.eq Univ (apply (apply Z (f Z)) (g Z)) (apply (g Z) (apply (apply (f Z) (f Z)) (g Z)))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#f. -#g. -#k. -#s. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#f ##. +#g ##. +#k ##. +#s ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL004-3.ma b/helm/software/matita/contribs/ng_TPTP/COL004-3.ma index 267efd5f8..b7674b26b 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL004-3.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL004-3.ma @@ -50,27 +50,27 @@ include "logic/equality.ma". (* ----This is the U equivalent *) ntheorem prove_u_combinator: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀k:Univ. ∀s:Univ. ∀x:Univ. ∀y:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply k X) Y) X. -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).eq Univ (apply (apply (apply (apply s (apply k (apply s (apply (apply s k) k)))) (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))) x) y) (apply y (apply (apply x x) y)) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).eq Univ (apply (apply (apply (apply s (apply k (apply s (apply (apply s k) k)))) (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))) x) y) (apply y (apply (apply x x) y))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#k. -#s. -#x. -#y. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#k ##. +#s ##. +#x ##. +#y ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL005-1.ma b/helm/software/matita/contribs/ng_TPTP/COL005-1.ma index ce19aae47..b0bb545aa 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL005-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL005-1.ma @@ -56,29 +56,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_model: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀combinator:Univ. ∀s:Univ. ∀w:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#combinator. -#s. -#w. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#combinator ##. +#s ##. +#w ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL006-1.ma b/helm/software/matita/contribs/ng_TPTP/COL006-1.ma index 6e8a16f6c..ae34cf1f7 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL006-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL006-1.ma @@ -46,29 +46,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀f:∀_:Univ.Univ. ∀k:Univ. ∀s:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply k X) Y) X. -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y))) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y)))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#f. -#k. -#s. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#f ##. +#k ##. +#s ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL006-5.ma b/helm/software/matita/contribs/ng_TPTP/COL006-5.ma index f63155f86..5978e2293 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL006-5.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL006-5.ma @@ -48,7 +48,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_strong_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀fixed_pt:Univ. ∀k:Univ. @@ -56,21 +56,21 @@ ntheorem prove_strong_fixed_point: ∀strong_fixed_point:Univ. ∀H0:eq Univ strong_fixed_point (apply (apply s (apply k (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))) (apply (apply s (apply k (apply (apply s s) (apply s k)))) (apply (apply s (apply k s)) k))). ∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply k X) Y) X. -∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt)) +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#fixed_pt. -#k. -#s. -#strong_fixed_point. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#fixed_pt ##. +#k ##. +#s ##. +#strong_fixed_point ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL006-6.ma b/helm/software/matita/contribs/ng_TPTP/COL006-6.ma index e464b4296..f9904be94 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL006-6.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL006-6.ma @@ -48,7 +48,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_strong_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀fixed_pt:Univ. ∀k:Univ. @@ -56,21 +56,21 @@ ntheorem prove_strong_fixed_point: ∀strong_fixed_point:Univ. ∀H0:eq Univ strong_fixed_point (apply (apply s (apply k (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))) (apply (apply s (apply (apply s (apply k s)) k)) (apply k (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))). ∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply k X) Y) X. -∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt)) +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#fixed_pt. -#k. -#s. -#strong_fixed_point. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#fixed_pt ##. +#k ##. +#s ##. +#strong_fixed_point ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL006-7.ma b/helm/software/matita/contribs/ng_TPTP/COL006-7.ma index 9209d1dc2..03263eb97 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL006-7.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL006-7.ma @@ -48,7 +48,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_strong_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀fixed_pt:Univ. ∀k:Univ. @@ -56,21 +56,21 @@ ntheorem prove_strong_fixed_point: ∀strong_fixed_point:Univ. ∀H0:eq Univ strong_fixed_point (apply (apply s (apply k (apply (apply (apply s s) (apply (apply s k) k)) (apply (apply s s) (apply s k))))) (apply (apply s (apply k s)) k)). ∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply k X) Y) X. -∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt)) +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#fixed_pt. -#k. -#s. -#strong_fixed_point. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#fixed_pt ##. +#k ##. +#s ##. +#strong_fixed_point ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL007-1.ma b/helm/software/matita/contribs/ng_TPTP/COL007-1.ma index d8c586f79..2f4a422d7 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL007-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL007-1.ma @@ -50,24 +50,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀combinator:Univ. ∀l:Univ. -∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply l X) Y) (apply X (apply Y Y)).∃Y:Univ.eq Univ Y (apply combinator Y) +∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply l X) Y) (apply X (apply Y Y)).∃Y:Univ.eq Univ Y (apply combinator Y)) . -#Univ. -#X. -#Y. -#apply. -#combinator. -#l. -#H0. -napply ex_intro[ -nid2: -nauto by H0; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#apply ##. +#combinator ##. +#l ##. +#H0 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL008-1.ma b/helm/software/matita/contribs/ng_TPTP/COL008-1.ma index 9ed5066f1..9ce669458 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL008-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL008-1.ma @@ -54,29 +54,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀combinator:Univ. ∀m:Univ. ∀H0:∀X:Univ.eq Univ (apply m X) (apply X X). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#combinator. -#m. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#combinator ##. +#m ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL009-1.ma b/helm/software/matita/contribs/ng_TPTP/COL009-1.ma index 14d0418f6..42c6ea098 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL009-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL009-1.ma @@ -52,29 +52,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀combinator:Univ. ∀l2:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply l2 X) Y) (apply Y (apply X X)). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#combinator. -#l2. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#combinator ##. +#l2 ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL010-1.ma b/helm/software/matita/contribs/ng_TPTP/COL010-1.ma index 8eb20e755..0a17e7973 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL010-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL010-1.ma @@ -52,29 +52,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀combinator:Univ. ∀s2:Univ. ∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s2 X) Y) Z) (apply (apply X Z) (apply Y Y)). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#combinator. -#s2. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#combinator ##. +#s2 ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL011-1.ma b/helm/software/matita/contribs/ng_TPTP/COL011-1.ma index 5563c8efd..e9789da85 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL011-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL011-1.ma @@ -52,29 +52,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀combinator:Univ. ∀o:Univ. ∀q1:Univ. ∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply q1 X) Y) Z) (apply X (apply Z Y)). -∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply o X) Y) (apply Y (apply X Y)).∃Y:Univ.eq Univ Y (apply combinator Y) +∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply o X) Y) (apply Y (apply X Y)).∃Y:Univ.eq Univ Y (apply combinator Y)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#combinator. -#o. -#q1. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#combinator ##. +#o ##. +#q1 ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL012-1.ma b/helm/software/matita/contribs/ng_TPTP/COL012-1.ma index e5ddd0330..48afb4418 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL012-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL012-1.ma @@ -50,24 +50,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀combinator:Univ. ∀u:Univ. -∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply u X) Y) (apply Y (apply (apply X X) Y)).∃Y:Univ.eq Univ Y (apply combinator Y) +∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply u X) Y) (apply Y (apply (apply X X) Y)).∃Y:Univ.eq Univ Y (apply combinator Y)) . -#Univ. -#X. -#Y. -#apply. -#combinator. -#u. -#H0. -napply ex_intro[ -nid2: -nauto by H0; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#apply ##. +#combinator ##. +#u ##. +#H0 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL013-1.ma b/helm/software/matita/contribs/ng_TPTP/COL013-1.ma index 62384c11d..769322cfb 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL013-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL013-1.ma @@ -52,29 +52,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀combinator:Univ. ∀l:Univ. ∀s:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply l X) Y) (apply X (apply Y Y)). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#combinator. -#l. -#s. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#combinator ##. +#l ##. +#s ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL014-1.ma b/helm/software/matita/contribs/ng_TPTP/COL014-1.ma index a2deaa971..4b5322bdd 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL014-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL014-1.ma @@ -52,28 +52,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀combinator:Univ. ∀l:Univ. ∀o:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply o X) Y) (apply Y (apply X Y)). -∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply l X) Y) (apply X (apply Y Y)).∃Y:Univ.eq Univ Y (apply combinator Y) +∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply l X) Y) (apply X (apply Y Y)).∃Y:Univ.eq Univ Y (apply combinator Y)) . -#Univ. -#X. -#Y. -#apply. -#combinator. -#l. -#o. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#apply ##. +#combinator ##. +#l ##. +#o ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL015-1.ma b/helm/software/matita/contribs/ng_TPTP/COL015-1.ma index 90c3d7c1d..f4744b4a8 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL015-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL015-1.ma @@ -50,29 +50,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀combinator:Univ. ∀m:Univ. ∀q:Univ. ∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply q X) Y) Z) (apply Y (apply X Z)). -∀H1:∀X:Univ.eq Univ (apply m X) (apply X X).∃Y:Univ.eq Univ Y (apply combinator Y) +∀H1:∀X:Univ.eq Univ (apply m X) (apply X X).∃Y:Univ.eq Univ Y (apply combinator Y)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#combinator. -#m. -#q. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#combinator ##. +#m ##. +#q ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL016-1.ma b/helm/software/matita/contribs/ng_TPTP/COL016-1.ma index 5aed7bcd6..4f3c8dee7 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL016-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL016-1.ma @@ -52,7 +52,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀combinator:Univ. @@ -60,25 +60,24 @@ ntheorem prove_fixed_point: ∀m:Univ. ∀H0:∀X:Univ.eq Univ (apply m X) (apply X X). ∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply l X) Y) (apply X (apply Y Y)). -∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y) +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#combinator. -#l. -#m. -#H0. -#H1. -#H2. -napply ex_intro[ -nid2: -nauto by H0,H1,H2; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#combinator ##. +#l ##. +#m ##. +#H0 ##. +#H1 ##. +#H2 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL017-1.ma b/helm/software/matita/contribs/ng_TPTP/COL017-1.ma index b605e2546..fca3e5539 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL017-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL017-1.ma @@ -52,7 +52,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀combinator:Univ. @@ -60,25 +60,24 @@ ntheorem prove_fixed_point: ∀t:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X). ∀H1:∀X:Univ.eq Univ (apply m X) (apply X X). -∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y) +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#combinator. -#m. -#t. -#H0. -#H1. -#H2. -napply ex_intro[ -nid2: -nauto by H0,H1,H2; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#combinator ##. +#m ##. +#t ##. +#H0 ##. +#H1 ##. +#H2 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL018-1.ma b/helm/software/matita/contribs/ng_TPTP/COL018-1.ma index 1736cfd65..76b226988 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL018-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL018-1.ma @@ -52,7 +52,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀combinator:Univ. ∀l:Univ. @@ -60,25 +60,24 @@ ntheorem prove_fixed_point: ∀w:Univ. ∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply q X) Y) Z) (apply Y (apply X Z)). ∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y). -∀H2:∀X:Univ.∀Y:Univ.eq Univ (apply (apply l X) Y) (apply X (apply Y Y)).∃Y:Univ.eq Univ Y (apply combinator Y) +∀H2:∀X:Univ.∀Y:Univ.eq Univ (apply (apply l X) Y) (apply X (apply Y Y)).∃Y:Univ.eq Univ Y (apply combinator Y)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#combinator. -#l. -#q. -#w. -#H0. -#H1. -#H2. -napply ex_intro[ -nid2: -nauto by H0,H1,H2; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#combinator ##. +#l ##. +#q ##. +#w ##. +#H0 ##. +#H1 ##. +#H2 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL019-1.ma b/helm/software/matita/contribs/ng_TPTP/COL019-1.ma index 1ea3c6a48..a95d1674c 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL019-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL019-1.ma @@ -52,7 +52,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀combinator:Univ. @@ -60,25 +60,24 @@ ntheorem prove_fixed_point: ∀t:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X). ∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)). -∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y) +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#combinator. -#s. -#t. -#H0. -#H1. -#H2. -napply ex_intro[ -nid2: -nauto by H0,H1,H2; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#combinator ##. +#s ##. +#t ##. +#H0 ##. +#H1 ##. +#H2 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL020-1.ma b/helm/software/matita/contribs/ng_TPTP/COL020-1.ma index ba7a4682d..2142718c7 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL020-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL020-1.ma @@ -52,7 +52,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀c:Univ. @@ -60,25 +60,24 @@ ntheorem prove_fixed_point: ∀s:Univ. ∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply c X) Y) Z) (apply (apply X Z) Y). ∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)). -∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y) +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#c. -#combinator. -#s. -#H0. -#H1. -#H2. -napply ex_intro[ -nid2: -nauto by H0,H1,H2; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#c ##. +#combinator ##. +#s ##. +#H0 ##. +#H1 ##. +#H2 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL021-1.ma b/helm/software/matita/contribs/ng_TPTP/COL021-1.ma index 08ffe6a60..c51a4752d 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL021-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL021-1.ma @@ -52,7 +52,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀combinator:Univ. @@ -60,25 +60,24 @@ ntheorem prove_fixed_point: ∀v:Univ. ∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply v X) Y) Z) (apply (apply Z X) Y). ∀H1:∀X:Univ.eq Univ (apply m X) (apply X X). -∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y) +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#combinator. -#m. -#v. -#H0. -#H1. -#H2. -napply ex_intro[ -nid2: -nauto by H0,H1,H2; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#combinator ##. +#m ##. +#v ##. +#H0 ##. +#H1 ##. +#H2 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL022-1.ma b/helm/software/matita/contribs/ng_TPTP/COL022-1.ma index ce9b20741..b7d5d8942 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL022-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL022-1.ma @@ -52,7 +52,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀combinator:Univ. @@ -60,25 +60,24 @@ ntheorem prove_fixed_point: ∀o:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply o X) Y) (apply Y (apply X Y)). ∀H1:∀X:Univ.eq Univ (apply m X) (apply X X). -∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y) +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#combinator. -#m. -#o. -#H0. -#H1. -#H2. -napply ex_intro[ -nid2: -nauto by H0,H1,H2; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#combinator ##. +#m ##. +#o ##. +#H0 ##. +#H1 ##. +#H2 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL023-1.ma b/helm/software/matita/contribs/ng_TPTP/COL023-1.ma index 2de4901e1..58bc6da21 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL023-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL023-1.ma @@ -52,29 +52,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀combinator:Univ. ∀n:Univ. ∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply n X) Y) Z) (apply (apply (apply X Z) Y) Z). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#combinator. -#n. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#combinator ##. +#n ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL024-1.ma b/helm/software/matita/contribs/ng_TPTP/COL024-1.ma index 627e64f4c..daa1e7b18 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL024-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL024-1.ma @@ -52,7 +52,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀c:Univ. @@ -60,25 +60,24 @@ ntheorem prove_fixed_point: ∀m:Univ. ∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply c X) Y) Z) (apply (apply X Z) Y). ∀H1:∀X:Univ.eq Univ (apply m X) (apply X X). -∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y) +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#c. -#combinator. -#m. -#H0. -#H1. -#H2. -napply ex_intro[ -nid2: -nauto by H0,H1,H2; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#c ##. +#combinator ##. +#m ##. +#H0 ##. +#H1 ##. +#H2 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL025-1.ma b/helm/software/matita/contribs/ng_TPTP/COL025-1.ma index c1c724954..fe13f5022 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL025-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL025-1.ma @@ -54,29 +54,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀combinator:Univ. ∀w:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#combinator. -#w. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#combinator ##. +#w ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL026-1.ma b/helm/software/matita/contribs/ng_TPTP/COL026-1.ma index efb2ac389..3ad640da1 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL026-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL026-1.ma @@ -52,29 +52,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀combinator:Univ. ∀w1:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w1 X) Y) (apply (apply Y X) X). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#combinator. -#w1. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#combinator ##. +#w1 ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL027-1.ma b/helm/software/matita/contribs/ng_TPTP/COL027-1.ma index 1f6eed676..a843dbe6c 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL027-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL027-1.ma @@ -52,29 +52,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀combinator:Univ. ∀h:Univ. ∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply h X) Y) Z) (apply (apply (apply X Y) Z) Y). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#combinator. -#h. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#combinator ##. +#h ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL029-1.ma b/helm/software/matita/contribs/ng_TPTP/COL029-1.ma index 724792270..2b8dd1498 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL029-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL029-1.ma @@ -54,24 +54,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀f:∀_:Univ.Univ. ∀u:Univ. -∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply u X) Y) (apply Y (apply (apply X X) Y)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y))) +∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply u X) Y) (apply Y (apply (apply X X) Y)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y)))) . -#Univ. -#X. -#Y. -#apply. -#f. -#u. -#H0. -napply ex_intro[ -nid2: -nauto by H0; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#apply ##. +#f ##. +#u ##. +#H0 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL030-1.ma b/helm/software/matita/contribs/ng_TPTP/COL030-1.ma index 75809d664..f5f7104dd 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL030-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL030-1.ma @@ -52,29 +52,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀f:∀_:Univ.Univ. ∀l:Univ. ∀s:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply l X) Y) (apply X (apply Y Y)). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y))) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y)))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#f. -#l. -#s. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#f ##. +#l ##. +#s ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL031-1.ma b/helm/software/matita/contribs/ng_TPTP/COL031-1.ma index d21c29e50..07453fb04 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL031-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL031-1.ma @@ -52,28 +52,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀f:∀_:Univ.Univ. ∀l:Univ. ∀o:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply o X) Y) (apply Y (apply X Y)). -∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply l X) Y) (apply X (apply Y Y)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y))) +∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply l X) Y) (apply X (apply Y Y)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y)))) . -#Univ. -#X. -#Y. -#apply. -#f. -#l. -#o. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#apply ##. +#f ##. +#l ##. +#o ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL032-1.ma b/helm/software/matita/contribs/ng_TPTP/COL032-1.ma index ee19a662c..68e4a66b1 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL032-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL032-1.ma @@ -52,29 +52,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀f:∀_:Univ.Univ. ∀m:Univ. ∀q:Univ. ∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply q X) Y) Z) (apply Y (apply X Z)). -∀H1:∀X:Univ.eq Univ (apply m X) (apply X X).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y))) +∀H1:∀X:Univ.eq Univ (apply m X) (apply X X).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y)))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#f. -#m. -#q. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#f ##. +#m ##. +#q ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL033-1.ma b/helm/software/matita/contribs/ng_TPTP/COL033-1.ma index 961826c37..bb0b03389 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL033-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL033-1.ma @@ -52,7 +52,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀f:∀_:Univ.Univ. @@ -60,25 +60,24 @@ ntheorem prove_fixed_point: ∀m:Univ. ∀H0:∀X:Univ.eq Univ (apply m X) (apply X X). ∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply l X) Y) (apply X (apply Y Y)). -∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y))) +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y)))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#f. -#l. -#m. -#H0. -#H1. -#H2. -napply ex_intro[ -nid2: -nauto by H0,H1,H2; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#f ##. +#l ##. +#m ##. +#H0 ##. +#H1 ##. +#H2 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL034-1.ma b/helm/software/matita/contribs/ng_TPTP/COL034-1.ma index 151dbbc7b..8ec76f290 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL034-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL034-1.ma @@ -52,7 +52,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀f:∀_:Univ.Univ. @@ -60,25 +60,24 @@ ntheorem prove_fixed_point: ∀t:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X). ∀H1:∀X:Univ.eq Univ (apply m X) (apply X X). -∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y))) +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y)))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#f. -#m. -#t. -#H0. -#H1. -#H2. -napply ex_intro[ -nid2: -nauto by H0,H1,H2; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#f ##. +#m ##. +#t ##. +#H0 ##. +#H1 ##. +#H2 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL035-1.ma b/helm/software/matita/contribs/ng_TPTP/COL035-1.ma index 04a96291d..f85a40796 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL035-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL035-1.ma @@ -52,7 +52,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀f:∀_:Univ.Univ. ∀l:Univ. @@ -60,25 +60,24 @@ ntheorem prove_fixed_point: ∀w:Univ. ∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply q X) Y) Z) (apply Y (apply X Z)). ∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y). -∀H2:∀X:Univ.∀Y:Univ.eq Univ (apply (apply l X) Y) (apply X (apply Y Y)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y))) +∀H2:∀X:Univ.∀Y:Univ.eq Univ (apply (apply l X) Y) (apply X (apply Y Y)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y)))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#f. -#l. -#q. -#w. -#H0. -#H1. -#H2. -napply ex_intro[ -nid2: -nauto by H0,H1,H2; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#f ##. +#l ##. +#q ##. +#w ##. +#H0 ##. +#H1 ##. +#H2 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL036-1.ma b/helm/software/matita/contribs/ng_TPTP/COL036-1.ma index cf7eadc9e..9c220cccc 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL036-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL036-1.ma @@ -52,7 +52,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀f:∀_:Univ.Univ. @@ -60,25 +60,24 @@ ntheorem prove_fixed_point: ∀t:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X). ∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)). -∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y))) +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y)))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#f. -#s. -#t. -#H0. -#H1. -#H2. -napply ex_intro[ -nid2: -nauto by H0,H1,H2; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#f ##. +#s ##. +#t ##. +#H0 ##. +#H1 ##. +#H2 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL037-1.ma b/helm/software/matita/contribs/ng_TPTP/COL037-1.ma index 0e466d643..1d688f683 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL037-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL037-1.ma @@ -52,7 +52,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀c:Univ. @@ -60,25 +60,24 @@ ntheorem prove_fixed_point: ∀s:Univ. ∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply c X) Y) Z) (apply (apply X Z) Y). ∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)). -∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y))) +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y)))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#c. -#f. -#s. -#H0. -#H1. -#H2. -napply ex_intro[ -nid2: -nauto by H0,H1,H2; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#c ##. +#f ##. +#s ##. +#H0 ##. +#H1 ##. +#H2 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL038-1.ma b/helm/software/matita/contribs/ng_TPTP/COL038-1.ma index ae0ba46d1..c121a04f8 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL038-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL038-1.ma @@ -52,7 +52,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀f:∀_:Univ.Univ. @@ -60,25 +60,24 @@ ntheorem prove_fixed_point: ∀v:Univ. ∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply v X) Y) Z) (apply (apply Z X) Y). ∀H1:∀X:Univ.eq Univ (apply m X) (apply X X). -∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y))) +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y)))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#f. -#m. -#v. -#H0. -#H1. -#H2. -napply ex_intro[ -nid2: -nauto by H0,H1,H2; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#f ##. +#m ##. +#v ##. +#H0 ##. +#H1 ##. +#H2 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL039-1.ma b/helm/software/matita/contribs/ng_TPTP/COL039-1.ma index 08aea64e2..4918b6b05 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL039-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL039-1.ma @@ -52,7 +52,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀f:∀_:Univ.Univ. @@ -60,25 +60,24 @@ ntheorem prove_fixed_point: ∀o:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply o X) Y) (apply Y (apply X Y)). ∀H1:∀X:Univ.eq Univ (apply m X) (apply X X). -∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y))) +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y)))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#f. -#m. -#o. -#H0. -#H1. -#H2. -napply ex_intro[ -nid2: -nauto by H0,H1,H2; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#f ##. +#m ##. +#o ##. +#H0 ##. +#H1 ##. +#H2 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL041-1.ma b/helm/software/matita/contribs/ng_TPTP/COL041-1.ma index 95d8e9b6a..e03054e83 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL041-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL041-1.ma @@ -52,7 +52,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀c:Univ. @@ -60,25 +60,24 @@ ntheorem prove_fixed_point: ∀m:Univ. ∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply c X) Y) Z) (apply (apply X Z) Y). ∀H1:∀X:Univ.eq Univ (apply m X) (apply X X). -∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y))) +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y)))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#c. -#f. -#m. -#H0. -#H1. -#H2. -napply ex_intro[ -nid2: -nauto by H0,H1,H2; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#c ##. +#f ##. +#m ##. +#H0 ##. +#H1 ##. +#H2 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL042-1.ma b/helm/software/matita/contribs/ng_TPTP/COL042-1.ma index 540da8d38..80c0a8eaa 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL042-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL042-1.ma @@ -56,29 +56,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀f:∀_:Univ.Univ. ∀w1:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w1 X) Y) (apply (apply Y X) X). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y))) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y)))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#f. -#w1. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#f ##. +#w1 ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL042-6.ma b/helm/software/matita/contribs/ng_TPTP/COL042-6.ma index d651b9a71..510e0e327 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL042-6.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL042-6.ma @@ -50,7 +50,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_strong_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀fixed_pt:Univ. @@ -58,21 +58,21 @@ ntheorem prove_strong_fixed_point: ∀w1:Univ. ∀H0:eq Univ strong_fixed_point (apply (apply b (apply (apply b (apply (apply b (apply w1 w1)) (apply b w1))) b)) b). ∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w1 X) Y) (apply (apply Y X) X). -∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt)) +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#fixed_pt. -#strong_fixed_point. -#w1. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#fixed_pt ##. +#strong_fixed_point ##. +#w1 ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL042-7.ma b/helm/software/matita/contribs/ng_TPTP/COL042-7.ma index e5242e4a4..a918648bb 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL042-7.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL042-7.ma @@ -50,7 +50,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_strong_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀fixed_pt:Univ. @@ -58,21 +58,21 @@ ntheorem prove_strong_fixed_point: ∀w1:Univ. ∀H0:eq Univ strong_fixed_point (apply (apply b (apply (apply b (apply w1 w1)) (apply b w1))) (apply (apply b b) b)). ∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w1 X) Y) (apply (apply Y X) X). -∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt)) +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#fixed_pt. -#strong_fixed_point. -#w1. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#fixed_pt ##. +#strong_fixed_point ##. +#w1 ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL042-8.ma b/helm/software/matita/contribs/ng_TPTP/COL042-8.ma index 1405102ea..45c3e3f73 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL042-8.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL042-8.ma @@ -50,7 +50,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_strong_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀fixed_pt:Univ. @@ -58,21 +58,21 @@ ntheorem prove_strong_fixed_point: ∀w1:Univ. ∀H0:eq Univ strong_fixed_point (apply (apply b (apply (apply b (apply w1 w1)) (apply (apply b (apply b w1)) b))) b). ∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w1 X) Y) (apply (apply Y X) X). -∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt)) +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#fixed_pt. -#strong_fixed_point. -#w1. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#fixed_pt ##. +#strong_fixed_point ##. +#w1 ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL042-9.ma b/helm/software/matita/contribs/ng_TPTP/COL042-9.ma index f401eafe3..14c63a54f 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL042-9.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL042-9.ma @@ -50,7 +50,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_strong_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀fixed_pt:Univ. @@ -58,21 +58,21 @@ ntheorem prove_strong_fixed_point: ∀w1:Univ. ∀H0:eq Univ strong_fixed_point (apply (apply b (apply w1 w1)) (apply (apply b (apply b w1)) (apply (apply b b) b))). ∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w1 X) Y) (apply (apply Y X) X). -∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt)) +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#fixed_pt. -#strong_fixed_point. -#w1. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#fixed_pt ##. +#strong_fixed_point ##. +#w1 ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL043-1.ma b/helm/software/matita/contribs/ng_TPTP/COL043-1.ma index b3cf607c1..dd293cc18 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL043-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL043-1.ma @@ -60,29 +60,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀f:∀_:Univ.Univ. ∀h:Univ. ∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply h X) Y) Z) (apply (apply (apply X Y) Z) Y). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y))) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y)))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#f. -#h. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#f ##. +#h ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL043-3.ma b/helm/software/matita/contribs/ng_TPTP/COL043-3.ma index 56a2344dd..a2db90239 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL043-3.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL043-3.ma @@ -52,7 +52,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_strong_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀fixed_pt:Univ. @@ -60,21 +60,21 @@ ntheorem prove_strong_fixed_point: ∀strong_fixed_point:Univ. ∀H0:eq Univ strong_fixed_point (apply (apply b (apply (apply b (apply (apply h (apply (apply b (apply (apply b h) (apply b b))) (apply h (apply (apply b h) (apply b b))))) h)) b)) b). ∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply h X) Y) Z) (apply (apply (apply X Y) Z) Y). -∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt)) +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#fixed_pt. -#h. -#strong_fixed_point. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#fixed_pt ##. +#h ##. +#strong_fixed_point ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL044-1.ma b/helm/software/matita/contribs/ng_TPTP/COL044-1.ma index 75ccabb43..9179224ce 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL044-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL044-1.ma @@ -60,29 +60,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀f:∀_:Univ.Univ. ∀n:Univ. ∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply n X) Y) Z) (apply (apply (apply X Z) Y) Z). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y))) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y)))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#f. -#n. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#f ##. +#n ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL044-6.ma b/helm/software/matita/contribs/ng_TPTP/COL044-6.ma index b0443cc89..333690ef8 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL044-6.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL044-6.ma @@ -50,7 +50,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_strong_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀fixed_pt:Univ. @@ -58,21 +58,21 @@ ntheorem prove_strong_fixed_point: ∀strong_fixed_point:Univ. ∀H0:eq Univ strong_fixed_point (apply (apply b (apply (apply b (apply (apply n (apply (apply b b) (apply (apply n (apply (apply b b) n)) n))) n)) b)) b). ∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply n X) Y) Z) (apply (apply (apply X Z) Y) Z). -∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt)) +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#fixed_pt. -#n. -#strong_fixed_point. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#fixed_pt ##. +#n ##. +#strong_fixed_point ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL044-7.ma b/helm/software/matita/contribs/ng_TPTP/COL044-7.ma index 257c88e50..3fb4d5fea 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL044-7.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL044-7.ma @@ -50,7 +50,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_strong_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀fixed_pt:Univ. @@ -58,21 +58,21 @@ ntheorem prove_strong_fixed_point: ∀strong_fixed_point:Univ. ∀H0:eq Univ strong_fixed_point (apply (apply b (apply (apply b (apply (apply n (apply (apply b b) (apply (apply n (apply n (apply b b))) n))) n)) b)) b). ∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply n X) Y) Z) (apply (apply (apply X Z) Y) Z). -∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt)) +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#fixed_pt. -#n. -#strong_fixed_point. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#fixed_pt ##. +#n ##. +#strong_fixed_point ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL044-8.ma b/helm/software/matita/contribs/ng_TPTP/COL044-8.ma index 156d1b536..e365ec387 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL044-8.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL044-8.ma @@ -50,7 +50,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_strong_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀fixed_pt:Univ. @@ -58,21 +58,21 @@ ntheorem prove_strong_fixed_point: ∀strong_fixed_point:Univ. ∀H0:eq Univ strong_fixed_point (apply (apply b (apply (apply b (apply (apply n (apply n (apply (apply b (apply b b)) (apply n (apply (apply b b) n))))) n)) b)) b). ∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply n X) Y) Z) (apply (apply (apply X Z) Y) Z). -∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt)) +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#fixed_pt. -#n. -#strong_fixed_point. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#fixed_pt ##. +#n ##. +#strong_fixed_point ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL044-9.ma b/helm/software/matita/contribs/ng_TPTP/COL044-9.ma index f47030a27..a4ccf59f4 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL044-9.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL044-9.ma @@ -50,7 +50,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_strong_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀fixed_pt:Univ. @@ -58,21 +58,21 @@ ntheorem prove_strong_fixed_point: ∀strong_fixed_point:Univ. ∀H0:eq Univ strong_fixed_point (apply (apply b (apply (apply b (apply (apply n (apply n (apply (apply b (apply b b)) (apply n (apply n (apply b b)))))) n)) b)) b). ∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply n X) Y) Z) (apply (apply (apply X Z) Y) Z). -∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt)) +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#fixed_pt. -#n. -#strong_fixed_point. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#fixed_pt ##. +#n ##. +#strong_fixed_point ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL045-1.ma b/helm/software/matita/contribs/ng_TPTP/COL045-1.ma index 4fdcdee33..0fe670684 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL045-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL045-1.ma @@ -52,7 +52,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀combinator:Univ. @@ -60,25 +60,24 @@ ntheorem prove_fixed_point: ∀s:Univ. ∀H0:∀X:Univ.eq Univ (apply m X) (apply X X). ∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)). -∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y) +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#combinator. -#m. -#s. -#H0. -#H1. -#H2. -napply ex_intro[ -nid2: -nauto by H0,H1,H2; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#combinator ##. +#m ##. +#s ##. +#H0 ##. +#H1 ##. +#H2 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL046-1.ma b/helm/software/matita/contribs/ng_TPTP/COL046-1.ma index bd8ec6d56..066beb34a 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL046-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL046-1.ma @@ -52,7 +52,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀f:∀_:Univ.Univ. @@ -60,25 +60,24 @@ ntheorem prove_fixed_point: ∀s:Univ. ∀H0:∀X:Univ.eq Univ (apply m X) (apply X X). ∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)). -∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y))) +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y)))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#f. -#m. -#s. -#H0. -#H1. -#H2. -napply ex_intro[ -nid2: -nauto by H0,H1,H2; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#f ##. +#m ##. +#s ##. +#H0 ##. +#H1 ##. +#H2 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL047-1.ma b/helm/software/matita/contribs/ng_TPTP/COL047-1.ma index b13f82d1a..027a0488b 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL047-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL047-1.ma @@ -54,29 +54,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_model: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀f:∀_:Univ.Univ. ∀l:Univ. ∀q:Univ. ∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply q X) Y) Z) (apply Y (apply X Z)). -∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply l X) Y) (apply X (apply Y Y)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y))) +∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply l X) Y) (apply X (apply Y Y)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y)))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#f. -#l. -#q. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#f ##. +#l ##. +#q ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL048-1.ma b/helm/software/matita/contribs/ng_TPTP/COL048-1.ma index bce67c079..0e91efe67 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL048-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL048-1.ma @@ -52,7 +52,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀combinator:Univ. @@ -60,25 +60,24 @@ ntheorem prove_fixed_point: ∀w:Univ. ∀H0:∀X:Univ.eq Univ (apply m X) (apply X X). ∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y). -∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y) +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#combinator. -#m. -#w. -#H0. -#H1. -#H2. -napply ex_intro[ -nid2: -nauto by H0,H1,H2; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#combinator ##. +#m ##. +#w ##. +#H0 ##. +#H1 ##. +#H2 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL049-1.ma b/helm/software/matita/contribs/ng_TPTP/COL049-1.ma index 169eaaa40..1929e30a8 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL049-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL049-1.ma @@ -72,7 +72,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_strong_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀f:∀_:Univ.Univ. @@ -80,25 +80,24 @@ ntheorem prove_strong_fixed_point: ∀w:Univ. ∀H0:∀X:Univ.eq Univ (apply m X) (apply X X). ∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y). -∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y))) +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y)))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#f. -#m. -#w. -#H0. -#H1. -#H2. -napply ex_intro[ -nid2: -nauto by H0,H1,H2; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#f ##. +#m ##. +#w ##. +#H0 ##. +#H1 ##. +#H2 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL050-1.ma b/helm/software/matita/contribs/ng_TPTP/COL050-1.ma index d5008d12a..fff36d95b 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL050-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL050-1.ma @@ -70,29 +70,28 @@ include "logic/equality.ma". (* ---- -[response(A,y) = y]. *) ntheorem prove_all_fond_of_another: - ∀Univ:Type.∀W:Univ.∀X:Univ.∀Y:Univ. + (∀Univ:Type.∀W:Univ.∀X:Univ.∀Y:Univ. ∀a:Univ. ∀compose:∀_:Univ.∀_:Univ.Univ. ∀mocking_bird:Univ. ∀response:∀_:Univ.∀_:Univ.Univ. ∀H0:∀W:Univ.∀X:Univ.∀Y:Univ.eq Univ (response (compose X Y) W) (response X (response Y W)). -∀H1:∀Y:Univ.eq Univ (response mocking_bird Y) (response Y Y).∃Y:Univ.eq Univ (response a Y) Y +∀H1:∀Y:Univ.eq Univ (response mocking_bird Y) (response Y Y).∃Y:Univ.eq Univ (response a Y) Y) . -#Univ. -#W. -#X. -#Y. -#a. -#compose. -#mocking_bird. -#response. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#W ##. +#X ##. +#Y ##. +#a ##. +#compose ##. +#mocking_bird ##. +#response ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL051-1.ma b/helm/software/matita/contribs/ng_TPTP/COL051-1.ma index d13e3a273..2d51c3845 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL051-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL051-1.ma @@ -66,27 +66,26 @@ include "logic/equality.ma". (* ---- FAx -[response(x,x) = x]. *) ntheorem prove_the_bird_exists: - ∀Univ:Type.∀W:Univ.∀X:Univ.∀Y:Univ. + (∀Univ:Type.∀W:Univ.∀X:Univ.∀Y:Univ. ∀compose:∀_:Univ.∀_:Univ.Univ. ∀mocking_bird:Univ. ∀response:∀_:Univ.∀_:Univ.Univ. ∀H0:∀W:Univ.∀X:Univ.∀Y:Univ.eq Univ (response (compose X Y) W) (response X (response Y W)). -∀H1:∀Y:Univ.eq Univ (response mocking_bird Y) (response Y Y).∃X:Univ.eq Univ (response X X) X +∀H1:∀Y:Univ.eq Univ (response mocking_bird Y) (response Y Y).∃X:Univ.eq Univ (response X X) X) . -#Univ. -#W. -#X. -#Y. -#compose. -#mocking_bird. -#response. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#W ##. +#X ##. +#Y ##. +#compose ##. +#mocking_bird ##. +#response ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL052-1.ma b/helm/software/matita/contribs/ng_TPTP/COL052-1.ma index c207b57dc..0a3889b2d 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL052-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL052-1.ma @@ -74,7 +74,7 @@ include "logic/equality.ma". (* ---- -(response(A,v) = response(odd_bird,v)). *) ntheorem prove_a_is_agreeable: - ∀Univ:Type.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ. + (∀Univ:Type.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ. ∀a:Univ. ∀c:Univ. ∀common_bird:∀_:Univ.Univ. @@ -82,26 +82,25 @@ ntheorem prove_a_is_agreeable: ∀odd_bird:Univ. ∀response:∀_:Univ.∀_:Univ.Univ. ∀H0:∀X:Univ.eq Univ (response c (common_bird X)) (response X (common_bird X)). -∀H1:∀W:Univ.∀X:Univ.∀Y:Univ.eq Univ (response (compose X Y) W) (response X (response Y W)).∃V:Univ.eq Univ (response a V) (response odd_bird V) +∀H1:∀W:Univ.∀X:Univ.∀Y:Univ.eq Univ (response (compose X Y) W) (response X (response Y W)).∃V:Univ.eq Univ (response a V) (response odd_bird V)) . -#Univ. -#V. -#W. -#X. -#Y. -#a. -#c. -#common_bird. -#compose. -#odd_bird. -#response. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#V ##. +#W ##. +#X ##. +#Y ##. +#a ##. +#c ##. +#common_bird ##. +#compose ##. +#odd_bird ##. +#response ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* ----C composes A with B. WHY is this here? *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL053-1.ma b/helm/software/matita/contribs/ng_TPTP/COL053-1.ma index 9a4b215d2..cdc2673c0 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL053-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL053-1.ma @@ -68,32 +68,31 @@ include "logic/equality.ma". (* ---- -[(u)f(u) = A(B((C)f(u)))]. *) ntheorem prove_bird_exists: - ∀Univ:Type.∀U:Univ.∀W:Univ.∀X:Univ.∀Y:Univ. + (∀Univ:Type.∀U:Univ.∀W:Univ.∀X:Univ.∀Y:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀compose:∀_:Univ.∀_:Univ.Univ. ∀f:∀_:Univ.Univ. ∀response:∀_:Univ.∀_:Univ.Univ. -∀H0:∀W:Univ.∀X:Univ.∀Y:Univ.eq Univ (response (compose X Y) W) (response X (response Y W)).∃U:Univ.eq Univ (response U (f U)) (response a (response b (response c (f U)))) +∀H0:∀W:Univ.∀X:Univ.∀Y:Univ.eq Univ (response (compose X Y) W) (response X (response Y W)).∃U:Univ.eq Univ (response U (f U)) (response a (response b (response c (f U))))) . -#Univ. -#U. -#W. -#X. -#Y. -#a. -#b. -#c. -#compose. -#f. -#response. -#H0. -napply ex_intro[ -nid2: -nauto by H0; -nid| -skip] +#Univ ##. +#U ##. +#W ##. +#X ##. +#Y ##. +#a ##. +#b ##. +#c ##. +#compose ##. +#f ##. +#response ##. +#H0 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL056-1.ma b/helm/software/matita/contribs/ng_TPTP/COL056-1.ma index fc787c7db..c12e91f31 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL056-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL056-1.ma @@ -70,7 +70,7 @@ include "logic/equality.ma". (* ---- (AB = C) and (AC = B) and -(wv = v). *) ntheorem prove_there_exists_a_happy_bird: - ∀Univ:Type.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ. + (∀Univ:Type.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -78,30 +78,28 @@ ntheorem prove_there_exists_a_happy_bird: ∀response:∀_:Univ.∀_:Univ.Univ. ∀H0:eq Univ (response a c) b. ∀H1:eq Univ (response a b) c. -∀H2:∀W:Univ.∀X:Univ.∀Y:Univ.eq Univ (response (compose X Y) W) (response X (response Y W)).∃V:Univ.∃W:Univ.eq Univ (response W V) V +∀H2:∀W:Univ.∀X:Univ.∀Y:Univ.eq Univ (response (compose X Y) W) (response X (response Y W)).∃V:Univ.∃W:Univ.eq Univ (response W V) V) . -#Univ. -#V. -#W. -#X. -#Y. -#a. -#b. -#c. -#compose. -#response. -#H0. -#H1. -#H2. -napply ex_intro[ -nid2: -napply ex_intro[ -nid2: -nauto by H0,H1,H2; -nid| -skip] -nid| -skip] +#Univ ##. +#V ##. +#W ##. +#X ##. +#Y ##. +#a ##. +#b ##. +#c ##. +#compose ##. +#response ##. +#H0 ##. +#H1 ##. +#H2 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2 ##; +##| ##skip ##] +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL057-1.ma b/helm/software/matita/contribs/ng_TPTP/COL057-1.ma index 9ad810fa2..cd91cb7e5 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL057-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL057-1.ma @@ -48,7 +48,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_strong_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀c:Univ. @@ -58,27 +58,26 @@ ntheorem prove_strong_fixed_point: ∀H0:∀X:Univ.eq Univ (apply i X) X. ∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply c X) Y) Z) (apply (apply X Z) Y). ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)). -∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y))) +∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y)))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#c. -#f. -#i. -#s. -#H0. -#H1. -#H2. -#H3. -napply ex_intro[ -nid2: -nauto by H0,H1,H2,H3; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#c ##. +#f ##. +#i ##. +#s ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2,H3 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL058-1.ma b/helm/software/matita/contribs/ng_TPTP/COL058-1.ma index d454217b7..372edc9e1 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL058-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL058-1.ma @@ -52,23 +52,22 @@ include "logic/equality.ma". (* ---- Hypothesis: There exists a bird x that is fond of itself. *) ntheorem prove_the_bird_exists: - ∀Univ:Type.∀X:Univ.∀X1:Univ.∀X2:Univ. + (∀Univ:Type.∀X:Univ.∀X1:Univ.∀X2:Univ. ∀lark:Univ. ∀response:∀_:Univ.∀_:Univ.Univ. -∀H0:∀X1:Univ.∀X2:Univ.eq Univ (response (response lark X1) X2) (response X1 (response X2 X2)).∃X:Univ.eq Univ (response X X) X +∀H0:∀X1:Univ.∀X2:Univ.eq Univ (response (response lark X1) X2) (response X1 (response X2 X2)).∃X:Univ.eq Univ (response X X) X) . -#Univ. -#X. -#X1. -#X2. -#lark. -#response. -#H0. -napply ex_intro[ -nid2: -nauto by H0; -nid| -skip] +#Univ ##. +#X ##. +#X1 ##. +#X2 ##. +#lark ##. +#response ##. +#H0 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL058-2.ma b/helm/software/matita/contribs/ng_TPTP/COL058-2.ma index be4dc09f2..4ebcf330f 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL058-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL058-2.ma @@ -56,18 +56,18 @@ include "logic/equality.ma". (* ---- Hypothesis: This bird is egocentric *) ntheorem prove_the_bird_exists: - ∀Univ:Type.∀X1:Univ.∀X2:Univ. + (∀Univ:Type.∀X1:Univ.∀X2:Univ. ∀lark:Univ. ∀response:∀_:Univ.∀_:Univ.Univ. -∀H0:∀X1:Univ.∀X2:Univ.eq Univ (response (response lark X1) X2) (response X1 (response X2 X2)).eq Univ (response (response (response lark (response (response lark (response lark lark)) (response lark (response lark lark)))) (response lark (response lark lark))) (response (response lark (response (response lark (response lark lark)) (response lark (response lark lark)))) (response lark (response lark lark)))) (response (response lark (response (response lark (response lark lark)) (response lark (response lark lark)))) (response lark (response lark lark))) +∀H0:∀X1:Univ.∀X2:Univ.eq Univ (response (response lark X1) X2) (response X1 (response X2 X2)).eq Univ (response (response (response lark (response (response lark (response lark lark)) (response lark (response lark lark)))) (response lark (response lark lark))) (response (response lark (response (response lark (response lark lark)) (response lark (response lark lark)))) (response lark (response lark lark)))) (response (response lark (response (response lark (response lark lark)) (response lark (response lark lark)))) (response lark (response lark lark)))) . -#Univ. -#X1. -#X2. -#lark. -#response. -#H0. -nauto by H0; +#Univ ##. +#X1 ##. +#X2 ##. +#lark ##. +#response ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL058-3.ma b/helm/software/matita/contribs/ng_TPTP/COL058-3.ma index dff033e64..80ac70256 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL058-3.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL058-3.ma @@ -56,18 +56,18 @@ include "logic/equality.ma". (* ---- Hypothesis: This bird is egocentric *) ntheorem prove_the_bird_exists: - ∀Univ:Type.∀X1:Univ.∀X2:Univ. + (∀Univ:Type.∀X1:Univ.∀X2:Univ. ∀lark:Univ. ∀response:∀_:Univ.∀_:Univ.Univ. -∀H0:∀X1:Univ.∀X2:Univ.eq Univ (response (response lark X1) X2) (response X1 (response X2 X2)).eq Univ (response (response (response (response lark lark) (response lark (response lark lark))) (response lark (response lark lark))) (response (response (response lark lark) (response lark (response lark lark))) (response lark (response lark lark)))) (response (response (response lark lark) (response lark (response lark lark))) (response lark (response lark lark))) +∀H0:∀X1:Univ.∀X2:Univ.eq Univ (response (response lark X1) X2) (response X1 (response X2 X2)).eq Univ (response (response (response (response lark lark) (response lark (response lark lark))) (response lark (response lark lark))) (response (response (response lark lark) (response lark (response lark lark))) (response lark (response lark lark)))) (response (response (response lark lark) (response lark (response lark lark))) (response lark (response lark lark)))) . -#Univ. -#X1. -#X2. -#lark. -#response. -#H0. -nauto by H0; +#Univ ##. +#X1 ##. +#X2 ##. +#lark ##. +#response ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL060-1.ma b/helm/software/matita/contribs/ng_TPTP/COL060-1.ma index 3bd259a5e..832dab4b0 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL060-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL060-1.ma @@ -48,7 +48,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_q_combinator: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀f:∀_:Univ.Univ. @@ -56,25 +56,24 @@ ntheorem prove_q_combinator: ∀h:∀_:Univ.Univ. ∀t:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃X:Univ.eq Univ (apply (apply (apply X (f X)) (g X)) (h X)) (apply (g X) (apply (f X) (h X))) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃X:Univ.eq Univ (apply (apply (apply X (f X)) (g X)) (h X)) (apply (g X) (apply (f X) (h X)))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#f. -#g. -#h. -#t. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#f ##. +#g ##. +#h ##. +#t ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL060-2.ma b/helm/software/matita/contribs/ng_TPTP/COL060-2.ma index 17b724860..2c2852946 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL060-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL060-2.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----This is the q equivalent *) ntheorem prove_q_combinator: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀t:Univ. @@ -62,21 +62,21 @@ ntheorem prove_q_combinator: ∀y:Univ. ∀z:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t b)) (apply (apply b b) t)) x) y) z) (apply y (apply x z)) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t b)) (apply (apply b b) t)) x) y) z) (apply y (apply x z))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#t. -#x. -#y. -#z. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#t ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL060-3.ma b/helm/software/matita/contribs/ng_TPTP/COL060-3.ma index cfcdd6896..e5a6e4d27 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL060-3.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL060-3.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----This is the q equivalent *) ntheorem prove_q_combinator: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀t:Univ. @@ -62,21 +62,21 @@ ntheorem prove_q_combinator: ∀y:Univ. ∀z:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t b)) b)) t) x) y) z) (apply y (apply x z)) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t b)) b)) t) x) y) z) (apply y (apply x z))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#t. -#x. -#y. -#z. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#t ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL061-1.ma b/helm/software/matita/contribs/ng_TPTP/COL061-1.ma index 142f8115c..ac488654f 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL061-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL061-1.ma @@ -48,7 +48,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_q1_combinator: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀f:∀_:Univ.Univ. @@ -56,25 +56,24 @@ ntheorem prove_q1_combinator: ∀h:∀_:Univ.Univ. ∀t:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃X:Univ.eq Univ (apply (apply (apply X (f X)) (g X)) (h X)) (apply (f X) (apply (h X) (g X))) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃X:Univ.eq Univ (apply (apply (apply X (f X)) (g X)) (h X)) (apply (f X) (apply (h X) (g X)))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#f. -#g. -#h. -#t. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#f ##. +#g ##. +#h ##. +#t ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL061-2.ma b/helm/software/matita/contribs/ng_TPTP/COL061-2.ma index 1ec0e4eb0..7cc6acc5d 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL061-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL061-2.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----This is the Q1 equivalent *) ntheorem prove_q1_combinator: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀t:Univ. @@ -62,21 +62,21 @@ ntheorem prove_q1_combinator: ∀y:Univ. ∀z:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t t)) (apply (apply b b) b)) x) y) z) (apply x (apply z y)) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t t)) (apply (apply b b) b)) x) y) z) (apply x (apply z y))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#t. -#x. -#y. -#z. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#t ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL061-3.ma b/helm/software/matita/contribs/ng_TPTP/COL061-3.ma index 3975f8e65..375ec4b6c 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL061-3.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL061-3.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----This is the Q1 equivalent *) ntheorem prove_q1_combinator: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀t:Univ. @@ -62,21 +62,21 @@ ntheorem prove_q1_combinator: ∀y:Univ. ∀z:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t t)) b)) b) x) y) z) (apply x (apply z y)) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t t)) b)) b) x) y) z) (apply x (apply z y))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#t. -#x. -#y. -#z. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#t ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL062-1.ma b/helm/software/matita/contribs/ng_TPTP/COL062-1.ma index a564ce77a..f42a3ed9c 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL062-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL062-1.ma @@ -48,7 +48,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_c_combinator: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀f:∀_:Univ.Univ. @@ -56,25 +56,24 @@ ntheorem prove_c_combinator: ∀h:∀_:Univ.Univ. ∀t:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃X:Univ.eq Univ (apply (apply (apply X (f X)) (g X)) (h X)) (apply (apply (f X) (h X)) (g X)) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃X:Univ.eq Univ (apply (apply (apply X (f X)) (g X)) (h X)) (apply (apply (f X) (h X)) (g X))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#f. -#g. -#h. -#t. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#f ##. +#g ##. +#h ##. +#t ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL062-2.ma b/helm/software/matita/contribs/ng_TPTP/COL062-2.ma index ac06cb782..4af6a0aa4 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL062-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL062-2.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----This is the C equivalent *) ntheorem prove_c_combinator: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀t:Univ. @@ -62,21 +62,21 @@ ntheorem prove_c_combinator: ∀y:Univ. ∀z:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t)) x) y) z) (apply (apply x z) y) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t)) x) y) z) (apply (apply x z) y)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#t. -#x. -#y. -#z. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#t ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL062-3.ma b/helm/software/matita/contribs/ng_TPTP/COL062-3.ma index 4b5896e86..3945065fe 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL062-3.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL062-3.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----This is the C equivalent *) ntheorem prove_c_combinator: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀t:Univ. @@ -62,21 +62,21 @@ ntheorem prove_c_combinator: ∀y:Univ. ∀z:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t (apply (apply b b) t))) b)) t) x) y) z) (apply (apply x z) y) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t (apply (apply b b) t))) b)) t) x) y) z) (apply (apply x z) y)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#t. -#x. -#y. -#z. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#t ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL063-1.ma b/helm/software/matita/contribs/ng_TPTP/COL063-1.ma index 386c7fa1e..22e868b2e 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL063-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL063-1.ma @@ -48,7 +48,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_f_combinator: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀f:∀_:Univ.Univ. @@ -56,25 +56,24 @@ ntheorem prove_f_combinator: ∀h:∀_:Univ.Univ. ∀t:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃X:Univ.eq Univ (apply (apply (apply X (f X)) (g X)) (h X)) (apply (apply (h X) (g X)) (f X)) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃X:Univ.eq Univ (apply (apply (apply X (f X)) (g X)) (h X)) (apply (apply (h X) (g X)) (f X))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#f. -#g. -#h. -#t. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#f ##. +#g ##. +#h ##. +#t ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL063-2.ma b/helm/software/matita/contribs/ng_TPTP/COL063-2.ma index eabd5ed4a..3f7cf870a 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL063-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL063-2.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----This is the F equivalent *) ntheorem prove_f_combinator: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀t:Univ. @@ -62,21 +62,21 @@ ntheorem prove_f_combinator: ∀y:Univ. ∀z:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t))) x) y) z) (apply (apply z y) x) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t))) x) y) z) (apply (apply z y) x)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#t. -#x. -#y. -#z. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#t ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL063-3.ma b/helm/software/matita/contribs/ng_TPTP/COL063-3.ma index ab43d8730..45b2479ef 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL063-3.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL063-3.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----This is the F equivalent *) ntheorem prove_f_combinator: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀t:Univ. @@ -62,21 +62,21 @@ ntheorem prove_f_combinator: ∀y:Univ. ∀z:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t t)) b)) (apply (apply b b) t)) x) y) z) (apply (apply z y) x) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t t)) b)) (apply (apply b b) t)) x) y) z) (apply (apply z y) x)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#t. -#x. -#y. -#z. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#t ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL063-4.ma b/helm/software/matita/contribs/ng_TPTP/COL063-4.ma index 66775e4f6..eb3d9050e 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL063-4.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL063-4.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----This is the F equivalent *) ntheorem prove_f_combinator: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀t:Univ. @@ -62,21 +62,21 @@ ntheorem prove_f_combinator: ∀y:Univ. ∀z:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t t)) (apply (apply b (apply (apply b b) b)) t)) x) y) z) (apply (apply z y) x) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t t)) (apply (apply b (apply (apply b b) b)) t)) x) y) z) (apply (apply z y) x)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#t. -#x. -#y. -#z. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#t ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL063-5.ma b/helm/software/matita/contribs/ng_TPTP/COL063-5.ma index c40232544..a49f38c46 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL063-5.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL063-5.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----This is the F equivalent *) ntheorem prove_f_combinator: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀t:Univ. @@ -62,21 +62,21 @@ ntheorem prove_f_combinator: ∀y:Univ. ∀z:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t t)) (apply (apply b b) b))) t) x) y) z) (apply (apply z y) x) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t t)) (apply (apply b b) b))) t) x) y) z) (apply (apply z y) x)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#t. -#x. -#y. -#z. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#t ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL063-6.ma b/helm/software/matita/contribs/ng_TPTP/COL063-6.ma index 185eca552..e68938685 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL063-6.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL063-6.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----This is the F equivalent *) ntheorem prove_f_combinator: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀t:Univ. @@ -62,21 +62,21 @@ ntheorem prove_f_combinator: ∀y:Univ. ∀z:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply (apply b (apply t t)) b)) b)) t) x) y) z) (apply (apply z y) x) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply (apply b (apply t t)) b)) b)) t) x) y) z) (apply (apply z y) x)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#t. -#x. -#y. -#z. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#t ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL064-1.ma b/helm/software/matita/contribs/ng_TPTP/COL064-1.ma index bdbeb0d6a..1c835c7d6 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL064-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL064-1.ma @@ -48,7 +48,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_v_combinator: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀f:∀_:Univ.Univ. @@ -56,25 +56,24 @@ ntheorem prove_v_combinator: ∀h:∀_:Univ.Univ. ∀t:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃X:Univ.eq Univ (apply (apply (apply X (f X)) (g X)) (h X)) (apply (apply (h X) (f X)) (g X)) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃X:Univ.eq Univ (apply (apply (apply X (f X)) (g X)) (h X)) (apply (apply (h X) (f X)) (g X))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#f. -#g. -#h. -#t. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#f ##. +#g ##. +#h ##. +#t ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL064-2.ma b/helm/software/matita/contribs/ng_TPTP/COL064-2.ma index 5085f254a..ce5e18f7e 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL064-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL064-2.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----This is the V equivalent *) ntheorem prove_v_combinator: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀t:Univ. @@ -62,21 +62,21 @@ ntheorem prove_v_combinator: ∀y:Univ. ∀z:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t))) x) y) z) (apply (apply z x) y) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t))) x) y) z) (apply (apply z x) y)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#t. -#x. -#y. -#z. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#t ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL064-3.ma b/helm/software/matita/contribs/ng_TPTP/COL064-3.ma index 2637df2c8..899546ff7 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL064-3.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL064-3.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----This is the V equivalent *) ntheorem prove_v_combinator: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀t:Univ. @@ -62,21 +62,21 @@ ntheorem prove_v_combinator: ∀y:Univ. ∀z:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t (apply (apply b b) t))) b)) (apply (apply b b) t)) x) y) z) (apply (apply z x) y) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t (apply (apply b b) t))) b)) (apply (apply b b) t)) x) y) z) (apply (apply z x) y)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#t. -#x. -#y. -#z. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#t ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL064-4.ma b/helm/software/matita/contribs/ng_TPTP/COL064-4.ma index 627a49e08..112191847 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL064-4.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL064-4.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----This is the V equivalent *) ntheorem prove_v_combinator: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀t:Univ. @@ -62,21 +62,21 @@ ntheorem prove_v_combinator: ∀y:Univ. ∀z:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b (apply (apply b b) b)) t)) x) y) z) (apply (apply z x) y) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b (apply (apply b b) b)) t)) x) y) z) (apply (apply z x) y)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#t. -#x. -#y. -#z. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#t ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL064-5.ma b/helm/software/matita/contribs/ng_TPTP/COL064-5.ma index cd5be1749..a31880641 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL064-5.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL064-5.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----This is the V equivalent *) ntheorem prove_v_combinator: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀t:Univ. @@ -62,21 +62,21 @@ ntheorem prove_v_combinator: ∀y:Univ. ∀z:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) b))) t) x) y) z) (apply (apply z x) y) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) b))) t) x) y) z) (apply (apply z x) y)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#t. -#x. -#y. -#z. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#t ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL064-6.ma b/helm/software/matita/contribs/ng_TPTP/COL064-6.ma index ef77186b1..c85a9a273 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL064-6.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL064-6.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----This is the V equivalent *) ntheorem prove_v_combinator: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀t:Univ. @@ -62,21 +62,21 @@ ntheorem prove_v_combinator: ∀y:Univ. ∀z:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply (apply b (apply t (apply (apply b b) t))) b)) b)) t) x) y) z) (apply (apply z x) y) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply (apply b (apply t (apply (apply b b) t))) b)) b)) t) x) y) z) (apply (apply z x) y)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#t. -#x. -#y. -#z. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#t ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL064-7.ma b/helm/software/matita/contribs/ng_TPTP/COL064-7.ma index 2a836b1cf..096520b6d 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL064-7.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL064-7.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----This is the V equivalent *) ntheorem prove_v_combinator: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀t:Univ. @@ -62,21 +62,21 @@ ntheorem prove_v_combinator: ∀y:Univ. ∀z:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b t) t))) x) y) z) (apply (apply z x) y) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b t) t))) x) y) z) (apply (apply z x) y)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#t. -#x. -#y. -#z. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#t ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL064-8.ma b/helm/software/matita/contribs/ng_TPTP/COL064-8.ma index dc9c52374..3fc8ac894 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL064-8.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL064-8.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----This is the V equivalent *) ntheorem prove_v_combinator: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀t:Univ. @@ -62,21 +62,21 @@ ntheorem prove_v_combinator: ∀y:Univ. ∀z:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t (apply (apply b b) t))) b)) (apply (apply b t) t)) x) y) z) (apply (apply z x) y) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t (apply (apply b b) t))) b)) (apply (apply b t) t)) x) y) z) (apply (apply z x) y)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#t. -#x. -#y. -#z. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#t ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL064-9.ma b/helm/software/matita/contribs/ng_TPTP/COL064-9.ma index 47b5d02fc..58ce254ee 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL064-9.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL064-9.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----This is the V equivalent *) ntheorem prove_v_combinator: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀t:Univ. @@ -62,21 +62,21 @@ ntheorem prove_v_combinator: ∀y:Univ. ∀z:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b (apply (apply b b) t)) t)) x) y) z) (apply (apply z x) y) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b (apply (apply b b) t)) t)) x) y) z) (apply (apply z x) y)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#t. -#x. -#y. -#z. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#t ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL065-1.ma b/helm/software/matita/contribs/ng_TPTP/COL065-1.ma index 3154381b3..ec1d0e7e4 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL065-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL065-1.ma @@ -48,7 +48,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_g_combinator: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀f:∀_:Univ.Univ. @@ -57,26 +57,25 @@ ntheorem prove_g_combinator: ∀i:∀_:Univ.Univ. ∀t:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃X:Univ.eq Univ (apply (apply (apply (apply X (f X)) (g X)) (h X)) (i X)) (apply (apply (f X) (i X)) (apply (g X) (h X))) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃X:Univ.eq Univ (apply (apply (apply (apply X (f X)) (g X)) (h X)) (i X)) (apply (apply (f X) (i X)) (apply (g X) (h X)))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#f. -#g. -#h. -#i. -#t. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#f ##. +#g ##. +#h ##. +#i ##. +#t ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL066-1.ma b/helm/software/matita/contribs/ng_TPTP/COL066-1.ma index ed5438bf3..df168dc73 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL066-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL066-1.ma @@ -48,7 +48,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p_combinator: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀f:∀_:Univ.Univ. @@ -58,27 +58,26 @@ ntheorem prove_p_combinator: ∀w:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y). ∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply q X) Y) Z) (apply Y (apply X Z)). -∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃X:Univ.eq Univ (apply (apply (apply (apply X (f X)) (g X)) (g X)) (h X)) (apply (apply (f X) (g X)) (apply (apply (f X) (g X)) (h X))) +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃X:Univ.eq Univ (apply (apply (apply (apply X (f X)) (g X)) (g X)) (h X)) (apply (apply (f X) (g X)) (apply (apply (f X) (g X)) (h X)))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#f. -#g. -#h. -#q. -#w. -#H0. -#H1. -#H2. -napply ex_intro[ -nid2: -nauto by H0,H1,H2; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#f ##. +#g ##. +#h ##. +#q ##. +#w ##. +#H0 ##. +#H1 ##. +#H2 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL066-2.ma b/helm/software/matita/contribs/ng_TPTP/COL066-2.ma index 295d9a3c0..aec24cecf 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL066-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL066-2.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----This is the P equivalent *) ntheorem prove_p_combinator: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀q:Univ. @@ -64,23 +64,23 @@ ntheorem prove_p_combinator: ∀z:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y). ∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply q X) Y) Z) (apply Y (apply X Z)). -∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply (apply q q) (apply w (apply q (apply q q)))) x) y) y) z) (apply (apply x y) (apply (apply x y) z)) +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply (apply q q) (apply w (apply q (apply q q)))) x) y) y) z) (apply (apply x y) (apply (apply x y) z))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#q. -#w. -#x. -#y. -#z. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#q ##. +#w ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL066-3.ma b/helm/software/matita/contribs/ng_TPTP/COL066-3.ma index f8bed5745..c012ed78e 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL066-3.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL066-3.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----This is the P equivalent *) ntheorem prove_p_combinator: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀q:Univ. @@ -64,23 +64,23 @@ ntheorem prove_p_combinator: ∀z:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y). ∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply q X) Y) Z) (apply Y (apply X Z)). -∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply (apply b (apply w (apply q (apply q q)))) q) x) y) y) z) (apply (apply x y) (apply (apply x y) z)) +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply (apply b (apply w (apply q (apply q q)))) q) x) y) y) z) (apply (apply x y) (apply (apply x y) z))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#q. -#w. -#x. -#y. -#z. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#q ##. +#w ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL067-1.ma b/helm/software/matita/contribs/ng_TPTP/COL067-1.ma index a8ca83454..d600aeca4 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL067-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL067-1.ma @@ -50,29 +50,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀f:∀_:Univ.Univ. ∀s:Univ. ∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y))) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y)))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#f. -#s. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#f ##. +#s ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL068-1.ma b/helm/software/matita/contribs/ng_TPTP/COL068-1.ma index 3f2b1b5a7..3982cf18c 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL068-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL068-1.ma @@ -48,29 +48,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀combinator:Univ. ∀s:Univ. ∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#combinator. -#s. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#combinator ##. +#s ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL069-1.ma b/helm/software/matita/contribs/ng_TPTP/COL069-1.ma index 242f45e35..f99a6397e 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL069-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL069-1.ma @@ -50,29 +50,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀f:∀_:Univ.Univ. ∀l:Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply l X) Y) (apply X (apply Y Y)). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y))) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y)))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#f. -#l. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#f ##. +#l ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL070-1.ma b/helm/software/matita/contribs/ng_TPTP/COL070-1.ma index 38b0d8182..56102f9df 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL070-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL070-1.ma @@ -50,29 +50,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀combinator:Univ. ∀n1:Univ. ∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply n1 X) Y) Z) (apply (apply (apply X Y) Y) Z).∃Y:Univ.eq Univ Y (apply combinator Y) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply n1 X) Y) Z) (apply (apply (apply X Y) Y) Z).∃Y:Univ.eq Univ Y (apply combinator Y)) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#combinator. -#n1. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#combinator ##. +#n1 ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL071-1.ma b/helm/software/matita/contribs/ng_TPTP/COL071-1.ma index 6a0ff4c1d..e0fde516c 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL071-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL071-1.ma @@ -50,29 +50,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀f:∀_:Univ.Univ. ∀n:Univ. ∀q:Univ. ∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply q X) Y) Z) (apply Y (apply X Z)). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply n X) Y) Z) (apply (apply (apply X Z) Y) Z).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y))) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply n X) Y) Z) (apply (apply (apply X Z) Y) Z).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y)))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#f. -#n. -#q. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#f ##. +#n ##. +#q ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL073-1.ma b/helm/software/matita/contribs/ng_TPTP/COL073-1.ma index 84af50345..6a4224fb0 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL073-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL073-1.ma @@ -54,29 +54,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_strong_fixed_point: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀f:∀_:Univ.Univ. ∀n1:Univ. ∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply n1 X) Y) Z) (apply (apply (apply X Y) Y) Z).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y))) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply n1 X) Y) Z) (apply (apply (apply X Y) Y) Z).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y)))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#f. -#n1. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#f ##. +#n1 ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL075-2.ma b/helm/software/matita/contribs/ng_TPTP/COL075-2.ma index 7c1e12d2d..a8caccead 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL075-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL075-2.ma @@ -66,31 +66,30 @@ include "logic/equality.ma". (* ----Subsitution axioms *) ntheorem prove_diagonal_combinator: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀abstraction:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:∀_:Univ.Univ. ∀c:∀_:Univ.Univ. ∀k:Univ. ∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply abstraction X) Y) Z) (apply (apply X (apply k Z)) (apply Y Z)). -∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply k X) Y) X.∃Y:Univ.eq Univ (apply (apply Y (b Y)) (c Y)) (apply (b Y) (b Y)) +∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply k X) Y) X.∃Y:Univ.eq Univ (apply (apply Y (b Y)) (c Y)) (apply (b Y) (b Y))) . -#Univ. -#X. -#Y. -#Z. -#abstraction. -#apply. -#b. -#c. -#k. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#abstraction ##. +#apply ##. +#b ##. +#c ##. +#k ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL083-1.ma b/helm/software/matita/contribs/ng_TPTP/COL083-1.ma index 070037025..621896348 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL083-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL083-1.ma @@ -42,33 +42,31 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_birds_are_compatible_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀compose:∀_:Univ.∀_:Univ.Univ. ∀mocking_bird:Univ. ∀response:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (response (compose A B) C) (response A (response B C)). -∀H1:∀A:Univ.eq Univ (response mocking_bird A) (response A A).∃A:Univ.∃B:Univ.eq Univ (response a A) B +∀H1:∀A:Univ.eq Univ (response mocking_bird A) (response A A).∃A:Univ.∃B:Univ.eq Univ (response a A) B) . -#Univ. -#A. -#B. -#C. -#a. -#compose. -#mocking_bird. -#response. -#H0. -#H1. -napply ex_intro[ -nid2: -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] -nid| -skip] +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#compose ##. +#mocking_bird ##. +#response ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL084-1.ma b/helm/software/matita/contribs/ng_TPTP/COL084-1.ma index f8c072eb3..1b5115363 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL084-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL084-1.ma @@ -42,33 +42,31 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_birds_are_compatible_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀b:Univ. ∀compose:∀_:Univ.∀_:Univ.Univ. ∀mocking_bird:Univ. ∀response:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (response (compose A B) C) (response A (response B C)). -∀H1:∀A:Univ.eq Univ (response mocking_bird A) (response A A).∃A:Univ.∃B:Univ.eq Univ (response b B) A +∀H1:∀A:Univ.eq Univ (response mocking_bird A) (response A A).∃A:Univ.∃B:Univ.eq Univ (response b B) A) . -#Univ. -#A. -#B. -#C. -#b. -#compose. -#mocking_bird. -#response. -#H0. -#H1. -napply ex_intro[ -nid2: -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] -nid| -skip] +#Univ ##. +#A ##. +#B ##. +#C ##. +#b ##. +#compose ##. +#mocking_bird ##. +#response ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL085-1.ma b/helm/software/matita/contribs/ng_TPTP/COL085-1.ma index c42c18008..a1aba169f 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL085-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL085-1.ma @@ -42,28 +42,26 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_happiness_1: - ∀Univ:Type.∀A:Univ.∀B:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ. ∀a:Univ. ∀b:Univ. ∀response:∀_:Univ.∀_:Univ.Univ. -∀H0:eq Univ (response a b) b.∃A:Univ.∃B:Univ.eq Univ (response a A) B +∀H0:eq Univ (response a b) b.∃A:Univ.∃B:Univ.eq Univ (response a A) B) . -#Univ. -#A. -#B. -#a. -#b. -#response. -#H0. -napply ex_intro[ -nid2: -napply ex_intro[ -nid2: -nauto by H0; -nid| -skip] -nid| -skip] +#Univ ##. +#A ##. +#B ##. +#a ##. +#b ##. +#response ##. +#H0 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0 ##; +##| ##skip ##] +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL086-1.ma b/helm/software/matita/contribs/ng_TPTP/COL086-1.ma index a5230029b..25034b472 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL086-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL086-1.ma @@ -42,28 +42,26 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_happiness_2: - ∀Univ:Type.∀A:Univ.∀B:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ. ∀a:Univ. ∀b:Univ. ∀response:∀_:Univ.∀_:Univ.Univ. -∀H0:eq Univ (response a b) b.∃A:Univ.∃B:Univ.eq Univ (response a B) A +∀H0:eq Univ (response a b) b.∃A:Univ.∃B:Univ.eq Univ (response a B) A) . -#Univ. -#A. -#B. -#a. -#b. -#response. -#H0. -napply ex_intro[ -nid2: -napply ex_intro[ -nid2: -nauto by H0; -nid| -skip] -nid| -skip] +#Univ ##. +#A ##. +#B ##. +#a ##. +#b ##. +#response ##. +#H0 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0 ##; +##| ##skip ##] +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/COL087-1.ma b/helm/software/matita/contribs/ng_TPTP/COL087-1.ma index 519a4493f..759663233 100644 --- a/helm/software/matita/contribs/ng_TPTP/COL087-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/COL087-1.ma @@ -48,29 +48,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem strong_fixpoint: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀apply:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀f:∀_:Univ.Univ. ∀m:Univ. ∀H0:∀X:Univ.eq Univ (apply m X) (apply X X). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y))) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y)))) . -#Univ. -#X. -#Y. -#Z. -#apply. -#b. -#f. -#m. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#f ##. +#m ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP001-2.ma b/helm/software/matita/contribs/ng_TPTP/GRP001-2.ma index d6af7f0ae..62d43484c 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP001-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP001-2.ma @@ -124,7 +124,7 @@ include "logic/equality.ma". (* ----Redundant two axioms *) ntheorem prove_b_times_a_is_c: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -137,26 +137,26 @@ ntheorem prove_b_times_a_is_c: ∀H3:∀X:Univ.eq Univ (multiply X identity) X. ∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H5:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H6:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply b a) c +∀H6:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply b a) c) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -nauto by H0,H1,H2,H3,H4,H5,H6; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +nauto by H0,H1,H2,H3,H4,H5,H6 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP001-4.ma b/helm/software/matita/contribs/ng_TPTP/GRP001-4.ma index dcf656eba..4c8585c23 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP001-4.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP001-4.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----There exists an identity element 'e' defined below. *) ntheorem prove_b_times_a_is_c: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -63,22 +63,22 @@ ntheorem prove_b_times_a_is_c: ∀H0:eq Univ (multiply a b) c. ∀H1:∀X:Univ.eq Univ (multiply X X) identity. ∀H2:∀X:Univ.eq Univ (multiply identity X) X. -∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).eq Univ (multiply b a) c +∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).eq Univ (multiply b a) c) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#identity. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#identity ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP002-2.ma b/helm/software/matita/contribs/ng_TPTP/GRP002-2.ma index fbe01c78c..7d2d0f3b4 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP002-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP002-2.ma @@ -122,7 +122,7 @@ include "logic/equality.ma". (* ----This hypothesis is omitted in the ANL source version *) ntheorem prove_k_times_inverse_b_is_e: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -143,34 +143,34 @@ ntheorem prove_k_times_inverse_b_is_e: ∀H7:∀X:Univ.eq Univ (multiply X identity) X. ∀H8:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H9:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H10:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply k (inverse b)) identity +∀H10:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply k (inverse b)) identity) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#h. -#identity. -#inverse. -#j. -#k. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#h ##. +#identity ##. +#inverse ##. +#j ##. +#k ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP002-3.ma b/helm/software/matita/contribs/ng_TPTP/GRP002-3.ma index 9051aaa60..76250c141 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP002-3.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP002-3.ma @@ -136,7 +136,7 @@ include "logic/equality.ma". (* ----Definition of the commutator *) ntheorem prove_commutator: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀commutator:∀_:Univ.∀_:Univ.Univ. @@ -147,24 +147,24 @@ ntheorem prove_commutator: ∀H1:∀X:Univ.∀Y:Univ.eq Univ (commutator X Y) (multiply X (multiply Y (multiply (inverse X) (inverse Y)))). ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H3:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H4:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (commutator (commutator a b) b) identity +∀H4:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (commutator (commutator a b) b) identity) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#commutator. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -nauto by H0,H1,H2,H3,H4; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#commutator ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +nauto by H0,H1,H2,H3,H4 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP002-4.ma b/helm/software/matita/contribs/ng_TPTP/GRP002-4.ma index 7f2fa4d42..f4cb1b59d 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP002-4.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP002-4.ma @@ -136,7 +136,7 @@ include "logic/equality.ma". (* ----Definition of the commutator *) ntheorem prove_commutator: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀commutator:∀_:Univ.∀_:Univ.Univ. @@ -149,26 +149,26 @@ ntheorem prove_commutator: ∀H3:∀X:Univ.eq Univ (multiply X identity) X. ∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H5:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H6:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (commutator (commutator a b) b) identity +∀H6:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (commutator (commutator a b) b) identity) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#commutator. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -nauto by H0,H1,H2,H3,H4,H5,H6; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#commutator ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +nauto by H0,H1,H2,H3,H4,H5,H6 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP010-4.ma b/helm/software/matita/contribs/ng_TPTP/GRP010-4.ma index f302f70d6..995e8f914 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP010-4.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP010-4.ma @@ -50,7 +50,7 @@ include "logic/equality.ma". (* ----There exists an identity element 'e' defined below. *) ntheorem prove_b_times_c_is_e: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀b:Univ. ∀c:Univ. ∀identity:Univ. @@ -59,22 +59,22 @@ ntheorem prove_b_times_c_is_e: ∀H0:eq Univ (multiply c b) identity. ∀H1:∀X:Univ.eq Univ (multiply (inverse X) X) identity. ∀H2:∀X:Univ.eq Univ (multiply identity X) X. -∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).eq Univ (multiply b c) identity +∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).eq Univ (multiply b c) identity) . -#Univ. -#X. -#Y. -#Z. -#b. -#c. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#b ##. +#c ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP011-4.ma b/helm/software/matita/contribs/ng_TPTP/GRP011-4.ma index 8e239b162..58c2ed1ed 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP011-4.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP011-4.ma @@ -50,7 +50,7 @@ include "logic/equality.ma". (* ----There exists an identity element *) ntheorem prove_left_cancellation: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀b:Univ. ∀c:Univ. ∀d:Univ. @@ -60,23 +60,23 @@ ntheorem prove_left_cancellation: ∀H0:eq Univ (multiply b c) (multiply d c). ∀H1:∀X:Univ.eq Univ (multiply (inverse X) X) identity. ∀H2:∀X:Univ.eq Univ (multiply identity X) X. -∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).eq Univ b d +∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).eq Univ b d) . -#Univ. -#X. -#Y. -#Z. -#b. -#c. -#d. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#b ##. +#c ##. +#d ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP012-4.ma b/helm/software/matita/contribs/ng_TPTP/GRP012-4.ma index a56976bfa..e4f7c3cff 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP012-4.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP012-4.ma @@ -114,7 +114,7 @@ include "logic/equality.ma". (* ----Redundant two axioms *) ntheorem prove_inverse_of_product_is_product_of_inverses: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀identity:Univ. @@ -124,23 +124,23 @@ ntheorem prove_inverse_of_product_is_product_of_inverses: ∀H1:∀X:Univ.eq Univ (multiply X identity) X. ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H3:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H4:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (inverse (multiply a b)) (multiply (inverse b) (inverse a)) +∀H4:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (inverse (multiply a b)) (multiply (inverse b) (inverse a))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -nauto by H0,H1,H2,H3,H4; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +nauto by H0,H1,H2,H3,H4 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP014-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP014-1.ma index aa83df8bc..a18fecb4e 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP014-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP014-1.ma @@ -56,26 +56,26 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_associativity: - ∀Univ:Type.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (inverse (multiply (multiply (inverse (multiply (inverse Y) (multiply (inverse X) W))) Z) (inverse (multiply Y Z))))) W.eq Univ (multiply a (multiply b c)) (multiply (multiply a b) c) +∀H0:∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (inverse (multiply (multiply (inverse (multiply (inverse Y) (multiply (inverse X) W))) Z) (inverse (multiply Y Z))))) W.eq Univ (multiply a (multiply b c)) (multiply (multiply a b) c)) . -#Univ. -#W. -#X. -#Y. -#Z. -#a. -#b. -#c. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#W ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP022-2.ma b/helm/software/matita/contribs/ng_TPTP/GRP022-2.ma index 6dab8aacb..fc9000626 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP022-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP022-2.ma @@ -116,7 +116,7 @@ include "logic/equality.ma". (* ----Redundant two axioms *) ntheorem prove_inverse_of_inverse_is_original: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀identity:Univ. ∀inverse:∀_:Univ.Univ. @@ -125,22 +125,22 @@ ntheorem prove_inverse_of_inverse_is_original: ∀H1:∀X:Univ.eq Univ (multiply X identity) X. ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H3:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H4:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (inverse (inverse a)) a +∀H4:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (inverse (inverse a)) a) . -#Univ. -#X. -#Y. -#Z. -#a. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -nauto by H0,H1,H2,H3,H4; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +nauto by H0,H1,H2,H3,H4 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP023-2.ma b/helm/software/matita/contribs/ng_TPTP/GRP023-2.ma index b5e55b39a..13bfa941d 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP023-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP023-2.ma @@ -112,7 +112,7 @@ include "logic/equality.ma". (* ----Redundant two axioms *) ntheorem prove_inverse_of_id_is_id: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀identity:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. @@ -120,21 +120,21 @@ ntheorem prove_inverse_of_id_is_id: ∀H1:∀X:Univ.eq Univ (multiply X identity) X. ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H3:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H4:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (inverse identity) identity +∀H4:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (inverse identity) identity) . -#Univ. -#X. -#Y. -#Z. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -nauto by H0,H1,H2,H3,H4; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +nauto by H0,H1,H2,H3,H4 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP024-5.ma b/helm/software/matita/contribs/ng_TPTP/GRP024-5.ma index 6b73428f5..68e336f06 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP024-5.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP024-5.ma @@ -124,7 +124,7 @@ include "logic/equality.ma". (* ----Denial of conclusion: *) ntheorem prove_center: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -136,25 +136,25 @@ ntheorem prove_center: ∀H1:∀X:Univ.∀Y:Univ.eq Univ (commutator X Y) (multiply (inverse X) (multiply (inverse Y) (multiply X Y))). ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H3:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H4:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply a (commutator b c)) (multiply (commutator b c) a) +∀H4:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply a (commutator b c)) (multiply (commutator b c) a)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#commutator. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -nauto by H0,H1,H2,H3,H4; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#commutator ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +nauto by H0,H1,H2,H3,H4 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP114-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP114-1.ma index d404bd47f..9af6d8905 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP114-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP114-1.ma @@ -124,7 +124,7 @@ include "logic/equality.ma". (* ----This axiom is a lemma *) ntheorem prove_product: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀identity:Univ. ∀intersection:∀_:Univ.∀_:Univ.Univ. @@ -152,41 +152,41 @@ ntheorem prove_product: ∀H16:eq Univ (inverse identity) identity. ∀H17:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H18:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H19:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply (positive_part a) (negative_part a)) a +∀H19:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply (positive_part a) (negative_part a)) a) . -#Univ. -#X. -#Y. -#Z. -#a. -#identity. -#intersection. -#inverse. -#multiply. -#negative_part. -#positive_part. -#union. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -#H18. -#H19. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#identity ##. +#intersection ##. +#inverse ##. +#multiply ##. +#negative_part ##. +#positive_part ##. +#union ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +#H19 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP115-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP115-1.ma index 9d54e5069..e8d2b3cc4 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP115-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP115-1.ma @@ -42,21 +42,21 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_order3: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀identity:Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (multiply (multiply X (multiply (multiply X Y) Z)) (multiply identity (multiply Z Z)))) Y.eq Univ (multiply a (multiply a a)) identity +∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (multiply (multiply X (multiply (multiply X Y) Z)) (multiply identity (multiply Z Z)))) Y.eq Univ (multiply a (multiply a a)) identity) . -#Univ. -#X. -#Y. -#Z. -#a. -#identity. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#identity ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP116-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP116-1.ma index 38048d795..3ba7d2a3d 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP116-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP116-1.ma @@ -42,21 +42,21 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_order3: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀identity:Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (multiply (multiply X (multiply (multiply X Y) Z)) (multiply identity (multiply Z Z)))) Y.eq Univ (multiply identity a) a +∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (multiply (multiply X (multiply (multiply X Y) Z)) (multiply identity (multiply Z Z)))) Y.eq Univ (multiply identity a) a) . -#Univ. -#X. -#Y. -#Z. -#a. -#identity. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#identity ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP117-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP117-1.ma index d794f935f..58d7577c2 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP117-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP117-1.ma @@ -42,21 +42,21 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_order3: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀identity:Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (multiply (multiply X (multiply (multiply X Y) Z)) (multiply identity (multiply Z Z)))) Y.eq Univ (multiply a identity) a +∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (multiply (multiply X (multiply (multiply X Y) Z)) (multiply identity (multiply Z Z)))) Y.eq Univ (multiply a identity) a) . -#Univ. -#X. -#Y. -#Z. -#a. -#identity. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#identity ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP118-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP118-1.ma index 2d6944b01..a0487adf7 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP118-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP118-1.ma @@ -42,25 +42,25 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_order3: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀identity:Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (multiply (multiply X (multiply (multiply X Y) Z)) (multiply identity (multiply Z Z)))) Y.eq Univ (multiply (multiply a b) c) (multiply a (multiply b c)) +∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (multiply (multiply X (multiply (multiply X Y) Z)) (multiply identity (multiply Z Z)))) Y.eq Univ (multiply (multiply a b) c) (multiply a (multiply b c))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#identity. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#identity ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP119-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP119-1.ma index d0f86c4bc..c598dbad6 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP119-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP119-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_order4: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀identity:Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:eq Univ (multiply identity identity) identity. -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply Y (multiply (multiply Y (multiply (multiply Y Y) (multiply X Z))) (multiply Z (multiply Z Z)))) X.eq Univ (multiply a (multiply a (multiply a a))) identity +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply Y (multiply (multiply Y (multiply (multiply Y Y) (multiply X Z))) (multiply Z (multiply Z Z)))) X.eq Univ (multiply a (multiply a (multiply a a))) identity) . -#Univ. -#X. -#Y. -#Z. -#a. -#identity. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#identity ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP120-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP120-1.ma index 91b597b50..6f3661aa5 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP120-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP120-1.ma @@ -42,23 +42,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_order3: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀identity:Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:eq Univ (multiply identity identity) identity. -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply Y (multiply (multiply Y (multiply (multiply Y Y) (multiply X Z))) (multiply Z (multiply Z Z)))) X.eq Univ (multiply identity a) a +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply Y (multiply (multiply Y (multiply (multiply Y Y) (multiply X Z))) (multiply Z (multiply Z Z)))) X.eq Univ (multiply identity a) a) . -#Univ. -#X. -#Y. -#Z. -#a. -#identity. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#identity ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP121-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP121-1.ma index 7721e1a23..e037e78f1 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP121-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP121-1.ma @@ -42,23 +42,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_order3: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀identity:Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:eq Univ (multiply identity identity) identity. -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply Y (multiply (multiply Y (multiply (multiply Y Y) (multiply X Z))) (multiply Z (multiply Z Z)))) X.eq Univ (multiply a identity) a +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply Y (multiply (multiply Y (multiply (multiply Y Y) (multiply X Z))) (multiply Z (multiply Z Z)))) X.eq Univ (multiply a identity) a) . -#Univ. -#X. -#Y. -#Z. -#a. -#identity. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#identity ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP122-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP122-1.ma index 72bea841f..a67858ac7 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP122-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP122-1.ma @@ -42,27 +42,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_order3: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀identity:Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:eq Univ (multiply identity identity) identity. -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply Y (multiply (multiply Y (multiply (multiply Y Y) (multiply X Z))) (multiply Z (multiply Z Z)))) X.eq Univ (multiply (multiply a b) c) (multiply a (multiply b c)) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply Y (multiply (multiply Y (multiply (multiply Y Y) (multiply X Z))) (multiply Z (multiply Z Z)))) X.eq Univ (multiply (multiply a b) c) (multiply a (multiply b c))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#identity. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#identity ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP136-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP136-1.ma index 19343581a..1e120e4c3 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP136-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP136-1.ma @@ -168,7 +168,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_ax_antisyma: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -192,37 +192,37 @@ ntheorem prove_ax_antisyma: ∀H13:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H15:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ a b +∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ a b) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP137-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP137-1.ma index 8e3ff36b1..97da5c292 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP137-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP137-1.ma @@ -168,7 +168,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_ax_antisymb: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -192,37 +192,37 @@ ntheorem prove_ax_antisymb: ∀H13:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H15:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ a b +∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ a b) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP138-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP138-1.ma index da10ca89e..5733d2bf5 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP138-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP138-1.ma @@ -172,7 +172,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_ax_glb1a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -197,38 +197,38 @@ ntheorem prove_ax_glb1a: ∀H13:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H15:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (greatest_lower_bound a b) c) (greatest_lower_bound a b) +∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (greatest_lower_bound a b) c) (greatest_lower_bound a b)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP139-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP139-1.ma index 892a1d93f..4e8621700 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP139-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP139-1.ma @@ -172,7 +172,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_ax_glb1b: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -197,38 +197,38 @@ ntheorem prove_ax_glb1b: ∀H13:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H15:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (greatest_lower_bound a b) c) c +∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (greatest_lower_bound a b) c) c) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP140-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP140-1.ma index f44966918..f38c01b99 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP140-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP140-1.ma @@ -172,7 +172,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_ax_glb1c: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -197,38 +197,38 @@ ntheorem prove_ax_glb1c: ∀H13:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H15:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (greatest_lower_bound a b) c) (greatest_lower_bound a b) +∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (greatest_lower_bound a b) c) (greatest_lower_bound a b)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP141-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP141-1.ma index 3a9efdc56..fe60aece6 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP141-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP141-1.ma @@ -172,7 +172,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_ax_glb1d: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -197,38 +197,38 @@ ntheorem prove_ax_glb1d: ∀H13:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H15:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (greatest_lower_bound a b) c) c +∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (greatest_lower_bound a b) c) c) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP142-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP142-1.ma index 696c40d28..9e8f84875 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP142-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP142-1.ma @@ -168,7 +168,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_ax_glb2a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -190,35 +190,35 @@ ntheorem prove_ax_glb2a: ∀H11:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H13:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (greatest_lower_bound a b) a) a +∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (greatest_lower_bound a b) a) a) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP143-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP143-1.ma index 8d2cd6a95..5aa44fcab 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP143-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP143-1.ma @@ -168,7 +168,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_ax_glb2b: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -190,35 +190,35 @@ ntheorem prove_ax_glb2b: ∀H11:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H13:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (greatest_lower_bound a b) a) (greatest_lower_bound a b) +∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (greatest_lower_bound a b) a) (greatest_lower_bound a b)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP144-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP144-1.ma index 4bed00c2f..f2ac45391 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP144-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP144-1.ma @@ -168,7 +168,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_ax_glb3a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -190,35 +190,35 @@ ntheorem prove_ax_glb3a: ∀H11:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H13:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (greatest_lower_bound a b) b) b +∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (greatest_lower_bound a b) b) b) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP145-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP145-1.ma index cfa89a081..1efa5a3b5 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP145-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP145-1.ma @@ -168,7 +168,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_ax_glb3b: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -190,35 +190,35 @@ ntheorem prove_ax_glb3b: ∀H11:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H13:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (greatest_lower_bound a b) b) (greatest_lower_bound a b) +∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (greatest_lower_bound a b) b) (greatest_lower_bound a b)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP146-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP146-1.ma index e676ec5c5..5056afbaf 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP146-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP146-1.ma @@ -172,7 +172,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_ax_lub1a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -197,38 +197,38 @@ ntheorem prove_ax_lub1a: ∀H13:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H15:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (least_upper_bound a b) c) c +∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (least_upper_bound a b) c) c) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP147-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP147-1.ma index 3a13169d6..1e1696011 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP147-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP147-1.ma @@ -172,7 +172,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_ax_lub1b: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -197,38 +197,38 @@ ntheorem prove_ax_lub1b: ∀H13:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H15:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (least_upper_bound a b) c) (least_upper_bound a b) +∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (least_upper_bound a b) c) (least_upper_bound a b)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP148-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP148-1.ma index 8079025c3..73ba41a11 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP148-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP148-1.ma @@ -172,7 +172,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_ax_lub1c: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -197,38 +197,38 @@ ntheorem prove_ax_lub1c: ∀H13:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H15:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (least_upper_bound a b) c) (least_upper_bound a b) +∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (least_upper_bound a b) c) (least_upper_bound a b)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP149-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP149-1.ma index 579a6dad3..c0f0387da 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP149-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP149-1.ma @@ -172,7 +172,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_ax_lub1d: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -197,38 +197,38 @@ ntheorem prove_ax_lub1d: ∀H13:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H15:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (least_upper_bound a b) c) c +∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (least_upper_bound a b) c) c) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP150-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP150-1.ma index 4b52a5567..cba62705d 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP150-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP150-1.ma @@ -168,7 +168,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_ax_lub2a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -190,35 +190,35 @@ ntheorem prove_ax_lub2a: ∀H11:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H13:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound a (least_upper_bound a b)) (least_upper_bound a b) +∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound a (least_upper_bound a b)) (least_upper_bound a b)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP151-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP151-1.ma index 7bec899cc..4447e1c96 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP151-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP151-1.ma @@ -168,7 +168,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_ax_lub2b: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -190,35 +190,35 @@ ntheorem prove_ax_lub2b: ∀H11:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H13:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound a (least_upper_bound a b)) a +∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound a (least_upper_bound a b)) a) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP152-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP152-1.ma index c6514c8e9..f30b220af 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP152-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP152-1.ma @@ -168,7 +168,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_ax_lub3a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -190,35 +190,35 @@ ntheorem prove_ax_lub3a: ∀H11:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H13:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound b (least_upper_bound a b)) (least_upper_bound a b) +∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound b (least_upper_bound a b)) (least_upper_bound a b)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP153-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP153-1.ma index 38f3721d4..3dffded8b 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP153-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP153-1.ma @@ -168,7 +168,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_ax_lub3b: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -190,35 +190,35 @@ ntheorem prove_ax_lub3b: ∀H11:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H13:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound b (least_upper_bound a b)) b +∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound b (least_upper_bound a b)) b) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP154-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP154-1.ma index de2ed811b..30e56c601 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP154-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP154-1.ma @@ -172,7 +172,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_ax_mono1a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -196,37 +196,37 @@ ntheorem prove_ax_mono1a: ∀H12:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H13:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H14:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply a c) (multiply b c)) (multiply b c) +∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply a c) (multiply b c)) (multiply b c)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP155-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP155-1.ma index 0e15d404f..8b7e460b6 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP155-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP155-1.ma @@ -168,7 +168,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_ax_mono1b: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -192,37 +192,37 @@ ntheorem prove_ax_mono1b: ∀H12:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H13:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H14:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (multiply a c) (multiply b c)) (multiply a c) +∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (multiply a c) (multiply b c)) (multiply a c)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP156-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP156-1.ma index 33ae99453..07c9a473e 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP156-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP156-1.ma @@ -172,7 +172,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_ax_mono1c: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -196,37 +196,37 @@ ntheorem prove_ax_mono1c: ∀H12:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H13:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H14:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (multiply a c) (multiply b c)) (multiply a c) +∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (multiply a c) (multiply b c)) (multiply a c)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP157-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP157-1.ma index 009ad1fcc..124b0417d 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP157-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP157-1.ma @@ -168,7 +168,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_ax_mono2a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -192,37 +192,37 @@ ntheorem prove_ax_mono2a: ∀H12:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H13:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H14:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply c a) (multiply c b)) (multiply c b) +∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply c a) (multiply c b)) (multiply c b)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP158-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP158-1.ma index fe85a7425..27ddf587c 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP158-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP158-1.ma @@ -168,7 +168,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_ax_mono2b: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -192,37 +192,37 @@ ntheorem prove_ax_mono2b: ∀H12:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H13:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H14:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (multiply c a) (multiply c b)) (multiply c a) +∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (multiply c a) (multiply c b)) (multiply c a)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP159-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP159-1.ma index 569b25b05..9f4e648e9 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP159-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP159-1.ma @@ -168,7 +168,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_ax_mono2c: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -192,37 +192,37 @@ ntheorem prove_ax_mono2c: ∀H12:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H13:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H14:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply c a) (multiply c b)) (multiply c b) +∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply c a) (multiply c b)) (multiply c b)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP160-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP160-1.ma index 21fbbc7da..9c35783f0 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP160-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP160-1.ma @@ -168,7 +168,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_ax_refla: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -189,34 +189,34 @@ ntheorem prove_ax_refla: ∀H11:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H13:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound a a) a +∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound a a) a) . -#Univ. -#X. -#Y. -#Z. -#a. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP161-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP161-1.ma index a49bd76e3..bb8b43c50 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP161-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP161-1.ma @@ -168,7 +168,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_ax_reflb: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -189,34 +189,34 @@ ntheorem prove_ax_reflb: ∀H11:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H13:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound a a) a +∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound a a) a) . -#Univ. -#X. -#Y. -#Z. -#a. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP162-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP162-1.ma index c1c487fb5..050bbab3f 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP162-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP162-1.ma @@ -168,7 +168,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_ax_transa: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -193,38 +193,38 @@ ntheorem prove_ax_transa: ∀H13:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H15:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound a c) c +∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound a c) c) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP163-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP163-1.ma index 988b042da..00792f6cd 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP163-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP163-1.ma @@ -168,7 +168,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_ax_transb: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -193,38 +193,38 @@ ntheorem prove_ax_transb: ∀H13:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H15:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound a c) a +∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound a c) a) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP164-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP164-1.ma index 0adb6f862..db03e8daf 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP164-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP164-1.ma @@ -170,7 +170,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_distrnu: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -193,36 +193,36 @@ ntheorem prove_distrnu: ∀H11:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H13:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound a (greatest_lower_bound b c)) (greatest_lower_bound (least_upper_bound a b) (least_upper_bound a c)) +∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound a (greatest_lower_bound b c)) (greatest_lower_bound (least_upper_bound a b) (least_upper_bound a c))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP164-2.ma b/helm/software/matita/contribs/ng_TPTP/GRP164-2.ma index 40c0aed3d..2b561b8d6 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP164-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP164-2.ma @@ -168,7 +168,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_distrun: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -191,36 +191,36 @@ ntheorem prove_distrun: ∀H11:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H13:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound a (least_upper_bound b c)) (least_upper_bound (greatest_lower_bound a b) (greatest_lower_bound a c)) +∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound a (least_upper_bound b c)) (least_upper_bound (greatest_lower_bound a b) (greatest_lower_bound a c))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP165-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP165-1.ma index 0c142332b..9505005d6 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP165-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP165-1.ma @@ -170,7 +170,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_lat1a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -192,35 +192,35 @@ ntheorem prove_lat1a: ∀H12:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H13:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H14:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound a (multiply a a)) (multiply a a) +∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound a (multiply a a)) (multiply a a)) . -#Univ. -#X. -#Y. -#Z. -#a. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP165-2.ma b/helm/software/matita/contribs/ng_TPTP/GRP165-2.ma index 2ef6abeaf..6f507672f 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP165-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP165-2.ma @@ -172,7 +172,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_lat1b: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -194,35 +194,35 @@ ntheorem prove_lat1b: ∀H12:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H13:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H14:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound a (multiply a a)) a +∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound a (multiply a a)) a) . -#Univ. -#X. -#Y. -#Z. -#a. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP166-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP166-1.ma index c99ae6fb1..59a9b6e3e 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP166-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP166-1.ma @@ -170,7 +170,7 @@ include "logic/equality.ma". (* ----[Dah95] says this is redundant. *) ntheorem prove_lat2a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -194,37 +194,37 @@ ntheorem prove_lat2a: ∀H13:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H15:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound a (multiply a b)) (multiply a b) +∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound a (multiply a b)) (multiply a b)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP166-2.ma b/helm/software/matita/contribs/ng_TPTP/GRP166-2.ma index 4159b95a7..e29e4ac3d 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP166-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP166-2.ma @@ -168,7 +168,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_lat2b: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -192,37 +192,37 @@ ntheorem prove_lat2b: ∀H13:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H15:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound a (multiply a b)) a +∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound a (multiply a b)) a) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP166-3.ma b/helm/software/matita/contribs/ng_TPTP/GRP166-3.ma index cbe04c5f9..233f93507 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP166-3.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP166-3.ma @@ -168,7 +168,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_lat3a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -192,37 +192,37 @@ ntheorem prove_lat3a: ∀H13:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H15:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound a (multiply b a)) (multiply b a) +∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound a (multiply b a)) (multiply b a)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP166-4.ma b/helm/software/matita/contribs/ng_TPTP/GRP166-4.ma index 8db74f3ac..171044468 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP166-4.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP166-4.ma @@ -170,7 +170,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_lat3b: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -194,37 +194,37 @@ ntheorem prove_lat3b: ∀H13:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H15:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound a (multiply b a)) a +∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound a (multiply b a)) a) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP167-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP167-1.ma index 4694e622b..916ec306c 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP167-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP167-1.ma @@ -186,7 +186,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_lat4: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -213,40 +213,40 @@ ntheorem prove_lat4: ∀H15:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H16:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H17:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H18:∀X:Univ.eq Univ (multiply identity X) X.eq Univ a (multiply (positive_part a) (negative_part a)) +∀H18:∀X:Univ.eq Univ (multiply identity X) X.eq Univ a (multiply (positive_part a) (negative_part a))) . -#Univ. -#X. -#Y. -#Z. -#a. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#negative_part. -#positive_part. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -#H18. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#negative_part ##. +#positive_part ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP167-2.ma b/helm/software/matita/contribs/ng_TPTP/GRP167-2.ma index 046df6030..b77fa68fa 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP167-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP167-2.ma @@ -170,7 +170,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_lat4: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -200,43 +200,43 @@ ntheorem prove_lat4: ∀H18:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H19:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H20:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H21:∀X:Univ.eq Univ (multiply identity X) X.eq Univ a (multiply (positive_part a) (negative_part a)) +∀H21:∀X:Univ.eq Univ (multiply identity X) X.eq Univ a (multiply (positive_part a) (negative_part a))) . -#Univ. -#X. -#Y. -#Z. -#a. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#negative_part. -#positive_part. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -#H18. -#H19. -#H20. -#H21. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#negative_part ##. +#positive_part ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +#H19 ##. +#H20 ##. +#H21 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP167-3.ma b/helm/software/matita/contribs/ng_TPTP/GRP167-3.ma index 15bfdf007..c695f895c 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP167-3.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP167-3.ma @@ -174,7 +174,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p19: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -195,34 +195,34 @@ ntheorem prove_p19: ∀H11:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H13:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ a (multiply (least_upper_bound a identity) (greatest_lower_bound a identity)) +∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ a (multiply (least_upper_bound a identity) (greatest_lower_bound a identity))) . -#Univ. -#X. -#Y. -#Z. -#a. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP167-4.ma b/helm/software/matita/contribs/ng_TPTP/GRP167-4.ma index ea46a3e4b..346cf559f 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP167-4.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP167-4.ma @@ -170,7 +170,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p19: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -194,37 +194,37 @@ ntheorem prove_p19: ∀H14:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H15:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H16:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ a (multiply (least_upper_bound a identity) (greatest_lower_bound a identity)) +∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ a (multiply (least_upper_bound a identity) (greatest_lower_bound a identity))) . -#Univ. -#X. -#Y. -#Z. -#a. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP167-5.ma b/helm/software/matita/contribs/ng_TPTP/GRP167-5.ma index 90256d155..d859a0d05 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP167-5.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP167-5.ma @@ -182,7 +182,7 @@ include "logic/equality.ma". (* ----Extra lemma *) ntheorem prove_lat4: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -210,43 +210,43 @@ ntheorem prove_lat4: ∀H16:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H17:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H18:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H19:∀X:Univ.eq Univ (multiply identity X) X.eq Univ a (multiply (positive_part a) (negative_part a)) +∀H19:∀X:Univ.eq Univ (multiply identity X) X.eq Univ a (multiply (positive_part a) (negative_part a))) . -#Univ. -#A. -#B. -#X. -#Y. -#Z. -#a. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#negative_part. -#positive_part. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -#H18. -#H19. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19; +#Univ ##. +#A ##. +#B ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#negative_part ##. +#positive_part ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +#H19 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP168-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP168-1.ma index 4b9267a39..548494c01 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP168-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP168-1.ma @@ -176,7 +176,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p01a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -200,37 +200,37 @@ ntheorem prove_p01a: ∀H12:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H13:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H14:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply (inverse c) (multiply a c)) (multiply (inverse c) (multiply b c))) (multiply (inverse c) (multiply b c)) +∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply (inverse c) (multiply a c)) (multiply (inverse c) (multiply b c))) (multiply (inverse c) (multiply b c))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP168-2.ma b/helm/software/matita/contribs/ng_TPTP/GRP168-2.ma index b2b0127d6..dd3ad6732 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP168-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP168-2.ma @@ -172,7 +172,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p01b: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -196,37 +196,37 @@ ntheorem prove_p01b: ∀H12:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H13:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H14:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (multiply (inverse c) (multiply a c)) (multiply (inverse c) (multiply b c))) (multiply (inverse c) (multiply a c)) +∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (multiply (inverse c) (multiply a c)) (multiply (inverse c) (multiply b c))) (multiply (inverse c) (multiply a c))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP169-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP169-1.ma index 683edea64..c0767e8d7 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP169-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP169-1.ma @@ -174,7 +174,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p02a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -197,36 +197,36 @@ ntheorem prove_p02a: ∀H12:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H13:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H14:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound a b) a +∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound a b) a) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP169-2.ma b/helm/software/matita/contribs/ng_TPTP/GRP169-2.ma index 5fbdc304a..43081c98b 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP169-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP169-2.ma @@ -172,7 +172,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p02b: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -195,36 +195,36 @@ ntheorem prove_p02b: ∀H12:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H13:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H14:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound a b) b +∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound a b) b) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP170-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP170-1.ma index a8faaad65..e75339b7a 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP170-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP170-1.ma @@ -166,7 +166,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p03a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -192,39 +192,39 @@ ntheorem prove_p03a: ∀H13:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H15:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply a c) (multiply b d)) (multiply b d) +∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply a c) (multiply b d)) (multiply b d)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP170-2.ma b/helm/software/matita/contribs/ng_TPTP/GRP170-2.ma index 8dc90be52..fdb5ce834 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP170-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP170-2.ma @@ -168,7 +168,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p03b: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -194,39 +194,39 @@ ntheorem prove_p03b: ∀H13:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H15:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (multiply a c) (multiply b d)) (multiply a c) +∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (multiply a c) (multiply b d)) (multiply a c)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP170-3.ma b/helm/software/matita/contribs/ng_TPTP/GRP170-3.ma index e0e8d061a..8fc3de379 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP170-3.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP170-3.ma @@ -168,7 +168,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p03c: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -194,39 +194,39 @@ ntheorem prove_p03c: ∀H13:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H15:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (multiply a c) (multiply b d)) (multiply a c) +∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (multiply a c) (multiply b d)) (multiply a c)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP170-4.ma b/helm/software/matita/contribs/ng_TPTP/GRP170-4.ma index 8a5892177..6dc53a8f9 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP170-4.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP170-4.ma @@ -170,7 +170,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p03d: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -196,39 +196,39 @@ ntheorem prove_p03d: ∀H13:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H15:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply a c) (multiply b d)) (multiply b d) +∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply a c) (multiply b d)) (multiply b d)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP171-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP171-1.ma index 74cf7fd88..7d53d8cc9 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP171-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP171-1.ma @@ -166,7 +166,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p04a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -190,37 +190,37 @@ ntheorem prove_p04a: ∀H13:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H15:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound identity (multiply a b)) (multiply a b) +∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound identity (multiply a b)) (multiply a b)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP171-2.ma b/helm/software/matita/contribs/ng_TPTP/GRP171-2.ma index 2b11ef019..246b366d0 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP171-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP171-2.ma @@ -168,7 +168,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p04c: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -192,37 +192,37 @@ ntheorem prove_p04c: ∀H13:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H15:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound identity (multiply a b)) identity +∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound identity (multiply a b)) identity) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP172-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP172-1.ma index ec686cafa..412fe5ed5 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP172-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP172-1.ma @@ -166,7 +166,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p04b: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -190,37 +190,37 @@ ntheorem prove_p04b: ∀H13:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H15:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound identity (multiply a b)) identity +∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound identity (multiply a b)) identity) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP172-2.ma b/helm/software/matita/contribs/ng_TPTP/GRP172-2.ma index 7496f87ba..91fe45d0e 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP172-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP172-2.ma @@ -168,7 +168,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p04d: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -192,37 +192,37 @@ ntheorem prove_p04d: ∀H13:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H15:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound identity (multiply a b)) (multiply a b) +∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound identity (multiply a b)) (multiply a b)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP173-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP173-1.ma index f52533d9f..f5414bb70 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP173-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP173-1.ma @@ -176,7 +176,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p05a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -199,36 +199,36 @@ ntheorem prove_p05a: ∀H13:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H15:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ identity a +∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ identity a) . -#Univ. -#X. -#Y. -#Z. -#a. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP174-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP174-1.ma index 6fd8802ca..81f34c62a 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP174-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP174-1.ma @@ -170,7 +170,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p05b: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -193,36 +193,36 @@ ntheorem prove_p05b: ∀H13:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H15:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ identity a +∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ identity a) . -#Univ. -#X. -#Y. -#Z. -#a. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP175-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP175-1.ma index a0b5ba182..655ce7476 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP175-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP175-1.ma @@ -166,7 +166,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p06a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -189,36 +189,36 @@ ntheorem prove_p06a: ∀H12:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H13:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H14:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound identity (multiply (inverse a) (multiply b a))) (multiply (inverse a) (multiply b a)) +∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound identity (multiply (inverse a) (multiply b a))) (multiply (inverse a) (multiply b a))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP175-2.ma b/helm/software/matita/contribs/ng_TPTP/GRP175-2.ma index 61a329cbc..ac4105e0d 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP175-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP175-2.ma @@ -168,7 +168,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p06b: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -191,36 +191,36 @@ ntheorem prove_p06b: ∀H12:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H13:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H14:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound identity (multiply (inverse a) (multiply b a))) identity +∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound identity (multiply (inverse a) (multiply b a))) identity) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP175-3.ma b/helm/software/matita/contribs/ng_TPTP/GRP175-3.ma index ab51a55a2..8d580533a 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP175-3.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP175-3.ma @@ -170,7 +170,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p06c: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -193,36 +193,36 @@ ntheorem prove_p06c: ∀H12:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H13:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H14:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound identity (multiply (inverse a) (multiply b a))) identity +∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound identity (multiply (inverse a) (multiply b a))) identity) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP175-4.ma b/helm/software/matita/contribs/ng_TPTP/GRP175-4.ma index cac62b59a..639d55c3c 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP175-4.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP175-4.ma @@ -170,7 +170,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p06d: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -193,36 +193,36 @@ ntheorem prove_p06d: ∀H12:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H13:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H14:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound identity (multiply (inverse a) (multiply b a))) (multiply (inverse a) (multiply b a)) +∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound identity (multiply (inverse a) (multiply b a))) (multiply (inverse a) (multiply b a))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP176-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP176-1.ma index 577a4e0bf..a42bec615 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP176-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP176-1.ma @@ -180,7 +180,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p07: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -204,37 +204,37 @@ ntheorem prove_p07: ∀H11:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H13:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply c (multiply (least_upper_bound a b) d)) (least_upper_bound (multiply c (multiply a d)) (multiply c (multiply b d))) +∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply c (multiply (least_upper_bound a b) d)) (least_upper_bound (multiply c (multiply a d)) (multiply c (multiply b d)))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP176-2.ma b/helm/software/matita/contribs/ng_TPTP/GRP176-2.ma index 49e34fa8d..ad72b49c2 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP176-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP176-2.ma @@ -170,7 +170,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p07: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -195,38 +195,38 @@ ntheorem prove_p07: ∀H12:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H13:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H14:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply c (multiply (least_upper_bound a b) d)) (least_upper_bound (multiply c (multiply a d)) (multiply c (multiply b d))) +∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply c (multiply (least_upper_bound a b) d)) (least_upper_bound (multiply c (multiply a d)) (multiply c (multiply b d)))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP177-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP177-1.ma index 12622b08b..72ae87b92 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP177-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP177-1.ma @@ -170,7 +170,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p08a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -196,39 +196,39 @@ ntheorem prove_p08a: ∀H14:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H15:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H16:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (greatest_lower_bound a (multiply b c)) (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))) (multiply (greatest_lower_bound a b) (greatest_lower_bound a c)) +∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (greatest_lower_bound a (multiply b c)) (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))) (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP177-2.ma b/helm/software/matita/contribs/ng_TPTP/GRP177-2.ma index a21b9e054..031f800dc 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP177-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP177-2.ma @@ -172,7 +172,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p08b: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -198,39 +198,39 @@ ntheorem prove_p08b: ∀H14:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H15:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H16:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (greatest_lower_bound a (multiply b c)) (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))) (greatest_lower_bound a (multiply b c)) +∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (greatest_lower_bound a (multiply b c)) (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))) (greatest_lower_bound a (multiply b c))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP178-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP178-1.ma index 135635cd9..0e9af2c6d 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP178-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP178-1.ma @@ -170,7 +170,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p09a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -197,40 +197,40 @@ ntheorem prove_p09a: ∀H15:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H16:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H17:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H18:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound a (multiply b c)) (greatest_lower_bound a c) +∀H18:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound a (multiply b c)) (greatest_lower_bound a c)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -#H18. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP178-2.ma b/helm/software/matita/contribs/ng_TPTP/GRP178-2.ma index 6530ef07b..73274af8e 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP178-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP178-2.ma @@ -172,7 +172,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p09b: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -199,40 +199,40 @@ ntheorem prove_p09b: ∀H15:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H16:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H17:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H18:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound a (multiply b c)) (greatest_lower_bound a c) +∀H18:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound a (multiply b c)) (greatest_lower_bound a c)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -#H18. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP179-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP179-1.ma index 2e41855c6..2580773e6 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP179-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP179-1.ma @@ -170,7 +170,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p10: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -192,35 +192,35 @@ ntheorem prove_p10: ∀H11:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H13:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (inverse (least_upper_bound a b)) (greatest_lower_bound (inverse a) (inverse b)) +∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (inverse (least_upper_bound a b)) (greatest_lower_bound (inverse a) (inverse b))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP179-2.ma b/helm/software/matita/contribs/ng_TPTP/GRP179-2.ma index 1a47cd5c0..69e141f96 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP179-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP179-2.ma @@ -172,7 +172,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p18: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -193,34 +193,34 @@ ntheorem prove_p18: ∀H11:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H13:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (inverse a) identity) (inverse (greatest_lower_bound a identity)) +∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (inverse a) identity) (inverse (greatest_lower_bound a identity))) . -#Univ. -#X. -#Y. -#Z. -#a. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP179-3.ma b/helm/software/matita/contribs/ng_TPTP/GRP179-3.ma index f2c385e9a..f6d5a79b7 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP179-3.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP179-3.ma @@ -172,7 +172,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p18: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -196,37 +196,37 @@ ntheorem prove_p18: ∀H14:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H15:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H16:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (inverse a) identity) (inverse (greatest_lower_bound a identity)) +∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (inverse a) identity) (inverse (greatest_lower_bound a identity))) . -#Univ. -#X. -#Y. -#Z. -#a. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP180-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP180-1.ma index c873f5e2d..6f7cd1a93 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP180-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP180-1.ma @@ -174,7 +174,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p11: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -196,35 +196,35 @@ ntheorem prove_p11: ∀H11:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H13:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply a (multiply (inverse (greatest_lower_bound a b)) b)) (least_upper_bound a b) +∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply a (multiply (inverse (greatest_lower_bound a b)) b)) (least_upper_bound a b)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP180-2.ma b/helm/software/matita/contribs/ng_TPTP/GRP180-2.ma index b4168829b..905898200 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP180-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP180-2.ma @@ -170,7 +170,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p11: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -195,38 +195,38 @@ ntheorem prove_p11: ∀H14:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H15:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H16:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply a (multiply (inverse (greatest_lower_bound a b)) b)) (least_upper_bound a b) +∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply a (multiply (inverse (greatest_lower_bound a b)) b)) (least_upper_bound a b)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP181-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP181-1.ma index e48f12638..da9b6888a 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP181-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP181-1.ma @@ -174,7 +174,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p12: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -199,38 +199,38 @@ ntheorem prove_p12: ∀H13:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H15:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ a b +∀H16:∀X:Univ.eq Univ (multiply identity X) X.eq Univ a b) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP181-2.ma b/helm/software/matita/contribs/ng_TPTP/GRP181-2.ma index f0e2365b5..7407c1c13 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP181-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP181-2.ma @@ -170,7 +170,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p12: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -198,41 +198,41 @@ ntheorem prove_p12: ∀H16:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H17:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H18:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H19:∀X:Univ.eq Univ (multiply identity X) X.eq Univ a b +∀H19:∀X:Univ.eq Univ (multiply identity X) X.eq Univ a b) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -#H18. -#H19. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +#H19 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP181-3.ma b/helm/software/matita/contribs/ng_TPTP/GRP181-3.ma index d22179466..64eeac2bd 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP181-3.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP181-3.ma @@ -174,7 +174,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p12x: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -201,40 +201,40 @@ ntheorem prove_p12x: ∀H15:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H16:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H17:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H18:∀X:Univ.eq Univ (multiply identity X) X.eq Univ a b +∀H18:∀X:Univ.eq Univ (multiply identity X) X.eq Univ a b) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -#H18. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP181-4.ma b/helm/software/matita/contribs/ng_TPTP/GRP181-4.ma index 0a0329787..af9b4262b 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP181-4.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP181-4.ma @@ -170,7 +170,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p12x: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -200,43 +200,43 @@ ntheorem prove_p12x: ∀H18:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H19:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H20:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H21:∀X:Univ.eq Univ (multiply identity X) X.eq Univ a b +∀H21:∀X:Univ.eq Univ (multiply identity X) X.eq Univ a b) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -#H18. -#H19. -#H20. -#H21. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +#H19 ##. +#H20 ##. +#H21 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP182-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP182-1.ma index 8d0029e3f..9a29c9b37 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP182-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP182-1.ma @@ -190,7 +190,7 @@ include "logic/equality.ma". (* ----This is Dahn's clause *) ntheorem prove_p17a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -211,34 +211,34 @@ ntheorem prove_p17a: ∀H11:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H13:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound identity (greatest_lower_bound a identity)) identity +∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound identity (greatest_lower_bound a identity)) identity) . -#Univ. -#X. -#Y. -#Z. -#a. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP182-2.ma b/helm/software/matita/contribs/ng_TPTP/GRP182-2.ma index bb7057f22..347a98b4f 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP182-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP182-2.ma @@ -186,7 +186,7 @@ include "logic/equality.ma". (* ----This is Dahn's clause *) ntheorem prove_p17a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -210,37 +210,37 @@ ntheorem prove_p17a: ∀H14:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H15:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H16:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound identity (greatest_lower_bound a identity)) identity +∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound identity (greatest_lower_bound a identity)) identity) . -#Univ. -#X. -#Y. -#Z. -#a. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP182-3.ma b/helm/software/matita/contribs/ng_TPTP/GRP182-3.ma index 4d5c4f691..6d6d119f8 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP182-3.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP182-3.ma @@ -176,7 +176,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p17b: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -197,34 +197,34 @@ ntheorem prove_p17b: ∀H11:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H13:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound identity (least_upper_bound a identity)) identity +∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound identity (least_upper_bound a identity)) identity) . -#Univ. -#X. -#Y. -#Z. -#a. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP182-4.ma b/helm/software/matita/contribs/ng_TPTP/GRP182-4.ma index 661c0f38d..f6ad9fccf 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP182-4.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP182-4.ma @@ -172,7 +172,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p17b: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -196,37 +196,37 @@ ntheorem prove_p17b: ∀H14:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H15:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H16:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound identity (least_upper_bound a identity)) identity +∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound identity (least_upper_bound a identity)) identity) . -#Univ. -#X. -#Y. -#Z. -#a. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP183-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP183-1.ma index b27354b13..126f03204 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP183-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP183-1.ma @@ -172,7 +172,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p20: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -193,34 +193,34 @@ ntheorem prove_p20: ∀H11:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H13:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (least_upper_bound a identity) (inverse (greatest_lower_bound a identity))) identity +∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (least_upper_bound a identity) (inverse (greatest_lower_bound a identity))) identity) . -#Univ. -#X. -#Y. -#Z. -#a. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP183-2.ma b/helm/software/matita/contribs/ng_TPTP/GRP183-2.ma index 0ee28d262..0c2a7a4f7 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP183-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP183-2.ma @@ -166,7 +166,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p20: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -190,37 +190,37 @@ ntheorem prove_p20: ∀H14:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H15:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H16:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (least_upper_bound a identity) (inverse (greatest_lower_bound a identity))) identity +∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (least_upper_bound a identity) (inverse (greatest_lower_bound a identity))) identity) . -#Univ. -#X. -#Y. -#Z. -#a. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP183-3.ma b/helm/software/matita/contribs/ng_TPTP/GRP183-3.ma index e9200701b..74b35d96e 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP183-3.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP183-3.ma @@ -172,7 +172,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_20x: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -193,34 +193,34 @@ ntheorem prove_20x: ∀H11:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H13:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (least_upper_bound a identity) (least_upper_bound (inverse a) identity)) identity +∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (least_upper_bound a identity) (least_upper_bound (inverse a) identity)) identity) . -#Univ. -#X. -#Y. -#Z. -#a. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP183-4.ma b/helm/software/matita/contribs/ng_TPTP/GRP183-4.ma index 75a490a88..1f42a1582 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP183-4.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP183-4.ma @@ -168,7 +168,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_20x: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -192,37 +192,37 @@ ntheorem prove_20x: ∀H14:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H15:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H16:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (least_upper_bound a identity) (least_upper_bound (inverse a) identity)) identity +∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (least_upper_bound a identity) (least_upper_bound (inverse a) identity)) identity) . -#Univ. -#X. -#Y. -#Z. -#a. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP184-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP184-1.ma index 6d14b4d95..c8d8b40f7 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP184-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP184-1.ma @@ -174,7 +174,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p21: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -195,34 +195,34 @@ ntheorem prove_p21: ∀H11:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H13:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply (least_upper_bound a identity) (inverse (greatest_lower_bound a identity))) (multiply (inverse (greatest_lower_bound a identity)) (least_upper_bound a identity)) +∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply (least_upper_bound a identity) (inverse (greatest_lower_bound a identity))) (multiply (inverse (greatest_lower_bound a identity)) (least_upper_bound a identity))) . -#Univ. -#X. -#Y. -#Z. -#a. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP184-2.ma b/helm/software/matita/contribs/ng_TPTP/GRP184-2.ma index 7e8bec897..e9c470469 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP184-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP184-2.ma @@ -166,7 +166,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p21: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -190,37 +190,37 @@ ntheorem prove_p21: ∀H14:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H15:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H16:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply (least_upper_bound a identity) (inverse (greatest_lower_bound a identity))) (multiply (inverse (greatest_lower_bound a identity)) (least_upper_bound a identity)) +∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply (least_upper_bound a identity) (inverse (greatest_lower_bound a identity))) (multiply (inverse (greatest_lower_bound a identity)) (least_upper_bound a identity))) . -#Univ. -#X. -#Y. -#Z. -#a. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP184-3.ma b/helm/software/matita/contribs/ng_TPTP/GRP184-3.ma index 29af55149..a9152c5cb 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP184-3.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP184-3.ma @@ -170,7 +170,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p21x: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -191,34 +191,34 @@ ntheorem prove_p21x: ∀H11:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H13:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply (least_upper_bound a identity) (inverse (greatest_lower_bound a identity))) (multiply (inverse (greatest_lower_bound a identity)) (least_upper_bound a identity)) +∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply (least_upper_bound a identity) (inverse (greatest_lower_bound a identity))) (multiply (inverse (greatest_lower_bound a identity)) (least_upper_bound a identity))) . -#Univ. -#X. -#Y. -#Z. -#a. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP184-4.ma b/helm/software/matita/contribs/ng_TPTP/GRP184-4.ma index 94ef33401..03d3a6cbd 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP184-4.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP184-4.ma @@ -166,7 +166,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p21x: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -192,39 +192,39 @@ ntheorem prove_p21x: ∀H16:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H17:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H18:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H19:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply (least_upper_bound a identity) (inverse (greatest_lower_bound a identity))) (multiply (inverse (greatest_lower_bound a identity)) (least_upper_bound a identity)) +∀H19:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply (least_upper_bound a identity) (inverse (greatest_lower_bound a identity))) (multiply (inverse (greatest_lower_bound a identity)) (least_upper_bound a identity))) . -#Univ. -#X. -#Y. -#Z. -#a. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -#H18. -#H19. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +#H19 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP185-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP185-1.ma index feaea23ab..508e97b4b 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP185-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP185-1.ma @@ -170,7 +170,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p22a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -192,35 +192,35 @@ ntheorem prove_p22a: ∀H11:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H13:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity))) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) +∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity))) (multiply (least_upper_bound a identity) (least_upper_bound b identity))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP185-2.ma b/helm/software/matita/contribs/ng_TPTP/GRP185-2.ma index 056a1aeed..b5cb8dd12 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP185-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP185-2.ma @@ -166,7 +166,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p22a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -191,38 +191,38 @@ ntheorem prove_p22a: ∀H14:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H15:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H16:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity))) (multiply (least_upper_bound a identity) (least_upper_bound b identity)) +∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity))) (multiply (least_upper_bound a identity) (least_upper_bound b identity))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP185-3.ma b/helm/software/matita/contribs/ng_TPTP/GRP185-3.ma index 727a57c95..6e7ed1546 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP185-3.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP185-3.ma @@ -172,7 +172,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p22b: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -194,35 +194,35 @@ ntheorem prove_p22b: ∀H11:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H13:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity))) (least_upper_bound (multiply a b) identity) +∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity))) (least_upper_bound (multiply a b) identity)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP185-4.ma b/helm/software/matita/contribs/ng_TPTP/GRP185-4.ma index 97bbbad37..d69bbc32a 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP185-4.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP185-4.ma @@ -168,7 +168,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p22b: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -193,38 +193,38 @@ ntheorem prove_p22b: ∀H14:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H15:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H16:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity))) (least_upper_bound (multiply a b) identity) +∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity))) (least_upper_bound (multiply a b) identity)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP186-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP186-1.ma index b9065e655..9d1f4c821 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP186-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP186-1.ma @@ -172,7 +172,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p23: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -194,35 +194,35 @@ ntheorem prove_p23: ∀H11:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H13:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply a b) identity) (multiply a (inverse (greatest_lower_bound a (inverse b)))) +∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply a b) identity) (multiply a (inverse (greatest_lower_bound a (inverse b))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP186-2.ma b/helm/software/matita/contribs/ng_TPTP/GRP186-2.ma index 56a9f5aa2..f09153bd4 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP186-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP186-2.ma @@ -168,7 +168,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p23: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -193,38 +193,38 @@ ntheorem prove_p23: ∀H14:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H15:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H16:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply a b) identity) (multiply a (inverse (greatest_lower_bound a (inverse b)))) +∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply a b) identity) (multiply a (inverse (greatest_lower_bound a (inverse b))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP186-3.ma b/helm/software/matita/contribs/ng_TPTP/GRP186-3.ma index 8ce7ed2dc..473ade104 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP186-3.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP186-3.ma @@ -172,7 +172,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p23x: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -194,35 +194,35 @@ ntheorem prove_p23x: ∀H11:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H13:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply a b) identity) (multiply a (least_upper_bound (inverse a) b)) +∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply a b) identity) (multiply a (least_upper_bound (inverse a) b))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP186-4.ma b/helm/software/matita/contribs/ng_TPTP/GRP186-4.ma index cbe8fcb56..119e94cf8 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP186-4.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP186-4.ma @@ -168,7 +168,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p23x: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -193,38 +193,38 @@ ntheorem prove_p23x: ∀H14:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H15:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H16:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply a b) identity) (multiply a (least_upper_bound (inverse a) b)) +∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply a b) identity) (multiply a (least_upper_bound (inverse a) b))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP187-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP187-1.ma index 4ff4bf1e6..4a6ce12a8 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP187-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP187-1.ma @@ -170,7 +170,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p33: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -193,36 +193,36 @@ ntheorem prove_p33: ∀H12:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H13:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H14:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply a b) (multiply b a) +∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply a b) (multiply b a)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP188-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP188-1.ma index c2a7a25e0..869146080 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP188-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP188-1.ma @@ -170,7 +170,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p38a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -192,35 +192,35 @@ ntheorem prove_p38a: ∀H11:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H13:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound b (least_upper_bound a b)) (least_upper_bound a b) +∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound b (least_upper_bound a b)) (least_upper_bound a b)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP188-2.ma b/helm/software/matita/contribs/ng_TPTP/GRP188-2.ma index 35910e4d8..ce0ea9cfb 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP188-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP188-2.ma @@ -166,7 +166,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p38a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -191,38 +191,38 @@ ntheorem prove_p38a: ∀H14:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H15:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H16:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound b (least_upper_bound a b)) (least_upper_bound a b) +∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound b (least_upper_bound a b)) (least_upper_bound a b)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP189-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP189-1.ma index 67d211741..cbde5bacf 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP189-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP189-1.ma @@ -170,7 +170,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p38b: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -192,35 +192,35 @@ ntheorem prove_p38b: ∀H11:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H13:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound b (least_upper_bound a b)) b +∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound b (least_upper_bound a b)) b) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP189-2.ma b/helm/software/matita/contribs/ng_TPTP/GRP189-2.ma index 24d4af94c..efdff2a17 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP189-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP189-2.ma @@ -166,7 +166,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p38b: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -191,38 +191,38 @@ ntheorem prove_p38b: ∀H14:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H15:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H16:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound b (least_upper_bound a b)) b +∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound b (least_upper_bound a b)) b) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP190-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP190-1.ma index 60133e1cc..6073397a9 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP190-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP190-1.ma @@ -170,7 +170,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p39a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -193,36 +193,36 @@ ntheorem prove_p39a: ∀H12:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H13:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H14:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (inverse a) (inverse b)) (inverse b) +∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (inverse a) (inverse b)) (inverse b)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP190-2.ma b/helm/software/matita/contribs/ng_TPTP/GRP190-2.ma index a67ac33f6..568d839ce 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP190-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP190-2.ma @@ -172,7 +172,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p39c: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -195,36 +195,36 @@ ntheorem prove_p39c: ∀H12:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H13:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H14:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (inverse a) (inverse b)) (inverse a) +∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (inverse a) (inverse b)) (inverse a)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP191-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP191-1.ma index 598666b24..a3efe8803 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP191-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP191-1.ma @@ -170,7 +170,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p39b: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -193,36 +193,36 @@ ntheorem prove_p39b: ∀H12:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H13:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H14:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (inverse a) (inverse b)) (inverse a) +∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (inverse a) (inverse b)) (inverse a)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP191-2.ma b/helm/software/matita/contribs/ng_TPTP/GRP191-2.ma index efd9f7868..e9ef675d4 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP191-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP191-2.ma @@ -172,7 +172,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p39d: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -195,36 +195,36 @@ ntheorem prove_p39d: ∀H12:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H13:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H14:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (inverse a) (inverse b)) (inverse b) +∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (inverse a) (inverse b)) (inverse b)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP192-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP192-1.ma index d3119d594..d3a311579 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP192-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP192-1.ma @@ -168,7 +168,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p40a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. @@ -191,36 +191,36 @@ ntheorem prove_p40a: ∀H12:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H13:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H14:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply a b) (multiply b a) +∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply a b) (multiply b a)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP193-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP193-1.ma index 94626fdeb..e3defd275 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP193-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP193-1.ma @@ -166,7 +166,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p8_9a: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -194,41 +194,41 @@ ntheorem prove_p8_9a: ∀H16:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H17:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H18:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H19:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound a (multiply b c)) (greatest_lower_bound a c) +∀H19:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound a (multiply b c)) (greatest_lower_bound a c)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -#H18. -#H19. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +#H19 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP193-2.ma b/helm/software/matita/contribs/ng_TPTP/GRP193-2.ma index 2f7104b2b..e27884732 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP193-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP193-2.ma @@ -168,7 +168,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_p8_9b: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -196,41 +196,41 @@ ntheorem prove_p8_9b: ∀H16:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). ∀H17:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). ∀H18:∀X:Univ.eq Univ (multiply (inverse X) X) identity. -∀H19:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound a (multiply b c)) (greatest_lower_bound a c) +∀H19:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound a (multiply b c)) (greatest_lower_bound a c)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#greatest_lower_bound. -#identity. -#inverse. -#least_upper_bound. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -#H18. -#H19. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +#H19 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP195-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP195-1.ma index 202eb45ba..171bc3a77 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP195-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP195-1.ma @@ -100,23 +100,23 @@ include "logic/equality.ma". (* ----Denial of conclusion: *) ntheorem prove_this: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (multiply X (multiply Y Y)) (multiply Y (multiply Y X)). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).eq Univ (multiply a (multiply b (multiply a (multiply b (multiply a (multiply b (multiply a b))))))) (multiply a (multiply a (multiply a (multiply a (multiply b (multiply b (multiply b b))))))) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).eq Univ (multiply a (multiply b (multiply a (multiply b (multiply a (multiply b (multiply a b))))))) (multiply a (multiply a (multiply a (multiply a (multiply b (multiply b (multiply b b)))))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP196-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP196-1.ma index fc24baa5a..551f70a33 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP196-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP196-1.ma @@ -104,23 +104,23 @@ include "logic/equality.ma". (* ----Denial of conclusion: *) ntheorem prove_this: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (multiply X (multiply Y (multiply Y Y))) (multiply Y (multiply Y (multiply Y X))). -∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).eq Univ (multiply a (multiply b (multiply a (multiply b (multiply a (multiply b (multiply a (multiply b (multiply a (multiply b (multiply a (multiply b (multiply a (multiply b (multiply a (multiply b (multiply a b))))))))))))))))) (multiply a (multiply a (multiply a (multiply a (multiply a (multiply a (multiply a (multiply a (multiply a (multiply b (multiply b (multiply b (multiply b (multiply b (multiply b (multiply b (multiply b b))))))))))))))))) +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).eq Univ (multiply a (multiply b (multiply a (multiply b (multiply a (multiply b (multiply a (multiply b (multiply a (multiply b (multiply a (multiply b (multiply a (multiply b (multiply a (multiply b (multiply a b))))))))))))))))) (multiply a (multiply a (multiply a (multiply a (multiply a (multiply a (multiply a (multiply a (multiply a (multiply b (multiply b (multiply b (multiply b (multiply b (multiply b (multiply b (multiply b b)))))))))))))))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP200-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP200-1.ma index 25f07202c..a82996bb0 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP200-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP200-1.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----Denial of Moufang-2: *) ntheorem prove_moufang2: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -72,31 +72,31 @@ ntheorem prove_moufang2: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (left_division X (multiply X Y)) Y. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply X (left_division X Y)) Y. ∀H7:∀X:Univ.eq Univ (multiply X identity) X. -∀H8:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply (multiply (multiply a b) c) b) (multiply a (multiply b (multiply c b))) +∀H8:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply (multiply (multiply a b) c) b) (multiply a (multiply b (multiply c b)))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#identity. -#left_division. -#left_inverse. -#multiply. -#right_division. -#right_inverse. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#identity ##. +#left_division ##. +#left_inverse ##. +#multiply ##. +#right_division ##. +#right_inverse ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP201-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP201-1.ma index cfe181627..9d7247d78 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP201-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP201-1.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----Denial of Moufang-3: *) ntheorem prove_moufang3: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -72,31 +72,31 @@ ntheorem prove_moufang3: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (left_division X (multiply X Y)) Y. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply X (left_division X Y)) Y. ∀H7:∀X:Univ.eq Univ (multiply X identity) X. -∀H8:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply (multiply (multiply a b) a) c) (multiply a (multiply b (multiply a c))) +∀H8:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply (multiply (multiply a b) a) c) (multiply a (multiply b (multiply a c)))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#identity. -#left_division. -#left_inverse. -#multiply. -#right_division. -#right_inverse. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#identity ##. +#left_division ##. +#left_inverse ##. +#multiply ##. +#right_division ##. +#right_inverse ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP202-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP202-1.ma index f8a1496c8..3718f3591 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP202-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP202-1.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----Denial of Moufang-1 *) ntheorem prove_moufang1: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -72,31 +72,31 @@ ntheorem prove_moufang1: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (left_division X (multiply X Y)) Y. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply X (left_division X Y)) Y. ∀H7:∀X:Univ.eq Univ (multiply X identity) X. -∀H8:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply (multiply a (multiply b c)) a) (multiply (multiply a b) (multiply c a)) +∀H8:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply (multiply a (multiply b c)) a) (multiply (multiply a b) (multiply c a))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#identity. -#left_division. -#left_inverse. -#multiply. -#right_division. -#right_inverse. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#identity ##. +#left_division ##. +#left_inverse ##. +#multiply ##. +#right_division ##. +#right_inverse ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP203-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP203-1.ma index 6b841f5ad..dcfbcec4a 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP203-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP203-1.ma @@ -52,7 +52,7 @@ include "logic/equality.ma". (* ----Denial of Moufang-2: *) ntheorem prove_moufang2: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -61,22 +61,22 @@ ntheorem prove_moufang2: ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply (multiply X Y) X) Z) (multiply X (multiply Y (multiply X Z))). ∀H1:∀X:Univ.eq Univ (multiply (left_inverse X) X) identity. -∀H2:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply (multiply (multiply a b) c) b) (multiply a (multiply b (multiply c b))) +∀H2:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply (multiply (multiply a b) c) b) (multiply a (multiply b (multiply c b)))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#identity. -#left_inverse. -#multiply. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#identity ##. +#left_inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP204-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP204-1.ma index d624beeef..60099d38d 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP204-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP204-1.ma @@ -52,7 +52,7 @@ include "logic/equality.ma". (* ----Denial of Moufang-2: *) ntheorem prove_moufang2: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -61,22 +61,22 @@ ntheorem prove_moufang2: ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X (multiply Y Z)) X) (multiply (multiply X Y) (multiply Z X)). ∀H1:∀X:Univ.eq Univ (multiply (left_inverse X) X) identity. -∀H2:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply (multiply (multiply a b) c) b) (multiply a (multiply b (multiply c b))) +∀H2:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply (multiply (multiply a b) c) b) (multiply a (multiply b (multiply c b)))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#identity. -#left_inverse. -#multiply. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#identity ##. +#left_inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP205-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP205-1.ma index dfbae70ec..b03156f38 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP205-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP205-1.ma @@ -48,7 +48,7 @@ include "logic/equality.ma". (* ----Denial of Moufang-4 *) ntheorem prove_moufang4: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀identity:Univ. ∀left_division:∀_:Univ.∀_:Univ.Univ. ∀left_inverse:∀_:Univ.Univ. @@ -66,31 +66,31 @@ ntheorem prove_moufang4: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (left_division X (multiply X Y)) Y. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply X (left_division X Y)) Y. ∀H7:∀X:Univ.eq Univ (multiply X identity) X. -∀H8:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply x (multiply (multiply y z) x)) (multiply (multiply x y) (multiply z x)) +∀H8:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply x (multiply (multiply y z) x)) (multiply (multiply x y) (multiply z x))) . -#Univ. -#X. -#Y. -#Z. -#identity. -#left_division. -#left_inverse. -#multiply. -#right_division. -#right_inverse. -#x. -#y. -#z. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#identity ##. +#left_division ##. +#left_inverse ##. +#multiply ##. +#right_division ##. +#right_inverse ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP206-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP206-1.ma index 0d343edd1..5de616891 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP206-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP206-1.ma @@ -48,7 +48,7 @@ include "logic/equality.ma". (* ----Denial of Moufang-1 *) ntheorem prove_moufang1: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -66,31 +66,31 @@ ntheorem prove_moufang1: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (left_division X (multiply X Y)) Y. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply X (left_division X Y)) Y. ∀H7:∀X:Univ.eq Univ (multiply X identity) X. -∀H8:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply (multiply a (multiply b c)) a) (multiply (multiply a b) (multiply c a)) +∀H8:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply (multiply a (multiply b c)) a) (multiply (multiply a b) (multiply c a))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#identity. -#left_division. -#left_inverse. -#multiply. -#right_division. -#right_inverse. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#identity ##. +#left_division ##. +#left_inverse ##. +#multiply ##. +#right_division ##. +#right_inverse ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP207-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP207-1.ma index 775456ace..01417f057 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP207-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP207-1.ma @@ -46,27 +46,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem try_prove_this_axiom: - ∀Univ:Type.∀U:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀Y:Univ.∀Z:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀u:Univ. ∀x:Univ. ∀y:Univ. ∀z:Univ. -∀H0:∀U:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply U (inverse (multiply Y (multiply (multiply (multiply Z (inverse Z)) (inverse (multiply U Y))) U)))) U.eq Univ (multiply x (inverse (multiply y (multiply (multiply (multiply z (inverse z)) (inverse (multiply u y))) x)))) u +∀H0:∀U:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply U (inverse (multiply Y (multiply (multiply (multiply Z (inverse Z)) (inverse (multiply U Y))) U)))) U.eq Univ (multiply x (inverse (multiply y (multiply (multiply (multiply z (inverse z)) (inverse (multiply u y))) x)))) u) . -#Univ. -#U. -#Y. -#Z. -#inverse. -#multiply. -#u. -#x. -#y. -#z. -#H0. -nauto by H0; +#Univ ##. +#U ##. +#Y ##. +#Z ##. +#inverse ##. +#multiply ##. +#u ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP403-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP403-1.ma index 59154df6d..c1a846e3b 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP403-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP403-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀b1:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A (inverse (multiply (inverse (multiply (inverse (multiply A B)) C)) (inverse (multiply B (multiply (inverse B) B)))))) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A (inverse (multiply (inverse (multiply (inverse (multiply A B)) C)) (inverse (multiply B (multiply (inverse B) B)))))) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#a1. -#b1. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#b1 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP404-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP404-1.ma index 99617dd26..27892e412 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP404-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP404-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀b2:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A (inverse (multiply (inverse (multiply (inverse (multiply A B)) C)) (inverse (multiply B (multiply (inverse B) B)))))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A (inverse (multiply (inverse (multiply (inverse (multiply A B)) C)) (inverse (multiply B (multiply (inverse B) B)))))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#b2. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#b2 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP405-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP405-1.ma index 60a08cb36..2c84a68cd 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP405-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP405-1.ma @@ -44,25 +44,25 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A (inverse (multiply (inverse (multiply (inverse (multiply A B)) C)) (inverse (multiply B (multiply (inverse B) B)))))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A (inverse (multiply (inverse (multiply (inverse (multiply A B)) C)) (inverse (multiply B (multiply (inverse B) B)))))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP406-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP406-1.ma index 4cfd212be..c384f4990 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP406-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP406-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀b1:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A (inverse (multiply (inverse (multiply (inverse (multiply A B)) C)) (multiply (inverse B) (multiply (inverse B) B))))) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A (inverse (multiply (inverse (multiply (inverse (multiply A B)) C)) (multiply (inverse B) (multiply (inverse B) B))))) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#a1. -#b1. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#b1 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP407-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP407-1.ma index 228156069..0a859e333 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP407-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP407-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀b2:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A (inverse (multiply (inverse (multiply (inverse (multiply A B)) C)) (multiply (inverse B) (multiply (inverse B) B))))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A (inverse (multiply (inverse (multiply (inverse (multiply A B)) C)) (multiply (inverse B) (multiply (inverse B) B))))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#b2. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#b2 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP408-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP408-1.ma index 66d36a65b..3d62add9a 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP408-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP408-1.ma @@ -44,25 +44,25 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A (inverse (multiply (inverse (multiply (inverse (multiply A B)) C)) (multiply (inverse B) (multiply (inverse B) B))))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A (inverse (multiply (inverse (multiply (inverse (multiply A B)) C)) (multiply (inverse B) (multiply (inverse B) B))))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP409-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP409-1.ma index b1505e5bb..122eba57f 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP409-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP409-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀b1:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply (multiply (inverse (multiply A (inverse (multiply B C)))) (multiply A (inverse C))) (inverse (multiply (inverse C) C))) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply (multiply (inverse (multiply A (inverse (multiply B C)))) (multiply A (inverse C))) (inverse (multiply (inverse C) C))) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#a1. -#b1. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#b1 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP410-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP410-1.ma index fae41be08..5d914a711 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP410-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP410-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀b2:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply (multiply (inverse (multiply A (inverse (multiply B C)))) (multiply A (inverse C))) (inverse (multiply (inverse C) C))) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply (multiply (inverse (multiply A (inverse (multiply B C)))) (multiply A (inverse C))) (inverse (multiply (inverse C) C))) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#b2. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#b2 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP411-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP411-1.ma index 94642882f..2391565a8 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP411-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP411-1.ma @@ -44,25 +44,25 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply (multiply (inverse (multiply A (inverse (multiply B C)))) (multiply A (inverse C))) (inverse (multiply (inverse C) C))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply (multiply (inverse (multiply A (inverse (multiply B C)))) (multiply A (inverse C))) (inverse (multiply (inverse C) C))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP412-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP412-1.ma index da06b00b2..26b8636fd 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP412-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP412-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀b1:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A (inverse (multiply (multiply (multiply (inverse B) B) (inverse (multiply (inverse (multiply A (inverse B))) C))) B))) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A (inverse (multiply (multiply (multiply (inverse B) B) (inverse (multiply (inverse (multiply A (inverse B))) C))) B))) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#a1. -#b1. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#b1 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP413-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP413-1.ma index 0a34e56b2..2ed604489 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP413-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP413-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀b2:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A (inverse (multiply (multiply (multiply (inverse B) B) (inverse (multiply (inverse (multiply A (inverse B))) C))) B))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A (inverse (multiply (multiply (multiply (inverse B) B) (inverse (multiply (inverse (multiply A (inverse B))) C))) B))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#b2. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#b2 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP414-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP414-1.ma index 1a41958a4..8b73eb633 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP414-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP414-1.ma @@ -44,25 +44,25 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A (inverse (multiply (multiply (multiply (inverse B) B) (inverse (multiply (inverse (multiply A (inverse B))) C))) B))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A (inverse (multiply (multiply (multiply (inverse B) B) (inverse (multiply (inverse (multiply A (inverse B))) C))) B))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP415-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP415-1.ma index 6166de9a4..3796fa9a1 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP415-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP415-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀b1:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (multiply A (inverse (multiply (inverse (multiply (inverse (multiply B A)) (multiply B (inverse C)))) (inverse (multiply (inverse A) A)))))) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (multiply A (inverse (multiply (inverse (multiply (inverse (multiply B A)) (multiply B (inverse C)))) (inverse (multiply (inverse A) A)))))) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#a1. -#b1. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#b1 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP416-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP416-1.ma index 2613f6f0d..a5a6ed68f 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP416-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP416-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀b2:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (multiply A (inverse (multiply (inverse (multiply (inverse (multiply B A)) (multiply B (inverse C)))) (inverse (multiply (inverse A) A)))))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (multiply A (inverse (multiply (inverse (multiply (inverse (multiply B A)) (multiply B (inverse C)))) (inverse (multiply (inverse A) A)))))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#b2. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#b2 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP417-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP417-1.ma index 8c972ced5..bf844f5c1 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP417-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP417-1.ma @@ -44,25 +44,25 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (multiply A (inverse (multiply (inverse (multiply (inverse (multiply B A)) (multiply B (inverse C)))) (inverse (multiply (inverse A) A)))))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (multiply A (inverse (multiply (inverse (multiply (inverse (multiply B A)) (multiply B (inverse C)))) (inverse (multiply (inverse A) A)))))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP418-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP418-1.ma index 64cd7d53a..2928861fb 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP418-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP418-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀b1:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (multiply (inverse (multiply A (inverse (multiply (inverse B) (inverse (multiply C (inverse (multiply (inverse C) C)))))))) (multiply A C))) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (multiply (inverse (multiply A (inverse (multiply (inverse B) (inverse (multiply C (inverse (multiply (inverse C) C)))))))) (multiply A C))) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#a1. -#b1. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#b1 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP419-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP419-1.ma index 285ca5c74..3fe58e557 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP419-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP419-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀b2:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (multiply (inverse (multiply A (inverse (multiply (inverse B) (inverse (multiply C (inverse (multiply (inverse C) C)))))))) (multiply A C))) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (multiply (inverse (multiply A (inverse (multiply (inverse B) (inverse (multiply C (inverse (multiply (inverse C) C)))))))) (multiply A C))) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#b2. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#b2 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP420-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP420-1.ma index 41b129f05..61c77ba3a 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP420-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP420-1.ma @@ -44,25 +44,25 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (multiply (inverse (multiply A (inverse (multiply (inverse B) (inverse (multiply C (inverse (multiply (inverse C) C)))))))) (multiply A C))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (multiply (inverse (multiply A (inverse (multiply (inverse B) (inverse (multiply C (inverse (multiply (inverse C) C)))))))) (multiply A C))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP421-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP421-1.ma index e7003cb6d..a7f5cc373 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP421-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP421-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀b1:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (multiply (inverse (multiply A (inverse (multiply (inverse B) (multiply (inverse C) (inverse (multiply (inverse C) C))))))) (multiply A C))) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (multiply (inverse (multiply A (inverse (multiply (inverse B) (multiply (inverse C) (inverse (multiply (inverse C) C))))))) (multiply A C))) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#a1. -#b1. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#b1 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP422-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP422-1.ma index 2c30562d2..5beca64ed 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP422-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP422-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀b2:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (multiply (inverse (multiply A (inverse (multiply (inverse B) (multiply (inverse C) (inverse (multiply (inverse C) C))))))) (multiply A C))) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (multiply (inverse (multiply A (inverse (multiply (inverse B) (multiply (inverse C) (inverse (multiply (inverse C) C))))))) (multiply A C))) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#b2. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#b2 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP423-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP423-1.ma index 1735e7304..1f0ffef3e 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP423-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP423-1.ma @@ -44,25 +44,25 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (multiply (inverse (multiply A (inverse (multiply (inverse B) (multiply (inverse C) (inverse (multiply (inverse C) C))))))) (multiply A C))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (multiply (inverse (multiply A (inverse (multiply (inverse B) (multiply (inverse C) (inverse (multiply (inverse C) C))))))) (multiply A C))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP424-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP424-1.ma index 25c979c77..bc6009efd 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP424-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP424-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀b1:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply (inverse (multiply (inverse (multiply A (inverse (multiply (inverse B) C)))) (multiply A (inverse C)))) (inverse (multiply (inverse C) C))) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply (inverse (multiply (inverse (multiply A (inverse (multiply (inverse B) C)))) (multiply A (inverse C)))) (inverse (multiply (inverse C) C))) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#a1. -#b1. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#b1 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP425-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP425-1.ma index 50629626a..3f94985b0 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP425-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP425-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀b2:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply (inverse (multiply (inverse (multiply A (inverse (multiply (inverse B) C)))) (multiply A (inverse C)))) (inverse (multiply (inverse C) C))) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply (inverse (multiply (inverse (multiply A (inverse (multiply (inverse B) C)))) (multiply A (inverse C)))) (inverse (multiply (inverse C) C))) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#b2. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#b2 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP426-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP426-1.ma index b059dc613..366d63359 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP426-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP426-1.ma @@ -44,25 +44,25 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply (inverse (multiply (inverse (multiply A (inverse (multiply (inverse B) C)))) (multiply A (inverse C)))) (inverse (multiply (inverse C) C))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply (inverse (multiply (inverse (multiply A (inverse (multiply (inverse B) C)))) (multiply A (inverse C)))) (inverse (multiply (inverse C) C))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP427-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP427-1.ma index ea2715006..1774ca7a1 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP427-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP427-1.ma @@ -44,24 +44,24 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a1:Univ. ∀b1:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (multiply A (inverse (multiply (multiply (inverse (multiply (inverse B) (multiply (inverse A) C))) D) (inverse (multiply B D))))) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (multiply A (inverse (multiply (multiply (inverse (multiply (inverse B) (multiply (inverse A) C))) D) (inverse (multiply B D))))) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#D. -#a1. -#b1. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a1 ##. +#b1 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP428-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP428-1.ma index 65121fafa..f2be7561e 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP428-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP428-1.ma @@ -44,24 +44,24 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a2:Univ. ∀b2:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (multiply A (inverse (multiply (multiply (inverse (multiply (inverse B) (multiply (inverse A) C))) D) (inverse (multiply B D))))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (multiply A (inverse (multiply (multiply (inverse (multiply (inverse B) (multiply (inverse A) C))) D) (inverse (multiply B D))))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#D. -#a2. -#b2. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a2 ##. +#b2 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP429-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP429-1.ma index 8c8aba521..1c9deecb3 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP429-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP429-1.ma @@ -44,26 +44,26 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (multiply A (inverse (multiply (multiply (inverse (multiply (inverse B) (multiply (inverse A) C))) D) (inverse (multiply B D))))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (multiply A (inverse (multiply (multiply (inverse (multiply (inverse B) (multiply (inverse A) C))) D) (inverse (multiply B D))))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#D. -#a3. -#b3. -#c3. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a3 ##. +#b3 ##. +#c3 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP430-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP430-1.ma index bda066f0d..fce734387 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP430-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP430-1.ma @@ -44,24 +44,24 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a1:Univ. ∀b1:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (multiply A (inverse (multiply B (multiply (multiply (multiply C (inverse C)) (inverse (multiply D B))) A)))) D.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (multiply A (inverse (multiply B (multiply (multiply (multiply C (inverse C)) (inverse (multiply D B))) A)))) D.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#D. -#a1. -#b1. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a1 ##. +#b1 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP431-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP431-1.ma index 1e6a8334d..fb04939f7 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP431-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP431-1.ma @@ -44,24 +44,24 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a2:Univ. ∀b2:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (multiply A (inverse (multiply B (multiply (multiply (multiply C (inverse C)) (inverse (multiply D B))) A)))) D.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (multiply A (inverse (multiply B (multiply (multiply (multiply C (inverse C)) (inverse (multiply D B))) A)))) D.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#D. -#a2. -#b2. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a2 ##. +#b2 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP432-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP432-1.ma index fe272fa68..f05e33430 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP432-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP432-1.ma @@ -44,26 +44,26 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (multiply A (inverse (multiply B (multiply (multiply (multiply C (inverse C)) (inverse (multiply D B))) A)))) D.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (multiply A (inverse (multiply B (multiply (multiply (multiply C (inverse C)) (inverse (multiply D B))) A)))) D.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#D. -#a3. -#b3. -#c3. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a3 ##. +#b3 ##. +#c3 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP433-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP433-1.ma index d1ba563a3..180ff8070 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP433-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP433-1.ma @@ -42,24 +42,24 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a1:Univ. ∀b1:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (multiply (multiply (multiply (inverse (multiply (multiply A B) C)) A) B) (multiply D (inverse D)))) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (multiply (multiply (multiply (inverse (multiply (multiply A B) C)) A) B) (multiply D (inverse D)))) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#D. -#a1. -#b1. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a1 ##. +#b1 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP434-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP434-1.ma index b120a08cc..217d2cebe 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP434-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP434-1.ma @@ -42,24 +42,24 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a2:Univ. ∀b2:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (multiply (multiply (multiply (inverse (multiply (multiply A B) C)) A) B) (multiply D (inverse D)))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (multiply (multiply (multiply (inverse (multiply (multiply A B) C)) A) B) (multiply D (inverse D)))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#D. -#a2. -#b2. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a2 ##. +#b2 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP435-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP435-1.ma index 84f56d45b..38ff3370e 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP435-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP435-1.ma @@ -42,26 +42,26 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (multiply (multiply (multiply (inverse (multiply (multiply A B) C)) A) B) (multiply D (inverse D)))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (multiply (multiply (multiply (inverse (multiply (multiply A B) C)) A) B) (multiply D (inverse D)))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#D. -#a3. -#b3. -#c3. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a3 ##. +#b3 ##. +#c3 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP436-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP436-1.ma index c84110d26..7c76e7806 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP436-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP436-1.ma @@ -42,24 +42,24 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a1:Univ. ∀b1:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (multiply A (inverse (multiply B (multiply C (multiply (multiply (inverse C) (inverse (multiply D B))) A))))) D.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (multiply A (inverse (multiply B (multiply C (multiply (multiply (inverse C) (inverse (multiply D B))) A))))) D.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#D. -#a1. -#b1. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a1 ##. +#b1 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP437-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP437-1.ma index befd20302..e32843f6b 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP437-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP437-1.ma @@ -42,24 +42,24 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a2:Univ. ∀b2:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (multiply A (inverse (multiply B (multiply C (multiply (multiply (inverse C) (inverse (multiply D B))) A))))) D.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (multiply A (inverse (multiply B (multiply C (multiply (multiply (inverse C) (inverse (multiply D B))) A))))) D.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#D. -#a2. -#b2. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a2 ##. +#b2 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP438-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP438-1.ma index b985457db..eb3af1e28 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP438-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP438-1.ma @@ -42,26 +42,26 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (multiply A (inverse (multiply B (multiply C (multiply (multiply (inverse C) (inverse (multiply D B))) A))))) D.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (multiply A (inverse (multiply B (multiply C (multiply (multiply (inverse C) (inverse (multiply D B))) A))))) D.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#D. -#a3. -#b3. -#c3. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a3 ##. +#b3 ##. +#c3 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP439-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP439-1.ma index 28d9a8f29..957ea1f26 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP439-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP439-1.ma @@ -42,24 +42,24 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a1:Univ. ∀b1:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (multiply A (multiply B (multiply (multiply (inverse B) C) (inverse (multiply D (multiply A C))))))) D.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (multiply A (multiply B (multiply (multiply (inverse B) C) (inverse (multiply D (multiply A C))))))) D.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#D. -#a1. -#b1. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a1 ##. +#b1 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP440-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP440-1.ma index ed9efb426..40a3e03e1 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP440-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP440-1.ma @@ -42,24 +42,24 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a2:Univ. ∀b2:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (multiply A (multiply B (multiply (multiply (inverse B) C) (inverse (multiply D (multiply A C))))))) D.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (multiply A (multiply B (multiply (multiply (inverse B) C) (inverse (multiply D (multiply A C))))))) D.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#D. -#a2. -#b2. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a2 ##. +#b2 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP441-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP441-1.ma index 6c1b7689f..40cd925f7 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP441-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP441-1.ma @@ -42,26 +42,26 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (multiply A (multiply B (multiply (multiply (inverse B) C) (inverse (multiply D (multiply A C))))))) D.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (multiply A (multiply B (multiply (multiply (inverse B) C) (inverse (multiply D (multiply A C))))))) D.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#D. -#a3. -#b3. -#c3. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a3 ##. +#b3 ##. +#c3 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP442-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP442-1.ma index df3e7d2dd..355689cd5 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP442-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP442-1.ma @@ -42,24 +42,24 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a1:Univ. ∀b1:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (multiply A (multiply B (multiply (multiply C (inverse C)) (inverse (multiply D (multiply A B))))))) D.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (multiply A (multiply B (multiply (multiply C (inverse C)) (inverse (multiply D (multiply A B))))))) D.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#D. -#a1. -#b1. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a1 ##. +#b1 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP443-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP443-1.ma index 19659a24a..9e5c02baa 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP443-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP443-1.ma @@ -42,24 +42,24 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a2:Univ. ∀b2:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (multiply A (multiply B (multiply (multiply C (inverse C)) (inverse (multiply D (multiply A B))))))) D.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (multiply A (multiply B (multiply (multiply C (inverse C)) (inverse (multiply D (multiply A B))))))) D.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#D. -#a2. -#b2. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a2 ##. +#b2 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP444-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP444-1.ma index 7911163a2..b975a65ed 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP444-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP444-1.ma @@ -42,26 +42,26 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (multiply A (multiply B (multiply (multiply C (inverse C)) (inverse (multiply D (multiply A B))))))) D.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (multiply A (multiply B (multiply (multiply C (inverse C)) (inverse (multiply D (multiply A B))))))) D.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#D. -#a3. -#b3. -#c3. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a3 ##. +#b3 ##. +#c3 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP445-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP445-1.ma index 6d9fd1bc9..8418608c5 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP445-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP445-1.ma @@ -44,7 +44,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀b1:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. @@ -52,21 +52,21 @@ ntheorem prove_these_axioms_1: ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A). ∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)). -∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide (divide A A) B) C) (divide (divide (divide A A) A) C))) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide (divide A A) B) C) (divide (divide (divide A A) A) C))) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#a1. -#b1. -#divide. -#inverse. -#multiply. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#b1 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP446-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP446-1.ma index 71cc757ee..a2017d6b2 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP446-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP446-1.ma @@ -44,7 +44,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀b2:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. @@ -52,21 +52,21 @@ ntheorem prove_these_axioms_2: ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A). ∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)). -∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide (divide A A) B) C) (divide (divide (divide A A) A) C))) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide (divide A A) B) C) (divide (divide (divide A A) A) C))) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#b2. -#divide. -#inverse. -#multiply. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#b2 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP447-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP447-1.ma index 916466da5..02d75901e 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP447-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP447-1.ma @@ -44,7 +44,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -53,22 +53,22 @@ ntheorem prove_these_axioms_3: ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A). ∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)). -∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide (divide A A) B) C) (divide (divide (divide A A) A) C))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide (divide A A) B) C) (divide (divide (divide A A) A) C))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#divide. -#inverse. -#multiply. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP448-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP448-1.ma index a148e15ce..adbc9e1f2 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP448-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP448-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀b1:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. @@ -50,21 +50,21 @@ ntheorem prove_these_axioms_1: ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A). ∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)). -∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide (divide B B) B) C) (divide (divide (divide B B) A) C))) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide (divide B B) B) C) (divide (divide (divide B B) A) C))) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#a1. -#b1. -#divide. -#inverse. -#multiply. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#b1 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP449-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP449-1.ma index 56086be0d..66e697654 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP449-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP449-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀b2:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. @@ -50,21 +50,21 @@ ntheorem prove_these_axioms_2: ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A). ∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)). -∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide (divide B B) B) C) (divide (divide (divide B B) A) C))) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide (divide B B) B) C) (divide (divide (divide B B) A) C))) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#b2. -#divide. -#inverse. -#multiply. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#b2 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP450-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP450-1.ma index 30345590f..c9e403d71 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP450-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP450-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -51,22 +51,22 @@ ntheorem prove_these_axioms_3: ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A). ∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)). -∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide (divide B B) B) C) (divide (divide (divide B B) A) C))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide (divide B B) B) C) (divide (divide (divide B B) A) C))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#divide. -#inverse. -#multiply. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP451-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP451-1.ma index b34de13b8..25112e82a 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP451-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP451-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀b1:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. @@ -50,21 +50,21 @@ ntheorem prove_these_axioms_1: ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A). ∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)). -∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide (divide A A) (divide A (divide B (divide (divide (divide A A) A) C)))) C) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide (divide A A) (divide A (divide B (divide (divide (divide A A) A) C)))) C) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#a1. -#b1. -#divide. -#inverse. -#multiply. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#b1 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP452-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP452-1.ma index 7d72af84b..a4425d166 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP452-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP452-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀b2:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. @@ -50,21 +50,21 @@ ntheorem prove_these_axioms_2: ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A). ∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)). -∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide (divide A A) (divide A (divide B (divide (divide (divide A A) A) C)))) C) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide (divide A A) (divide A (divide B (divide (divide (divide A A) A) C)))) C) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#b2. -#divide. -#inverse. -#multiply. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#b2 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP453-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP453-1.ma index 2132d98b6..0636f2c49 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP453-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP453-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -51,22 +51,22 @@ ntheorem prove_these_axioms_3: ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A). ∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)). -∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide (divide A A) (divide A (divide B (divide (divide (divide A A) A) C)))) C) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide (divide A A) (divide A (divide B (divide (divide (divide A A) A) C)))) C) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#divide. -#inverse. -#multiply. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP454-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP454-1.ma index 87c212d97..4575c0bef 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP454-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP454-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -51,22 +51,22 @@ ntheorem prove_these_axioms_1: ∀H0:∀A:Univ.eq Univ identity (divide A A). ∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity (divide A (divide B (divide (divide (divide A A) A) C)))) C) B.eq Univ (multiply (inverse a1) a1) identity +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity (divide A (divide B (divide (divide (divide A A) A) C)))) C) B.eq Univ (multiply (inverse a1) a1) identity) . -#Univ. -#A. -#B. -#C. -#a1. -#divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP455-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP455-1.ma index 761dd43c9..c8e7f698b 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP455-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP455-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -51,22 +51,22 @@ ntheorem prove_these_axioms_2: ∀H0:∀A:Univ.eq Univ identity (divide A A). ∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity (divide A (divide B (divide (divide (divide A A) A) C)))) C) B.eq Univ (multiply identity a2) a2 +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity (divide A (divide B (divide (divide (divide A A) A) C)))) C) B.eq Univ (multiply identity a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP456-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP456-1.ma index ec7d503db..96c3c2435 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP456-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP456-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -53,24 +53,24 @@ ntheorem prove_these_axioms_3: ∀H0:∀A:Univ.eq Univ identity (divide A A). ∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity (divide A (divide B (divide (divide (divide A A) A) C)))) C) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity (divide A (divide B (divide (divide (divide A A) A) C)))) C) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP457-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP457-1.ma index 3605339eb..807aa273f 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP457-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP457-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -51,22 +51,22 @@ ntheorem prove_these_axioms_1: ∀H0:∀A:Univ.eq Univ identity (divide A A). ∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide (divide A A) (divide A (divide B (divide (divide identity A) C)))) C) B.eq Univ (multiply (inverse a1) a1) identity +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide (divide A A) (divide A (divide B (divide (divide identity A) C)))) C) B.eq Univ (multiply (inverse a1) a1) identity) . -#Univ. -#A. -#B. -#C. -#a1. -#divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP458-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP458-1.ma index c176d88df..755039a31 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP458-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP458-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -51,22 +51,22 @@ ntheorem prove_these_axioms_2: ∀H0:∀A:Univ.eq Univ identity (divide A A). ∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide (divide A A) (divide A (divide B (divide (divide identity A) C)))) C) B.eq Univ (multiply identity a2) a2 +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide (divide A A) (divide A (divide B (divide (divide identity A) C)))) C) B.eq Univ (multiply identity a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP459-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP459-1.ma index c62e8ec36..41156cec1 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP459-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP459-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -53,24 +53,24 @@ ntheorem prove_these_axioms_3: ∀H0:∀A:Univ.eq Univ identity (divide A A). ∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide (divide A A) (divide A (divide B (divide (divide identity A) C)))) C) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide (divide A A) (divide A (divide B (divide (divide identity A) C)))) C) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP460-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP460-1.ma index 040b43f0f..94eda6ef5 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP460-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP460-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -51,22 +51,22 @@ ntheorem prove_these_axioms_1: ∀H0:∀A:Univ.eq Univ identity (divide A A). ∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide identity B) C) (divide (divide (divide A A) A) C))) B.eq Univ (multiply (inverse a1) a1) identity +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide identity B) C) (divide (divide (divide A A) A) C))) B.eq Univ (multiply (inverse a1) a1) identity) . -#Univ. -#A. -#B. -#C. -#a1. -#divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP461-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP461-1.ma index 9caff9e2c..0b9679075 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP461-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP461-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -51,22 +51,22 @@ ntheorem prove_these_axioms_2: ∀H0:∀A:Univ.eq Univ identity (divide A A). ∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide identity B) C) (divide (divide (divide A A) A) C))) B.eq Univ (multiply identity a2) a2 +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide identity B) C) (divide (divide (divide A A) A) C))) B.eq Univ (multiply identity a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP462-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP462-1.ma index 544cf7608..46b5ab7dc 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP462-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP462-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -53,24 +53,24 @@ ntheorem prove_these_axioms_3: ∀H0:∀A:Univ.eq Univ identity (divide A A). ∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide identity B) C) (divide (divide (divide A A) A) C))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide identity B) C) (divide (divide (divide A A) A) C))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP463-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP463-1.ma index f08e037b9..96a391484 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP463-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP463-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -51,22 +51,22 @@ ntheorem prove_these_axioms_1: ∀H0:∀A:Univ.eq Univ identity (divide A A). ∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide (divide A A) B) C) (divide (divide identity A) C))) B.eq Univ (multiply (inverse a1) a1) identity +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide (divide A A) B) C) (divide (divide identity A) C))) B.eq Univ (multiply (inverse a1) a1) identity) . -#Univ. -#A. -#B. -#C. -#a1. -#divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP464-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP464-1.ma index 8f9c131d6..af4d64b73 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP464-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP464-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -51,22 +51,22 @@ ntheorem prove_these_axioms_2: ∀H0:∀A:Univ.eq Univ identity (divide A A). ∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide (divide A A) B) C) (divide (divide identity A) C))) B.eq Univ (multiply identity a2) a2 +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide (divide A A) B) C) (divide (divide identity A) C))) B.eq Univ (multiply identity a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP465-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP465-1.ma index aed21ebbf..299e71ccb 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP465-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP465-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -53,24 +53,24 @@ ntheorem prove_these_axioms_3: ∀H0:∀A:Univ.eq Univ identity (divide A A). ∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide (divide A A) B) C) (divide (divide identity A) C))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide (divide A A) B) C) (divide (divide identity A) C))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP466-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP466-1.ma index 4d4a4e63d..f766a182a 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP466-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP466-1.ma @@ -42,28 +42,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a1:Univ. ∀b1:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (divide A A) (divide B (divide (divide C (divide D B)) (inverse D)))) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (divide A A) (divide B (divide (divide C (divide D B)) (inverse D)))) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#D. -#a1. -#b1. -#divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a1 ##. +#b1 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP467-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP467-1.ma index 8a475fb53..13aed9a51 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP467-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP467-1.ma @@ -42,28 +42,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a2:Univ. ∀b2:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (divide A A) (divide B (divide (divide C (divide D B)) (inverse D)))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (divide A A) (divide B (divide (divide C (divide D B)) (inverse D)))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#D. -#a2. -#b2. -#divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a2 ##. +#b2 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP468-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP468-1.ma index 95ba27cde..26ab05aeb 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP468-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP468-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -50,22 +50,22 @@ ntheorem prove_these_axioms_3: ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (divide A A) (divide B (divide (divide C (divide D B)) (inverse D)))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (divide A A) (divide B (divide (divide C (divide D B)) (inverse D)))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#D. -#a3. -#b3. -#c3. -#divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a3 ##. +#b3 ##. +#c3 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP469-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP469-1.ma index 30496da52..a06761fcb 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP469-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP469-1.ma @@ -42,28 +42,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a1:Univ. ∀b1:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (inverse (divide A (divide B (divide C D)))) (divide (divide D C) A)) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (inverse (divide A (divide B (divide C D)))) (divide (divide D C) A)) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#D. -#a1. -#b1. -#divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a1 ##. +#b1 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP470-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP470-1.ma index 9eb7fd417..1c068958b 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP470-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP470-1.ma @@ -42,28 +42,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a2:Univ. ∀b2:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (inverse (divide A (divide B (divide C D)))) (divide (divide D C) A)) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (inverse (divide A (divide B (divide C D)))) (divide (divide D C) A)) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#D. -#a2. -#b2. -#divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a2 ##. +#b2 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP471-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP471-1.ma index ed9cea8b6..ba9538fd6 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP471-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP471-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -50,22 +50,22 @@ ntheorem prove_these_axioms_3: ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (inverse (divide A (divide B (divide C D)))) (divide (divide D C) A)) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (inverse (divide A (divide B (divide C D)))) (divide (divide D C) A)) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#D. -#a3. -#b3. -#c3. -#divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a3 ##. +#b3 ##. +#c3 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP472-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP472-1.ma index f45a230f7..79a4a5be1 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP472-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP472-1.ma @@ -42,28 +42,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a1:Univ. ∀b1:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (divide (inverse (divide A B)) (divide (divide C D) A)) (divide D C)) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (divide (inverse (divide A B)) (divide (divide C D) A)) (divide D C)) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#D. -#a1. -#b1. -#divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a1 ##. +#b1 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP473-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP473-1.ma index ecdd2d0bb..c2368b582 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP473-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP473-1.ma @@ -42,28 +42,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a2:Univ. ∀b2:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (divide (inverse (divide A B)) (divide (divide C D) A)) (divide D C)) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (divide (inverse (divide A B)) (divide (divide C D) A)) (divide D C)) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#D. -#a2. -#b2. -#divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a2 ##. +#b2 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP474-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP474-1.ma index 7828b5a79..c3f0ccff2 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP474-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP474-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -50,22 +50,22 @@ ntheorem prove_these_axioms_3: ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (divide (inverse (divide A B)) (divide (divide C D) A)) (divide D C)) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (divide (inverse (divide A B)) (divide (divide C D) A)) (divide D C)) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#D. -#a3. -#b3. -#c3. -#divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a3 ##. +#b3 ##. +#c3 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP475-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP475-1.ma index 96bb54619..2822352fd 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP475-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP475-1.ma @@ -42,28 +42,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a1:Univ. ∀b1:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (inverse (divide (divide (divide A B) C) (divide D C))) (divide B A)) D.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (inverse (divide (divide (divide A B) C) (divide D C))) (divide B A)) D.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#D. -#a1. -#b1. -#divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a1 ##. +#b1 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP476-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP476-1.ma index b84d82ef0..69aad5885 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP476-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP476-1.ma @@ -42,28 +42,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a2:Univ. ∀b2:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (inverse (divide (divide (divide A B) C) (divide D C))) (divide B A)) D.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (inverse (divide (divide (divide A B) C) (divide D C))) (divide B A)) D.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#D. -#a2. -#b2. -#divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a2 ##. +#b2 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP477-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP477-1.ma index 66ef3278c..0a1ef109a 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP477-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP477-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -50,22 +50,22 @@ ntheorem prove_these_axioms_3: ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (inverse (divide (divide (divide A B) C) (divide D C))) (divide B A)) D.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (inverse (divide (divide (divide A B) C) (divide D C))) (divide B A)) D.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#D. -#a3. -#b3. -#c3. -#divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a3 ##. +#b3 ##. +#c3 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP478-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP478-1.ma index 451efce96..ac8d7d52b 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP478-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP478-1.ma @@ -42,28 +42,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a1:Univ. ∀b1:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (inverse (divide (divide (divide A A) B) (divide C (divide B D)))) D) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (inverse (divide (divide (divide A A) B) (divide C (divide B D)))) D) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#D. -#a1. -#b1. -#divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a1 ##. +#b1 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP479-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP479-1.ma index b18f0cc11..96ae39859 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP479-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP479-1.ma @@ -42,28 +42,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a2:Univ. ∀b2:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (inverse (divide (divide (divide A A) B) (divide C (divide B D)))) D) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (inverse (divide (divide (divide A A) B) (divide C (divide B D)))) D) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#D. -#a2. -#b2. -#divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a2 ##. +#b2 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP480-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP480-1.ma index b5b5ba50b..9786e751c 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP480-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP480-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -50,22 +50,22 @@ ntheorem prove_these_axioms_3: ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (inverse (divide (divide (divide A A) B) (divide C (divide B D)))) D) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (inverse (divide (divide (divide A A) B) (divide C (divide B D)))) D) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#D. -#a3. -#b3. -#c3. -#divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a3 ##. +#b3 ##. +#c3 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP481-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP481-1.ma index e69260458..12bee4871 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP481-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP481-1.ma @@ -44,7 +44,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a1:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -53,23 +53,23 @@ ntheorem prove_these_axioms_1: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (double_divide (double_divide (double_divide A (double_divide B identity)) (double_divide (double_divide C (double_divide D (double_divide D identity))) (double_divide A identity))) B) C.eq Univ (multiply (inverse a1) a1) identity +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (double_divide (double_divide (double_divide A (double_divide B identity)) (double_divide (double_divide C (double_divide D (double_divide D identity))) (double_divide A identity))) B) C.eq Univ (multiply (inverse a1) a1) identity) . -#Univ. -#A. -#B. -#C. -#D. -#a1. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a1 ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP482-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP482-1.ma index 3fc4b9df4..de47ea5b7 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP482-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP482-1.ma @@ -44,7 +44,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a2:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -53,23 +53,23 @@ ntheorem prove_these_axioms_2: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (double_divide (double_divide (double_divide A (double_divide B identity)) (double_divide (double_divide C (double_divide D (double_divide D identity))) (double_divide A identity))) B) C.eq Univ (multiply identity a2) a2 +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (double_divide (double_divide (double_divide A (double_divide B identity)) (double_divide (double_divide C (double_divide D (double_divide D identity))) (double_divide A identity))) B) C.eq Univ (multiply identity a2) a2) . -#Univ. -#A. -#B. -#C. -#D. -#a2. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a2 ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP483-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP483-1.ma index bf9af7de8..6396b3304 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP483-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP483-1.ma @@ -44,7 +44,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -55,25 +55,25 @@ ntheorem prove_these_axioms_3: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (double_divide (double_divide (double_divide A (double_divide B identity)) (double_divide (double_divide C (double_divide D (double_divide D identity))) (double_divide A identity))) B) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (double_divide (double_divide (double_divide A (double_divide B identity)) (double_divide (double_divide C (double_divide D (double_divide D identity))) (double_divide A identity))) B) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#D. -#a3. -#b3. -#c3. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a3 ##. +#b3 ##. +#c3 ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP484-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP484-1.ma index 294db2870..09b0e091c 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP484-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP484-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -51,22 +51,22 @@ ntheorem prove_these_axioms_1: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide A B) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply (inverse a1) a1) identity +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide A B) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply (inverse a1) a1) identity) . -#Univ. -#A. -#B. -#C. -#a1. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP485-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP485-1.ma index 4248746f4..59569d979 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP485-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP485-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -51,22 +51,22 @@ ntheorem prove_these_axioms_2: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide A B) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply identity a2) a2 +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide A B) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply identity a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP486-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP486-1.ma index 469282c73..470bf8f63 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP486-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP486-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -53,24 +53,24 @@ ntheorem prove_these_axioms_3: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide A B) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide A B) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP487-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP487-1.ma index a276d8fd0..8d27572b7 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP487-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP487-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -51,22 +51,22 @@ ntheorem prove_these_axioms_1: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide A (double_divide (double_divide (double_divide identity (double_divide (double_divide A identity) (double_divide B C))) B) identity)) C.eq Univ (multiply (inverse a1) a1) identity +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide A (double_divide (double_divide (double_divide identity (double_divide (double_divide A identity) (double_divide B C))) B) identity)) C.eq Univ (multiply (inverse a1) a1) identity) . -#Univ. -#A. -#B. -#C. -#a1. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP488-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP488-1.ma index 9df211881..dced1b098 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP488-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP488-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -51,22 +51,22 @@ ntheorem prove_these_axioms_2: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide A (double_divide (double_divide (double_divide identity (double_divide (double_divide A identity) (double_divide B C))) B) identity)) C.eq Univ (multiply identity a2) a2 +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide A (double_divide (double_divide (double_divide identity (double_divide (double_divide A identity) (double_divide B C))) B) identity)) C.eq Univ (multiply identity a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP489-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP489-1.ma index 7e5d03efa..42408cd44 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP489-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP489-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -53,24 +53,24 @@ ntheorem prove_these_axioms_3: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide A (double_divide (double_divide (double_divide identity (double_divide (double_divide A identity) (double_divide B C))) B) identity)) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide A (double_divide (double_divide (double_divide identity (double_divide (double_divide A identity) (double_divide B C))) B) identity)) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP490-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP490-1.ma index 6d2768164..5c1ae9bd6 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP490-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP490-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -51,22 +51,22 @@ ntheorem prove_these_axioms_1: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide identity A) (double_divide identity (double_divide (double_divide (double_divide A B) identity) (double_divide C B)))) C.eq Univ (multiply (inverse a1) a1) identity +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide identity A) (double_divide identity (double_divide (double_divide (double_divide A B) identity) (double_divide C B)))) C.eq Univ (multiply (inverse a1) a1) identity) . -#Univ. -#A. -#B. -#C. -#a1. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP491-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP491-1.ma index ef3420d08..93fd41467 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP491-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP491-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -51,22 +51,22 @@ ntheorem prove_these_axioms_2: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide identity A) (double_divide identity (double_divide (double_divide (double_divide A B) identity) (double_divide C B)))) C.eq Univ (multiply identity a2) a2 +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide identity A) (double_divide identity (double_divide (double_divide (double_divide A B) identity) (double_divide C B)))) C.eq Univ (multiply identity a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP492-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP492-1.ma index ed941d373..d44f5da17 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP492-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP492-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -53,24 +53,24 @@ ntheorem prove_these_axioms_3: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide identity A) (double_divide identity (double_divide (double_divide (double_divide A B) identity) (double_divide C B)))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide identity A) (double_divide identity (double_divide (double_divide (double_divide A B) identity) (double_divide C B)))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP493-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP493-1.ma index c3db76a92..3c7bdabbc 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP493-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP493-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -51,22 +51,22 @@ ntheorem prove_these_axioms_1: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide identity A) (double_divide (double_divide (double_divide B C) (double_divide identity identity)) (double_divide A C))) B.eq Univ (multiply (inverse a1) a1) identity +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide identity A) (double_divide (double_divide (double_divide B C) (double_divide identity identity)) (double_divide A C))) B.eq Univ (multiply (inverse a1) a1) identity) . -#Univ. -#A. -#B. -#C. -#a1. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP494-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP494-1.ma index a9eecedfd..f0526a191 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP494-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP494-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -51,22 +51,22 @@ ntheorem prove_these_axioms_2: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide identity A) (double_divide (double_divide (double_divide B C) (double_divide identity identity)) (double_divide A C))) B.eq Univ (multiply identity a2) a2 +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide identity A) (double_divide (double_divide (double_divide B C) (double_divide identity identity)) (double_divide A C))) B.eq Univ (multiply identity a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP495-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP495-1.ma index 87aa0e17f..4b45ef052 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP495-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP495-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -53,24 +53,24 @@ ntheorem prove_these_axioms_3: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide identity A) (double_divide (double_divide (double_divide B C) (double_divide identity identity)) (double_divide A C))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide identity A) (double_divide (double_divide (double_divide B C) (double_divide identity identity)) (double_divide A C))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP496-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP496-1.ma index 149cb514a..0eb5a5462 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP496-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP496-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -51,22 +51,22 @@ ntheorem prove_these_axioms_1: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide identity (double_divide A (double_divide B identity))) (double_divide (double_divide B (double_divide C A)) identity)) C.eq Univ (multiply (inverse a1) a1) identity +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide identity (double_divide A (double_divide B identity))) (double_divide (double_divide B (double_divide C A)) identity)) C.eq Univ (multiply (inverse a1) a1) identity) . -#Univ. -#A. -#B. -#C. -#a1. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP497-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP497-1.ma index 43830cc38..2c33f0a2c 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP497-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP497-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -51,22 +51,22 @@ ntheorem prove_these_axioms_2: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide identity (double_divide A (double_divide B identity))) (double_divide (double_divide B (double_divide C A)) identity)) C.eq Univ (multiply identity a2) a2 +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide identity (double_divide A (double_divide B identity))) (double_divide (double_divide B (double_divide C A)) identity)) C.eq Univ (multiply identity a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP498-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP498-1.ma index 9955b5dee..c54add805 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP498-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP498-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -53,24 +53,24 @@ ntheorem prove_these_axioms_3: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide identity (double_divide A (double_divide B identity))) (double_divide (double_divide B (double_divide C A)) identity)) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide identity (double_divide A (double_divide B identity))) (double_divide (double_divide B (double_divide C A)) identity)) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP499-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP499-1.ma index 1bc0c3566..88f2839ae 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP499-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP499-1.ma @@ -42,28 +42,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a1:Univ. ∀b1:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (double_divide (inverse A) (inverse (double_divide (inverse (double_divide A (double_divide B C))) (double_divide D (double_divide B D))))) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (double_divide (inverse A) (inverse (double_divide (inverse (double_divide A (double_divide B C))) (double_divide D (double_divide B D))))) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#D. -#a1. -#b1. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a1 ##. +#b1 ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP500-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP500-1.ma index ebdcf71a2..0527d9b82 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP500-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP500-1.ma @@ -42,28 +42,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a2:Univ. ∀b2:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (double_divide (inverse A) (inverse (double_divide (inverse (double_divide A (double_divide B C))) (double_divide D (double_divide B D))))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (double_divide (inverse A) (inverse (double_divide (inverse (double_divide A (double_divide B C))) (double_divide D (double_divide B D))))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#D. -#a2. -#b2. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a2 ##. +#b2 ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP501-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP501-1.ma index 35ca44ccd..8a7c5dd80 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP501-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP501-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -50,22 +50,22 @@ ntheorem prove_these_axioms_3: ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (double_divide (inverse A) (inverse (double_divide (inverse (double_divide A (double_divide B C))) (double_divide D (double_divide B D))))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (double_divide (inverse A) (inverse (double_divide (inverse (double_divide A (double_divide B C))) (double_divide D (double_divide B D))))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#D. -#a3. -#b3. -#c3. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a3 ##. +#b3 ##. +#c3 ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP502-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP502-1.ma index eaed7714d..9773ff32c 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP502-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP502-1.ma @@ -42,28 +42,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a1:Univ. ∀b1:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (double_divide (double_divide A (inverse (double_divide B C))) (double_divide (inverse B) (inverse (double_divide D (double_divide A D))))) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (double_divide (double_divide A (inverse (double_divide B C))) (double_divide (inverse B) (inverse (double_divide D (double_divide A D))))) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#D. -#a1. -#b1. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a1 ##. +#b1 ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP503-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP503-1.ma index c6b851778..0e36105a6 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP503-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP503-1.ma @@ -42,28 +42,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a2:Univ. ∀b2:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (double_divide (double_divide A (inverse (double_divide B C))) (double_divide (inverse B) (inverse (double_divide D (double_divide A D))))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (double_divide (double_divide A (inverse (double_divide B C))) (double_divide (inverse B) (inverse (double_divide D (double_divide A D))))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#D. -#a2. -#b2. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a2 ##. +#b2 ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP504-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP504-1.ma index 046317341..68dcd94eb 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP504-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP504-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -50,22 +50,22 @@ ntheorem prove_these_axioms_3: ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (double_divide (double_divide A (inverse (double_divide B C))) (double_divide (inverse B) (inverse (double_divide D (double_divide A D))))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (double_divide (double_divide A (inverse (double_divide B C))) (double_divide (inverse B) (inverse (double_divide D (double_divide A D))))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#D. -#a3. -#b3. -#c3. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a3 ##. +#b3 ##. +#c3 ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP505-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP505-1.ma index 175871056..38d84e467 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP505-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP505-1.ma @@ -46,26 +46,26 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ. ∀a1:Univ. ∀b1:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (multiply (inverse (multiply (inverse (multiply (inverse (multiply A B)) (multiply B A))) (multiply (inverse (multiply C D)) (multiply C (inverse (multiply (multiply E (inverse F)) (inverse D))))))) F) E.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (multiply (inverse (multiply (inverse (multiply (inverse (multiply A B)) (multiply B A))) (multiply (inverse (multiply C D)) (multiply C (inverse (multiply (multiply E (inverse F)) (inverse D))))))) F) E.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#D. -#E. -#F. -#a1. -#b1. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#E ##. +#F ##. +#a1 ##. +#b1 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP506-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP506-1.ma index c9c29eb94..d88a0420f 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP506-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP506-1.ma @@ -46,26 +46,26 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ. ∀a2:Univ. ∀b2:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (multiply (inverse (multiply (inverse (multiply (inverse (multiply A B)) (multiply B A))) (multiply (inverse (multiply C D)) (multiply C (inverse (multiply (multiply E (inverse F)) (inverse D))))))) F) E.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (multiply (inverse (multiply (inverse (multiply (inverse (multiply A B)) (multiply B A))) (multiply (inverse (multiply C D)) (multiply C (inverse (multiply (multiply E (inverse F)) (inverse D))))))) F) E.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#D. -#E. -#F. -#a2. -#b2. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#E ##. +#F ##. +#a2 ##. +#b2 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP507-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP507-1.ma index bba15764f..cc576198f 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP507-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP507-1.ma @@ -46,28 +46,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (multiply (inverse (multiply (inverse (multiply (inverse (multiply A B)) (multiply B A))) (multiply (inverse (multiply C D)) (multiply C (inverse (multiply (multiply E (inverse F)) (inverse D))))))) F) E.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (multiply (inverse (multiply (inverse (multiply (inverse (multiply A B)) (multiply B A))) (multiply (inverse (multiply C D)) (multiply C (inverse (multiply (multiply E (inverse F)) (inverse D))))))) F) E.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#D. -#E. -#F. -#a3. -#b3. -#c3. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#E ##. +#F ##. +#a3 ##. +#b3 ##. +#c3 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP508-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP508-1.ma index f39469bac..51bff57f1 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP508-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP508-1.ma @@ -48,26 +48,26 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_4: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ. ∀a:Univ. ∀b:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (multiply (inverse (multiply (inverse (multiply (inverse (multiply A B)) (multiply B A))) (multiply (inverse (multiply C D)) (multiply C (inverse (multiply (multiply E (inverse F)) (inverse D))))))) F) E.eq Univ (multiply a b) (multiply b a) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (multiply (inverse (multiply (inverse (multiply (inverse (multiply A B)) (multiply B A))) (multiply (inverse (multiply C D)) (multiply C (inverse (multiply (multiply E (inverse F)) (inverse D))))))) F) E.eq Univ (multiply a b) (multiply b a)) . -#Univ. -#A. -#B. -#C. -#D. -#E. -#F. -#a. -#b. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#E ##. +#F ##. +#a ##. +#b ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP509-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP509-1.ma index 554bf348f..153d2a305 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP509-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP509-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀b1:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply (multiply (multiply A B) C) (inverse (multiply A C))) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply (multiply (multiply A B) C) (inverse (multiply A C))) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#a1. -#b1. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#b1 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP510-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP510-1.ma index 9233ad4ca..3853ee252 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP510-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP510-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀b2:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply (multiply (multiply A B) C) (inverse (multiply A C))) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply (multiply (multiply A B) C) (inverse (multiply A C))) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#b2. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#b2 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP511-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP511-1.ma index d25661700..3817828bc 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP511-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP511-1.ma @@ -44,25 +44,25 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply (multiply (multiply A B) C) (inverse (multiply A C))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply (multiply (multiply A B) C) (inverse (multiply A C))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP512-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP512-1.ma index 287b790ef..a0444ed59 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP512-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP512-1.ma @@ -46,23 +46,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_4: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply (multiply (multiply A B) C) (inverse (multiply A C))) B.eq Univ (multiply a b) (multiply b a) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply (multiply (multiply A B) C) (inverse (multiply A C))) B.eq Univ (multiply a b) (multiply b a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP513-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP513-1.ma index 422d45132..621b7c960 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP513-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP513-1.ma @@ -42,23 +42,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀b1:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A (multiply (multiply B C) (inverse (multiply A C)))) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A (multiply (multiply B C) (inverse (multiply A C)))) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#a1. -#b1. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#b1 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP514-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP514-1.ma index 4deb56ec7..68482523b 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP514-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP514-1.ma @@ -42,23 +42,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀b2:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A (multiply (multiply B C) (inverse (multiply A C)))) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A (multiply (multiply B C) (inverse (multiply A C)))) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#b2. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#b2 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP515-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP515-1.ma index 7beb00cb2..fb351a296 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP515-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP515-1.ma @@ -42,25 +42,25 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A (multiply (multiply B C) (inverse (multiply A C)))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A (multiply (multiply B C) (inverse (multiply A C)))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP516-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP516-1.ma index 7dfb86338..9e3016c6d 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP516-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP516-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_4: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A (multiply (multiply B C) (inverse (multiply A C)))) B.eq Univ (multiply a b) (multiply b a) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A (multiply (multiply B C) (inverse (multiply A C)))) B.eq Univ (multiply a b) (multiply b a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP517-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP517-1.ma index 50b756fb1..9d6b2cfc1 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP517-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP517-1.ma @@ -42,23 +42,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀b1:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A (multiply (multiply (inverse (multiply A B)) C) B)) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A (multiply (multiply (inverse (multiply A B)) C) B)) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#a1. -#b1. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#b1 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP518-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP518-1.ma index 3942acf63..e479db4d5 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP518-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP518-1.ma @@ -42,23 +42,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀b2:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A (multiply (multiply (inverse (multiply A B)) C) B)) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A (multiply (multiply (inverse (multiply A B)) C) B)) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#b2. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#b2 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP519-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP519-1.ma index c41563030..1f6df982e 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP519-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP519-1.ma @@ -42,25 +42,25 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A (multiply (multiply (inverse (multiply A B)) C) B)) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A (multiply (multiply (inverse (multiply A B)) C) B)) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP520-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP520-1.ma index ce16cd7cb..ac9b9e0e4 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP520-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP520-1.ma @@ -44,23 +44,23 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_4: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A (multiply (multiply (inverse (multiply A B)) C) B)) C.eq Univ (multiply a b) (multiply b a) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A (multiply (multiply (inverse (multiply A B)) C) B)) C.eq Univ (multiply a b) (multiply b a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#inverse. -#multiply. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP521-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP521-1.ma index bbf1c91c8..686429dcc 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP521-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP521-1.ma @@ -44,7 +44,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀b1:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. @@ -52,21 +52,21 @@ ntheorem prove_these_axioms_1: ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A). ∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)). -∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide B (divide C (divide A B)))) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide B (divide C (divide A B)))) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#a1. -#b1. -#divide. -#inverse. -#multiply. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#b1 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP522-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP522-1.ma index c7ad818a0..c6dbff145 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP522-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP522-1.ma @@ -44,7 +44,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀b2:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. @@ -52,21 +52,21 @@ ntheorem prove_these_axioms_2: ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A). ∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)). -∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide B (divide C (divide A B)))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide B (divide C (divide A B)))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#b2. -#divide. -#inverse. -#multiply. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#b2 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP523-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP523-1.ma index 750944fa1..d7cb870f9 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP523-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP523-1.ma @@ -44,7 +44,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -53,22 +53,22 @@ ntheorem prove_these_axioms_3: ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A). ∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)). -∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide B (divide C (divide A B)))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide B (divide C (divide A B)))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#divide. -#inverse. -#multiply. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP524-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP524-1.ma index fb7ed0745..31f1d82f2 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP524-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP524-1.ma @@ -46,7 +46,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_4: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. @@ -54,21 +54,21 @@ ntheorem prove_these_axioms_4: ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A). ∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)). -∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide B (divide C (divide A B)))) C.eq Univ (multiply a b) (multiply b a) +∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide B (divide C (divide A B)))) C.eq Univ (multiply a b) (multiply b a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#divide. -#inverse. -#multiply. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP525-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP525-1.ma index e6b23b370..426c25c53 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP525-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP525-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀b1:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. @@ -50,21 +50,21 @@ ntheorem prove_these_axioms_1: ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A). ∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)). -∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide A B) (divide C B))) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide A B) (divide C B))) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#a1. -#b1. -#divide. -#inverse. -#multiply. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#b1 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP526-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP526-1.ma index 8bbcd06ef..18da54689 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP526-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP526-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀b2:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. @@ -50,21 +50,21 @@ ntheorem prove_these_axioms_2: ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A). ∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)). -∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide A B) (divide C B))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide A B) (divide C B))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#b2. -#divide. -#inverse. -#multiply. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#b2 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP527-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP527-1.ma index 0ee5db0e0..79cfce82e 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP527-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP527-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -51,22 +51,22 @@ ntheorem prove_these_axioms_3: ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A). ∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)). -∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide A B) (divide C B))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide A B) (divide C B))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#divide. -#inverse. -#multiply. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP528-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP528-1.ma index c08b96853..d3933fe4c 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP528-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP528-1.ma @@ -44,7 +44,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_4: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. @@ -52,21 +52,21 @@ ntheorem prove_these_axioms_4: ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A). ∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)). -∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide A B) (divide C B))) C.eq Univ (multiply a b) (multiply b a) +∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide A B) (divide C B))) C.eq Univ (multiply a b) (multiply b a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#divide. -#inverse. -#multiply. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP529-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP529-1.ma index 0d6078694..70d1fe54b 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP529-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP529-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀b1:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. @@ -50,21 +50,21 @@ ntheorem prove_these_axioms_1: ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A). ∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)). -∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide A (divide B C)) (divide A B)) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide A (divide B C)) (divide A B)) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#a1. -#b1. -#divide. -#inverse. -#multiply. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#b1 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP530-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP530-1.ma index 81350f0a0..7f832564d 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP530-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP530-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀b2:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. @@ -50,21 +50,21 @@ ntheorem prove_these_axioms_2: ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A). ∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)). -∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide A (divide B C)) (divide A B)) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide A (divide B C)) (divide A B)) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#b2. -#divide. -#inverse. -#multiply. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#b2 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP531-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP531-1.ma index 523f3a462..5cace15ea 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP531-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP531-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -51,22 +51,22 @@ ntheorem prove_these_axioms_3: ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A). ∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)). -∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide A (divide B C)) (divide A B)) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide A (divide B C)) (divide A B)) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#divide. -#inverse. -#multiply. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP532-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP532-1.ma index 1ad011502..29dfc5e56 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP532-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP532-1.ma @@ -44,7 +44,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_4: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. @@ -52,21 +52,21 @@ ntheorem prove_these_axioms_4: ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A). ∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)). -∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide A (divide B C)) (divide A B)) C.eq Univ (multiply a b) (multiply b a) +∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide A (divide B C)) (divide A B)) C.eq Univ (multiply a b) (multiply b a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#divide. -#inverse. -#multiply. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP533-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP533-1.ma index 1640a8325..d3dd5ef43 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP533-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP533-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀b1:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. @@ -52,23 +52,23 @@ ntheorem prove_these_axioms_1: ∀H0:∀A:Univ.eq Univ identity (divide A A). ∀H1:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A). ∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide A (divide (divide A B) C)) B) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide A (divide (divide A B) C)) B) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#a1. -#b1. -#divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#b1 ##. +#divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP534-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP534-1.ma index 977f361ae..b247615c0 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP534-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP534-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀b2:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. @@ -52,23 +52,23 @@ ntheorem prove_these_axioms_2: ∀H0:∀A:Univ.eq Univ identity (divide A A). ∀H1:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A). ∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide A (divide (divide A B) C)) B) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide A (divide (divide A B) C)) B) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#b2. -#divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#b2 ##. +#divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP535-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP535-1.ma index cdc9a5fba..a177853f2 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP535-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP535-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -53,24 +53,24 @@ ntheorem prove_these_axioms_3: ∀H0:∀A:Univ.eq Univ identity (divide A A). ∀H1:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A). ∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide A (divide (divide A B) C)) B) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide A (divide (divide A B) C)) B) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP536-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP536-1.ma index 1b8aac15b..a811cff52 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP536-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP536-1.ma @@ -44,7 +44,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_4: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. @@ -54,23 +54,23 @@ ntheorem prove_these_axioms_4: ∀H0:∀A:Univ.eq Univ identity (divide A A). ∀H1:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A). ∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide A (divide (divide A B) C)) B) C.eq Univ (multiply a b) (multiply b a) +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide A (divide (divide A B) C)) B) C.eq Univ (multiply a b) (multiply b a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP537-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP537-1.ma index 7fee7faf8..36020a8c9 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP537-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP537-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀b1:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. @@ -52,23 +52,23 @@ ntheorem prove_these_axioms_1: ∀H0:∀A:Univ.eq Univ identity (divide A A). ∀H1:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A). ∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide A B) (divide (divide A C) B)) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide A B) (divide (divide A C) B)) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#a1. -#b1. -#divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#b1 ##. +#divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP538-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP538-1.ma index f08441aad..650d873c8 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP538-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP538-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀b2:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. @@ -52,23 +52,23 @@ ntheorem prove_these_axioms_2: ∀H0:∀A:Univ.eq Univ identity (divide A A). ∀H1:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A). ∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide A B) (divide (divide A C) B)) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide A B) (divide (divide A C) B)) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#b2. -#divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#b2 ##. +#divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP539-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP539-1.ma index 99c06f984..52bcf01f7 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP539-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP539-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -53,24 +53,24 @@ ntheorem prove_these_axioms_3: ∀H0:∀A:Univ.eq Univ identity (divide A A). ∀H1:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A). ∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide A B) (divide (divide A C) B)) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide A B) (divide (divide A C) B)) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP540-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP540-1.ma index 7768c1cff..b71de165c 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP540-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP540-1.ma @@ -44,7 +44,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_4: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. @@ -54,23 +54,23 @@ ntheorem prove_these_axioms_4: ∀H0:∀A:Univ.eq Univ identity (divide A A). ∀H1:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A). ∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide A B) (divide (divide A C) B)) C.eq Univ (multiply a b) (multiply b a) +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide A B) (divide (divide A C) B)) C.eq Univ (multiply a b) (multiply b a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP541-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP541-1.ma index 9c86fe372..afdf8b338 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP541-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP541-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀b1:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. @@ -52,23 +52,23 @@ ntheorem prove_these_axioms_1: ∀H0:∀A:Univ.eq Univ identity (divide A A). ∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity (divide (divide (divide A B) C) A)) C) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity (divide (divide (divide A B) C) A)) C) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#a1. -#b1. -#divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#b1 ##. +#divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP542-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP542-1.ma index 360fc06bb..1ae6d15a1 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP542-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP542-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀b2:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. @@ -52,23 +52,23 @@ ntheorem prove_these_axioms_2: ∀H0:∀A:Univ.eq Univ identity (divide A A). ∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity (divide (divide (divide A B) C) A)) C) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity (divide (divide (divide A B) C) A)) C) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#b2. -#divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#b2 ##. +#divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP543-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP543-1.ma index 947a0c584..41806e718 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP543-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP543-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -53,24 +53,24 @@ ntheorem prove_these_axioms_3: ∀H0:∀A:Univ.eq Univ identity (divide A A). ∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity (divide (divide (divide A B) C) A)) C) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity (divide (divide (divide A B) C) A)) C) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP544-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP544-1.ma index b28e35e06..438323ec6 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP544-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP544-1.ma @@ -44,7 +44,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_4: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. @@ -54,23 +54,23 @@ ntheorem prove_these_axioms_4: ∀H0:∀A:Univ.eq Univ identity (divide A A). ∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity (divide (divide (divide A B) C) A)) C) B.eq Univ (multiply a b) (multiply b a) +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity (divide (divide (divide A B) C) A)) C) B.eq Univ (multiply a b) (multiply b a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP545-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP545-1.ma index e2bd3d947..e9dcf10fe 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP545-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP545-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀b1:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. @@ -52,23 +52,23 @@ ntheorem prove_these_axioms_1: ∀H0:∀A:Univ.eq Univ identity (divide A A). ∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity (divide A B)) (divide (divide B C) A)) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity (divide A B)) (divide (divide B C) A)) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#a1. -#b1. -#divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#b1 ##. +#divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP546-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP546-1.ma index 7432a8b28..980de2272 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP546-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP546-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀b2:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. @@ -52,23 +52,23 @@ ntheorem prove_these_axioms_2: ∀H0:∀A:Univ.eq Univ identity (divide A A). ∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity (divide A B)) (divide (divide B C) A)) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity (divide A B)) (divide (divide B C) A)) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#b2. -#divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#b2 ##. +#divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP547-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP547-1.ma index ba39a6705..c57439378 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP547-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP547-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -53,24 +53,24 @@ ntheorem prove_these_axioms_3: ∀H0:∀A:Univ.eq Univ identity (divide A A). ∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity (divide A B)) (divide (divide B C) A)) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity (divide A B)) (divide (divide B C) A)) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP548-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP548-1.ma index c5c404e8c..e4c1eb274 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP548-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP548-1.ma @@ -44,7 +44,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_4: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. @@ -54,23 +54,23 @@ ntheorem prove_these_axioms_4: ∀H0:∀A:Univ.eq Univ identity (divide A A). ∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity (divide A B)) (divide (divide B C) A)) C.eq Univ (multiply a b) (multiply b a) +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity (divide A B)) (divide (divide B C) A)) C.eq Univ (multiply a b) (multiply b a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP549-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP549-1.ma index 359109f79..8ac514124 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP549-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP549-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀b1:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. @@ -52,23 +52,23 @@ ntheorem prove_these_axioms_1: ∀H0:∀A:Univ.eq Univ identity (divide A A). ∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity A) (divide (divide (divide B A) C) B)) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity A) (divide (divide (divide B A) C) B)) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#a1. -#b1. -#divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#b1 ##. +#divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP550-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP550-1.ma index cbaef27d1..1ae00fd48 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP550-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP550-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀b2:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. @@ -52,23 +52,23 @@ ntheorem prove_these_axioms_2: ∀H0:∀A:Univ.eq Univ identity (divide A A). ∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity A) (divide (divide (divide B A) C) B)) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity A) (divide (divide (divide B A) C) B)) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#b2. -#divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#b2 ##. +#divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP551-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP551-1.ma index a8a530c87..ec9d53f8d 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP551-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP551-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -53,24 +53,24 @@ ntheorem prove_these_axioms_3: ∀H0:∀A:Univ.eq Univ identity (divide A A). ∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity A) (divide (divide (divide B A) C) B)) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity A) (divide (divide (divide B A) C) B)) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP552-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP552-1.ma index d1ee805da..a79f97d76 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP552-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP552-1.ma @@ -44,7 +44,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_4: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. @@ -54,23 +54,23 @@ ntheorem prove_these_axioms_4: ∀H0:∀A:Univ.eq Univ identity (divide A A). ∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity A) (divide (divide (divide B A) C) B)) C.eq Univ (multiply a b) (multiply b a) +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity A) (divide (divide (divide B A) C) B)) C.eq Univ (multiply a b) (multiply b a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP553-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP553-1.ma index 3e766fcc0..7065e5afa 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP553-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP553-1.ma @@ -42,27 +42,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀b1:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide A (inverse (divide B (divide A C)))) C) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide A (inverse (divide B (divide A C)))) C) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#a1. -#b1. -#divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#b1 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP554-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP554-1.ma index 5d7b7f593..6064e70e7 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP554-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP554-1.ma @@ -42,27 +42,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀b2:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide A (inverse (divide B (divide A C)))) C) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide A (inverse (divide B (divide A C)))) C) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#b2. -#divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#b2 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP555-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP555-1.ma index 624da5e46..0adc21920 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP555-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP555-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -50,21 +50,21 @@ ntheorem prove_these_axioms_3: ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide A (inverse (divide B (divide A C)))) C) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide A (inverse (divide B (divide A C)))) C) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP556-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP556-1.ma index b23168923..beca625fc 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP556-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP556-1.ma @@ -44,27 +44,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_4: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide A (inverse (divide B (divide A C)))) C) B.eq Univ (multiply a b) (multiply b a) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide A (inverse (divide B (divide A C)))) C) B.eq Univ (multiply a b) (multiply b a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP557-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP557-1.ma index 0d087c31e..995347628 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP557-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP557-1.ma @@ -42,27 +42,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀b1:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (inverse (divide (divide B C) (divide A C)))) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (inverse (divide (divide B C) (divide A C)))) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#a1. -#b1. -#divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#b1 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP558-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP558-1.ma index 9126baa77..05da7bfd5 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP558-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP558-1.ma @@ -42,27 +42,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀b2:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (inverse (divide (divide B C) (divide A C)))) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (inverse (divide (divide B C) (divide A C)))) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#b2. -#divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#b2 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP559-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP559-1.ma index ec9e14fca..3381519db 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP559-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP559-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -50,21 +50,21 @@ ntheorem prove_these_axioms_3: ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (inverse (divide (divide B C) (divide A C)))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (inverse (divide (divide B C) (divide A C)))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP560-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP560-1.ma index 312246d0f..e651ea723 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP560-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP560-1.ma @@ -44,27 +44,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_4: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (inverse (divide (divide B C) (divide A C)))) B.eq Univ (multiply a b) (multiply b a) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (inverse (divide (divide B C) (divide A C)))) B.eq Univ (multiply a b) (multiply b a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP561-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP561-1.ma index f2b8dc6fb..78825bcc3 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP561-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP561-1.ma @@ -42,27 +42,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀b1:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide (divide A (inverse B)) C) (divide A C)) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide (divide A (inverse B)) C) (divide A C)) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#a1. -#b1. -#divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#b1 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP562-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP562-1.ma index 0cab9e2db..abeb3dce5 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP562-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP562-1.ma @@ -42,27 +42,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀b2:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide (divide A (inverse B)) C) (divide A C)) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide (divide A (inverse B)) C) (divide A C)) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#b2. -#divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#b2 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP563-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP563-1.ma index 7608d32e3..e259171a4 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP563-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP563-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -50,21 +50,21 @@ ntheorem prove_these_axioms_3: ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide (divide A (inverse B)) C) (divide A C)) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide (divide A (inverse B)) C) (divide A C)) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP564-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP564-1.ma index 83cfba553..6bfde9b04 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP564-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP564-1.ma @@ -44,27 +44,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_4: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide (divide A (inverse B)) C) (divide A C)) B.eq Univ (multiply a b) (multiply b a) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide (divide A (inverse B)) C) (divide A C)) B.eq Univ (multiply a b) (multiply b a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP565-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP565-1.ma index 28b8fcc2f..ad1e0a6d1 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP565-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP565-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -51,22 +51,22 @@ ntheorem prove_these_axioms_1: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide A C)) (double_divide identity C))) (double_divide identity identity)) B.eq Univ (multiply (inverse a1) a1) identity +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide A C)) (double_divide identity C))) (double_divide identity identity)) B.eq Univ (multiply (inverse a1) a1) identity) . -#Univ. -#A. -#B. -#C. -#a1. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP566-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP566-1.ma index 887f25172..0363aac1e 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP566-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP566-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -51,22 +51,22 @@ ntheorem prove_these_axioms_2: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide A C)) (double_divide identity C))) (double_divide identity identity)) B.eq Univ (multiply identity a2) a2 +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide A C)) (double_divide identity C))) (double_divide identity identity)) B.eq Univ (multiply identity a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP567-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP567-1.ma index 6321b9b98..39b6b7e3d 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP567-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP567-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -53,24 +53,24 @@ ntheorem prove_these_axioms_3: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide A C)) (double_divide identity C))) (double_divide identity identity)) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide A C)) (double_divide identity C))) (double_divide identity identity)) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP568-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP568-1.ma index 0ed4770dd..749631010 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP568-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP568-1.ma @@ -44,7 +44,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_4: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. @@ -54,23 +54,23 @@ ntheorem prove_these_axioms_4: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide A C)) (double_divide identity C))) (double_divide identity identity)) B.eq Univ (multiply a b) (multiply b a) +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide A C)) (double_divide identity C))) (double_divide identity identity)) B.eq Univ (multiply a b) (multiply b a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP569-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP569-1.ma index ae7a50018..5b74f4371 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP569-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP569-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -51,22 +51,22 @@ ntheorem prove_these_axioms_1: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide A C)) (double_divide C identity))) (double_divide identity identity)) B.eq Univ (multiply (inverse a1) a1) identity +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide A C)) (double_divide C identity))) (double_divide identity identity)) B.eq Univ (multiply (inverse a1) a1) identity) . -#Univ. -#A. -#B. -#C. -#a1. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP570-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP570-1.ma index 68dbffab1..513f2fcdd 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP570-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP570-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -51,22 +51,22 @@ ntheorem prove_these_axioms_2: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide A C)) (double_divide C identity))) (double_divide identity identity)) B.eq Univ (multiply identity a2) a2 +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide A C)) (double_divide C identity))) (double_divide identity identity)) B.eq Univ (multiply identity a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP571-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP571-1.ma index 6d7f12251..88f9820db 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP571-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP571-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -53,24 +53,24 @@ ntheorem prove_these_axioms_3: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide A C)) (double_divide C identity))) (double_divide identity identity)) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide A C)) (double_divide C identity))) (double_divide identity identity)) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP572-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP572-1.ma index 92199becd..af70347bd 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP572-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP572-1.ma @@ -44,7 +44,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_4: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. @@ -54,23 +54,23 @@ ntheorem prove_these_axioms_4: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide A C)) (double_divide C identity))) (double_divide identity identity)) B.eq Univ (multiply a b) (multiply b a) +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide A C)) (double_divide C identity))) (double_divide identity identity)) B.eq Univ (multiply a b) (multiply b a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP573-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP573-1.ma index c73992b92..21a357f86 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP573-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP573-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -51,22 +51,22 @@ ntheorem prove_these_axioms_1: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide C A)) (double_divide C identity))) (double_divide identity identity)) B.eq Univ (multiply (inverse a1) a1) identity +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide C A)) (double_divide C identity))) (double_divide identity identity)) B.eq Univ (multiply (inverse a1) a1) identity) . -#Univ. -#A. -#B. -#C. -#a1. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP574-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP574-1.ma index 8747fba41..be30a4612 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP574-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP574-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -51,22 +51,22 @@ ntheorem prove_these_axioms_2: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide C A)) (double_divide C identity))) (double_divide identity identity)) B.eq Univ (multiply identity a2) a2 +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide C A)) (double_divide C identity))) (double_divide identity identity)) B.eq Univ (multiply identity a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP575-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP575-1.ma index 3abc8c0ef..bb1acf06d 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP575-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP575-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -53,24 +53,24 @@ ntheorem prove_these_axioms_3: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide C A)) (double_divide C identity))) (double_divide identity identity)) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide C A)) (double_divide C identity))) (double_divide identity identity)) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP576-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP576-1.ma index 21471d50b..b9c0057f3 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP576-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP576-1.ma @@ -44,7 +44,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_4: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. @@ -54,23 +54,23 @@ ntheorem prove_these_axioms_4: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide C A)) (double_divide C identity))) (double_divide identity identity)) B.eq Univ (multiply a b) (multiply b a) +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide C A)) (double_divide C identity))) (double_divide identity identity)) B.eq Univ (multiply a b) (multiply b a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP577-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP577-1.ma index 3af4b7563..b585afcdf 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP577-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP577-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -51,22 +51,22 @@ ntheorem prove_these_axioms_1: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide B A) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply (inverse a1) a1) identity +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide B A) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply (inverse a1) a1) identity) . -#Univ. -#A. -#B. -#C. -#a1. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP578-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP578-1.ma index 79e7e896e..97e7da5c5 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP578-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP578-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -51,22 +51,22 @@ ntheorem prove_these_axioms_2: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide B A) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply identity a2) a2 +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide B A) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply identity a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP579-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP579-1.ma index 15c5f1b0e..8d745e162 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP579-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP579-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -53,24 +53,24 @@ ntheorem prove_these_axioms_3: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide B A) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide B A) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP580-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP580-1.ma index df48bb1b8..70ddefa16 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP580-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP580-1.ma @@ -44,7 +44,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_4: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. @@ -54,23 +54,23 @@ ntheorem prove_these_axioms_4: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide B A) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply a b) (multiply b a) +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide B A) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply a b) (multiply b a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP581-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP581-1.ma index f7e228ba5..ff5b2d353 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP581-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP581-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -51,22 +51,22 @@ ntheorem prove_these_axioms_1: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide identity B) (double_divide C (double_divide B A)))) (double_divide identity identity)) C.eq Univ (multiply (inverse a1) a1) identity +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide identity B) (double_divide C (double_divide B A)))) (double_divide identity identity)) C.eq Univ (multiply (inverse a1) a1) identity) . -#Univ. -#A. -#B. -#C. -#a1. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP582-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP582-1.ma index 086989b3f..5d65580b9 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP582-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP582-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀identity:Univ. @@ -51,22 +51,22 @@ ntheorem prove_these_axioms_2: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide identity B) (double_divide C (double_divide B A)))) (double_divide identity identity)) C.eq Univ (multiply identity a2) a2 +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide identity B) (double_divide C (double_divide B A)))) (double_divide identity identity)) C.eq Univ (multiply identity a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP583-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP583-1.ma index 250841225..e24aa930c 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP583-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP583-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -53,24 +53,24 @@ ntheorem prove_these_axioms_3: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide identity B) (double_divide C (double_divide B A)))) (double_divide identity identity)) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide identity B) (double_divide C (double_divide B A)))) (double_divide identity identity)) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP584-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP584-1.ma index df363bcb2..3407ff886 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP584-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP584-1.ma @@ -44,7 +44,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_4: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. @@ -54,23 +54,23 @@ ntheorem prove_these_axioms_4: ∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)). ∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity). ∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity). -∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide identity B) (double_divide C (double_divide B A)))) (double_divide identity identity)) C.eq Univ (multiply a b) (multiply b a) +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide identity B) (double_divide C (double_divide B A)))) (double_divide identity identity)) C.eq Univ (multiply a b) (multiply b a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#double_divide. -#identity. -#inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#double_divide ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP585-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP585-1.ma index adcb802b9..a2b52eb26 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP585-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP585-1.ma @@ -42,27 +42,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀b1:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide A (inverse (double_divide (inverse (double_divide (double_divide A B) (inverse C))) B))) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide A (inverse (double_divide (inverse (double_divide (double_divide A B) (inverse C))) B))) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#a1. -#b1. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#b1 ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP586-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP586-1.ma index 3d7d13fbc..1bf2de2e3 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP586-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP586-1.ma @@ -42,27 +42,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀b2:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide A (inverse (double_divide (inverse (double_divide (double_divide A B) (inverse C))) B))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide A (inverse (double_divide (inverse (double_divide (double_divide A B) (inverse C))) B))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#b2. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#b2 ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP587-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP587-1.ma index f3dd0d6c0..e15f2c40f 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP587-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP587-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -50,21 +50,21 @@ ntheorem prove_these_axioms_3: ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide A (inverse (double_divide (inverse (double_divide (double_divide A B) (inverse C))) B))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide A (inverse (double_divide (inverse (double_divide (double_divide A B) (inverse C))) B))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP588-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP588-1.ma index f400339f4..cf745feff 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP588-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP588-1.ma @@ -44,27 +44,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_4: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide A (inverse (double_divide (inverse (double_divide (double_divide A B) (inverse C))) B))) C.eq Univ (multiply a b) (multiply b a) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide A (inverse (double_divide (inverse (double_divide (double_divide A B) (inverse C))) B))) C.eq Univ (multiply a b) (multiply b a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP589-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP589-1.ma index 8bac910e9..d7bddccf0 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP589-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP589-1.ma @@ -42,27 +42,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀b1:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (inverse (double_divide (double_divide A B) (inverse (double_divide A (inverse C))))) B) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (inverse (double_divide (double_divide A B) (inverse (double_divide A (inverse C))))) B) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#a1. -#b1. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#b1 ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP590-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP590-1.ma index 162f71f6e..c4c5dc975 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP590-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP590-1.ma @@ -42,27 +42,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀b2:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (inverse (double_divide (double_divide A B) (inverse (double_divide A (inverse C))))) B) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (inverse (double_divide (double_divide A B) (inverse (double_divide A (inverse C))))) B) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#b2. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#b2 ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP591-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP591-1.ma index 986f8eb49..f213912e6 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP591-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP591-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -50,21 +50,21 @@ ntheorem prove_these_axioms_3: ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (inverse (double_divide (double_divide A B) (inverse (double_divide A (inverse C))))) B) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (inverse (double_divide (double_divide A B) (inverse (double_divide A (inverse C))))) B) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP592-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP592-1.ma index f92e44b36..988e5982a 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP592-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP592-1.ma @@ -44,27 +44,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_4: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (inverse (double_divide (double_divide A B) (inverse (double_divide A (inverse C))))) B) C.eq Univ (multiply a b) (multiply b a) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (inverse (double_divide (double_divide A B) (inverse (double_divide A (inverse C))))) B) C.eq Univ (multiply a b) (multiply b a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP593-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP593-1.ma index 75b0cfa3f..b5f88158e 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP593-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP593-1.ma @@ -42,27 +42,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀b1:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (double_divide (double_divide A B) (inverse (double_divide A (inverse (double_divide C B)))))) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (double_divide (double_divide A B) (inverse (double_divide A (inverse (double_divide C B)))))) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#a1. -#b1. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#b1 ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP594-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP594-1.ma index 29b8955b9..e25ca8bb1 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP594-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP594-1.ma @@ -42,27 +42,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀b2:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (double_divide (double_divide A B) (inverse (double_divide A (inverse (double_divide C B)))))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (double_divide (double_divide A B) (inverse (double_divide A (inverse (double_divide C B)))))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#b2. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#b2 ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP595-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP595-1.ma index ef861880f..a494643cc 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP595-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP595-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -50,21 +50,21 @@ ntheorem prove_these_axioms_3: ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (double_divide (double_divide A B) (inverse (double_divide A (inverse (double_divide C B)))))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (double_divide (double_divide A B) (inverse (double_divide A (inverse (double_divide C B)))))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP596-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP596-1.ma index 1dbcc169f..8a1a88fbf 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP596-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP596-1.ma @@ -44,27 +44,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_4: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (double_divide (double_divide A B) (inverse (double_divide A (inverse (double_divide C B)))))) C.eq Univ (multiply a b) (multiply b a) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (double_divide (double_divide A B) (inverse (double_divide A (inverse (double_divide C B)))))) C.eq Univ (multiply a b) (multiply b a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP597-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP597-1.ma index 7e83dfc60..603c3ecd3 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP597-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP597-1.ma @@ -42,27 +42,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀b1:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A B) (inverse (double_divide A (inverse (double_divide (inverse C) B))))) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A B) (inverse (double_divide A (inverse (double_divide (inverse C) B))))) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#a1. -#b1. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#b1 ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP598-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP598-1.ma index 2d679efdf..b29ef7584 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP598-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP598-1.ma @@ -42,27 +42,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀b2:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A B) (inverse (double_divide A (inverse (double_divide (inverse C) B))))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A B) (inverse (double_divide A (inverse (double_divide (inverse C) B))))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#b2. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#b2 ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP599-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP599-1.ma index 2c0e2ab89..76f4aeb7a 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP599-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP599-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -50,21 +50,21 @@ ntheorem prove_these_axioms_3: ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A B) (inverse (double_divide A (inverse (double_divide (inverse C) B))))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A B) (inverse (double_divide A (inverse (double_divide (inverse C) B))))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP600-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP600-1.ma index 8c9d233b2..43379ae22 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP600-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP600-1.ma @@ -44,27 +44,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_4: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A B) (inverse (double_divide A (inverse (double_divide (inverse C) B))))) C.eq Univ (multiply a b) (multiply b a) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A B) (inverse (double_divide A (inverse (double_divide (inverse C) B))))) C.eq Univ (multiply a b) (multiply b a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP601-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP601-1.ma index fcb6f9f76..a880b04bc 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP601-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP601-1.ma @@ -42,27 +42,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀b1:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (double_divide (inverse (double_divide A (inverse (double_divide B (double_divide A C))))) C)) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (double_divide (inverse (double_divide A (inverse (double_divide B (double_divide A C))))) C)) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#a1. -#b1. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#b1 ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP602-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP602-1.ma index 8f8d7fc89..2aec07734 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP602-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP602-1.ma @@ -42,27 +42,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀b2:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (double_divide (inverse (double_divide A (inverse (double_divide B (double_divide A C))))) C)) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (double_divide (inverse (double_divide A (inverse (double_divide B (double_divide A C))))) C)) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#b2. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#b2 ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP603-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP603-1.ma index 2d18b4a1c..476e04eae 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP603-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP603-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -50,21 +50,21 @@ ntheorem prove_these_axioms_3: ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (double_divide (inverse (double_divide A (inverse (double_divide B (double_divide A C))))) C)) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (double_divide (inverse (double_divide A (inverse (double_divide B (double_divide A C))))) C)) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP604-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP604-1.ma index 73b8041c6..ad89f1391 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP604-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP604-1.ma @@ -44,27 +44,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_4: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (double_divide (inverse (double_divide A (inverse (double_divide B (double_divide A C))))) C)) B.eq Univ (multiply a b) (multiply b a) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (double_divide (inverse (double_divide A (inverse (double_divide B (double_divide A C))))) C)) B.eq Univ (multiply a b) (multiply b a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP605-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP605-1.ma index f44ef9d5f..1666dafab 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP605-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP605-1.ma @@ -42,27 +42,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀b1:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (inverse (double_divide A (inverse (double_divide (inverse B) (double_divide A C))))) C) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (inverse (double_divide A (inverse (double_divide (inverse B) (double_divide A C))))) C) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#a1. -#b1. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#b1 ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP606-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP606-1.ma index 062699c62..83f737da3 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP606-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP606-1.ma @@ -42,27 +42,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀b2:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (inverse (double_divide A (inverse (double_divide (inverse B) (double_divide A C))))) C) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (inverse (double_divide A (inverse (double_divide (inverse B) (double_divide A C))))) C) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#b2. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#b2 ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP607-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP607-1.ma index 76b353367..59dbab99e 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP607-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP607-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -50,21 +50,21 @@ ntheorem prove_these_axioms_3: ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (inverse (double_divide A (inverse (double_divide (inverse B) (double_divide A C))))) C) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (inverse (double_divide A (inverse (double_divide (inverse B) (double_divide A C))))) C) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP608-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP608-1.ma index 6fde1bd12..9aea5f8f6 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP608-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP608-1.ma @@ -44,27 +44,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_4: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (inverse (double_divide A (inverse (double_divide (inverse B) (double_divide A C))))) C) B.eq Univ (multiply a b) (multiply b a) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (inverse (double_divide A (inverse (double_divide (inverse B) (double_divide A C))))) C) B.eq Univ (multiply a b) (multiply b a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP609-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP609-1.ma index a3859b4dd..e31dcc063 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP609-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP609-1.ma @@ -42,27 +42,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀b1:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (double_divide (inverse (double_divide (inverse (double_divide A B)) C)) (double_divide A C))) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (double_divide (inverse (double_divide (inverse (double_divide A B)) C)) (double_divide A C))) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#a1. -#b1. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#b1 ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP610-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP610-1.ma index 026c82b15..3af39c420 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP610-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP610-1.ma @@ -42,27 +42,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀b2:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (double_divide (inverse (double_divide (inverse (double_divide A B)) C)) (double_divide A C))) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (double_divide (inverse (double_divide (inverse (double_divide A B)) C)) (double_divide A C))) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#b2. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#b2 ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP611-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP611-1.ma index b9eec35d7..53390659c 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP611-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP611-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -50,21 +50,21 @@ ntheorem prove_these_axioms_3: ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (double_divide (inverse (double_divide (inverse (double_divide A B)) C)) (double_divide A C))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (double_divide (inverse (double_divide (inverse (double_divide A B)) C)) (double_divide A C))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP612-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP612-1.ma index 9c0e214d4..260692377 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP612-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP612-1.ma @@ -44,27 +44,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_4: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (double_divide (inverse (double_divide (inverse (double_divide A B)) C)) (double_divide A C))) B.eq Univ (multiply a b) (multiply b a) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (double_divide (inverse (double_divide (inverse (double_divide A B)) C)) (double_divide A C))) B.eq Univ (multiply a b) (multiply b a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP613-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP613-1.ma index 7eb3cf678..0f9434900 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP613-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP613-1.ma @@ -42,27 +42,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a1:Univ. ∀b1:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (inverse (double_divide (inverse (double_divide A (inverse B))) C)) (double_divide A C)) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (inverse (double_divide (inverse (double_divide A (inverse B))) C)) (double_divide A C)) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)) . -#Univ. -#A. -#B. -#C. -#a1. -#b1. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a1 ##. +#b1 ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP614-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP614-1.ma index 5a26002fb..fb7392af4 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP614-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP614-1.ma @@ -42,27 +42,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a2:Univ. ∀b2:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (inverse (double_divide (inverse (double_divide A (inverse B))) C)) (double_divide A C)) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (inverse (double_divide (inverse (double_divide A (inverse B))) C)) (double_divide A C)) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) . -#Univ. -#A. -#B. -#C. -#a2. -#b2. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#b2 ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP615-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP615-1.ma index f9e2303ec..1132b2d80 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP615-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP615-1.ma @@ -42,7 +42,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a3:Univ. ∀b3:Univ. ∀c3:Univ. @@ -50,21 +50,21 @@ ntheorem prove_these_axioms_3: ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (inverse (double_divide (inverse (double_divide A (inverse B))) C)) (double_divide A C)) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (inverse (double_divide (inverse (double_divide A (inverse B))) C)) (double_divide A C)) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) . -#Univ. -#A. -#B. -#C. -#a3. -#b3. -#c3. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/GRP616-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP616-1.ma index 9293a5525..3467a37f3 100644 --- a/helm/software/matita/contribs/ng_TPTP/GRP616-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/GRP616-1.ma @@ -44,27 +44,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_these_axioms_4: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀double_divide:∀_:Univ.∀_:Univ.Univ. ∀inverse:∀_:Univ.Univ. ∀multiply:∀_:Univ.∀_:Univ.Univ. ∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)). -∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (inverse (double_divide (inverse (double_divide A (inverse B))) C)) (double_divide A C)) B.eq Univ (multiply a b) (multiply b a) +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (inverse (double_divide (inverse (double_divide A (inverse B))) C)) (double_divide A C)) B.eq Univ (multiply a b) (multiply b a)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#double_divide. -#inverse. -#multiply. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#double_divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT006-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT006-1.ma index 230d42770..c9fe28094 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT006-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT006-1.ma @@ -52,27 +52,27 @@ include "logic/equality.ma". (* ----Denial of the conclusion: *) ntheorem prove_associativity_of_meet: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀join:∀_:Univ.∀_:Univ.Univ. ∀meet:∀_:Univ.∀_:Univ.Univ. ∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet X (join Y Z)) (join (meet Z X) (meet Y X)). -∀H1:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X.eq Univ (meet (meet a b) c) (meet a (meet b c)) +∀H1:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X.eq Univ (meet (meet a b) c) (meet a (meet b c))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT007-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT007-1.ma index 4b9d7b6a1..4b4830b65 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT007-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT007-1.ma @@ -52,27 +52,27 @@ include "logic/equality.ma". (* ----Denial of the conclusion: *) ntheorem prove_associativity_of_join: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀join:∀_:Univ.∀_:Univ.Univ. ∀meet:∀_:Univ.∀_:Univ.Univ. ∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet X (join Y Z)) (join (meet Z X) (meet Y X)). -∀H1:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X.eq Univ (join (join a b) c) (join a (join b c)) +∀H1:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X.eq Univ (join (join a b) c) (join a (join b c))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT008-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT008-1.ma index 66f91939d..70d6caeba 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT008-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT008-1.ma @@ -52,25 +52,25 @@ include "logic/equality.ma". (* ----Denial of the conclusion: *) ntheorem prove_absorbtion_dual: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀join:∀_:Univ.∀_:Univ.Univ. ∀meet:∀_:Univ.∀_:Univ.Univ. ∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet X (join Y Z)) (join (meet Z X) (meet Y X)). -∀H1:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X.eq Univ (join a (meet a b)) a +∀H1:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X.eq Univ (join a (meet a b)) a) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#join. -#meet. -#H0. -#H1. -nauto by H0,H1; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT009-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT009-1.ma index ff81bcdfb..53836a655 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT009-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT009-1.ma @@ -102,7 +102,7 @@ include "logic/equality.ma". (* ----Denial of ordinary distributivity. *) ntheorem prove_distributivity: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -116,27 +116,27 @@ ntheorem prove_distributivity: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet b c)) (meet (join a b) (join a c)) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet b c)) (meet (join a b) (join a c))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT010-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT010-1.ma index 4a41eaee9..3818ff648 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT010-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT010-1.ma @@ -100,7 +100,7 @@ include "logic/equality.ma". (* ----Denial of the conclusion: *) ntheorem prove_this: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -117,31 +117,31 @@ ntheorem prove_this: ∀H7:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H8:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H9:∀X:Univ.eq Univ (join X X) X. -∀H10:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (meet (join b c) (join b d))) (meet (meet a (meet (join b c) (join b d))) (join (meet a (join b (meet c d))) (join (meet a c) (meet a d)))) +∀H10:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (meet (join b c) (join b d))) (meet (meet a (meet (join b c) (join b d))) (join (meet a (join b (meet c d))) (join (meet a c) (meet a d))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT011-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT011-1.ma index cd9041cba..309702acc 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT011-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT011-1.ma @@ -106,7 +106,7 @@ include "logic/equality.ma". (* ----Denial that meet1 and meet2 are the same: *) ntheorem prove_meets_are_same: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀join:∀_:Univ.∀_:Univ.Univ. @@ -124,31 +124,31 @@ ntheorem prove_meets_are_same: ∀H9:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H10:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H11:∀X:Univ.eq Univ (join X X) X. -∀H12:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a b) (meet2 a b) +∀H12:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a b) (meet2 a b)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#join. -#meet. -#meet2. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#join ##. +#meet ##. +#meet2 ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT012-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT012-1.ma index 6bf4ffcab..80f90acc3 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT012-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT012-1.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----Denial of conclusion: *) ntheorem prove_commutativity_of_meet: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀join:∀_:Univ.∀_:Univ.Univ. @@ -62,21 +62,21 @@ ntheorem prove_commutativity_of_meet: ∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (meet (join X Y) (join Y Z)) Y) Y. ∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (join (meet X Y) (meet Y Z)) Y) Y. ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet X (join Y (join X Z))) X. -∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join X (meet Y (meet X Z))) X.eq Univ (meet b a) (meet a b) +∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join X (meet Y (meet X Z))) X.eq Univ (meet b a) (meet a b)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT013-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT013-1.ma index b1b1d0c63..09f42fbeb 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT013-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT013-1.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----Denial of conclusion: *) ntheorem prove_associativity_of_meet: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -63,22 +63,22 @@ ntheorem prove_associativity_of_meet: ∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (meet (join X Y) (join Y Z)) Y) Y. ∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (join (meet X Y) (meet Y Z)) Y) Y. ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet X (join Y (join X Z))) X. -∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join X (meet Y (meet X Z))) X.eq Univ (meet (meet a b) c) (meet a (meet b c)) +∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join X (meet Y (meet X Z))) X.eq Univ (meet (meet a b) c) (meet a (meet b c))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT014-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT014-1.ma index 99e5955c6..705578d84 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT014-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT014-1.ma @@ -54,7 +54,7 @@ include "logic/equality.ma". (* ----Denial of conclusion: *) ntheorem prove_absorbtion: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀join:∀_:Univ.∀_:Univ.Univ. @@ -62,21 +62,21 @@ ntheorem prove_absorbtion: ∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (meet (join X Y) (join Y Z)) Y) Y. ∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (join (meet X Y) (meet Y Z)) Y) Y. ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet X (join Y (join X Z))) X. -∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join X (meet Y (meet X Z))) X.eq Univ (meet a (join a b)) a +∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join X (meet Y (meet X Z))) X.eq Univ (meet a (join a b)) a) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT016-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT016-1.ma index 9da1b618a..e93daaa95 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT016-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT016-1.ma @@ -104,7 +104,7 @@ include "logic/equality.ma". (* ----Denial of equation E1 *) ntheorem prove_e1: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀complement:∀_:Univ.Univ. @@ -121,30 +121,30 @@ ntheorem prove_e1: ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X). ∀H7:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H8:∀X:Univ.eq Univ (meet (complement X) X) n0. -∀H9:∀X:Univ.eq Univ (join (complement X) X) n1.eq Univ (join (complement (join (meet a (complement b)) (complement a))) (join (meet a (complement b)) (join (meet (complement a) (meet (join a (complement b)) (join a b))) (meet (complement a) (complement (meet (join a (complement b)) (join a b))))))) n1 +∀H9:∀X:Univ.eq Univ (join (complement X) X) n1.eq Univ (join (complement (join (meet a (complement b)) (complement a))) (join (meet a (complement b)) (join (meet (complement a) (meet (join a (complement b)) (join a b))) (meet (complement a) (complement (meet (join a (complement b)) (join a b))))))) n1) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#complement. -#join. -#meet. -#n0. -#n1. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#complement ##. +#join ##. +#meet ##. +#n0 ##. +#n1 ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT017-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT017-1.ma index 0c1216286..1bf610418 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT017-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT017-1.ma @@ -102,7 +102,7 @@ include "logic/equality.ma". (* ----Denial of equation E2 *) ntheorem prove_e2: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀complement:∀_:Univ.Univ. @@ -119,30 +119,30 @@ ntheorem prove_e2: ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X). ∀H7:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H8:∀X:Univ.eq Univ (meet (complement X) X) n0. -∀H9:∀X:Univ.eq Univ (join (complement X) X) n1.eq Univ (join a (join (meet (complement a) (meet (join a (complement b)) (join a b))) (meet (complement a) (join (meet (complement a) b) (meet (complement a) (complement b)))))) n1 +∀H9:∀X:Univ.eq Univ (join (complement X) X) n1.eq Univ (join a (join (meet (complement a) (meet (join a (complement b)) (join a b))) (meet (complement a) (join (meet (complement a) b) (meet (complement a) (complement b)))))) n1) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#complement. -#join. -#meet. -#n0. -#n1. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#complement ##. +#join ##. +#meet ##. +#n0 ##. +#n1 ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT018-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT018-1.ma index e3b88368d..c00d5b361 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT018-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT018-1.ma @@ -102,7 +102,7 @@ include "logic/equality.ma". (* ----Denial of equation E3 *) ntheorem prove_e3: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀complement:∀_:Univ.Univ. @@ -119,30 +119,30 @@ ntheorem prove_e3: ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X). ∀H7:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H8:∀X:Univ.eq Univ (meet (complement X) X) n0. -∀H9:∀X:Univ.eq Univ (join (complement X) X) n1.eq Univ (join (complement (join (join (meet (complement a) b) (meet (complement a) (complement b))) (meet a (join (complement a) b)))) (join (complement a) b)) n1 +∀H9:∀X:Univ.eq Univ (join (complement X) X) n1.eq Univ (join (complement (join (join (meet (complement a) b) (meet (complement a) (complement b))) (meet a (join (complement a) b)))) (join (complement a) b)) n1) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#complement. -#join. -#meet. -#n0. -#n1. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#complement ##. +#join ##. +#meet ##. +#n0 ##. +#n1 ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT019-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT019-1.ma index 098916872..c061a967c 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT019-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT019-1.ma @@ -98,7 +98,7 @@ include "logic/equality.ma". (* ----Denial of the corresponding dual distributivity law: *) ntheorem prove_distributivity_law_dual: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -112,27 +112,27 @@ ntheorem prove_distributivity_law_dual: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X). ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X). ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet b c)) (meet (join a b) (join a c)) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet b c)) (meet (join a b) (join a c))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT020-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT020-1.ma index 36b341f4d..a0afabbe2 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT020-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT020-1.ma @@ -98,7 +98,7 @@ include "logic/equality.ma". (* ----Denial of ordinary distributivity: *) ntheorem prove_distributivity: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -112,27 +112,27 @@ ntheorem prove_distributivity: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X). ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X). ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b c)) (join (meet a b) (meet a c)) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b c)) (join (meet a b) (meet a c))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT021-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT021-1.ma index ad011cf99..40883faa0 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT021-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT021-1.ma @@ -98,7 +98,7 @@ include "logic/equality.ma". (* ----Denial of distributivity: *) ntheorem prove_distributivity: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -112,27 +112,27 @@ ntheorem prove_distributivity: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X). ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X). ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b c)) (join (meet a b) (meet a c)) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b c)) (join (meet a b) (meet a c))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT022-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT022-1.ma index 99b716108..12095c661 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT022-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT022-1.ma @@ -102,7 +102,7 @@ include "logic/equality.ma". (* ----Denial of ordinary equational modularity: *) ntheorem prove_modularity: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -116,27 +116,27 @@ ntheorem prove_modularity: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X). ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X). ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (join (meet a b) (meet a c)) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (join (meet a b) (meet a c))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT023-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT023-1.ma index 785e8a9ff..d49c1913b 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT023-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT023-1.ma @@ -98,7 +98,7 @@ include "logic/equality.ma". (* ----Denial of ordinary equational modularity: *) ntheorem prove_modularity: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -112,27 +112,27 @@ ntheorem prove_modularity: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X). ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X). ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (join (meet a b) (meet a c)) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (join (meet a b) (meet a c))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT024-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT024-1.ma index 6e3419f56..a6d415ee4 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT024-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT024-1.ma @@ -106,7 +106,7 @@ include "logic/equality.ma". (* ----Denial that meet1 and meet2 are the same: *) ntheorem prove_meets_equal: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀join:∀_:Univ.∀_:Univ.Univ. @@ -124,31 +124,31 @@ ntheorem prove_meets_equal: ∀H9:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X). ∀H10:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X). ∀H11:∀X:Univ.eq Univ (join X X) X. -∀H12:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a b) (meet2 a b) +∀H12:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a b) (meet2 a b)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#join. -#meet. -#meet2. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#join ##. +#meet ##. +#meet2 ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT025-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT025-1.ma index e212ec9e6..3f8b30b4a 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT025-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT025-1.ma @@ -56,7 +56,7 @@ include "logic/equality.ma". (* ----Denial of meet=meet2. *) ntheorem prove_meets_equal: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀join:∀_:Univ.∀_:Univ.Univ. @@ -75,32 +75,32 @@ ntheorem prove_meets_equal: ∀H10:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H11:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H12:∀X:Univ.eq Univ (join X X) X. -∀H13:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a b) (meet2 a b) +∀H13:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a b) (meet2 a b)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#join. -#meet. -#meet2. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#join ##. +#meet ##. +#meet2 ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT026-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT026-1.ma index 7711cfb0e..c15c8dd2e 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT026-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT026-1.ma @@ -100,7 +100,7 @@ include "logic/equality.ma". (* ----Denial of associativity of meet: *) ntheorem prove_associativity_of_meet: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -112,25 +112,25 @@ ntheorem prove_associativity_of_meet: ∀H3:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X). ∀H4:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X). ∀H5:∀X:Univ.eq Univ (join X X) X. -∀H6:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet (meet a b) c) (meet a (meet b c)) +∀H6:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet (meet a b) c) (meet a (meet b c))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -nauto by H0,H1,H2,H3,H4,H5,H6; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +nauto by H0,H1,H2,H3,H4,H5,H6 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT027-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT027-1.ma index 3fa60ade7..a60194d91 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT027-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT027-1.ma @@ -100,7 +100,7 @@ include "logic/equality.ma". (* ----Denial of associativity of join: *) ntheorem prove_associativity_of_join: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -112,25 +112,25 @@ ntheorem prove_associativity_of_join: ∀H3:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X). ∀H4:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X). ∀H5:∀X:Univ.eq Univ (join X X) X. -∀H6:∀X:Univ.eq Univ (meet X X) X.eq Univ (join (join a b) c) (join a (join b c)) +∀H6:∀X:Univ.eq Univ (meet X X) X.eq Univ (join (join a b) c) (join a (join b c))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -nauto by H0,H1,H2,H3,H4,H5,H6; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +nauto by H0,H1,H2,H3,H4,H5,H6 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT028-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT028-1.ma index 230168e14..14d6cdeee 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT028-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT028-1.ma @@ -104,7 +104,7 @@ include "logic/equality.ma". (* ----Denial of meet=meet2: *) ntheorem name: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀join:∀_:Univ.∀_:Univ.Univ. @@ -119,28 +119,28 @@ ntheorem name: ∀H6:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X). ∀H7:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X). ∀H8:∀X:Univ.eq Univ (join X X) X. -∀H9:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a b) (meet2 a b) +∀H9:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a b) (meet2 a b)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#join. -#meet. -#meet2. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#join ##. +#meet ##. +#meet2 ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT031-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT031-1.ma index 91182d8b2..450d27802 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT031-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT031-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem dist_join: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀join:∀_:Univ.∀_:Univ.Univ. ∀meet:∀_:Univ.∀_:Univ.Univ. ∀xx:Univ. @@ -110,27 +110,27 @@ ntheorem dist_join: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (join xx (meet yy zz)) (meet (join xx yy) (join xx zz)) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (join xx (meet yy zz)) (meet (join xx yy) (join xx zz))) . -#Univ. -#X. -#Y. -#Z. -#join. -#meet. -#xx. -#yy. -#zz. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#join ##. +#meet ##. +#xx ##. +#yy ##. +#zz ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT032-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT032-1.ma index 21825ff73..64b004449 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT032-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT032-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem dist_meet: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀join:∀_:Univ.∀_:Univ.Univ. ∀meet:∀_:Univ.∀_:Univ.Univ. ∀xx:Univ. @@ -110,27 +110,27 @@ ntheorem dist_meet: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet xx (join yy zz)) (join (meet xx yy) (meet xx zz)) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet xx (join yy zz)) (join (meet xx yy) (meet xx zz))) . -#Univ. -#X. -#Y. -#Z. -#join. -#meet. -#xx. -#yy. -#zz. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#join ##. +#meet ##. +#xx ##. +#yy ##. +#zz ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT033-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT033-1.ma index c4318d931..290ac6f5a 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT033-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT033-1.ma @@ -52,7 +52,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem idempotence_of_join: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀join:∀_:Univ.∀_:Univ.Univ. ∀meet:∀_:Univ.∀_:Univ.Univ. ∀xx:Univ. @@ -61,22 +61,22 @@ ntheorem idempotence_of_join: ∀H2:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X). ∀H3:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X). ∀H4:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. -∀H5:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X.eq Univ (join xx xx) xx +∀H5:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X.eq Univ (join xx xx) xx) . -#Univ. -#X. -#Y. -#Z. -#join. -#meet. -#xx. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -nauto by H0,H1,H2,H3,H4,H5; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#join ##. +#meet ##. +#xx ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +nauto by H0,H1,H2,H3,H4,H5 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT034-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT034-1.ma index ce4e27291..860439ac9 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT034-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT034-1.ma @@ -52,7 +52,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem idempotence_of_meet: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀join:∀_:Univ.∀_:Univ.Univ. ∀meet:∀_:Univ.∀_:Univ.Univ. ∀xx:Univ. @@ -61,22 +61,22 @@ ntheorem idempotence_of_meet: ∀H2:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X). ∀H3:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X). ∀H4:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. -∀H5:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X.eq Univ (meet xx xx) xx +∀H5:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X.eq Univ (meet xx xx) xx) . -#Univ. -#X. -#Y. -#Z. -#join. -#meet. -#xx. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -nauto by H0,H1,H2,H3,H4,H5; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#join ##. +#meet ##. +#xx ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +nauto by H0,H1,H2,H3,H4,H5 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT038-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT038-1.ma index 37fb8d7d5..dd0677fe5 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT038-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT038-1.ma @@ -106,7 +106,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem rhs: - ∀Univ:Type.∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀aa:Univ. ∀bb:Univ. ∀cc:Univ. @@ -130,40 +130,40 @@ ntheorem rhs: ∀H12:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H13:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H14:∀X:Univ.eq Univ (join X X) X. -∀H15:∀X:Univ.eq Univ (meet X X) X.eq Univ (f aa dd) (f cc dd) +∀H15:∀X:Univ.eq Univ (meet X X) X.eq Univ (f aa dd) (f cc dd)) . -#Univ. -#U. -#V. -#W. -#X. -#Y. -#Z. -#aa. -#bb. -#cc. -#dd. -#f. -#join. -#meet. -#n0. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15; +#Univ ##. +#U ##. +#V ##. +#W ##. +#X ##. +#Y ##. +#Z ##. +#aa ##. +#bb ##. +#cc ##. +#dd ##. +#f ##. +#join ##. +#meet ##. +#n0 ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT039-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT039-1.ma index 414f5bbdb..849a668c0 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT039-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT039-1.ma @@ -100,7 +100,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem rhs: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀join:∀_:Univ.∀_:Univ.Univ. ∀meet:∀_:Univ.∀_:Univ.Univ. ∀xx:Univ. @@ -116,29 +116,29 @@ ntheorem rhs: ∀H7:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H8:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H9:∀X:Univ.eq Univ (join X X) X. -∀H10:∀X:Univ.eq Univ (meet X X) X.eq Univ (join xx (meet yy zz)) (meet yy (join xx zz)) +∀H10:∀X:Univ.eq Univ (meet X X) X.eq Univ (join xx (meet yy zz)) (meet yy (join xx zz))) . -#Univ. -#X. -#Y. -#Z. -#join. -#meet. -#xx. -#yy. -#zz. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#join ##. +#meet ##. +#xx ##. +#yy ##. +#zz ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT039-2.ma b/helm/software/matita/contribs/ng_TPTP/LAT039-2.ma index 1cff13ba2..3898ab504 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT039-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT039-2.ma @@ -98,7 +98,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem rhs: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀join:∀_:Univ.∀_:Univ.Univ. ∀meet:∀_:Univ.∀_:Univ.Univ. ∀xx:Univ. @@ -114,29 +114,29 @@ ntheorem rhs: ∀H7:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H8:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H9:∀X:Univ.eq Univ (join X X) X. -∀H10:∀X:Univ.eq Univ (meet X X) X.eq Univ (join xx (meet yy zz)) (meet (join xx yy) (join xx zz)) +∀H10:∀X:Univ.eq Univ (meet X X) X.eq Univ (join xx (meet yy zz)) (meet (join xx yy) (join xx zz))) . -#Univ. -#X. -#Y. -#Z. -#join. -#meet. -#xx. -#yy. -#zz. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#join ##. +#meet ##. +#xx ##. +#yy ##. +#zz ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT040-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT040-1.ma index fd14ebbb7..c9377b192 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT040-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT040-1.ma @@ -98,7 +98,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem rhs: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀join:∀_:Univ.∀_:Univ.Univ. ∀meet:∀_:Univ.∀_:Univ.Univ. ∀xx:Univ. @@ -115,30 +115,30 @@ ntheorem rhs: ∀H8:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H9:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H10:∀X:Univ.eq Univ (join X X) X. -∀H11:∀X:Univ.eq Univ (meet X X) X.eq Univ yy zz +∀H11:∀X:Univ.eq Univ (meet X X) X.eq Univ yy zz) . -#Univ. -#X. -#Y. -#Z. -#join. -#meet. -#xx. -#yy. -#zz. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#join ##. +#meet ##. +#xx ##. +#yy ##. +#zz ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT042-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT042-1.ma index 3f0062418..670313caf 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT042-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT042-1.ma @@ -104,7 +104,7 @@ include "logic/equality.ma". (* ----Denial of modular law: *) ntheorem prove_modular_law: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -124,33 +124,33 @@ ntheorem prove_modular_law: ∀H8:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H9:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H10:∀X:Univ.eq Univ (join X X) X. -∀H11:∀X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet b (join a c))) (meet (join a b) (join a c)) +∀H11:∀X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet b (join a c))) (meet (join a b) (join a c))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#complement. -#join. -#meet. -#n0. -#n1. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#complement ##. +#join ##. +#meet ##. +#n0 ##. +#n1 ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT043-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT043-1.ma index 4f89b3bb8..e9e110e95 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT043-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT043-1.ma @@ -104,7 +104,7 @@ include "logic/equality.ma". (* ----Denial of compatability *) ntheorem prove_compatability_law: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀c:Univ. ∀complement:∀_:Univ.Univ. ∀d:Univ. @@ -123,32 +123,32 @@ ntheorem prove_compatability_law: ∀H8:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H9:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H10:∀X:Univ.eq Univ (join X X) X. -∀H11:∀X:Univ.eq Univ (meet X X) X.eq Univ (complement (join c d)) (meet (complement c) (complement d)) +∀H11:∀X:Univ.eq Univ (meet X X) X.eq Univ (complement (join c d)) (meet (complement c) (complement d))) . -#Univ. -#X. -#Y. -#Z. -#c. -#complement. -#d. -#join. -#meet. -#n0. -#n1. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#c ##. +#complement ##. +#d ##. +#join ##. +#meet ##. +#n0 ##. +#n1 ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT044-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT044-1.ma index 4f44c7cf1..1a304708f 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT044-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT044-1.ma @@ -104,7 +104,7 @@ include "logic/equality.ma". (* ----Denial of weak orthomodular law (10) *) ntheorem prove_weak_orthomodular_law: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀complement:∀_:Univ.Univ. @@ -125,34 +125,34 @@ ntheorem prove_weak_orthomodular_law: ∀H10:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H11:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H12:∀X:Univ.eq Univ (join X X) X. -∀H13:∀X:Univ.eq Univ (meet X X) X.eq Univ (join (meet (complement a) (join a b)) (join (complement b) (meet a b))) n1 +∀H13:∀X:Univ.eq Univ (meet X X) X.eq Univ (join (meet (complement a) (join a b)) (join (complement b) (meet a b))) n1) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#complement. -#join. -#meet. -#n0. -#n1. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#complement ##. +#join ##. +#meet ##. +#n0 ##. +#n1 ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT045-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT045-1.ma index bb7d59f21..8d071b019 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT045-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT045-1.ma @@ -104,7 +104,7 @@ include "logic/equality.ma". (* ----Denial of orthomodular law (8) *) ntheorem prove_orthomodular_law: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀complement:∀_:Univ.Univ. @@ -125,34 +125,34 @@ ntheorem prove_orthomodular_law: ∀H10:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H11:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H12:∀X:Univ.eq Univ (join X X) X. -∀H13:∀X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet (complement a) (join a b))) (join a b) +∀H13:∀X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet (complement a) (join a b))) (join a b)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#complement. -#join. -#meet. -#n0. -#n1. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#complement ##. +#join ##. +#meet ##. +#n0 ##. +#n1 ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT046-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT046-1.ma index 455824235..0ded34a1d 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT046-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT046-1.ma @@ -104,7 +104,7 @@ include "logic/equality.ma". (* ----Denial of distributivity (4) *) ntheorem prove_distributivity: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -126,35 +126,35 @@ ntheorem prove_distributivity: ∀H10:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H11:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H12:∀X:Univ.eq Univ (join X X) X. -∀H13:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b c)) (join (meet a b) (meet a c)) +∀H13:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b c)) (join (meet a b) (meet a c))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#complement. -#join. -#meet. -#n0. -#n1. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#complement ##. +#join ##. +#meet ##. +#n0 ##. +#n1 ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT047-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT047-1.ma index 652877488..71d57f861 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT047-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT047-1.ma @@ -98,7 +98,7 @@ include "logic/equality.ma". (* ----Denial of modularity (7) *) ntheorem prove_modularity: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -111,26 +111,26 @@ ntheorem prove_modularity: ∀H4:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H5:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H6:∀X:Univ.eq Univ (join X X) X. -∀H7:∀X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet b (join a c))) (meet (join a b) (join a c)) +∀H7:∀X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet b (join a c))) (meet (join a b) (join a c))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -nauto by H0,H1,H2,H3,H4,H5,H6,H7; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT048-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT048-1.ma index e98612595..53b296265 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT048-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT048-1.ma @@ -104,7 +104,7 @@ include "logic/equality.ma". (* ----Denial of orthomodular law (8) *) ntheorem prove_orthomodular_law: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀complement:∀_:Univ.Univ. @@ -125,34 +125,34 @@ ntheorem prove_orthomodular_law: ∀H10:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H11:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H12:∀X:Univ.eq Univ (join X X) X. -∀H13:∀X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet (complement a) (join a b))) (join a b) +∀H13:∀X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet (complement a) (join a b))) (join a b)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#complement. -#join. -#meet. -#n0. -#n1. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#complement ##. +#join ##. +#meet ##. +#n0 ##. +#n1 ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT049-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT049-1.ma index 6a9977343..3033e987f 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT049-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT049-1.ma @@ -102,7 +102,7 @@ include "logic/equality.ma". (* ----Denial of weak orthomodular law (10) *) ntheorem prove_weak_orthomodular_law: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀complement:∀_:Univ.Univ. @@ -122,33 +122,33 @@ ntheorem prove_weak_orthomodular_law: ∀H9:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H10:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H11:∀X:Univ.eq Univ (join X X) X. -∀H12:∀X:Univ.eq Univ (meet X X) X.eq Univ (join (meet (complement a) (join a b)) (join (complement b) (meet a b))) n1 +∀H12:∀X:Univ.eq Univ (meet X X) X.eq Univ (join (meet (complement a) (join a b)) (join (complement b) (meet a b))) n1) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#complement. -#join. -#meet. -#n0. -#n1. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#complement ##. +#join ##. +#meet ##. +#n0 ##. +#n1 ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT050-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT050-1.ma index 76ab9a495..1bdeb0c16 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT050-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT050-1.ma @@ -110,7 +110,7 @@ include "logic/equality.ma". (* ----Denial of modular law: *) ntheorem prove_modular_law: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -132,35 +132,35 @@ ntheorem prove_modular_law: ∀H10:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H11:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H12:∀X:Univ.eq Univ (join X X) X. -∀H13:∀X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet b (join a c))) (meet (join a b) (join a c)) +∀H13:∀X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet b (join a c))) (meet (join a b) (join a c))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#complement. -#join. -#meet. -#n0. -#n1. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#complement ##. +#join ##. +#meet ##. +#n0 ##. +#n1 ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT051-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT051-1.ma index f88678a03..aad2e25b7 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT051-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT051-1.ma @@ -102,7 +102,7 @@ include "logic/equality.ma". (* ----Denial of compatibility (6) *) ntheorem prove_compatibility_law: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀complement:∀_:Univ.Univ. @@ -120,31 +120,31 @@ ntheorem prove_compatibility_law: ∀H7:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H8:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H9:∀X:Univ.eq Univ (join X X) X. -∀H10:∀X:Univ.eq Univ (meet X X) X.eq Univ (complement (join a b)) (meet (complement a) (complement b)) +∀H10:∀X:Univ.eq Univ (meet X X) X.eq Univ (complement (join a b)) (meet (complement a) (complement b))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#complement. -#join. -#meet. -#n0. -#n1. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#complement ##. +#join ##. +#meet ##. +#n0 ##. +#n1 ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT052-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT052-1.ma index 5cde28496..2cbb344bf 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT052-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT052-1.ma @@ -104,7 +104,7 @@ include "logic/equality.ma". (* ----Denial of compatibility (6) *) ntheorem prove_compatibility_law: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀complement:∀_:Univ.Univ. @@ -123,32 +123,32 @@ ntheorem prove_compatibility_law: ∀H8:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H9:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H10:∀X:Univ.eq Univ (join X X) X. -∀H11:∀X:Univ.eq Univ (meet X X) X.eq Univ (complement (join a b)) (meet (complement a) (complement b)) +∀H11:∀X:Univ.eq Univ (meet X X) X.eq Univ (complement (join a b)) (meet (complement a) (complement b))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#complement. -#join. -#meet. -#n0. -#n1. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#complement ##. +#join ##. +#meet ##. +#n0 ##. +#n1 ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT053-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT053-1.ma index 26d40408f..fd95f1a51 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT053-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT053-1.ma @@ -110,7 +110,7 @@ include "logic/equality.ma". (* ----Denial of equation in question *) ntheorem prove_this: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀complement:∀_:Univ.Univ. @@ -131,34 +131,34 @@ ntheorem prove_this: ∀H10:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H11:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H12:∀X:Univ.eq Univ (join X X) X. -∀H13:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a (join (complement a) (meet a b))))) (meet a (join (complement a) (meet a b))) +∀H13:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a (join (complement a) (meet a b))))) (meet a (join (complement a) (meet a b)))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#complement. -#join. -#meet. -#n0. -#n1. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#complement ##. +#join ##. +#meet ##. +#n0 ##. +#n1 ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT054-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT054-1.ma index cf631367e..f8992eacb 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT054-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT054-1.ma @@ -108,7 +108,7 @@ include "logic/equality.ma". (* ----Denial of equation in question *) ntheorem prove_this: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀complement:∀_:Univ.Univ. @@ -128,33 +128,33 @@ ntheorem prove_this: ∀H9:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H10:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H11:∀X:Univ.eq Univ (join X X) X. -∀H12:∀X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet (complement b) (join (complement a) (meet (complement b) (join a (meet (complement b) (complement a))))))) (join a (meet (complement b) (join (complement a) (meet (complement b) (join a (meet (complement b) (join (complement a) (meet (complement b) a)))))))) +∀H12:∀X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet (complement b) (join (complement a) (meet (complement b) (join a (meet (complement b) (complement a))))))) (join a (meet (complement b) (join (complement a) (meet (complement b) (join a (meet (complement b) (join (complement a) (meet (complement b) a))))))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#complement. -#join. -#meet. -#n0. -#n1. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#complement ##. +#join ##. +#meet ##. +#n0 ##. +#n1 ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT062-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT062-1.ma index b4d3993d3..0cf86379e 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT062-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT062-1.ma @@ -98,7 +98,7 @@ include "logic/equality.ma". (* ----Denial of E51 *) ntheorem prove_e51: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀complement:∀_:Univ.Univ. @@ -116,33 +116,33 @@ ntheorem prove_e51: ∀H7:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H8:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H9:∀X:Univ.eq Univ (join X X) X. -∀H10:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet (join a (complement b)) (join (join (meet a b) (meet (complement a) b)) (meet (complement a) (complement b)))) (join (meet a b) (meet (complement a) (complement b))) +∀H10:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet (join a (complement b)) (join (join (meet a b) (meet (complement a) b)) (meet (complement a) (complement b)))) (join (meet a b) (meet (complement a) (complement b)))) . -#Univ. -#A. -#B. -#X. -#Y. -#Z. -#a. -#b. -#complement. -#join. -#meet. -#n0. -#n1. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10; +#Univ ##. +#A ##. +#B ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#complement ##. +#join ##. +#meet ##. +#n0 ##. +#n1 ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT063-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT063-1.ma index f79da4108..526ece0e2 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT063-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT063-1.ma @@ -98,7 +98,7 @@ include "logic/equality.ma". (* ----Denial of E62 *) ntheorem prove_e62: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀complement:∀_:Univ.Univ. @@ -116,33 +116,33 @@ ntheorem prove_e62: ∀H7:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H8:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H9:∀X:Univ.eq Univ (join X X) X. -∀H10:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a (join (complement a) (meet a b))))) (meet a (join (complement a) (meet a b))) +∀H10:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a (join (complement a) (meet a b))))) (meet a (join (complement a) (meet a b)))) . -#Univ. -#A. -#B. -#X. -#Y. -#Z. -#a. -#b. -#complement. -#join. -#meet. -#n0. -#n1. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10; +#Univ ##. +#A ##. +#B ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#complement ##. +#join ##. +#meet ##. +#n0 ##. +#n1 ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT070-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT070-1.ma index c2741e568..419daa259 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT070-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT070-1.ma @@ -48,24 +48,24 @@ include "logic/equality.ma". (* ----Denial of Sheffer stroke associativity *) ntheorem associativity: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀f:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f (f (f B A) (f A C)) D) (f A (f (f A (f (f B B) B)) C))) A.eq Univ (f a (f (f b c) (f b c))) (f c (f (f b a) (f b a))) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f (f (f B A) (f A C)) D) (f A (f (f A (f (f B B) B)) C))) A.eq Univ (f a (f (f b c) (f b c))) (f c (f (f b a) (f b a)))) . -#Univ. -#A. -#B. -#C. -#D. -#a. -#b. -#c. -#f. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a ##. +#b ##. +#c ##. +#f ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT071-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT071-1.ma index 0367a84a8..6e7245577 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT071-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT071-1.ma @@ -50,24 +50,24 @@ include "logic/equality.ma". (* ----Denial of Sheffer stroke associativity *) ntheorem associativity: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀f:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f B A) (f (f (f (f B A) A) (f C A)) (f (f A A) D))) A.eq Univ (f a (f (f b c) (f b c))) (f c (f (f b a) (f b a))) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f B A) (f (f (f (f B A) A) (f C A)) (f (f A A) D))) A.eq Univ (f a (f (f b c) (f b c))) (f c (f (f b a) (f b a)))) . -#Univ. -#A. -#B. -#C. -#D. -#a. -#b. -#c. -#f. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a ##. +#b ##. +#c ##. +#f ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT072-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT072-1.ma index 061fbcd3c..5dc838e98 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT072-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT072-1.ma @@ -50,24 +50,24 @@ include "logic/equality.ma". (* ----Denial of Sheffer stroke associativity *) ntheorem associativity: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀f:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f (f (f B A) (f A C)) D) (f A (f (f C (f (f A A) C)) C))) A.eq Univ (f a (f (f b c) (f b c))) (f c (f (f b a) (f b a))) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f (f (f B A) (f A C)) D) (f A (f (f C (f (f A A) C)) C))) A.eq Univ (f a (f (f b c) (f b c))) (f c (f (f b a) (f b a)))) . -#Univ. -#A. -#B. -#C. -#D. -#a. -#b. -#c. -#f. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a ##. +#b ##. +#c ##. +#f ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT073-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT073-1.ma index a794acc46..e225137b4 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT073-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT073-1.ma @@ -50,24 +50,24 @@ include "logic/equality.ma". (* ----Denial of Sheffer stroke modularity *) ntheorem modularity: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀f:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f (f B (f A B)) B) (f A (f C (f (f A B) (f (f C C) D))))) A.eq Univ (f a (f b (f a (f c c)))) (f a (f c (f a (f b b)))) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f (f B (f A B)) B) (f A (f C (f (f A B) (f (f C C) D))))) A.eq Univ (f a (f b (f a (f c c)))) (f a (f c (f a (f b b))))) . -#Univ. -#A. -#B. -#C. -#D. -#a. -#b. -#c. -#f. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a ##. +#b ##. +#c ##. +#f ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT074-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT074-1.ma index cad65bd02..1ef9a1b2c 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT074-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT074-1.ma @@ -50,24 +50,24 @@ include "logic/equality.ma". (* ----Denial of Sheffer stroke associativity *) ntheorem associativity: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀f:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f B A) (f (f (f A A) C) (f (f (f (f (f A B) C) C) A) (f A D)))) A.eq Univ (f a (f (f b c) (f b c))) (f c (f (f b a) (f b a))) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f B A) (f (f (f A A) C) (f (f (f (f (f A B) C) C) A) (f A D)))) A.eq Univ (f a (f (f b c) (f b c))) (f c (f (f b a) (f b a)))) . -#Univ. -#A. -#B. -#C. -#D. -#a. -#b. -#c. -#f. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a ##. +#b ##. +#c ##. +#f ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT075-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT075-1.ma index 3efa62ec6..3fd4856e7 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT075-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT075-1.ma @@ -50,24 +50,24 @@ include "logic/equality.ma". (* ----Denial of Sheffer stroke modularity *) ntheorem modularity: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀f:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f B A) (f (f (f A A) C) (f (f (f (f (f A B) C) C) A) (f A D)))) A.eq Univ (f a (f b (f a (f c c)))) (f a (f c (f a (f b b)))) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f B A) (f (f (f A A) C) (f (f (f (f (f A B) C) C) A) (f A D)))) A.eq Univ (f a (f b (f a (f c c)))) (f a (f c (f a (f b b))))) . -#Univ. -#A. -#B. -#C. -#D. -#a. -#b. -#c. -#f. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a ##. +#b ##. +#c ##. +#f ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT076-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT076-1.ma index bb9b8b9f7..f027a0762 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT076-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT076-1.ma @@ -50,24 +50,24 @@ include "logic/equality.ma". (* ----Denial of Sheffer stroke associativity *) ntheorem associativity: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀f:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f (f (f B A) (f C A)) D) (f A (f (f (f (f (f (f B B) A) C) C) A) B))) A.eq Univ (f a (f (f b c) (f b c))) (f c (f (f b a) (f b a))) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f (f (f B A) (f C A)) D) (f A (f (f (f (f (f (f B B) A) C) C) A) B))) A.eq Univ (f a (f (f b c) (f b c))) (f c (f (f b a) (f b a)))) . -#Univ. -#A. -#B. -#C. -#D. -#a. -#b. -#c. -#f. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a ##. +#b ##. +#c ##. +#f ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT077-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT077-1.ma index d37f4b169..c4d9441a5 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT077-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT077-1.ma @@ -50,24 +50,24 @@ include "logic/equality.ma". (* ----Denial of Sheffer stroke modularity *) ntheorem modularity: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀f:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f (f (f B A) (f C A)) D) (f A (f (f (f (f (f (f B B) A) C) C) A) B))) A.eq Univ (f a (f b (f a (f c c)))) (f a (f c (f a (f b b)))) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f (f (f B A) (f C A)) D) (f A (f (f (f (f (f (f B B) A) C) C) A) B))) A.eq Univ (f a (f b (f a (f c c)))) (f a (f c (f a (f b b))))) . -#Univ. -#A. -#B. -#C. -#D. -#a. -#b. -#c. -#f. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a ##. +#b ##. +#c ##. +#f ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT078-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT078-1.ma index 656c0bf40..af4604043 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT078-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT078-1.ma @@ -50,24 +50,24 @@ include "logic/equality.ma". (* ----Denial of Sheffer stroke associativity *) ntheorem associativity: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀f:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f (f (f B A) (f A C)) D) (f A (f (f (f B (f B (f (f C C) A))) A) C))) A.eq Univ (f a (f (f b c) (f b c))) (f c (f (f b a) (f b a))) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f (f (f B A) (f A C)) D) (f A (f (f (f B (f B (f (f C C) A))) A) C))) A.eq Univ (f a (f (f b c) (f b c))) (f c (f (f b a) (f b a)))) . -#Univ. -#A. -#B. -#C. -#D. -#a. -#b. -#c. -#f. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a ##. +#b ##. +#c ##. +#f ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT079-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT079-1.ma index 24ef05694..c8eef4278 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT079-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT079-1.ma @@ -50,24 +50,24 @@ include "logic/equality.ma". (* ----Denial of Sheffer stroke modularity *) ntheorem modularity: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀f:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f (f (f B A) (f A C)) D) (f A (f (f (f B (f B (f (f C C) A))) A) C))) A.eq Univ (f a (f b (f a (f c c)))) (f a (f c (f a (f b b)))) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f (f (f B A) (f A C)) D) (f A (f (f (f B (f B (f (f C C) A))) A) C))) A.eq Univ (f a (f b (f a (f c c)))) (f a (f c (f a (f b b))))) . -#Univ. -#A. -#B. -#C. -#D. -#a. -#b. -#c. -#f. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a ##. +#b ##. +#c ##. +#f ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT080-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT080-1.ma index 77ef4705c..f988251bc 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT080-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT080-1.ma @@ -44,25 +44,25 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_normal_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ. ∀a:Univ. ∀join:∀_:Univ.∀_:Univ.Univ. ∀meet:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet D B) (meet B E)) B)) (meet (join (meet B (meet (meet (join D (join B E)) (join F B)) B)) (meet G (join B (meet (meet (join D (join B E)) (join F B)) B)))) (join A (join (join (meet D B) (meet B E)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (meet a a) a +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet D B) (meet B E)) B)) (meet (join (meet B (meet (meet (join D (join B E)) (join F B)) B)) (meet G (join B (meet (meet (join D (join B E)) (join F B)) B)))) (join A (join (join (meet D B) (meet B E)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (meet a a) a) . -#Univ. -#A. -#B. -#C. -#D. -#E. -#F. -#G. -#a. -#join. -#meet. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#E ##. +#F ##. +#G ##. +#a ##. +#join ##. +#meet ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT081-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT081-1.ma index 195973ba3..1e0b7674a 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT081-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT081-1.ma @@ -44,27 +44,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_normal_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ. ∀a:Univ. ∀b:Univ. ∀join:∀_:Univ.∀_:Univ.Univ. âˆ€meet:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet D B) (meet B E)) B)) (meet (join (meet B (meet (meet (join D (join B E)) (join F B)) B)) (meet G (join B (meet (meet (join D (join B E)) (join F B)) B)))) (join A (join (join (meet D B) (meet B E)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (meet a b) (meet b a) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet D B) (meet B E)) B)) (meet (join (meet B (meet (meet (join D (join B E)) (join F B)) B)) (meet G (join B (meet (meet (join D (join B E)) (join F B)) B)))) (join A (join (join (meet D B) (meet B E)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (meet a b) (meet b a)) . -#Univ. -#A. -#B. -#C. -#D. -#E. -#F. -#G. -#a. -#b. -#join. -#meet. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#E ##. +#F ##. +#G ##. +#a ##. +#b ##. +#join ##. +#meet ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT082-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT082-1.ma index c7f79d5ab..4220f197a 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT082-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT082-1.ma @@ -44,29 +44,29 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_normal_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀join:∀_:Univ.∀_:Univ.Univ. ∀meet:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet D B) (meet B E)) B)) (meet (join (meet B (meet (meet (join D (join B E)) (join F B)) B)) (meet G (join B (meet (meet (join D (join B E)) (join F B)) B)))) (join A (join (join (meet D B) (meet B E)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (meet (meet a b) c) (meet a (meet b c)) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet D B) (meet B E)) B)) (meet (join (meet B (meet (meet (join D (join B E)) (join F B)) B)) (meet G (join B (meet (meet (join D (join B E)) (join F B)) B)))) (join A (join (join (meet D B) (meet B E)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (meet (meet a b) c) (meet a (meet b c))) . -#Univ. -#A. -#B. -#C. -#D. -#E. -#F. -#G. -#a. -#b. -#c. -#join. -#meet. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#E ##. +#F ##. +#G ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT083-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT083-1.ma index 4cb8b50ab..dfbde99b9 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT083-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT083-1.ma @@ -44,25 +44,25 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_normal_axioms_4: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ. ∀a:Univ. ∀join:∀_:Univ.∀_:Univ.Univ. ∀meet:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet D B) (meet B E)) B)) (meet (join (meet B (meet (meet (join D (join B E)) (join F B)) B)) (meet G (join B (meet (meet (join D (join B E)) (join F B)) B)))) (join A (join (join (meet D B) (meet B E)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (join a a) a +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet D B) (meet B E)) B)) (meet (join (meet B (meet (meet (join D (join B E)) (join F B)) B)) (meet G (join B (meet (meet (join D (join B E)) (join F B)) B)))) (join A (join (join (meet D B) (meet B E)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (join a a) a) . -#Univ. -#A. -#B. -#C. -#D. -#E. -#F. -#G. -#a. -#join. -#meet. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#E ##. +#F ##. +#G ##. +#a ##. +#join ##. +#meet ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT084-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT084-1.ma index 5ea52b573..98907f1d8 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT084-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT084-1.ma @@ -44,27 +44,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_normal_axioms_5: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ. ∀a:Univ. ∀b:Univ. ∀join:∀_:Univ.∀_:Univ.Univ. ∀meet:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet D B) (meet B E)) B)) (meet (join (meet B (meet (meet (join D (join B E)) (join F B)) B)) (meet G (join B (meet (meet (join D (join B E)) (join F B)) B)))) (join A (join (join (meet D B) (meet B E)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (join a b) (join b a) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet D B) (meet B E)) B)) (meet (join (meet B (meet (meet (join D (join B E)) (join F B)) B)) (meet G (join B (meet (meet (join D (join B E)) (join F B)) B)))) (join A (join (join (meet D B) (meet B E)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (join a b) (join b a)) . -#Univ. -#A. -#B. -#C. -#D. -#E. -#F. -#G. -#a. -#b. -#join. -#meet. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#E ##. +#F ##. +#G ##. +#a ##. +#b ##. +#join ##. +#meet ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT085-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT085-1.ma index 2245c79b8..1b6df28fd 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT085-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT085-1.ma @@ -44,29 +44,29 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_normal_axioms_6: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀join:∀_:Univ.∀_:Univ.Univ. ∀meet:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet D B) (meet B E)) B)) (meet (join (meet B (meet (meet (join D (join B E)) (join F B)) B)) (meet G (join B (meet (meet (join D (join B E)) (join F B)) B)))) (join A (join (join (meet D B) (meet B E)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (join (join a b) c) (join a (join b c)) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet D B) (meet B E)) B)) (meet (join (meet B (meet (meet (join D (join B E)) (join F B)) B)) (meet G (join B (meet (meet (join D (join B E)) (join F B)) B)))) (join A (join (join (meet D B) (meet B E)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (join (join a b) c) (join a (join b c))) . -#Univ. -#A. -#B. -#C. -#D. -#E. -#F. -#G. -#a. -#b. -#c. -#join. -#meet. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#E ##. +#F ##. +#G ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT086-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT086-1.ma index f12c2801d..541b4e86c 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT086-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT086-1.ma @@ -44,27 +44,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_normal_axioms_7: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ. ∀a:Univ. ∀b:Univ. ∀join:∀_:Univ.∀_:Univ.Univ. ∀meet:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet D B) (meet B E)) B)) (meet (join (meet B (meet (meet (join D (join B E)) (join F B)) B)) (meet G (join B (meet (meet (join D (join B E)) (join F B)) B)))) (join A (join (join (meet D B) (meet B E)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (meet a (join a b)) a +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet D B) (meet B E)) B)) (meet (join (meet B (meet (meet (join D (join B E)) (join F B)) B)) (meet G (join B (meet (meet (join D (join B E)) (join F B)) B)))) (join A (join (join (meet D B) (meet B E)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (meet a (join a b)) a) . -#Univ. -#A. -#B. -#C. -#D. -#E. -#F. -#G. -#a. -#b. -#join. -#meet. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#E ##. +#F ##. +#G ##. +#a ##. +#b ##. +#join ##. +#meet ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT087-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT087-1.ma index d59b01941..51c069943 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT087-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT087-1.ma @@ -44,27 +44,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_normal_axioms_8: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ. ∀a:Univ. ∀b:Univ. ∀join:∀_:Univ.∀_:Univ.Univ. ∀meet:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet D B) (meet B E)) B)) (meet (join (meet B (meet (meet (join D (join B E)) (join F B)) B)) (meet G (join B (meet (meet (join D (join B E)) (join F B)) B)))) (join A (join (join (meet D B) (meet B E)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (join a (meet a b)) a +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet D B) (meet B E)) B)) (meet (join (meet B (meet (meet (join D (join B E)) (join F B)) B)) (meet G (join B (meet (meet (join D (join B E)) (join F B)) B)))) (join A (join (join (meet D B) (meet B E)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (join a (meet a b)) a) . -#Univ. -#A. -#B. -#C. -#D. -#E. -#F. -#G. -#a. -#b. -#join. -#meet. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#E ##. +#F ##. +#G ##. +#a ##. +#b ##. +#join ##. +#meet ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT088-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT088-1.ma index cead215b5..7ab3ba553 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT088-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT088-1.ma @@ -44,7 +44,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_normal_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀join:∀_:Univ.∀_:Univ.Univ. ∀meet:∀_:Univ.∀_:Univ.Univ. @@ -52,21 +52,21 @@ ntheorem prove_normal_axioms_1: ∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (meet (meet (join A B) (join C A)) A) A. ∀H2:∀A:Univ.∀B:Univ.eq Univ (join (meet A B) (meet B (join A B))) B. ∀H3:∀A:Univ.∀B:Univ.eq Univ (join (meet A A) (meet B (join A A))) A. -∀H4:∀A:Univ.∀B:Univ.eq Univ (join (meet A B) (meet A (join A B))) A.eq Univ (meet a a) a +∀H4:∀A:Univ.∀B:Univ.eq Univ (join (meet A B) (meet A (join A B))) A.eq Univ (meet a a) a) . -#Univ. -#A. -#B. -#C. -#a. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -nauto by H0,H1,H2,H3,H4; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +nauto by H0,H1,H2,H3,H4 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT089-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT089-1.ma index 72cf2348f..3ef0067fb 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT089-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT089-1.ma @@ -44,7 +44,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_normal_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀join:∀_:Univ.∀_:Univ.Univ. @@ -53,22 +53,22 @@ ntheorem prove_normal_axioms_2: ∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (meet (meet (join A B) (join C A)) A) A. ∀H2:∀A:Univ.∀B:Univ.eq Univ (join (meet A B) (meet B (join A B))) B. ∀H3:∀A:Univ.∀B:Univ.eq Univ (join (meet A A) (meet B (join A A))) A. -∀H4:∀A:Univ.∀B:Univ.eq Univ (join (meet A B) (meet A (join A B))) A.eq Univ (meet b a) (meet a b) +∀H4:∀A:Univ.∀B:Univ.eq Univ (join (meet A B) (meet A (join A B))) A.eq Univ (meet b a) (meet a b)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -nauto by H0,H1,H2,H3,H4; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +nauto by H0,H1,H2,H3,H4 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT090-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT090-1.ma index 002a647e2..d55368558 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT090-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT090-1.ma @@ -44,7 +44,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_normal_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀join:∀_:Univ.∀_:Univ.Univ. ∀meet:∀_:Univ.∀_:Univ.Univ. @@ -52,21 +52,21 @@ ntheorem prove_normal_axioms_3: ∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (meet (meet (join A B) (join C A)) A) A. ∀H2:∀A:Univ.∀B:Univ.eq Univ (join (meet A B) (meet B (join A B))) B. ∀H3:∀A:Univ.∀B:Univ.eq Univ (join (meet A A) (meet B (join A A))) A. -∀H4:∀A:Univ.∀B:Univ.eq Univ (join (meet A B) (meet A (join A B))) A.eq Univ (join a a) a +∀H4:∀A:Univ.∀B:Univ.eq Univ (join (meet A B) (meet A (join A B))) A.eq Univ (join a a) a) . -#Univ. -#A. -#B. -#C. -#a. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -nauto by H0,H1,H2,H3,H4; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +nauto by H0,H1,H2,H3,H4 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT091-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT091-1.ma index 396afaf7c..0dff618da 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT091-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT091-1.ma @@ -44,7 +44,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_normal_axioms_4: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. ∀a:Univ. ∀b:Univ. ∀join:∀_:Univ.∀_:Univ.Univ. @@ -53,22 +53,22 @@ ntheorem prove_normal_axioms_4: ∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (meet (meet (join A B) (join C A)) A) A. ∀H2:∀A:Univ.∀B:Univ.eq Univ (join (meet A B) (meet B (join A B))) B. ∀H3:∀A:Univ.∀B:Univ.eq Univ (join (meet A A) (meet B (join A A))) A. -∀H4:∀A:Univ.∀B:Univ.eq Univ (join (meet A B) (meet A (join A B))) A.eq Univ (join b a) (join a b) +∀H4:∀A:Univ.∀B:Univ.eq Univ (join (meet A B) (meet A (join A B))) A.eq Univ (join b a) (join a b)) . -#Univ. -#A. -#B. -#C. -#a. -#b. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -nauto by H0,H1,H2,H3,H4; +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +nauto by H0,H1,H2,H3,H4 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT092-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT092-1.ma index 1a6a9f384..cb5a9d0a8 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT092-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT092-1.ma @@ -44,24 +44,24 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_wal_axioms_1: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ. ∀a:Univ. ∀join:∀_:Univ.∀_:Univ.Univ. ∀meet:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet B D) (meet E B)) B)) (meet (join (meet B (meet (meet (join B D) (join E B)) B)) (meet F (join B (meet (meet (join B D) (join E B)) B)))) (join A (join (join (meet B D) (meet E B)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (meet a a) a +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet B D) (meet E B)) B)) (meet (join (meet B (meet (meet (join B D) (join E B)) B)) (meet F (join B (meet (meet (join B D) (join E B)) B)))) (join A (join (join (meet B D) (meet E B)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (meet a a) a) . -#Univ. -#A. -#B. -#C. -#D. -#E. -#F. -#a. -#join. -#meet. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#E ##. +#F ##. +#a ##. +#join ##. +#meet ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT093-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT093-1.ma index a296cb8c7..4220ad468 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT093-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT093-1.ma @@ -44,26 +44,26 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_wal_axioms_2: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ. ∀a:Univ. ∀b:Univ. ∀join:∀_:Univ.∀_:Univ.Univ. ∀meet:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet B D) (meet E B)) B)) (meet (join (meet B (meet (meet (join B D) (join E B)) B)) (meet F (join B (meet (meet (join B D) (join E B)) B)))) (join A (join (join (meet B D) (meet E B)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (meet b a) (meet a b) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet B D) (meet E B)) B)) (meet (join (meet B (meet (meet (join B D) (join E B)) B)) (meet F (join B (meet (meet (join B D) (join E B)) B)))) (join A (join (join (meet B D) (meet E B)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (meet b a) (meet a b)) . -#Univ. -#A. -#B. -#C. -#D. -#E. -#F. -#a. -#b. -#join. -#meet. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#E ##. +#F ##. +#a ##. +#b ##. +#join ##. +#meet ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT094-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT094-1.ma index 6e9e3bd0d..5bb57b139 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT094-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT094-1.ma @@ -44,24 +44,24 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_wal_axioms_3: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ. ∀a:Univ. ∀join:∀_:Univ.∀_:Univ.Univ. ∀meet:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet B D) (meet E B)) B)) (meet (join (meet B (meet (meet (join B D) (join E B)) B)) (meet F (join B (meet (meet (join B D) (join E B)) B)))) (join A (join (join (meet B D) (meet E B)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (join a a) a +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet B D) (meet E B)) B)) (meet (join (meet B (meet (meet (join B D) (join E B)) B)) (meet F (join B (meet (meet (join B D) (join E B)) B)))) (join A (join (join (meet B D) (meet E B)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (join a a) a) . -#Univ. -#A. -#B. -#C. -#D. -#E. -#F. -#a. -#join. -#meet. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#E ##. +#F ##. +#a ##. +#join ##. +#meet ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT095-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT095-1.ma index 05837e059..13163eb1f 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT095-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT095-1.ma @@ -44,26 +44,26 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_wal_axioms_4: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ. ∀a:Univ. ∀b:Univ. ∀join:∀_:Univ.∀_:Univ.Univ. ∀meet:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet B D) (meet E B)) B)) (meet (join (meet B (meet (meet (join B D) (join E B)) B)) (meet F (join B (meet (meet (join B D) (join E B)) B)))) (join A (join (join (meet B D) (meet E B)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (join b a) (join a b) +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet B D) (meet E B)) B)) (meet (join (meet B (meet (meet (join B D) (join E B)) B)) (meet F (join B (meet (meet (join B D) (join E B)) B)))) (join A (join (join (meet B D) (meet E B)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (join b a) (join a b)) . -#Univ. -#A. -#B. -#C. -#D. -#E. -#F. -#a. -#b. -#join. -#meet. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#E ##. +#F ##. +#a ##. +#b ##. +#join ##. +#meet ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT096-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT096-1.ma index 6ba41ced4..887e06deb 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT096-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT096-1.ma @@ -44,28 +44,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_wal_axioms_5: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀join:∀_:Univ.∀_:Univ.Univ. ∀meet:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet B D) (meet E B)) B)) (meet (join (meet B (meet (meet (join B D) (join E B)) B)) (meet F (join B (meet (meet (join B D) (join E B)) B)))) (join A (join (join (meet B D) (meet E B)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (meet (meet (join a b) (join c b)) b) b +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet B D) (meet E B)) B)) (meet (join (meet B (meet (meet (join B D) (join E B)) B)) (meet F (join B (meet (meet (join B D) (join E B)) B)))) (join A (join (join (meet B D) (meet E B)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (meet (meet (join a b) (join c b)) b) b) . -#Univ. -#A. -#B. -#C. -#D. -#E. -#F. -#a. -#b. -#c. -#join. -#meet. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#E ##. +#F ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT097-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT097-1.ma index ae1b28e7c..c25e16a9d 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT097-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT097-1.ma @@ -44,28 +44,28 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_wal_axioms_6: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀join:∀_:Univ.∀_:Univ.Univ. ∀meet:∀_:Univ.∀_:Univ.Univ. -∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet B D) (meet E B)) B)) (meet (join (meet B (meet (meet (join B D) (join E B)) B)) (meet F (join B (meet (meet (join B D) (join E B)) B)))) (join A (join (join (meet B D) (meet E B)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (join (join (meet a b) (meet c b)) b) b +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet B D) (meet E B)) B)) (meet (join (meet B (meet (meet (join B D) (join E B)) B)) (meet F (join B (meet (meet (join B D) (join E B)) B)))) (join A (join (join (meet B D) (meet E B)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (join (join (meet a b) (meet c b)) b) b) . -#Univ. -#A. -#B. -#C. -#D. -#E. -#F. -#a. -#b. -#c. -#join. -#meet. -#H0. -nauto by H0; +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#E ##. +#F ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT098-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT098-1.ma index 2c86ca36b..4353e1809 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT098-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT098-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H3: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -110,27 +110,27 @@ ntheorem prove_H3: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet c (join b (meet a (join c (meet a b))))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet c (join b (meet a (join c (meet a b)))))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT099-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT099-1.ma index d79633e10..d266668c7 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT099-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT099-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H2: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -110,27 +110,27 @@ ntheorem prove_H2: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet c (join (meet a (join b c)) (meet b c))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet c (join (meet a (join b c)) (meet b c)))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT100-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT100-1.ma index a867faa01..3828f8ee6 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT100-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT100-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H4: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -111,28 +111,28 @@ ntheorem prove_H4: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a (join c d)))) (meet a (join b (meet (join a (meet b d)) (join c d)))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a (join c d)))) (meet a (join b (meet (join a (meet b d)) (join c d))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT101-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT101-1.ma index aa01c4e7c..b8bda8e04 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT101-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT101-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H10: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -110,27 +110,27 @@ ntheorem prove_H10: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet c (join a (meet b c))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet c (join a (meet b c)))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT102-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT102-1.ma index 6758a72e8..2826950d9 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT102-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT102-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H4: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -111,28 +111,28 @@ ntheorem prove_H4: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a (join c d)))) (meet a (join b (meet (join a (meet b d)) (join c d)))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a (join c d)))) (meet a (join b (meet (join a (meet b d)) (join c d))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT103-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT103-1.ma index 4245d9191..ae7bfd994 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT103-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT103-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H6: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -110,27 +110,27 @@ ntheorem prove_H6: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join (meet a (join b (meet a c))) (meet c (join a b)))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join (meet a (join b (meet a c))) (meet c (join a b))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT104-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT104-1.ma index 10cd2bfb4..41dc3124b 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT104-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT104-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H3: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -110,27 +110,27 @@ ntheorem prove_H3: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet c (join b (meet a (join c (meet a b))))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet c (join b (meet a (join c (meet a b)))))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT105-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT105-1.ma index ec6729955..98a5ed09a 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT105-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT105-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H10: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -110,27 +110,27 @@ ntheorem prove_H10: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet c (join a (meet b c))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet c (join a (meet b c)))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT106-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT106-1.ma index 7a637bf4e..29fbb08f6 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT106-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT106-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H3: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -110,27 +110,27 @@ ntheorem prove_H3: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet c (join b (meet a (join c (meet a b))))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet c (join b (meet a (join c (meet a b)))))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT107-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT107-1.ma index 4916dc861..604edac4b 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT107-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT107-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H17: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -110,27 +110,27 @@ ntheorem prove_H17: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join (meet a b) (meet a c))) (meet a (join (meet b (join a (meet b c))) (meet c (join a b)))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join (meet a b) (meet a c))) (meet a (join (meet b (join a (meet b c))) (meet c (join a b))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT108-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT108-1.ma index 6d4644f0e..0695bc7ca 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT108-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT108-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H42: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -111,29 +111,29 @@ ntheorem prove_H42: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join a d)))) (meet a (join b (meet c (join b (join d (meet a c)))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join a d)))) (meet a (join b (meet c (join b (join d (meet a c))))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT109-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT109-1.ma index 7d78e688c..c961d5c1f 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT109-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT109-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H40: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -111,29 +111,29 @@ ntheorem prove_H40: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join a d)))) (meet a (join b (meet c (join d (meet c (join a b)))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join a d)))) (meet a (join b (meet c (join d (meet c (join a b))))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT110-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT110-1.ma index e66e7defa..9b52222ec 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT110-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT110-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H42: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -111,29 +111,29 @@ ntheorem prove_H42: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join a d)))) (meet a (join b (meet c (join b (join d (meet a c)))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join a d)))) (meet a (join b (meet c (join b (join d (meet a c))))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT111-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT111-1.ma index bc54b9b25..890f4e14a 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT111-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT111-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H40: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -111,29 +111,29 @@ ntheorem prove_H40: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join a d)))) (meet a (join b (meet c (join d (meet c (join a b)))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join a d)))) (meet a (join b (meet c (join d (meet c (join a b))))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT112-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT112-1.ma index 181f30b9c..2a6b6b2b4 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT112-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT112-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H42: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -111,29 +111,29 @@ ntheorem prove_H42: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join a d)))) (meet a (join b (meet c (join b (join d (meet a c)))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join a d)))) (meet a (join b (meet c (join b (join d (meet a c))))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT113-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT113-1.ma index cb4867c6e..c2341dd77 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT113-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT113-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H40: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -111,29 +111,29 @@ ntheorem prove_H40: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join a d)))) (meet a (join b (meet c (join d (meet c (join a b)))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join a d)))) (meet a (join b (meet c (join d (meet c (join a b))))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT114-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT114-1.ma index 9fab125b4..31a584c73 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT114-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT114-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H56: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -110,27 +110,27 @@ ntheorem prove_H56: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (join (meet a b) (meet a (join b c))) (meet a (join b (meet (join a b) (join c (meet a b))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (join (meet a b) (meet a (join b c))) (meet a (join b (meet (join a b) (join c (meet a b)))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT115-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT115-1.ma index 60fa4849e..5f7b70a83 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT115-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT115-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H59: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -111,28 +111,28 @@ ntheorem prove_H59: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (meet (join b c) (join b d))) (meet a (join b (meet (join b d) (join c (meet a b))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (meet (join b c) (join b d))) (meet a (join b (meet (join b d) (join c (meet a b)))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT116-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT116-1.ma index dfe1746e6..c00022747 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT116-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT116-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H60: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -111,28 +111,28 @@ ntheorem prove_H60: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (meet (join b c) (join b d))) (meet a (join b (meet (join b c) (join d (meet a b))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (meet (join b c) (join b d))) (meet a (join b (meet (join b c) (join d (meet a b)))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT117-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT117-1.ma index ff81b0ed1..d9a71dac6 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT117-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT117-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H69: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -110,28 +110,28 @@ ntheorem prove_H69: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b c)) (join (meet a (join c (meet a b))) (meet a (join b (meet a c)))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b c)) (join (meet a (join c (meet a b))) (meet a (join b (meet a c))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT118-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT118-1.ma index d3ff1c7c8..73d42d96e 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT118-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT118-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H69: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -110,28 +110,28 @@ ntheorem prove_H69: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b c)) (join (meet a (join c (meet a b))) (meet a (join b (meet a c)))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b c)) (join (meet a (join c (meet a b))) (meet a (join b (meet a c))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT119-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT119-1.ma index 413dd2728..12710e360 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT119-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT119-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H3: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -110,27 +110,27 @@ ntheorem prove_H3: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet c (join b (meet a (join c (meet a b))))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet c (join b (meet a (join c (meet a b)))))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT120-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT120-1.ma index 8f1286219..a36dc39a2 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT120-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT120-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H58: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -110,27 +110,27 @@ ntheorem prove_H58: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b c)) (meet a (join b (meet (join a b) (join c (meet a b))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b c)) (meet a (join b (meet (join a b) (join c (meet a b)))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT121-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT121-1.ma index 611839b47..095c62960 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT121-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT121-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H55: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -110,27 +110,27 @@ ntheorem prove_H55: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet b (join a c))) (join a (meet b (join c (meet a (join c b))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet b (join a c))) (join a (meet b (join c (meet a (join c b)))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT122-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT122-1.ma index e588eec64..9691d8e91 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT122-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT122-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H55: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -110,27 +110,27 @@ ntheorem prove_H55: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet b (join a c))) (join a (meet b (join c (meet a (join c b))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet b (join a c))) (join a (meet b (join c (meet a (join c b)))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT123-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT123-1.ma index 997aa8715..6d6b3edcc 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT123-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT123-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H55: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -110,27 +110,27 @@ ntheorem prove_H55: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet b (join a c))) (join a (meet b (join c (meet a (join c b))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet b (join a c))) (join a (meet b (join c (meet a (join c b)))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT124-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT124-1.ma index 0bfb6c5a8..93a6ea79b 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT124-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT124-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H69: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -110,28 +110,28 @@ ntheorem prove_H69: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b c)) (join (meet a (join c (meet a b))) (meet a (join b (meet a c)))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b c)) (join (meet a (join c (meet a b))) (meet a (join b (meet a c))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT125-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT125-1.ma index aa1b10538..3e764db23 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT125-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT125-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H69: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -110,28 +110,28 @@ ntheorem prove_H69: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b c)) (join (meet a (join c (meet a b))) (meet a (join b (meet a c)))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b c)) (join (meet a (join c (meet a b))) (meet a (join b (meet a c))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT126-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT126-1.ma index 8ad7a515e..edd8e894f 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT126-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT126-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H69: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -110,28 +110,28 @@ ntheorem prove_H69: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b c)) (join (meet a (join c (meet a b))) (meet a (join b (meet a c)))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b c)) (join (meet a (join c (meet a b))) (meet a (join b (meet a c))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT127-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT127-1.ma index ed0229f4c..d09420bc3 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT127-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT127-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H6: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -110,27 +110,27 @@ ntheorem prove_H6: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join (meet a (join b (meet a c))) (meet c (join a b)))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join (meet a (join b (meet a c))) (meet c (join a b))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT128-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT128-1.ma index 2c33fd8f1..7e7520c19 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT128-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT128-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H3: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -110,27 +110,27 @@ ntheorem prove_H3: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet c (join b (meet a (join c (meet a b))))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet c (join b (meet a (join c (meet a b)))))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT129-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT129-1.ma index bb2ab891b..d46dd31a6 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT129-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT129-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H10: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -110,27 +110,27 @@ ntheorem prove_H10: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet c (join a (meet b c))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet c (join a (meet b c)))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT130-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT130-1.ma index cb4904b0f..74ef4b441 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT130-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT130-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H39: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -111,28 +111,28 @@ ntheorem prove_H39: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join a d)))) (meet a (join b (meet c (join d (meet a c))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join a d)))) (meet a (join b (meet c (join d (meet a c)))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT131-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT131-1.ma index 0c1795354..609ee7962 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT131-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT131-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H42: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -111,28 +111,28 @@ ntheorem prove_H42: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join a d)))) (meet a (join b (meet c (join b (join d (meet a c)))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join a d)))) (meet a (join b (meet c (join b (join d (meet a c))))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT132-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT132-1.ma index ff9c9b942..0d51e23b4 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT132-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT132-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H42: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -111,28 +111,28 @@ ntheorem prove_H42: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join a d)))) (meet a (join b (meet c (join b (join d (meet a c)))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join a d)))) (meet a (join b (meet c (join b (join d (meet a c))))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT133-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT133-1.ma index b32350e1f..c02168b72 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT133-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT133-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H6_dual: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -110,27 +110,27 @@ ntheorem prove_H6_dual: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet b (join a c))) (join a (meet (join a (meet b (join a c))) (join c (meet a b)))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet b (join a c))) (join a (meet (join a (meet b (join a c))) (join c (meet a b))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT134-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT134-1.ma index e6b97b84a..584a6f4ed 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT134-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT134-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H22_dual: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -110,27 +110,27 @@ ntheorem prove_H22_dual: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet (join a b) (join a c)) (join a (meet (join b (meet c (join a b))) (join c (meet a b)))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet (join a b) (join a c)) (join a (meet (join b (meet c (join a b))) (join c (meet a b))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT135-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT135-1.ma index 90d9f2d29..5ba5acdb4 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT135-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT135-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H39_dual: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -111,28 +111,28 @@ ntheorem prove_H39_dual: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet b (join c (meet a d)))) (join a (meet b (join c (meet d (join a c))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet b (join c (meet a d)))) (join a (meet b (join c (meet d (join a c)))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT136-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT136-1.ma index 426b2ec4e..b0a91612a 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT136-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT136-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H39_dual: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -111,28 +111,28 @@ ntheorem prove_H39_dual: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet b (join c (meet a d)))) (join a (meet b (join c (meet d (join a c))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet b (join c (meet a d)))) (join a (meet b (join c (meet d (join a c)))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT137-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT137-1.ma index a83226e9e..4cb884983 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT137-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT137-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H40_dual: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -111,28 +111,28 @@ ntheorem prove_H40_dual: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet b (join c (meet a d)))) (join a (meet b (join c (meet d (join c (meet a b)))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet b (join c (meet a d)))) (join a (meet b (join c (meet d (join c (meet a b))))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT138-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT138-1.ma index e6d9158dd..792085727 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT138-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT138-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H6: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -108,27 +108,27 @@ ntheorem prove_H6: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join (meet a (join b (meet a c))) (meet c (join a b)))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join (meet a (join b (meet a c))) (meet c (join a b))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT139-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT139-1.ma index 34dd4d2a8..33d0b75ee 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT139-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT139-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H10: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -108,27 +108,27 @@ ntheorem prove_H10: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet c (join a (meet b c))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet c (join a (meet b c)))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT140-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT140-1.ma index 73bea8e2f..ba6402d83 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT140-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT140-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H2: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -108,27 +108,27 @@ ntheorem prove_H2: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet c (join (meet a (join b c)) (meet b c))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet c (join (meet a (join b c)) (meet b c)))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT141-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT141-1.ma index 2e5a78df6..f3eebea8d 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT141-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT141-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H6: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -108,27 +108,27 @@ ntheorem prove_H6: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join (meet a (join b (meet a c))) (meet c (join a b)))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join (meet a (join b (meet a c))) (meet c (join a b))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT142-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT142-1.ma index e194c7ae6..8e46c0bb6 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT142-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT142-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H6: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -108,27 +108,27 @@ ntheorem prove_H6: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join (meet a (join b (meet a c))) (meet c (join a b)))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join (meet a (join b (meet a c))) (meet c (join a b))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT143-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT143-1.ma index 1e5e1ce96..a4aee6248 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT143-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT143-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H15: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -108,27 +108,27 @@ ntheorem prove_H15: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join (meet a b) (meet a c))) (meet a (join (meet a b) (join (meet a c) (meet c (join a b))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join (meet a b) (meet a c))) (meet a (join (meet a b) (join (meet a c) (meet c (join a b)))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT144-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT144-1.ma index b02006e00..fde21c0af 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT144-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT144-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H2: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -108,28 +108,28 @@ ntheorem prove_H2: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet c (join (meet a (join b c)) (meet b c))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet c (join (meet a (join b c)) (meet b c)))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT145-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT145-1.ma index 36d50b21f..b2cf6562d 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT145-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT145-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H6: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -108,28 +108,28 @@ ntheorem prove_H6: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join (meet a (join b (meet a c))) (meet c (join a b)))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join (meet a (join b (meet a c))) (meet c (join a b))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT146-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT146-1.ma index c1ba8a246..d9cdee383 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT146-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT146-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H28: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -109,29 +109,29 @@ ntheorem prove_H28: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a (meet c d)))) (meet a (join b (meet c (meet d (join a (meet b d)))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a (meet c d)))) (meet a (join b (meet c (meet d (join a (meet b d))))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT147-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT147-1.ma index 6c7cb44b0..61078e985 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT147-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT147-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H45: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -109,29 +109,29 @@ ntheorem prove_H45: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (meet b (join c (meet a d)))) (meet a (meet b (join c (meet d (join a (meet b c)))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (meet b (join c (meet a d)))) (meet a (meet b (join c (meet d (join a (meet b c))))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT148-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT148-1.ma index b6ac365f5..d46dbce07 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT148-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT148-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H7: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -108,28 +108,28 @@ ntheorem prove_H7: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet a (join (meet a b) (meet c (join a b)))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet a (join (meet a b) (meet c (join a b))))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT149-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT149-1.ma index 898c1590b..8e1ca28f1 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT149-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT149-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H43: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -109,29 +109,29 @@ ntheorem prove_H43: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join b d)))) (meet a (join b (meet c (join d (meet a (join b d)))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join b d)))) (meet a (join b (meet c (join d (meet a (join b d))))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT150-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT150-1.ma index 3cbf00fd4..c0745aa10 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT150-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT150-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H40: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -109,29 +109,29 @@ ntheorem prove_H40: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join a d)))) (meet a (join b (meet c (join d (meet c (join a b)))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join a d)))) (meet a (join b (meet c (join d (meet c (join a b))))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT151-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT151-1.ma index 4b251d134..4c354f65c 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT151-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT151-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H42: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -109,29 +109,29 @@ ntheorem prove_H42: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join a d)))) (meet a (join b (meet c (join b (join d (meet a c)))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join a d)))) (meet a (join b (meet c (join b (join d (meet a c))))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT152-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT152-1.ma index 439c2e6b8..3e9afcf29 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT152-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT152-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H6: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -108,28 +108,28 @@ ntheorem prove_H6: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join (meet a (join b (meet a c))) (meet c (join a b)))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join (meet a (join b (meet a c))) (meet c (join a b))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT153-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT153-1.ma index a654c4224..aa3e4e671 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT153-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT153-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H7: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -108,28 +108,28 @@ ntheorem prove_H7: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet a (join (meet a b) (meet c (join a b)))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet a (join (meet a b) (meet c (join a b))))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT154-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT154-1.ma index b01f13c89..641737ff9 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT154-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT154-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H6: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -108,28 +108,28 @@ ntheorem prove_H6: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join (meet a (join b (meet a c))) (meet c (join a b)))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join (meet a (join b (meet a c))) (meet c (join a b))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT155-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT155-1.ma index 825191b91..882cadec9 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT155-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT155-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H2: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -108,28 +108,28 @@ ntheorem prove_H2: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet c (join (meet a (join b c)) (meet b c))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet c (join (meet a (join b c)) (meet b c)))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT156-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT156-1.ma index c475084d9..a9c8faa77 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT156-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT156-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H6: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -108,28 +108,28 @@ ntheorem prove_H6: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join (meet a (join b (meet a c))) (meet c (join a b)))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join (meet a (join b (meet a c))) (meet c (join a b))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT157-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT157-1.ma index 6787d55a8..bd391cdb1 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT157-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT157-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H2: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -108,28 +108,28 @@ ntheorem prove_H2: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet c (join (meet a (join b c)) (meet b c))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet c (join (meet a (join b c)) (meet b c)))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT158-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT158-1.ma index dbed63471..bf59b4877 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT158-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT158-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H49: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -109,29 +109,29 @@ ntheorem prove_H49: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join a d)))) (meet a (join b (join (meet a c) (meet c (join b d))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join a d)))) (meet a (join b (join (meet a c) (meet c (join b d)))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT159-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT159-1.ma index 8de3d38c0..401f2f495 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT159-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT159-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H7: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -108,28 +108,28 @@ ntheorem prove_H7: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet a (join (meet a b) (meet c (join a b)))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet a (join (meet a b) (meet c (join a b))))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT160-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT160-1.ma index 54353ac5b..35462d6af 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT160-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT160-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H51: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -109,29 +109,29 @@ ntheorem prove_H51: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join a d)))) (meet a (join b (join (meet a c) (meet c d)))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join a d)))) (meet a (join b (join (meet a c) (meet c d))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT161-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT161-1.ma index 89ea72031..4a95ac7f2 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT161-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT161-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H59: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -109,28 +109,28 @@ ntheorem prove_H59: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (meet (join b c) (join b d))) (meet a (join b (meet (join b d) (join c (meet a b))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (meet (join b c) (join b d))) (meet a (join b (meet (join b d) (join c (meet a b)))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT162-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT162-1.ma index 993517a9c..e2ba632c7 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT162-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT162-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H73: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -109,28 +109,28 @@ ntheorem prove_H73: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (meet b (join c d))) (meet a (meet b (join c (meet a (join d (meet b c)))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (meet b (join c d))) (meet a (meet b (join c (meet a (join d (meet b c))))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT163-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT163-1.ma index 5050af7aa..0d68d0a02 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT163-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT163-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H32: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -109,29 +109,29 @@ ntheorem prove_H32: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a (meet c d)))) (meet a (join b (meet c (join (meet a d) (meet b d))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a (meet c d)))) (meet a (join b (meet c (join (meet a d) (meet b d)))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT164-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT164-1.ma index 0f65de1f9..2363cdec1 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT164-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT164-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H6: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -108,28 +108,28 @@ ntheorem prove_H6: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join (meet a (join b (meet a c))) (meet c (join a b)))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join (meet a (join b (meet a c))) (meet c (join a b))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT165-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT165-1.ma index 8c775947f..7af7f34f7 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT165-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT165-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H77: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -109,29 +109,29 @@ ntheorem prove_H77: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join b d)))) (meet a (join b (meet c (join d (meet a (meet b c)))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join b d)))) (meet a (join b (meet c (join d (meet a (meet b c))))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT166-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT166-1.ma index d20e91cc1..3ce05128b 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT166-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT166-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H78: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -109,29 +109,29 @@ ntheorem prove_H78: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join b d)))) (meet a (join b (meet c (join d (meet b (join a d)))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join b d)))) (meet a (join b (meet c (join d (meet b (join a d))))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT167-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT167-1.ma index 5d60167f5..7aa6a73dc 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT167-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT167-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H77: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -109,29 +109,29 @@ ntheorem prove_H77: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join b d)))) (meet a (join b (meet c (join d (meet a (meet b c)))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join b d)))) (meet a (join b (meet c (join d (meet a (meet b c))))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT168-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT168-1.ma index 706a86446..a96473cdd 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT168-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT168-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H58: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -108,27 +108,27 @@ ntheorem prove_H58: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b c)) (meet a (join b (meet (join a b) (join c (meet a b))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b c)) (meet a (join b (meet (join a b) (join c (meet a b)))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT169-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT169-1.ma index f1847dedf..4de3ff368 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT169-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT169-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H58: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -108,27 +108,27 @@ ntheorem prove_H58: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b c)) (meet a (join b (meet (join a b) (join c (meet a b))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b c)) (meet a (join b (meet (join a b) (join c (meet a b)))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT170-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT170-1.ma index fbd731567..eb7930fc4 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT170-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT170-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H58: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -108,28 +108,28 @@ ntheorem prove_H58: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b c)) (meet a (join b (meet (join a b) (join c (meet a b))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b c)) (meet a (join b (meet (join a b) (join c (meet a b)))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT171-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT171-1.ma index f3a1f681c..486ae563d 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT171-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT171-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H6: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -108,27 +108,27 @@ ntheorem prove_H6: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join (meet a (join b (meet a c))) (meet c (join a b)))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join (meet a (join b (meet a c))) (meet c (join a b))))) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT172-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT172-1.ma index e7389871c..9eb7912e8 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT172-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT172-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H32: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -109,29 +109,29 @@ ntheorem prove_H32: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a (meet c d)))) (meet a (join b (meet c (join (meet a d) (meet b d))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a (meet c d)))) (meet a (join b (meet c (join (meet a d) (meet b d)))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT173-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT173-1.ma index e49dc5a49..54da5bba7 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT173-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT173-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H40: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -109,29 +109,29 @@ ntheorem prove_H40: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join a d)))) (meet a (join b (meet c (join d (meet c (join a b)))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join a d)))) (meet a (join b (meet c (join d (meet c (join a b))))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT174-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT174-1.ma index 86201e93a..6ee4979ea 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT174-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT174-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H6: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -108,28 +108,28 @@ ntheorem prove_H6: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join (meet a (join b (meet a c))) (meet c (join a b)))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join (meet a (join b (meet a c))) (meet c (join a b))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT175-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT175-1.ma index dca001bf9..f7d1d9164 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT175-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT175-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H32: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -109,29 +109,29 @@ ntheorem prove_H32: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a (meet c d)))) (meet a (join b (meet c (join (meet a d) (meet b d))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a (meet c d)))) (meet a (join b (meet c (join (meet a d) (meet b d)))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT176-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT176-1.ma index fe0bdf3ee..53fe02b67 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT176-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT176-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H42: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -109,29 +109,29 @@ ntheorem prove_H42: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join a d)))) (meet a (join b (meet c (join b (join d (meet a c)))))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join a d)))) (meet a (join b (meet c (join b (join d (meet a c))))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LAT177-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT177-1.ma index 183a6c44f..b068d5047 100644 --- a/helm/software/matita/contribs/ng_TPTP/LAT177-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LAT177-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_H6: - ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. @@ -108,28 +108,28 @@ ntheorem prove_H6: ∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. ∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. ∀H7:∀X:Univ.eq Univ (join X X) X. -∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join (meet a (join b (meet a c))) (meet c (join a b)))) +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join (meet a (join b (meet a c))) (meet c (join a b))))) . -#Univ. -#U. -#X. -#Y. -#Z. -#a. -#b. -#c. -#join. -#meet. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8; +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/LCL109-2.ma b/helm/software/matita/contribs/ng_TPTP/LCL109-2.ma index f57e46a3b..b5eb0e620 100644 --- a/helm/software/matita/contribs/ng_TPTP/LCL109-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/LCL109-2.ma @@ -118,7 +118,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_wajsberg_mv_4: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀implies:∀_:Univ.∀_:Univ.Univ. @@ -127,22 +127,22 @@ ntheorem prove_wajsberg_mv_4: ∀H0:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth. ∀H1:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X). ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth. -∀H3:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies (implies (implies a b) (implies b a)) (implies b a)) truth +∀H3:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies (implies (implies a b) (implies b a)) (implies b a)) truth) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#implies. -#not. -#truth. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#implies ##. +#not ##. +#truth ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LCL109-6.ma b/helm/software/matita/contribs/ng_TPTP/LCL109-6.ma index 3b9d1042c..922e6b2f1 100644 --- a/helm/software/matita/contribs/ng_TPTP/LCL109-6.ma +++ b/helm/software/matita/contribs/ng_TPTP/LCL109-6.ma @@ -112,7 +112,7 @@ include "logic/equality.ma". (* ----Include the definition of implies in terms of xor and and_star *) ntheorem prove_wajsberg_mv_4: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀and_star:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. @@ -133,34 +133,34 @@ ntheorem prove_wajsberg_mv_4: ∀H9:∀X:Univ.eq Univ (and_star X truth) X. ∀H10:∀X:Univ.eq Univ (xor X X) falsehood. ∀H11:∀X:Univ.eq Univ (xor X falsehood) X. -∀H12:∀X:Univ.eq Univ (not X) (xor X truth).eq Univ (implies (implies (implies a b) (implies b a)) (implies b a)) truth +∀H12:∀X:Univ.eq Univ (not X) (xor X truth).eq Univ (implies (implies (implies a b) (implies b a)) (implies b a)) truth) . -#Univ. -#X. -#Y. -#Z. -#a. -#and_star. -#b. -#falsehood. -#implies. -#not. -#truth. -#xor. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#and_star ##. +#b ##. +#falsehood ##. +#implies ##. +#not ##. +#truth ##. +#xor ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LCL110-2.ma b/helm/software/matita/contribs/ng_TPTP/LCL110-2.ma index c88434c1a..2ed79d1ed 100644 --- a/helm/software/matita/contribs/ng_TPTP/LCL110-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/LCL110-2.ma @@ -104,7 +104,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_mv_24: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀implies:∀_:Univ.∀_:Univ.Univ. ∀not:∀_:Univ.Univ. ∀truth:Univ. @@ -112,21 +112,21 @@ ntheorem prove_mv_24: ∀H0:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth. ∀H1:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X). ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth. -∀H3:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies (not (not x)) x) truth +∀H3:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies (not (not x)) x) truth) . -#Univ. -#X. -#Y. -#Z. -#implies. -#not. -#truth. -#x. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#implies ##. +#not ##. +#truth ##. +#x ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LCL111-2.ma b/helm/software/matita/contribs/ng_TPTP/LCL111-2.ma index 6614e5692..dbf4d4fee 100644 --- a/helm/software/matita/contribs/ng_TPTP/LCL111-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/LCL111-2.ma @@ -108,7 +108,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_mv_25: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀implies:∀_:Univ.∀_:Univ.Univ. ∀not:∀_:Univ.Univ. ∀truth:Univ. @@ -118,23 +118,23 @@ ntheorem prove_mv_25: ∀H0:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth. ∀H1:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X). ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth. -∀H3:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies (implies x y) (implies (implies z x) (implies z y))) truth +∀H3:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies (implies x y) (implies (implies z x) (implies z y))) truth) . -#Univ. -#X. -#Y. -#Z. -#implies. -#not. -#truth. -#x. -#y. -#z. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#implies ##. +#not ##. +#truth ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LCL112-2.ma b/helm/software/matita/contribs/ng_TPTP/LCL112-2.ma index b3e51dc22..2cb8cdb58 100644 --- a/helm/software/matita/contribs/ng_TPTP/LCL112-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/LCL112-2.ma @@ -106,7 +106,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_mv_29: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀implies:∀_:Univ.∀_:Univ.Univ. ∀not:∀_:Univ.Univ. ∀truth:Univ. @@ -114,21 +114,21 @@ ntheorem prove_mv_29: ∀H0:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth. ∀H1:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X). ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth. -∀H3:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies x (not (not x))) truth +∀H3:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies x (not (not x))) truth) . -#Univ. -#X. -#Y. -#Z. -#implies. -#not. -#truth. -#x. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#implies ##. +#not ##. +#truth ##. +#x ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LCL113-2.ma b/helm/software/matita/contribs/ng_TPTP/LCL113-2.ma index a47824980..332865e64 100644 --- a/helm/software/matita/contribs/ng_TPTP/LCL113-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/LCL113-2.ma @@ -102,7 +102,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_mv_33: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀implies:∀_:Univ.∀_:Univ.Univ. ∀not:∀_:Univ.Univ. ∀truth:Univ. @@ -111,22 +111,22 @@ ntheorem prove_mv_33: ∀H0:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth. ∀H1:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X). ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth. -∀H3:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies (implies (not x) y) (implies (not y) x)) truth +∀H3:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies (implies (not x) y) (implies (not y) x)) truth) . -#Univ. -#X. -#Y. -#Z. -#implies. -#not. -#truth. -#x. -#y. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#implies ##. +#not ##. +#truth ##. +#x ##. +#y ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LCL114-2.ma b/helm/software/matita/contribs/ng_TPTP/LCL114-2.ma index bdbe0632d..8dacec0d6 100644 --- a/helm/software/matita/contribs/ng_TPTP/LCL114-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/LCL114-2.ma @@ -104,7 +104,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_mv_36: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀implies:∀_:Univ.∀_:Univ.Univ. ∀not:∀_:Univ.Univ. ∀truth:Univ. @@ -113,22 +113,22 @@ ntheorem prove_mv_36: ∀H0:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth. ∀H1:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X). ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth. -∀H3:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies (implies x y) (implies (not y) (not x))) truth +∀H3:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies (implies x y) (implies (not y) (not x))) truth) . -#Univ. -#X. -#Y. -#Z. -#implies. -#not. -#truth. -#x. -#y. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#implies ##. +#not ##. +#truth ##. +#x ##. +#y ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LCL115-2.ma b/helm/software/matita/contribs/ng_TPTP/LCL115-2.ma index aa510f786..9792c03e6 100644 --- a/helm/software/matita/contribs/ng_TPTP/LCL115-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/LCL115-2.ma @@ -102,7 +102,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_mv_39: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀implies:∀_:Univ.∀_:Univ.Univ. @@ -111,22 +111,22 @@ ntheorem prove_mv_39: ∀H0:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth. ∀H1:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X). ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth. -∀H3:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies (not (implies a b)) (not b)) truth +∀H3:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies (not (implies a b)) (not b)) truth) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#implies. -#not. -#truth. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#implies ##. +#not ##. +#truth ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LCL116-2.ma b/helm/software/matita/contribs/ng_TPTP/LCL116-2.ma index 3c69aa5ed..72a39a0a2 100644 --- a/helm/software/matita/contribs/ng_TPTP/LCL116-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/LCL116-2.ma @@ -102,7 +102,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_mv_50: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀implies:∀_:Univ.∀_:Univ.Univ. @@ -111,22 +111,22 @@ ntheorem prove_mv_50: ∀H0:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth. ∀H1:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X). ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth. -∀H3:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies (not a) (implies b (not (implies b a)))) truth +∀H3:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies (not a) (implies b (not (implies b a)))) truth) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#implies. -#not. -#truth. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#implies ##. +#not ##. +#truth ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LCL132-1.ma b/helm/software/matita/contribs/ng_TPTP/LCL132-1.ma index e1f0217a2..98aa1600c 100644 --- a/helm/software/matita/contribs/ng_TPTP/LCL132-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LCL132-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_wajsberg_lemma: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀implies:∀_:Univ.∀_:Univ.Univ. ∀not:∀_:Univ.Univ. ∀truth:Univ. @@ -102,21 +102,21 @@ ntheorem prove_wajsberg_lemma: ∀H0:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth. ∀H1:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X). ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth. -∀H3:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies x x) truth +∀H3:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies x x) truth) . -#Univ. -#X. -#Y. -#Z. -#implies. -#not. -#truth. -#x. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#implies ##. +#not ##. +#truth ##. +#x ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LCL133-1.ma b/helm/software/matita/contribs/ng_TPTP/LCL133-1.ma index 2500bc7e8..62c6e618e 100644 --- a/helm/software/matita/contribs/ng_TPTP/LCL133-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LCL133-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_wajsberg_lemma: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀implies:∀_:Univ.∀_:Univ.Univ. ∀not:∀_:Univ.Univ. ∀truth:Univ. @@ -104,23 +104,23 @@ ntheorem prove_wajsberg_lemma: ∀H1:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth. ∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X). ∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth. -∀H4:∀X:Univ.eq Univ (implies truth X) X.eq Univ x y +∀H4:∀X:Univ.eq Univ (implies truth X) X.eq Univ x y) . -#Univ. -#X. -#Y. -#Z. -#implies. -#not. -#truth. -#x. -#y. -#H0. -#H1. -#H2. -#H3. -#H4. -nauto by H0,H1,H2,H3,H4; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#implies ##. +#not ##. +#truth ##. +#x ##. +#y ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +nauto by H0,H1,H2,H3,H4 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LCL134-1.ma b/helm/software/matita/contribs/ng_TPTP/LCL134-1.ma index 147aa33e4..6526b1a20 100644 --- a/helm/software/matita/contribs/ng_TPTP/LCL134-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LCL134-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_wajsberg_lemma: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀implies:∀_:Univ.∀_:Univ.Univ. ∀not:∀_:Univ.Univ. ∀truth:Univ. @@ -102,21 +102,21 @@ ntheorem prove_wajsberg_lemma: ∀H0:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth. ∀H1:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X). ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth. -∀H3:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies x truth) truth +∀H3:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies x truth) truth) . -#Univ. -#X. -#Y. -#Z. -#implies. -#not. -#truth. -#x. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#implies ##. +#not ##. +#truth ##. +#x ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LCL135-1.ma b/helm/software/matita/contribs/ng_TPTP/LCL135-1.ma index fe981588f..e4fb0659f 100644 --- a/helm/software/matita/contribs/ng_TPTP/LCL135-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LCL135-1.ma @@ -102,7 +102,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_wajsberg_lemma: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀implies:∀_:Univ.∀_:Univ.Univ. ∀not:∀_:Univ.Univ. ∀truth:Univ. @@ -111,22 +111,22 @@ ntheorem prove_wajsberg_lemma: ∀H0:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth. ∀H1:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X). ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth. -∀H3:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies x (implies y x)) truth +∀H3:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies x (implies y x)) truth) . -#Univ. -#X. -#Y. -#Z. -#implies. -#not. -#truth. -#x. -#y. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#implies ##. +#not ##. +#truth ##. +#x ##. +#y ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LCL136-1.ma b/helm/software/matita/contribs/ng_TPTP/LCL136-1.ma index fe9a999e5..b3e65946d 100644 --- a/helm/software/matita/contribs/ng_TPTP/LCL136-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LCL136-1.ma @@ -102,7 +102,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_wajsberg_lemma: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀implies:∀_:Univ.∀_:Univ.Univ. ∀not:∀_:Univ.Univ. ∀truth:Univ. @@ -113,24 +113,24 @@ ntheorem prove_wajsberg_lemma: ∀H1:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth. ∀H2:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X). ∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth. -∀H4:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies x z) truth +∀H4:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies x z) truth) . -#Univ. -#X. -#Y. -#Z. -#implies. -#not. -#truth. -#x. -#y. -#z. -#H0. -#H1. -#H2. -#H3. -#H4. -nauto by H0,H1,H2,H3,H4; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#implies ##. +#not ##. +#truth ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +nauto by H0,H1,H2,H3,H4 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LCL137-1.ma b/helm/software/matita/contribs/ng_TPTP/LCL137-1.ma index 444b18427..a7b67ea38 100644 --- a/helm/software/matita/contribs/ng_TPTP/LCL137-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LCL137-1.ma @@ -100,7 +100,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_wajsberg_lemma: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀implies:∀_:Univ.∀_:Univ.Univ. ∀not:∀_:Univ.Univ. ∀truth:Univ. @@ -110,23 +110,23 @@ ntheorem prove_wajsberg_lemma: ∀H0:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth. ∀H1:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X). ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth. -∀H3:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies (implies (implies x y) y) (implies (implies y z) (implies x z))) truth +∀H3:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies (implies (implies x y) y) (implies (implies y z) (implies x z))) truth) . -#Univ. -#X. -#Y. -#Z. -#implies. -#not. -#truth. -#x. -#y. -#z. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#implies ##. +#not ##. +#truth ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LCL138-1.ma b/helm/software/matita/contribs/ng_TPTP/LCL138-1.ma index fb355b977..19dadd806 100644 --- a/helm/software/matita/contribs/ng_TPTP/LCL138-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LCL138-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_wajsberg_lemma: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀implies:∀_:Univ.∀_:Univ.Univ. ∀not:∀_:Univ.Univ. ∀truth:Univ. @@ -104,23 +104,23 @@ ntheorem prove_wajsberg_lemma: ∀H0:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth. ∀H1:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X). ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth. -∀H3:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies x (implies y z)) (implies y (implies x z)) +∀H3:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies x (implies y z)) (implies y (implies x z))) . -#Univ. -#X. -#Y. -#Z. -#implies. -#not. -#truth. -#x. -#y. -#z. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#implies ##. +#not ##. +#truth ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LCL139-1.ma b/helm/software/matita/contribs/ng_TPTP/LCL139-1.ma index 88e37963f..7da3696ae 100644 --- a/helm/software/matita/contribs/ng_TPTP/LCL139-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LCL139-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_wajsberg_lemma: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀implies:∀_:Univ.∀_:Univ.Univ. ∀not:∀_:Univ.Univ. ∀truth:Univ. @@ -102,21 +102,21 @@ ntheorem prove_wajsberg_lemma: ∀H0:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth. ∀H1:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X). ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth. -∀H3:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies x (not truth)) (not x) +∀H3:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies x (not truth)) (not x)) . -#Univ. -#X. -#Y. -#Z. -#implies. -#not. -#truth. -#x. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#implies ##. +#not ##. +#truth ##. +#x ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LCL140-1.ma b/helm/software/matita/contribs/ng_TPTP/LCL140-1.ma index 5315fcc0b..ef4988ea5 100644 --- a/helm/software/matita/contribs/ng_TPTP/LCL140-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LCL140-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_wajsberg_lemma: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀implies:∀_:Univ.∀_:Univ.Univ. ∀not:∀_:Univ.Univ. ∀truth:Univ. @@ -102,21 +102,21 @@ ntheorem prove_wajsberg_lemma: ∀H0:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth. ∀H1:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X). ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth. -∀H3:∀X:Univ.eq Univ (implies truth X) X.eq Univ (not (not x)) x +∀H3:∀X:Univ.eq Univ (implies truth X) X.eq Univ (not (not x)) x) . -#Univ. -#X. -#Y. -#Z. -#implies. -#not. -#truth. -#x. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#implies ##. +#not ##. +#truth ##. +#x ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LCL141-1.ma b/helm/software/matita/contribs/ng_TPTP/LCL141-1.ma index f00e2f8f9..942202886 100644 --- a/helm/software/matita/contribs/ng_TPTP/LCL141-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LCL141-1.ma @@ -102,7 +102,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_wajsberg_lemma: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀implies:∀_:Univ.∀_:Univ.Univ. ∀not:∀_:Univ.Univ. ∀truth:Univ. @@ -111,22 +111,22 @@ ntheorem prove_wajsberg_lemma: ∀H0:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth. ∀H1:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X). ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth. -∀H3:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies (not x) (not y)) (implies y x) +∀H3:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies (not x) (not y)) (implies y x)) . -#Univ. -#X. -#Y. -#Z. -#implies. -#not. -#truth. -#x. -#y. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#implies ##. +#not ##. +#truth ##. +#x ##. +#y ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LCL153-1.ma b/helm/software/matita/contribs/ng_TPTP/LCL153-1.ma index cae6ddc88..e3bd93a9a 100644 --- a/helm/software/matita/contribs/ng_TPTP/LCL153-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LCL153-1.ma @@ -200,7 +200,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_alternative_wajsberg_axiom: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀myand:∀_:Univ.∀_:Univ.Univ. ∀and_star:∀_:Univ.∀_:Univ.Univ. ∀falsehood:Univ. @@ -225,38 +225,38 @@ ntheorem prove_alternative_wajsberg_axiom: ∀H12:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth. ∀H13:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X). ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth. -∀H15:∀X:Univ.eq Univ (implies truth X) X.eq Univ (not x) (xor x truth) +∀H15:∀X:Univ.eq Univ (implies truth X) X.eq Univ (not x) (xor x truth)) . -#Univ. -#X. -#Y. -#Z. -#and. -#and_star. -#falsehood. -#implies. -#not. -#or. -#truth. -#x. -#xor. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#and ##. +#and_star ##. +#falsehood ##. +#implies ##. +#not ##. +#or ##. +#truth ##. +#x ##. +#xor ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LCL154-1.ma b/helm/software/matita/contribs/ng_TPTP/LCL154-1.ma index 4c1cb6839..e91668662 100644 --- a/helm/software/matita/contribs/ng_TPTP/LCL154-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LCL154-1.ma @@ -200,7 +200,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_alternative_wajsberg_axiom: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀myand:∀_:Univ.∀_:Univ.Univ. ∀and_star:∀_:Univ.∀_:Univ.Univ. ∀falsehood:Univ. @@ -225,38 +225,38 @@ ntheorem prove_alternative_wajsberg_axiom: ∀H12:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth. ∀H13:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X). ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth. -∀H15:∀X:Univ.eq Univ (implies truth X) X.eq Univ (xor x falsehood) x +∀H15:∀X:Univ.eq Univ (implies truth X) X.eq Univ (xor x falsehood) x) . -#Univ. -#X. -#Y. -#Z. -#and. -#and_star. -#falsehood. -#implies. -#not. -#or. -#truth. -#x. -#xor. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#and ##. +#and_star ##. +#falsehood ##. +#implies ##. +#not ##. +#or ##. +#truth ##. +#x ##. +#xor ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LCL155-1.ma b/helm/software/matita/contribs/ng_TPTP/LCL155-1.ma index aef193031..4835947c6 100644 --- a/helm/software/matita/contribs/ng_TPTP/LCL155-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LCL155-1.ma @@ -200,7 +200,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_alternative_wajsberg_axiom: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀myand:∀_:Univ.∀_:Univ.Univ. ∀and_star:∀_:Univ.∀_:Univ.Univ. ∀falsehood:Univ. @@ -225,38 +225,38 @@ ntheorem prove_alternative_wajsberg_axiom: ∀H12:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth. ∀H13:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X). ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth. -∀H15:∀X:Univ.eq Univ (implies truth X) X.eq Univ (xor x x) falsehood +∀H15:∀X:Univ.eq Univ (implies truth X) X.eq Univ (xor x x) falsehood) . -#Univ. -#X. -#Y. -#Z. -#and. -#and_star. -#falsehood. -#implies. -#not. -#or. -#truth. -#x. -#xor. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#and ##. +#and_star ##. +#falsehood ##. +#implies ##. +#not ##. +#or ##. +#truth ##. +#x ##. +#xor ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LCL156-1.ma b/helm/software/matita/contribs/ng_TPTP/LCL156-1.ma index 007fe42d6..cc526399f 100644 --- a/helm/software/matita/contribs/ng_TPTP/LCL156-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LCL156-1.ma @@ -200,7 +200,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_alternative_wajsberg_axiom: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀myand:∀_:Univ.∀_:Univ.Univ. ∀and_star:∀_:Univ.∀_:Univ.Univ. ∀falsehood:Univ. @@ -225,38 +225,38 @@ ntheorem prove_alternative_wajsberg_axiom: ∀H12:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth. ∀H13:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X). ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth. -∀H15:∀X:Univ.eq Univ (implies truth X) X.eq Univ (and_star x truth) x +∀H15:∀X:Univ.eq Univ (implies truth X) X.eq Univ (and_star x truth) x) . -#Univ. -#X. -#Y. -#Z. -#and. -#and_star. -#falsehood. -#implies. -#not. -#or. -#truth. -#x. -#xor. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#and ##. +#and_star ##. +#falsehood ##. +#implies ##. +#not ##. +#or ##. +#truth ##. +#x ##. +#xor ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LCL157-1.ma b/helm/software/matita/contribs/ng_TPTP/LCL157-1.ma index e104ae5e2..0cf3cdc31 100644 --- a/helm/software/matita/contribs/ng_TPTP/LCL157-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LCL157-1.ma @@ -200,7 +200,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_alternative_wajsberg_axiom: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀myand:∀_:Univ.∀_:Univ.Univ. ∀and_star:∀_:Univ.∀_:Univ.Univ. ∀falsehood:Univ. @@ -225,38 +225,38 @@ ntheorem prove_alternative_wajsberg_axiom: ∀H12:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth. ∀H13:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X). ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth. -∀H15:∀X:Univ.eq Univ (implies truth X) X.eq Univ (and_star x falsehood) falsehood +∀H15:∀X:Univ.eq Univ (implies truth X) X.eq Univ (and_star x falsehood) falsehood) . -#Univ. -#X. -#Y. -#Z. -#and. -#and_star. -#falsehood. -#implies. -#not. -#or. -#truth. -#x. -#xor. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#and ##. +#and_star ##. +#falsehood ##. +#implies ##. +#not ##. +#or ##. +#truth ##. +#x ##. +#xor ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LCL158-1.ma b/helm/software/matita/contribs/ng_TPTP/LCL158-1.ma index 5a4d483ee..3cb01d959 100644 --- a/helm/software/matita/contribs/ng_TPTP/LCL158-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LCL158-1.ma @@ -200,7 +200,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_alternative_wajsberg_axiom: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀myand:∀_:Univ.∀_:Univ.Univ. ∀and_star:∀_:Univ.∀_:Univ.Univ. ∀falsehood:Univ. @@ -225,38 +225,38 @@ ntheorem prove_alternative_wajsberg_axiom: ∀H12:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth. ∀H13:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X). ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth. -∀H15:∀X:Univ.eq Univ (implies truth X) X.eq Univ (and_star (xor truth x) x) falsehood +∀H15:∀X:Univ.eq Univ (implies truth X) X.eq Univ (and_star (xor truth x) x) falsehood) . -#Univ. -#X. -#Y. -#Z. -#and. -#and_star. -#falsehood. -#implies. -#not. -#or. -#truth. -#x. -#xor. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#and ##. +#and_star ##. +#falsehood ##. +#implies ##. +#not ##. +#or ##. +#truth ##. +#x ##. +#xor ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LCL159-1.ma b/helm/software/matita/contribs/ng_TPTP/LCL159-1.ma index 32f437b2b..450621a83 100644 --- a/helm/software/matita/contribs/ng_TPTP/LCL159-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LCL159-1.ma @@ -200,7 +200,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_alternative_wajsberg_axiom: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀myand:∀_:Univ.∀_:Univ.Univ. ∀and_star:∀_:Univ.∀_:Univ.Univ. ∀falsehood:Univ. @@ -226,39 +226,39 @@ ntheorem prove_alternative_wajsberg_axiom: ∀H12:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth. ∀H13:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X). ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth. -∀H15:∀X:Univ.eq Univ (implies truth X) X.eq Univ (xor x (xor truth y)) (xor (xor x truth) y) +∀H15:∀X:Univ.eq Univ (implies truth X) X.eq Univ (xor x (xor truth y)) (xor (xor x truth) y)) . -#Univ. -#X. -#Y. -#Z. -#and. -#and_star. -#falsehood. -#implies. -#not. -#or. -#truth. -#x. -#xor. -#y. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#and ##. +#and_star ##. +#falsehood ##. +#implies ##. +#not ##. +#or ##. +#truth ##. +#x ##. +#xor ##. +#y ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LCL160-1.ma b/helm/software/matita/contribs/ng_TPTP/LCL160-1.ma index d1e3d9f22..0b2d3dd00 100644 --- a/helm/software/matita/contribs/ng_TPTP/LCL160-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LCL160-1.ma @@ -200,7 +200,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_alternative_wajsberg_axiom: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀myand:∀_:Univ.∀_:Univ.Univ. ∀and_star:∀_:Univ.∀_:Univ.Univ. ∀falsehood:Univ. @@ -226,39 +226,39 @@ ntheorem prove_alternative_wajsberg_axiom: ∀H12:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth. ∀H13:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X). ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth. -∀H15:∀X:Univ.eq Univ (implies truth X) X.eq Univ (and_star (xor (and_star (xor truth x) y) truth) y) (and_star (xor (and_star (xor truth y) x) truth) x) +∀H15:∀X:Univ.eq Univ (implies truth X) X.eq Univ (and_star (xor (and_star (xor truth x) y) truth) y) (and_star (xor (and_star (xor truth y) x) truth) x)) . -#Univ. -#X. -#Y. -#Z. -#and. -#and_star. -#falsehood. -#implies. -#not. -#or. -#truth. -#x. -#xor. -#y. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#and ##. +#and_star ##. +#falsehood ##. +#implies ##. +#not ##. +#or ##. +#truth ##. +#x ##. +#xor ##. +#y ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LCL161-1.ma b/helm/software/matita/contribs/ng_TPTP/LCL161-1.ma index ebac3edfb..25fc7efb7 100644 --- a/helm/software/matita/contribs/ng_TPTP/LCL161-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LCL161-1.ma @@ -108,7 +108,7 @@ include "logic/equality.ma". (* ----Include the definition of implies in terms of xor and and_star *) ntheorem prove_wajsberg_axiom: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀and_star:∀_:Univ.∀_:Univ.Univ. ∀falsehood:Univ. ∀implies:∀_:Univ.∀_:Univ.Univ. @@ -128,33 +128,33 @@ ntheorem prove_wajsberg_axiom: ∀H9:∀X:Univ.eq Univ (and_star X truth) X. ∀H10:∀X:Univ.eq Univ (xor X X) falsehood. ∀H11:∀X:Univ.eq Univ (xor X falsehood) X. -∀H12:∀X:Univ.eq Univ (not X) (xor X truth).eq Univ (implies truth x) x +∀H12:∀X:Univ.eq Univ (not X) (xor X truth).eq Univ (implies truth x) x) . -#Univ. -#X. -#Y. -#Z. -#and_star. -#falsehood. -#implies. -#not. -#truth. -#x. -#xor. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#and_star ##. +#falsehood ##. +#implies ##. +#not ##. +#truth ##. +#x ##. +#xor ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LCL162-1.ma b/helm/software/matita/contribs/ng_TPTP/LCL162-1.ma index b1d9a7a82..9959c93fe 100644 --- a/helm/software/matita/contribs/ng_TPTP/LCL162-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LCL162-1.ma @@ -108,7 +108,7 @@ include "logic/equality.ma". (* ----Include the definition of implies in terms of xor and and_star *) ntheorem prove_wajsberg_axiom: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀and_star:∀_:Univ.∀_:Univ.Univ. ∀falsehood:Univ. ∀implies:∀_:Univ.∀_:Univ.Univ. @@ -130,35 +130,35 @@ ntheorem prove_wajsberg_axiom: ∀H9:∀X:Univ.eq Univ (and_star X truth) X. ∀H10:∀X:Univ.eq Univ (xor X X) falsehood. ∀H11:∀X:Univ.eq Univ (xor X falsehood) X. -∀H12:∀X:Univ.eq Univ (not X) (xor X truth).eq Univ (implies (implies x y) (implies (implies y z) (implies x z))) truth +∀H12:∀X:Univ.eq Univ (not X) (xor X truth).eq Univ (implies (implies x y) (implies (implies y z) (implies x z))) truth) . -#Univ. -#X. -#Y. -#Z. -#and_star. -#falsehood. -#implies. -#not. -#truth. -#x. -#xor. -#y. -#z. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#and_star ##. +#falsehood ##. +#implies ##. +#not ##. +#truth ##. +#x ##. +#xor ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LCL163-1.ma b/helm/software/matita/contribs/ng_TPTP/LCL163-1.ma index ce259e5d1..03ab41df7 100644 --- a/helm/software/matita/contribs/ng_TPTP/LCL163-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LCL163-1.ma @@ -108,7 +108,7 @@ include "logic/equality.ma". (* ----Include the definition of implies in terms of xor and and_star *) ntheorem prove_wajsberg_axiom: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀and_star:∀_:Univ.∀_:Univ.Univ. ∀falsehood:Univ. ∀implies:∀_:Univ.∀_:Univ.Univ. @@ -129,34 +129,34 @@ ntheorem prove_wajsberg_axiom: ∀H9:∀X:Univ.eq Univ (and_star X truth) X. ∀H10:∀X:Univ.eq Univ (xor X X) falsehood. ∀H11:∀X:Univ.eq Univ (xor X falsehood) X. -∀H12:∀X:Univ.eq Univ (not X) (xor X truth).eq Univ (implies (implies x y) y) (implies (implies y x) x) +∀H12:∀X:Univ.eq Univ (not X) (xor X truth).eq Univ (implies (implies x y) y) (implies (implies y x) x)) . -#Univ. -#X. -#Y. -#Z. -#and_star. -#falsehood. -#implies. -#not. -#truth. -#x. -#xor. -#y. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#and_star ##. +#falsehood ##. +#implies ##. +#not ##. +#truth ##. +#x ##. +#xor ##. +#y ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LCL164-1.ma b/helm/software/matita/contribs/ng_TPTP/LCL164-1.ma index 71b33f190..4e908ed5c 100644 --- a/helm/software/matita/contribs/ng_TPTP/LCL164-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LCL164-1.ma @@ -108,7 +108,7 @@ include "logic/equality.ma". (* ----Include the definition of implies in terms of xor and and_star *) ntheorem prove_wajsberg_axiom: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀and_star:∀_:Univ.∀_:Univ.Univ. ∀falsehood:Univ. ∀implies:∀_:Univ.∀_:Univ.Univ. @@ -129,34 +129,34 @@ ntheorem prove_wajsberg_axiom: ∀H9:∀X:Univ.eq Univ (and_star X truth) X. ∀H10:∀X:Univ.eq Univ (xor X X) falsehood. ∀H11:∀X:Univ.eq Univ (xor X falsehood) X. -∀H12:∀X:Univ.eq Univ (not X) (xor X truth).eq Univ (implies (implies (not x) (not y)) (implies y x)) truth +∀H12:∀X:Univ.eq Univ (not X) (xor X truth).eq Univ (implies (implies (not x) (not y)) (implies y x)) truth) . -#Univ. -#X. -#Y. -#Z. -#and_star. -#falsehood. -#implies. -#not. -#truth. -#x. -#xor. -#y. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#and_star ##. +#falsehood ##. +#implies ##. +#not ##. +#truth ##. +#x ##. +#xor ##. +#y ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LCL165-1.ma b/helm/software/matita/contribs/ng_TPTP/LCL165-1.ma index 1acd6646d..7c2d610d9 100644 --- a/helm/software/matita/contribs/ng_TPTP/LCL165-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LCL165-1.ma @@ -146,7 +146,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_wajsberg_ntheorem: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀myand:∀_:Univ.∀_:Univ.Univ. ∀implies:∀_:Univ.∀_:Univ.Univ. ∀not:∀_:Univ.Univ. @@ -162,29 +162,29 @@ ntheorem prove_wajsberg_ntheorem: ∀H6:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth. ∀H7:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X). ∀H8:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth. -∀H9:∀X:Univ.eq Univ (implies truth X) X.eq Univ (not (or (myand x (or x x)) (myand x x))) (myand (not x) (or (or (not x) (not x)) (myand (not x) (not x)))) +∀H9:∀X:Univ.eq Univ (implies truth X) X.eq Univ (not (or (myand x (or x x)) (myand x x))) (myand (not x) (or (or (not x) (not x)) (myand (not x) (not x))))) . -#Univ. -#X. -#Y. -#Z. -#and. -#implies. -#not. -#or. -#truth. -#x. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#and ##. +#implies ##. +#not ##. +#or ##. +#truth ##. +#x ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LDA001-1.ma b/helm/software/matita/contribs/ng_TPTP/LDA001-1.ma index 409b5d3fc..317d8fb64 100644 --- a/helm/software/matita/contribs/ng_TPTP/LDA001-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LDA001-1.ma @@ -46,7 +46,7 @@ include "logic/equality.ma". (* ----3*2*U = U*U*U *) ntheorem prove_equation: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀f:∀_:Univ.∀_:Univ.Univ. ∀n1:Univ. ∀n2:Univ. @@ -55,22 +55,22 @@ ntheorem prove_equation: ∀H0:eq Univ u (f n2 n2). ∀H1:eq Univ n3 (f n2 n1). ∀H2:eq Univ n2 (f n1 n1). -∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (f X (f Y Z)) (f (f X Y) (f X Z)).eq Univ (f (f n3 n2) u) (f (f u u) u) +∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (f X (f Y Z)) (f (f X Y) (f X Z)).eq Univ (f (f n3 n2) u) (f (f u u) u)) . -#Univ. -#X. -#Y. -#Z. -#f. -#n1. -#n2. -#n3. -#u. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#f ##. +#n1 ##. +#n2 ##. +#n3 ##. +#u ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LDA002-1.ma b/helm/software/matita/contribs/ng_TPTP/LDA002-1.ma index d715ed708..f99623f54 100644 --- a/helm/software/matita/contribs/ng_TPTP/LDA002-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/LDA002-1.ma @@ -46,7 +46,7 @@ include "logic/equality.ma". (* ----3*2*U2*(UU*UU) = U1*U3*(uU*UU) *) ntheorem prove_equation: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀f:∀_:Univ.∀_:Univ.Univ. @@ -69,36 +69,36 @@ ntheorem prove_equation: ∀H7:eq Univ u (f n2 n2). ∀H8:eq Univ n3 (f n2 n1). ∀H9:eq Univ n2 (f n1 n1). -∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (f X (f Y Z)) (f (f X Y) (f X Z)).eq Univ (f a v) (f b v) +∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (f X (f Y Z)) (f (f X Y) (f X Z)).eq Univ (f a v) (f b v)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#f. -#n1. -#n2. -#n3. -#u. -#u1. -#u2. -#u3. -#uu. -#v. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#f ##. +#n1 ##. +#n2 ##. +#n3 ##. +#u ##. +#u1 ##. +#u2 ##. +#u3 ##. +#uu ##. +#v ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/LDA007-3.ma b/helm/software/matita/contribs/ng_TPTP/LDA007-3.ma index 57ad1fac3..d7d4ed63f 100644 --- a/helm/software/matita/contribs/ng_TPTP/LDA007-3.ma +++ b/helm/software/matita/contribs/ng_TPTP/LDA007-3.ma @@ -50,7 +50,7 @@ include "logic/equality.ma". (* ----t(tsk) = tt(ts)(tk), where k=crit(t) *) ntheorem prove_equation: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀f:∀_:Univ.∀_:Univ.Univ. ∀k:Univ. ∀s:Univ. @@ -65,28 +65,28 @@ ntheorem prove_equation: ∀H2:eq Univ tt_ts (f tt ts). ∀H3:eq Univ ts (f t s). ∀H4:eq Univ tt (f t t). -∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (f X (f Y Z)) (f (f X Y) (f X Z)).eq Univ (f t tsk) (f tt_ts tk) +∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (f X (f Y Z)) (f (f X Y) (f X Z)).eq Univ (f t tsk) (f tt_ts tk)) . -#Univ. -#X. -#Y. -#Z. -#f. -#k. -#s. -#t. -#tk. -#ts. -#tsk. -#tt. -#tt_ts. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -nauto by H0,H1,H2,H3,H4,H5; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#f ##. +#k ##. +#s ##. +#t ##. +#tk ##. +#ts ##. +#tsk ##. +#tt ##. +#tt_ts ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +nauto by H0,H1,H2,H3,H4,H5 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG007-4.ma b/helm/software/matita/contribs/ng_TPTP/RNG007-4.ma index aeb930e1d..14452aa99 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG007-4.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG007-4.ma @@ -118,7 +118,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_inverse: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -138,33 +138,33 @@ ntheorem prove_inverse: ∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)). ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)). ∀H13:∀X:Univ.eq Univ (add (additive_inverse X) X) additive_identity. -∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (add a a) additive_identity +∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (add a a) additive_identity) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#additive_inverse. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG008-3.ma b/helm/software/matita/contribs/ng_TPTP/RNG008-3.ma index 2ec7c3393..d943757e0 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG008-3.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG008-3.ma @@ -122,7 +122,7 @@ include "logic/equality.ma". (* ----Right identity and inverse are dependent lemmas *) ntheorem prove_commutativity: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -147,38 +147,38 @@ ntheorem prove_commutativity: ∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)). ∀H15:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)). ∀H16:∀X:Univ.eq Univ (add (additive_inverse X) X) additive_identity. -∀H17:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply b a) c +∀H17:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply b a) c) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#additive_inverse. -#b. -#c. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#b ##. +#c ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG008-4.ma b/helm/software/matita/contribs/ng_TPTP/RNG008-4.ma index 1f635f79d..1132ca8e8 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG008-4.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG008-4.ma @@ -120,7 +120,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_commutativity: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -143,36 +143,36 @@ ntheorem prove_commutativity: ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)). ∀H13:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)). ∀H14:∀X:Univ.eq Univ (add (additive_inverse X) X) additive_identity. -∀H15:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply b a) c +∀H15:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply b a) c) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#additive_inverse. -#b. -#c. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#b ##. +#c ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG008-7.ma b/helm/software/matita/contribs/ng_TPTP/RNG008-7.ma index ea1b11082..97ad08d77 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG008-7.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG008-7.ma @@ -114,7 +114,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_commutativity: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -132,31 +132,31 @@ ntheorem prove_commutativity: ∀H7:∀X:Univ.eq Univ (add X (additive_inverse X)) additive_identity. ∀H8:∀X:Univ.eq Univ (add (additive_inverse X) X) additive_identity. ∀H9:∀X:Univ.eq Univ (add X additive_identity) X. -∀H10:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply b a) c +∀H10:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply b a) c) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#additive_inverse. -#b. -#c. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#b ##. +#c ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG009-5.ma b/helm/software/matita/contribs/ng_TPTP/RNG009-5.ma index c54e35210..b9634bf40 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG009-5.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG009-5.ma @@ -68,7 +68,7 @@ include "logic/equality.ma". (* ----Associativity of product *) ntheorem prove_commutativity: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -82,27 +82,27 @@ ntheorem prove_commutativity: ∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)). ∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)). ∀H6:∀X:Univ.eq Univ (add X (additive_inverse X)) additive_identity. -∀H7:∀X:Univ.eq Univ (add X additive_identity) X.eq Univ (multiply a b) (multiply b a) +∀H7:∀X:Univ.eq Univ (add X additive_identity) X.eq Univ (multiply a b) (multiply b a)) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#additive_inverse. -#b. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -nauto by H0,H1,H2,H3,H4,H5,H6,H7; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#b ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG009-7.ma b/helm/software/matita/contribs/ng_TPTP/RNG009-7.ma index 022e4e944..6fbab396e 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG009-7.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG009-7.ma @@ -108,7 +108,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_commutativity: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -126,31 +126,31 @@ ntheorem prove_commutativity: ∀H7:∀X:Univ.eq Univ (add X (additive_inverse X)) additive_identity. ∀H8:∀X:Univ.eq Univ (add (additive_inverse X) X) additive_identity. ∀H9:∀X:Univ.eq Univ (add X additive_identity) X. -∀H10:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply b a) c +∀H10:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply b a) c) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#additive_inverse. -#b. -#c. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#b ##. +#c ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG010-5.ma b/helm/software/matita/contribs/ng_TPTP/RNG010-5.ma index 20f0cbf02..53e71afc1 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG010-5.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG010-5.ma @@ -110,7 +110,7 @@ include "logic/equality.ma". (* ----Middle Moufang *) ntheorem prove_skew_symmetry: - ∀Univ:Type.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -147,51 +147,51 @@ ntheorem prove_skew_symmetry: ∀H22:∀X:Univ.eq Univ (add additive_identity X) X. ∀H23:∀X:Univ.eq Univ (add X additive_identity) X. ∀H24:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)). -∀H25:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (s a b c d) (additive_inverse (s b a c d)) +∀H25:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (s a b c d) (additive_inverse (s b a c d))) . -#Univ. -#W. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#additive_inverse. -#associator. -#b. -#c. -#commutator. -#d. -#multiply. -#s. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -#H18. -#H19. -#H20. -#H21. -#H22. -#H23. -#H24. -#H25. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21,H22,H23,H24,H25; +#Univ ##. +#W ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#b ##. +#c ##. +#commutator ##. +#d ##. +#multiply ##. +#s ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +#H19 ##. +#H20 ##. +#H21 ##. +#H22 ##. +#H23 ##. +#H24 ##. +#H25 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21,H22,H23,H24,H25 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG010-6.ma b/helm/software/matita/contribs/ng_TPTP/RNG010-6.ma index c0ca77876..6990c3dff 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG010-6.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG010-6.ma @@ -130,7 +130,7 @@ include "logic/equality.ma". (* ----Left Moufang *) ntheorem prove_skew_symmetry: - ∀Univ:Type.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -160,44 +160,44 @@ ntheorem prove_skew_symmetry: ∀H15:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H16:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H17:∀X:Univ.eq Univ (add X additive_identity) X. -∀H18:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (s a b c d) (additive_inverse (s b a c d)) +∀H18:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (s a b c d) (additive_inverse (s b a c d))) . -#Univ. -#W. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#additive_inverse. -#associator. -#b. -#c. -#commutator. -#d. -#multiply. -#s. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -#H18. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18; +#Univ ##. +#W ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#b ##. +#c ##. +#commutator ##. +#d ##. +#multiply ##. +#s ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG010-7.ma b/helm/software/matita/contribs/ng_TPTP/RNG010-7.ma index 855e088e5..33af94213 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG010-7.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG010-7.ma @@ -132,7 +132,7 @@ include "logic/equality.ma". (* ----Left Moufang *) ntheorem prove_skew_symmetry: - ∀Univ:Type.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -169,51 +169,51 @@ ntheorem prove_skew_symmetry: ∀H22:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H23:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H24:∀X:Univ.eq Univ (add X additive_identity) X. -∀H25:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (s a b c d) (additive_inverse (s b a c d)) +∀H25:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (s a b c d) (additive_inverse (s b a c d))) . -#Univ. -#W. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#additive_inverse. -#associator. -#b. -#c. -#commutator. -#d. -#multiply. -#s. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -#H18. -#H19. -#H20. -#H21. -#H22. -#H23. -#H24. -#H25. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21,H22,H23,H24,H25; +#Univ ##. +#W ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#b ##. +#c ##. +#commutator ##. +#d ##. +#multiply ##. +#s ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +#H19 ##. +#H20 ##. +#H21 ##. +#H22 ##. +#H23 ##. +#H24 ##. +#H25 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21,H22,H23,H24,H25 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG011-5.ma b/helm/software/matita/contribs/ng_TPTP/RNG011-5.ma index c64870849..967c509b4 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG011-5.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG011-5.ma @@ -86,7 +86,7 @@ include "logic/equality.ma". (* ----Middle associator identity *) ntheorem prove_equality: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -115,42 +115,42 @@ ntheorem prove_equality: ∀H17:∀X:Univ.eq Univ (add additive_identity X) X. ∀H18:∀X:Univ.eq Univ (add X additive_identity) X. ∀H19:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)). -∀H20:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply (multiply (associator a a b) a) (associator a a b)) additive_identity +∀H20:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply (multiply (associator a a b) a) (associator a a b)) additive_identity) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#additive_inverse. -#associator. -#b. -#commutator. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -#H18. -#H19. -#H20. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#b ##. +#commutator ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +#H19 ##. +#H20 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG012-6.ma b/helm/software/matita/contribs/ng_TPTP/RNG012-6.ma index 0966476be..418d692ac 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG012-6.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG012-6.ma @@ -110,7 +110,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_equation: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -133,36 +133,36 @@ ntheorem prove_equation: ∀H11:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H12:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H13:∀X:Univ.eq Univ (add X additive_identity) X. -∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply (additive_inverse a) (additive_inverse b)) (multiply a b) +∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply (additive_inverse a) (additive_inverse b)) (multiply a b)) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#additive_inverse. -#associator. -#b. -#commutator. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#b ##. +#commutator ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG013-6.ma b/helm/software/matita/contribs/ng_TPTP/RNG013-6.ma index 01cbc74c0..9115cb2ec 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG013-6.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG013-6.ma @@ -110,7 +110,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_equation: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -133,36 +133,36 @@ ntheorem prove_equation: ∀H11:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H12:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H13:∀X:Univ.eq Univ (add X additive_identity) X. -∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply (additive_inverse a) b) (additive_inverse (multiply a b)) +∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply (additive_inverse a) b) (additive_inverse (multiply a b))) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#additive_inverse. -#associator. -#b. -#commutator. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#b ##. +#commutator ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG014-6.ma b/helm/software/matita/contribs/ng_TPTP/RNG014-6.ma index 8567d448b..900a70dd3 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG014-6.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG014-6.ma @@ -110,7 +110,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_equation: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -133,36 +133,36 @@ ntheorem prove_equation: ∀H11:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H12:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H13:∀X:Univ.eq Univ (add X additive_identity) X. -∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply a (additive_inverse b)) (additive_inverse (multiply a b)) +∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply a (additive_inverse b)) (additive_inverse (multiply a b))) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#additive_inverse. -#associator. -#b. -#commutator. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#b ##. +#commutator ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG015-6.ma b/helm/software/matita/contribs/ng_TPTP/RNG015-6.ma index c9c45cf75..28af5b7b7 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG015-6.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG015-6.ma @@ -110,7 +110,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_distributivity: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -134,37 +134,37 @@ ntheorem prove_distributivity: ∀H11:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H12:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H13:∀X:Univ.eq Univ (add X additive_identity) X. -∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply x (add y (additive_inverse z))) (add (multiply x y) (additive_inverse (multiply x z))) +∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply x (add y (additive_inverse z))) (add (multiply x y) (additive_inverse (multiply x z)))) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#multiply. -#x. -#y. -#z. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG016-6.ma b/helm/software/matita/contribs/ng_TPTP/RNG016-6.ma index 59a382195..c13b880e9 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG016-6.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG016-6.ma @@ -110,7 +110,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_distributivity: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -134,37 +134,37 @@ ntheorem prove_distributivity: ∀H11:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H12:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H13:∀X:Univ.eq Univ (add X additive_identity) X. -∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply (add x (additive_inverse y)) z) (add (multiply x z) (additive_inverse (multiply y z))) +∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply (add x (additive_inverse y)) z) (add (multiply x z) (additive_inverse (multiply y z)))) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#multiply. -#x. -#y. -#z. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG017-6.ma b/helm/software/matita/contribs/ng_TPTP/RNG017-6.ma index fac210f4d..a7020501e 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG017-6.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG017-6.ma @@ -110,7 +110,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_distributivity: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -134,37 +134,37 @@ ntheorem prove_distributivity: ∀H11:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H12:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H13:∀X:Univ.eq Univ (add X additive_identity) X. -∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply (additive_inverse x) (add y z)) (add (additive_inverse (multiply x y)) (additive_inverse (multiply x z))) +∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply (additive_inverse x) (add y z)) (add (additive_inverse (multiply x y)) (additive_inverse (multiply x z)))) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#multiply. -#x. -#y. -#z. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG018-6.ma b/helm/software/matita/contribs/ng_TPTP/RNG018-6.ma index ee1d8d0e3..d4d23ee7e 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG018-6.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG018-6.ma @@ -110,7 +110,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_distributivity: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -134,37 +134,37 @@ ntheorem prove_distributivity: ∀H11:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H12:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H13:∀X:Univ.eq Univ (add X additive_identity) X. -∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply (add x y) (additive_inverse z)) (add (additive_inverse (multiply x z)) (additive_inverse (multiply y z))) +∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply (add x y) (additive_inverse z)) (add (additive_inverse (multiply x z)) (additive_inverse (multiply y z)))) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#multiply. -#x. -#y. -#z. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG019-6.ma b/helm/software/matita/contribs/ng_TPTP/RNG019-6.ma index c85dd9ef4..4fe2198a2 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG019-6.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG019-6.ma @@ -114,7 +114,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_linearised_form1: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -139,38 +139,38 @@ ntheorem prove_linearised_form1: ∀H11:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H12:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H13:∀X:Univ.eq Univ (add X additive_identity) X. -∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x y (add u v)) (add (associator x y u) (associator x y v)) +∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x y (add u v)) (add (associator x y u) (associator x y v))) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#multiply. -#u. -#v. -#x. -#y. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#u ##. +#v ##. +#x ##. +#y ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG019-7.ma b/helm/software/matita/contribs/ng_TPTP/RNG019-7.ma index d41fa2484..eae788ee4 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG019-7.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG019-7.ma @@ -116,7 +116,7 @@ include "logic/equality.ma". (* ----The next 7 clause are extra lemmas which Stevens found useful *) ntheorem prove_linearised_form1: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -148,45 +148,45 @@ ntheorem prove_linearised_form1: ∀H18:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H19:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H20:∀X:Univ.eq Univ (add X additive_identity) X. -∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x y (add u v)) (add (associator x y u) (associator x y v)) +∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x y (add u v)) (add (associator x y u) (associator x y v))) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#multiply. -#u. -#v. -#x. -#y. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -#H18. -#H19. -#H20. -#H21. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#u ##. +#v ##. +#x ##. +#y ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +#H19 ##. +#H20 ##. +#H21 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG020-6.ma b/helm/software/matita/contribs/ng_TPTP/RNG020-6.ma index f4c1a0f95..cfc07d85b 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG020-6.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG020-6.ma @@ -114,7 +114,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_linearised_form2: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -139,38 +139,38 @@ ntheorem prove_linearised_form2: ∀H11:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H12:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H13:∀X:Univ.eq Univ (add X additive_identity) X. -∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x (add u v) y) (add (associator x u y) (associator x v y)) +∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x (add u v) y) (add (associator x u y) (associator x v y))) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#multiply. -#u. -#v. -#x. -#y. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#u ##. +#v ##. +#x ##. +#y ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG020-7.ma b/helm/software/matita/contribs/ng_TPTP/RNG020-7.ma index 1159fafc9..2f9b9919c 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG020-7.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG020-7.ma @@ -116,7 +116,7 @@ include "logic/equality.ma". (* ----The next 7 clause are extra lemmas which Stevens found useful *) ntheorem prove_linearised_form2: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -148,45 +148,45 @@ ntheorem prove_linearised_form2: ∀H18:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H19:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H20:∀X:Univ.eq Univ (add X additive_identity) X. -∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x (add u v) y) (add (associator x u y) (associator x v y)) +∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x (add u v) y) (add (associator x u y) (associator x v y))) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#multiply. -#u. -#v. -#x. -#y. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -#H18. -#H19. -#H20. -#H21. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#u ##. +#v ##. +#x ##. +#y ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +#H19 ##. +#H20 ##. +#H21 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG021-6.ma b/helm/software/matita/contribs/ng_TPTP/RNG021-6.ma index 3879ebacd..d75d067cc 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG021-6.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG021-6.ma @@ -114,7 +114,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_linearised_form3: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -139,38 +139,38 @@ ntheorem prove_linearised_form3: ∀H11:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H12:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H13:∀X:Univ.eq Univ (add X additive_identity) X. -∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator (add u v) x y) (add (associator u x y) (associator v x y)) +∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator (add u v) x y) (add (associator u x y) (associator v x y))) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#multiply. -#u. -#v. -#x. -#y. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#u ##. +#v ##. +#x ##. +#y ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG021-7.ma b/helm/software/matita/contribs/ng_TPTP/RNG021-7.ma index f0dbb6042..1b5d524dc 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG021-7.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG021-7.ma @@ -116,7 +116,7 @@ include "logic/equality.ma". (* ----The next 7 clause are extra lemmas which Stevens found useful *) ntheorem prove_linearised_form3: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -148,45 +148,45 @@ ntheorem prove_linearised_form3: ∀H18:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H19:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H20:∀X:Univ.eq Univ (add X additive_identity) X. -∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator (add u v) x y) (add (associator u x y) (associator v x y)) +∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator (add u v) x y) (add (associator u x y) (associator v x y))) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#multiply. -#u. -#v. -#x. -#y. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -#H18. -#H19. -#H20. -#H21. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#u ##. +#v ##. +#x ##. +#y ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +#H19 ##. +#H20 ##. +#H21 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG023-6.ma b/helm/software/matita/contribs/ng_TPTP/RNG023-6.ma index 2d79a7ef8..f49becb37 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG023-6.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG023-6.ma @@ -114,7 +114,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_left_alternative: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -137,36 +137,36 @@ ntheorem prove_left_alternative: ∀H11:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H12:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H13:∀X:Univ.eq Univ (add X additive_identity) X. -∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x x y) additive_identity +∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x x y) additive_identity) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#multiply. -#x. -#y. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#x ##. +#y ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG023-7.ma b/helm/software/matita/contribs/ng_TPTP/RNG023-7.ma index 50ad5010d..20e7ad8d9 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG023-7.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG023-7.ma @@ -116,7 +116,7 @@ include "logic/equality.ma". (* ----The next 7 clause are extra lemmas which Stevens found useful *) ntheorem prove_left_alternative: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -146,43 +146,43 @@ ntheorem prove_left_alternative: ∀H18:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H19:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H20:∀X:Univ.eq Univ (add X additive_identity) X. -∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x x y) additive_identity +∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x x y) additive_identity) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#multiply. -#x. -#y. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -#H18. -#H19. -#H20. -#H21. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#x ##. +#y ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +#H19 ##. +#H20 ##. +#H21 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG024-6.ma b/helm/software/matita/contribs/ng_TPTP/RNG024-6.ma index 62f9e1acf..21016c6d9 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG024-6.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG024-6.ma @@ -114,7 +114,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_right_alternative: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -137,36 +137,36 @@ ntheorem prove_right_alternative: ∀H11:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H12:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H13:∀X:Univ.eq Univ (add X additive_identity) X. -∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x y y) additive_identity +∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x y y) additive_identity) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#multiply. -#x. -#y. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#x ##. +#y ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG024-7.ma b/helm/software/matita/contribs/ng_TPTP/RNG024-7.ma index cd32b61ea..44f5f92a6 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG024-7.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG024-7.ma @@ -116,7 +116,7 @@ include "logic/equality.ma". (* ----The next 7 clause are extra lemmas which Stevens found useful *) ntheorem prove_right_alternative: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -146,43 +146,43 @@ ntheorem prove_right_alternative: ∀H18:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H19:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H20:∀X:Univ.eq Univ (add X additive_identity) X. -∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x y y) additive_identity +∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x y y) additive_identity) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#multiply. -#x. -#y. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -#H18. -#H19. -#H20. -#H21. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#x ##. +#y ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +#H19 ##. +#H20 ##. +#H21 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG025-4.ma b/helm/software/matita/contribs/ng_TPTP/RNG025-4.ma index c48def0b8..3a62f36b0 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG025-4.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG025-4.ma @@ -114,7 +114,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_equation: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -138,37 +138,37 @@ ntheorem prove_equation: ∀H11:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H12:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H13:∀X:Univ.eq Univ (add X additive_identity) X. -∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (add (associator x y z) (associator x z y)) additive_identity +∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (add (associator x y z) (associator x z y)) additive_identity) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#multiply. -#x. -#y. -#z. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG025-5.ma b/helm/software/matita/contribs/ng_TPTP/RNG025-5.ma index 58c33d873..81e9f7a28 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG025-5.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG025-5.ma @@ -116,7 +116,7 @@ include "logic/equality.ma". (* ----The next 7 clause are extra lemmas which Stevens found useful *) ntheorem prove_equation: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -147,44 +147,44 @@ ntheorem prove_equation: ∀H18:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H19:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H20:∀X:Univ.eq Univ (add X additive_identity) X. -∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (add (associator x y z) (associator x z y)) additive_identity +∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (add (associator x y z) (associator x z y)) additive_identity) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#multiply. -#x. -#y. -#z. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -#H18. -#H19. -#H20. -#H21. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +#H19 ##. +#H20 ##. +#H21 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG025-6.ma b/helm/software/matita/contribs/ng_TPTP/RNG025-6.ma index 25108636e..822fc0578 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG025-6.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG025-6.ma @@ -114,7 +114,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_flexible_law: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -137,36 +137,36 @@ ntheorem prove_flexible_law: ∀H11:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H12:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H13:∀X:Univ.eq Univ (add X additive_identity) X. -∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x y x) additive_identity +∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x y x) additive_identity) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#multiply. -#x. -#y. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#x ##. +#y ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG025-7.ma b/helm/software/matita/contribs/ng_TPTP/RNG025-7.ma index 103e8a59d..db3270b15 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG025-7.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG025-7.ma @@ -116,7 +116,7 @@ include "logic/equality.ma". (* ----The next 7 clause are extra lemmas which Stevens found useful *) ntheorem prove_flexible_law: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -146,43 +146,43 @@ ntheorem prove_flexible_law: ∀H18:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H19:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H20:∀X:Univ.eq Univ (add X additive_identity) X. -∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x y x) additive_identity +∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x y x) additive_identity) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#multiply. -#x. -#y. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -#H18. -#H19. -#H20. -#H21. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#x ##. +#y ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +#H19 ##. +#H20 ##. +#H21 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG025-8.ma b/helm/software/matita/contribs/ng_TPTP/RNG025-8.ma index d8ff521a2..b2065c5b4 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG025-8.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG025-8.ma @@ -82,7 +82,7 @@ include "logic/equality.ma". (* ----Commutator *) ntheorem prove_flexible_law: - ∀Univ:Type.∀U:Univ.∀V:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀V:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -108,41 +108,41 @@ ntheorem prove_flexible_law: ∀H13:∀X:Univ.eq Univ (add X additive_identity) X. ∀H14:∀X:Univ.eq Univ (add additive_identity X) X. ∀H15:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (add Y Z)) (add (add X Y) Z). -∀H16:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (associator a b c) (associator a c b)) additive_identity +∀H16:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (associator a b c) (associator a c b)) additive_identity) . -#Univ. -#U. -#V. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#additive_inverse. -#associator. -#b. -#c. -#commutator. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16; +#Univ ##. +#U ##. +#V ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#b ##. +#c ##. +#commutator ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG025-9.ma b/helm/software/matita/contribs/ng_TPTP/RNG025-9.ma index 14474c2b2..0f415c015 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG025-9.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG025-9.ma @@ -84,7 +84,7 @@ include "logic/equality.ma". (* ----Commutator *) ntheorem prove_flexible_law: - ∀Univ:Type.∀U:Univ.∀V:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀U:Univ.∀V:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -117,48 +117,48 @@ ntheorem prove_flexible_law: ∀H20:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y (additive_inverse Z))) (add (multiply X Y) (additive_inverse (multiply X Z))). ∀H21:∀X:Univ.∀Y:Univ.eq Univ (multiply X (additive_inverse Y)) (additive_inverse (multiply X Y)). ∀H22:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) Y) (additive_inverse (multiply X Y)). -∀H23:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) (additive_inverse Y)) (multiply X Y).eq Univ (add (associator a b c) (associator a c b)) additive_identity +∀H23:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) (additive_inverse Y)) (multiply X Y).eq Univ (add (associator a b c) (associator a c b)) additive_identity) . -#Univ. -#U. -#V. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#additive_inverse. -#associator. -#b. -#c. -#commutator. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -#H18. -#H19. -#H20. -#H21. -#H22. -#H23. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21,H22,H23; +#Univ ##. +#U ##. +#V ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#b ##. +#c ##. +#commutator ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +#H19 ##. +#H20 ##. +#H21 ##. +#H22 ##. +#H23 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21,H22,H23 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG026-6.ma b/helm/software/matita/contribs/ng_TPTP/RNG026-6.ma index 02440d3d1..9bb3c1953 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG026-6.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG026-6.ma @@ -110,7 +110,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_teichmuller_identity: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -135,38 +135,38 @@ ntheorem prove_teichmuller_identity: ∀H11:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H12:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H13:∀X:Univ.eq Univ (add X additive_identity) X. -∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (add (add (associator (multiply a b) c d) (associator a b (multiply c d))) (additive_inverse (add (add (associator a (multiply b c) d) (multiply a (associator b c d))) (multiply (associator a b c) d)))) additive_identity +∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (add (add (associator (multiply a b) c d) (associator a b (multiply c d))) (additive_inverse (add (add (associator a (multiply b c) d) (multiply a (associator b c d))) (multiply (associator a b c) d)))) additive_identity) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#additive_inverse. -#associator. -#b. -#c. -#commutator. -#d. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#b ##. +#c ##. +#commutator ##. +#d ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG026-7.ma b/helm/software/matita/contribs/ng_TPTP/RNG026-7.ma index 08863a0da..9385d8b8d 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG026-7.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG026-7.ma @@ -112,7 +112,7 @@ include "logic/equality.ma". (* ----The next 7 clause are extra lemmas which Stevens found useful *) ntheorem prove_teichmuller_identity: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -144,45 +144,45 @@ ntheorem prove_teichmuller_identity: ∀H18:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H19:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H20:∀X:Univ.eq Univ (add X additive_identity) X. -∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (add (add (associator (multiply a b) c d) (associator a b (multiply c d))) (additive_inverse (add (add (associator a (multiply b c) d) (multiply a (associator b c d))) (multiply (associator a b c) d)))) additive_identity +∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (add (add (associator (multiply a b) c d) (associator a b (multiply c d))) (additive_inverse (add (add (associator a (multiply b c) d) (multiply a (associator b c d))) (multiply (associator a b c) d)))) additive_identity) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#additive_inverse. -#associator. -#b. -#c. -#commutator. -#d. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -#H18. -#H19. -#H20. -#H21. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#b ##. +#c ##. +#commutator ##. +#d ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +#H19 ##. +#H20 ##. +#H21 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG027-5.ma b/helm/software/matita/contribs/ng_TPTP/RNG027-5.ma index 32df52956..77bde2470 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG027-5.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG027-5.ma @@ -116,7 +116,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_right_moufang: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -140,37 +140,37 @@ ntheorem prove_right_moufang: ∀H11:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H12:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H13:∀X:Univ.eq Univ (add X additive_identity) X. -∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply cz (multiply cx (multiply cy cx))) (multiply (multiply (multiply cz cx) cy) cx) +∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply cz (multiply cx (multiply cy cx))) (multiply (multiply (multiply cz cx) cy) cx)) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#cx. -#cy. -#cz. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#cx ##. +#cy ##. +#cz ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG027-7.ma b/helm/software/matita/contribs/ng_TPTP/RNG027-7.ma index 037c7220f..48b4fe029 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG027-7.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG027-7.ma @@ -116,7 +116,7 @@ include "logic/equality.ma". (* ----The next 7 clause are extra lemmas which Stevens found useful *) ntheorem prove_right_moufang: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -147,44 +147,44 @@ ntheorem prove_right_moufang: ∀H18:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H19:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H20:∀X:Univ.eq Univ (add X additive_identity) X. -∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply cz (multiply cx (multiply cy cx))) (multiply (multiply (multiply cz cx) cy) cx) +∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply cz (multiply cx (multiply cy cx))) (multiply (multiply (multiply cz cx) cy) cx)) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#cx. -#cy. -#cz. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -#H18. -#H19. -#H20. -#H21. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#cx ##. +#cy ##. +#cz ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +#H19 ##. +#H20 ##. +#H21 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG027-8.ma b/helm/software/matita/contribs/ng_TPTP/RNG027-8.ma index d31485571..5b5eca6b6 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG027-8.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG027-8.ma @@ -118,7 +118,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_right_moufang: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -142,37 +142,37 @@ ntheorem prove_right_moufang: ∀H11:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H12:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H13:∀X:Univ.eq Univ (add X additive_identity) X. -∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x (multiply x y) z) (multiply (associator x y z) x) +∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x (multiply x y) z) (multiply (associator x y z) x)) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#multiply. -#x. -#y. -#z. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG027-9.ma b/helm/software/matita/contribs/ng_TPTP/RNG027-9.ma index fa034e3e0..24cd1a6aa 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG027-9.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG027-9.ma @@ -114,7 +114,7 @@ include "logic/equality.ma". (* ----The next 7 clause are extra lemmas which Stevens found useful *) ntheorem prove_right_moufang: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -145,44 +145,44 @@ ntheorem prove_right_moufang: ∀H18:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H19:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H20:∀X:Univ.eq Univ (add X additive_identity) X. -∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x (multiply x y) z) (multiply (associator x y z) x) +∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x (multiply x y) z) (multiply (associator x y z) x)) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#multiply. -#x. -#y. -#z. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -#H18. -#H19. -#H20. -#H21. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +#H19 ##. +#H20 ##. +#H21 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG028-5.ma b/helm/software/matita/contribs/ng_TPTP/RNG028-5.ma index 036ca92c7..dffec11c4 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG028-5.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG028-5.ma @@ -116,7 +116,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_left_moufang: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -140,37 +140,37 @@ ntheorem prove_left_moufang: ∀H11:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H12:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H13:∀X:Univ.eq Univ (add X additive_identity) X. -∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply (multiply cx (multiply cy cx)) cz) (multiply cx (multiply cy (multiply cx cz))) +∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply (multiply cx (multiply cy cx)) cz) (multiply cx (multiply cy (multiply cx cz)))) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#cx. -#cy. -#cz. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#cx ##. +#cy ##. +#cz ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG028-7.ma b/helm/software/matita/contribs/ng_TPTP/RNG028-7.ma index a760f4b5f..1259b372a 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG028-7.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG028-7.ma @@ -116,7 +116,7 @@ include "logic/equality.ma". (* ----The next 7 clause are extra lemmas which Stevens found useful *) ntheorem prove_left_moufang: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -147,44 +147,44 @@ ntheorem prove_left_moufang: ∀H18:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H19:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H20:∀X:Univ.eq Univ (add X additive_identity) X. -∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply (multiply cx (multiply cy cx)) cz) (multiply cx (multiply cy (multiply cx cz))) +∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply (multiply cx (multiply cy cx)) cz) (multiply cx (multiply cy (multiply cx cz)))) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#cx. -#cy. -#cz. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -#H18. -#H19. -#H20. -#H21. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#cx ##. +#cy ##. +#cz ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +#H19 ##. +#H20 ##. +#H21 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG028-8.ma b/helm/software/matita/contribs/ng_TPTP/RNG028-8.ma index d6aba11c0..ce8b28cbd 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG028-8.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG028-8.ma @@ -118,7 +118,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_left_moufang: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -142,37 +142,37 @@ ntheorem prove_left_moufang: ∀H11:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H12:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H13:∀X:Univ.eq Univ (add X additive_identity) X. -∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x (multiply y x) z) (multiply x (associator x y z)) +∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x (multiply y x) z) (multiply x (associator x y z))) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#multiply. -#x. -#y. -#z. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG028-9.ma b/helm/software/matita/contribs/ng_TPTP/RNG028-9.ma index 0f39aca0e..3a5a3f4a9 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG028-9.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG028-9.ma @@ -114,7 +114,7 @@ include "logic/equality.ma". (* ----The next 7 clause are extra lemmas which Stevens found useful *) ntheorem prove_left_moufang: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -145,44 +145,44 @@ ntheorem prove_left_moufang: ∀H18:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H19:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H20:∀X:Univ.eq Univ (add X additive_identity) X. -∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x (multiply y x) z) (multiply x (associator x y z)) +∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x (multiply y x) z) (multiply x (associator x y z))) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#multiply. -#x. -#y. -#z. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -#H18. -#H19. -#H20. -#H21. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +#H19 ##. +#H20 ##. +#H21 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG029-5.ma b/helm/software/matita/contribs/ng_TPTP/RNG029-5.ma index f95752bb3..80da263af 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG029-5.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG029-5.ma @@ -116,7 +116,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_middle_law: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -140,37 +140,37 @@ ntheorem prove_middle_law: ∀H11:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H12:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H13:∀X:Univ.eq Univ (add X additive_identity) X. -∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply (multiply cx cy) (multiply cz cx)) (multiply cx (multiply (multiply cy cz) cx)) +∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply (multiply cx cy) (multiply cz cx)) (multiply cx (multiply (multiply cy cz) cx))) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#cx. -#cy. -#cz. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#cx ##. +#cy ##. +#cz ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG029-6.ma b/helm/software/matita/contribs/ng_TPTP/RNG029-6.ma index 96332588f..73486f3d8 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG029-6.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG029-6.ma @@ -112,7 +112,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_middle_moufang: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -136,37 +136,37 @@ ntheorem prove_middle_moufang: ∀H11:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H12:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H13:∀X:Univ.eq Univ (add X additive_identity) X. -∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply (multiply x y) (multiply z x)) (multiply (multiply x (multiply y z)) x) +∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply (multiply x y) (multiply z x)) (multiply (multiply x (multiply y z)) x)) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#multiply. -#x. -#y. -#z. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG029-7.ma b/helm/software/matita/contribs/ng_TPTP/RNG029-7.ma index 5be18d2cc..7d1816ac6 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG029-7.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG029-7.ma @@ -114,7 +114,7 @@ include "logic/equality.ma". (* ----The next 7 clause are extra lemmas which Stevens found useful *) ntheorem prove_middle_moufang: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -145,44 +145,44 @@ ntheorem prove_middle_moufang: ∀H18:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H19:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H20:∀X:Univ.eq Univ (add X additive_identity) X. -∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply (multiply x y) (multiply z x)) (multiply (multiply x (multiply y z)) x) +∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply (multiply x y) (multiply z x)) (multiply (multiply x (multiply y z)) x)) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#multiply. -#x. -#y. -#z. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -#H18. -#H19. -#H20. -#H21. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +#H19 ##. +#H20 ##. +#H21 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG030-6.ma b/helm/software/matita/contribs/ng_TPTP/RNG030-6.ma index 7d136d32c..514d0a911 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG030-6.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG030-6.ma @@ -76,7 +76,7 @@ include "logic/equality.ma". (* ----Commutator *) ntheorem prove_conjecture_1: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -98,35 +98,35 @@ ntheorem prove_conjecture_1: ∀H10:∀X:Univ.eq Univ (add X additive_identity) X. ∀H11:∀X:Univ.eq Univ (add additive_identity X) X. ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (add Y Z)) (add (add X Y) Z). -∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (multiply (associator x x y) (multiply (associator x x y) (associator x x y))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) additive_identity +∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (multiply (associator x x y) (multiply (associator x x y) (associator x x y))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) additive_identity) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#multiply. -#x. -#y. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#x ##. +#y ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG030-7.ma b/helm/software/matita/contribs/ng_TPTP/RNG030-7.ma index 5731b42d9..fcc333735 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG030-7.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG030-7.ma @@ -78,7 +78,7 @@ include "logic/equality.ma". (* ----Commutator *) ntheorem prove_conjecture_1: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -107,42 +107,42 @@ ntheorem prove_conjecture_1: ∀H17:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y (additive_inverse Z))) (add (multiply X Y) (additive_inverse (multiply X Z))). ∀H18:∀X:Univ.∀Y:Univ.eq Univ (multiply X (additive_inverse Y)) (additive_inverse (multiply X Y)). ∀H19:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) Y) (additive_inverse (multiply X Y)). -∀H20:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) (additive_inverse Y)) (multiply X Y).eq Univ (add (multiply (associator x x y) (multiply (associator x x y) (associator x x y))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) additive_identity +∀H20:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) (additive_inverse Y)) (multiply X Y).eq Univ (add (multiply (associator x x y) (multiply (associator x x y) (associator x x y))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) additive_identity) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#multiply. -#x. -#y. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -#H18. -#H19. -#H20. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#x ##. +#y ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +#H19 ##. +#H20 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG031-6.ma b/helm/software/matita/contribs/ng_TPTP/RNG031-6.ma index b08210083..bb504c97d 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG031-6.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG031-6.ma @@ -78,7 +78,7 @@ include "logic/equality.ma". (* ----Commutator *) ntheorem prove_conjecture_2: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -100,35 +100,35 @@ ntheorem prove_conjecture_2: ∀H10:∀X:Univ.eq Univ (add X additive_identity) X. ∀H11:∀X:Univ.eq Univ (add additive_identity X) X. ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (add Y Z)) (add (add X Y) Z). -∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply (multiply (multiply (associator x x y) (associator x x y)) x) (multiply (associator x x y) (associator x x y))) additive_identity +∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply (multiply (multiply (associator x x y) (associator x x y)) x) (multiply (associator x x y) (associator x x y))) additive_identity) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#multiply. -#x. -#y. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#x ##. +#y ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG031-7.ma b/helm/software/matita/contribs/ng_TPTP/RNG031-7.ma index 36c7034e6..663fc2b71 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG031-7.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG031-7.ma @@ -82,7 +82,7 @@ include "logic/equality.ma". (* ----Commutator *) ntheorem prove_conjecture_2: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -111,42 +111,42 @@ ntheorem prove_conjecture_2: ∀H17:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y (additive_inverse Z))) (add (multiply X Y) (additive_inverse (multiply X Z))). ∀H18:∀X:Univ.∀Y:Univ.eq Univ (multiply X (additive_inverse Y)) (additive_inverse (multiply X Y)). ∀H19:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) Y) (additive_inverse (multiply X Y)). -∀H20:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) (additive_inverse Y)) (multiply X Y).eq Univ (multiply (multiply (multiply (associator x x y) (associator x x y)) x) (multiply (associator x x y) (associator x x y))) additive_identity +∀H20:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) (additive_inverse Y)) (multiply X Y).eq Univ (multiply (multiply (multiply (associator x x y) (associator x x y)) x) (multiply (associator x x y) (associator x x y))) additive_identity) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#multiply. -#x. -#y. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -#H18. -#H19. -#H20. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#x ##. +#y ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +#H19 ##. +#H20 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG032-6.ma b/helm/software/matita/contribs/ng_TPTP/RNG032-6.ma index 2d60f2834..8475d8391 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG032-6.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG032-6.ma @@ -76,7 +76,7 @@ include "logic/equality.ma". (* ----Commutator *) ntheorem prove_conjecture_3: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -98,35 +98,35 @@ ntheorem prove_conjecture_3: ∀H10:∀X:Univ.eq Univ (add X additive_identity) X. ∀H11:∀X:Univ.eq Univ (add additive_identity X) X. ∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (add Y Z)) (add (add X Y) Z). -∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (add (add (add (add (multiply (associator x x y) (multiply (associator x x y) (associator x x y))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) additive_identity +∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (add (add (add (add (multiply (associator x x y) (multiply (associator x x y) (associator x x y))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) additive_identity) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#multiply. -#x. -#y. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#x ##. +#y ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG032-7.ma b/helm/software/matita/contribs/ng_TPTP/RNG032-7.ma index db423664a..b3c67e18a 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG032-7.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG032-7.ma @@ -78,7 +78,7 @@ include "logic/equality.ma". (* ----Commutator *) ntheorem prove_conjecture_3: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -107,42 +107,42 @@ ntheorem prove_conjecture_3: ∀H17:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y (additive_inverse Z))) (add (multiply X Y) (additive_inverse (multiply X Z))). ∀H18:∀X:Univ.∀Y:Univ.eq Univ (multiply X (additive_inverse Y)) (additive_inverse (multiply X Y)). ∀H19:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) Y) (additive_inverse (multiply X Y)). -∀H20:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) (additive_inverse Y)) (multiply X Y).eq Univ (add (add (add (add (add (multiply (associator x x y) (multiply (associator x x y) (associator x x y))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) additive_identity +∀H20:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) (additive_inverse Y)) (multiply X Y).eq Univ (add (add (add (add (add (multiply (associator x x y) (multiply (associator x x y) (associator x x y))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) additive_identity) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#multiply. -#x. -#y. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -#H18. -#H19. -#H20. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#x ##. +#y ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +#H19 ##. +#H20 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG033-6.ma b/helm/software/matita/contribs/ng_TPTP/RNG033-6.ma index 02dd89c14..04f339737 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG033-6.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG033-6.ma @@ -110,7 +110,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_challenge: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -135,38 +135,38 @@ ntheorem prove_challenge: ∀H11:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H12:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H13:∀X:Univ.eq Univ (add X additive_identity) X. -∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (add (associator (multiply x y) z w) (associator x y (commutator z w))) (add (multiply x (associator y z w)) (multiply (associator x z w) y)) +∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (add (associator (multiply x y) z w) (associator x y (commutator z w))) (add (multiply x (associator y z w)) (multiply (associator x z w) y))) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#multiply. -#w. -#x. -#y. -#z. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#w ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG033-7.ma b/helm/software/matita/contribs/ng_TPTP/RNG033-7.ma index 60ff29fc1..12e30a3f5 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG033-7.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG033-7.ma @@ -112,7 +112,7 @@ include "logic/equality.ma". (* ----The next 7 clause are extra lemmas which Stevens found useful *) ntheorem prove_challenge: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -144,45 +144,45 @@ ntheorem prove_challenge: ∀H18:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H19:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H20:∀X:Univ.eq Univ (add X additive_identity) X. -∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (add (associator (multiply x y) z w) (associator x y (commutator z w))) (add (multiply x (associator y z w)) (multiply (associator x z w) y)) +∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (add (associator (multiply x y) z w) (associator x y (commutator z w))) (add (multiply x (associator y z w)) (multiply (associator x z w) y))) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#multiply. -#w. -#x. -#y. -#z. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -#H18. -#H19. -#H20. -#H21. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#w ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +#H19 ##. +#H20 ##. +#H21 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG033-8.ma b/helm/software/matita/contribs/ng_TPTP/RNG033-8.ma index 4010312f2..c295fe39b 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG033-8.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG033-8.ma @@ -116,7 +116,7 @@ include "logic/equality.ma". (* ----Right Moufang *) ntheorem prove_challenge: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -142,39 +142,39 @@ ntheorem prove_challenge: ∀H12:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H13:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H14:∀X:Univ.eq Univ (add X additive_identity) X. -∀H15:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (add (associator (multiply x y) z w) (associator x y (commutator z w))) (add (multiply x (associator y z w)) (multiply (associator x z w) y)) +∀H15:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (add (associator (multiply x y) z w) (associator x y (commutator z w))) (add (multiply x (associator y z w)) (multiply (associator x z w) y))) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#multiply. -#w. -#x. -#y. -#z. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#w ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG033-9.ma b/helm/software/matita/contribs/ng_TPTP/RNG033-9.ma index 93017c38c..9883ba974 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG033-9.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG033-9.ma @@ -118,7 +118,7 @@ include "logic/equality.ma". (* ----Right Moufang *) ntheorem prove_challenge: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. ∀additive_inverse:∀_:Univ.Univ. @@ -151,46 +151,46 @@ ntheorem prove_challenge: ∀H19:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. ∀H20:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. ∀H21:∀X:Univ.eq Univ (add X additive_identity) X. -∀H22:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (add (associator (multiply x y) z w) (associator x y (commutator z w))) (add (multiply x (associator y z w)) (multiply (associator x z w) y)) +∀H22:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (add (associator (multiply x y) z w) (associator x y (commutator z w))) (add (multiply x (associator y z w)) (multiply (associator x z w) y))) . -#Univ. -#X. -#Y. -#Z. -#add. -#additive_identity. -#additive_inverse. -#associator. -#commutator. -#multiply. -#w. -#x. -#y. -#z. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -#H11. -#H12. -#H13. -#H14. -#H15. -#H16. -#H17. -#H18. -#H19. -#H20. -#H21. -#H22. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21,H22; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#w ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +#H19 ##. +#H20 ##. +#H21 ##. +#H22 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21,H22 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG035-7.ma b/helm/software/matita/contribs/ng_TPTP/RNG035-7.ma index 06b2743f4..00a6466ec 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG035-7.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG035-7.ma @@ -104,7 +104,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_commutativity: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -122,31 +122,31 @@ ntheorem prove_commutativity: ∀H7:∀X:Univ.eq Univ (add X (additive_inverse X)) additive_identity. ∀H8:∀X:Univ.eq Univ (add (additive_inverse X) X) additive_identity. ∀H9:∀X:Univ.eq Univ (add X additive_identity) X. -∀H10:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply b a) c +∀H10:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply b a) c) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#additive_inverse. -#b. -#c. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#b ##. +#c ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/RNG036-7.ma b/helm/software/matita/contribs/ng_TPTP/RNG036-7.ma index 96e40b2f0..cb3a5d1a5 100644 --- a/helm/software/matita/contribs/ng_TPTP/RNG036-7.ma +++ b/helm/software/matita/contribs/ng_TPTP/RNG036-7.ma @@ -104,7 +104,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_commutativity: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀additive_identity:Univ. @@ -122,31 +122,31 @@ ntheorem prove_commutativity: ∀H7:∀X:Univ.eq Univ (add X (additive_inverse X)) additive_identity. ∀H8:∀X:Univ.eq Univ (add (additive_inverse X) X) additive_identity. ∀H9:∀X:Univ.eq Univ (add X additive_identity) X. -∀H10:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply b a) c +∀H10:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply b a) c) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#additive_identity. -#additive_inverse. -#b. -#c. -#multiply. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -#H6. -#H7. -#H8. -#H9. -#H10. -nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#b ##. +#c ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/ROB001-1.ma b/helm/software/matita/contribs/ng_TPTP/ROB001-1.ma index 9c782b0e0..5c5b99fd1 100644 --- a/helm/software/matita/contribs/ng_TPTP/ROB001-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/ROB001-1.ma @@ -94,27 +94,27 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_huntingtons_axiom: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. ∀negate:∀_:Univ.Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X. ∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)). -∀H2:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b +∀H2:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#b. -#negate. -#H0. -#H1. -#H2. -nauto by H0,H1,H2; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#b ##. +#negate ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/ROB002-1.ma b/helm/software/matita/contribs/ng_TPTP/ROB002-1.ma index 4efb8da76..3de7979ec 100644 --- a/helm/software/matita/contribs/ng_TPTP/ROB002-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/ROB002-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_huntingtons_axiom: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. @@ -102,21 +102,21 @@ ntheorem prove_huntingtons_axiom: ∀H0:∀X:Univ.eq Univ (negate (negate X)) X. ∀H1:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X. ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)). -∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b +∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#b. -#negate. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#b ##. +#negate ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/ROB003-1.ma b/helm/software/matita/contribs/ng_TPTP/ROB003-1.ma index fd10b5376..9f3fb004f 100644 --- a/helm/software/matita/contribs/ng_TPTP/ROB003-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/ROB003-1.ma @@ -108,7 +108,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_huntingtons_axiom: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. @@ -117,22 +117,22 @@ ntheorem prove_huntingtons_axiom: ∀H0:∀X:Univ.eq Univ (add X c) c. ∀H1:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X. ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)). -∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b +∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#b. -#c. -#negate. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#b ##. +#c ##. +#negate ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/ROB004-1.ma b/helm/software/matita/contribs/ng_TPTP/ROB004-1.ma index 981a05054..4b2757f55 100644 --- a/helm/software/matita/contribs/ng_TPTP/ROB004-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/ROB004-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_huntingtons_axiom: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. @@ -108,25 +108,25 @@ ntheorem prove_huntingtons_axiom: ∀H2:eq Univ (negate d) c. ∀H3:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X. ∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)). -∀H5:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b +∀H5:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#b. -#c. -#d. -#negate. -#H0. -#H1. -#H2. -#H3. -#H4. -#H5. -nauto by H0,H1,H2,H3,H4,H5; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#b ##. +#c ##. +#d ##. +#negate ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +nauto by H0,H1,H2,H3,H4,H5 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/ROB005-1.ma b/helm/software/matita/contribs/ng_TPTP/ROB005-1.ma index 01a7efe5f..d921ea73f 100644 --- a/helm/software/matita/contribs/ng_TPTP/ROB005-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/ROB005-1.ma @@ -116,7 +116,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_huntingtons_axiom: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. @@ -125,22 +125,22 @@ ntheorem prove_huntingtons_axiom: ∀H0:eq Univ (add c c) c. ∀H1:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X. ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)). -∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b +∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#b. -#c. -#negate. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#b ##. +#c ##. +#negate ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/ROB006-1.ma b/helm/software/matita/contribs/ng_TPTP/ROB006-1.ma index dc4810818..ab3f8aeea 100644 --- a/helm/software/matita/contribs/ng_TPTP/ROB006-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/ROB006-1.ma @@ -104,7 +104,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_huntingtons_axiom: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. @@ -114,23 +114,23 @@ ntheorem prove_huntingtons_axiom: ∀H0:eq Univ (add c d) d. ∀H1:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X. ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)). -∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b +∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#b. -#c. -#d. -#negate. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#b ##. +#c ##. +#d ##. +#negate ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/ROB006-2.ma b/helm/software/matita/contribs/ng_TPTP/ROB006-2.ma index 054ecfb45..49f37838b 100644 --- a/helm/software/matita/contribs/ng_TPTP/ROB006-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/ROB006-2.ma @@ -100,7 +100,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_idempotence: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀c:Univ. ∀d:Univ. @@ -108,25 +108,24 @@ ntheorem prove_idempotence: ∀H0:eq Univ (add c d) d. ∀H1:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X. ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)). -∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).∃X:Univ.eq Univ (add X X) X +∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).∃X:Univ.eq Univ (add X X) X) . -#Univ. -#X. -#Y. -#Z. -#add. -#c. -#d. -#negate. -#H0. -#H1. -#H2. -#H3. -napply ex_intro[ -nid2: -nauto by H0,H1,H2,H3; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#c ##. +#d ##. +#negate ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2,H3 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/ROB007-1.ma b/helm/software/matita/contribs/ng_TPTP/ROB007-1.ma index 93bc99301..01be6c2e5 100644 --- a/helm/software/matita/contribs/ng_TPTP/ROB007-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/ROB007-1.ma @@ -100,7 +100,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_huntingtons_axiom: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. @@ -108,21 +108,21 @@ ntheorem prove_huntingtons_axiom: ∀H0:eq Univ (negate (add a b)) (negate b). ∀H1:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X. ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)). -∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b +∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#b. -#negate. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#b ##. +#negate ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/ROB007-2.ma b/helm/software/matita/contribs/ng_TPTP/ROB007-2.ma index a3484ea03..ced2a0f36 100644 --- a/helm/software/matita/contribs/ng_TPTP/ROB007-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/ROB007-2.ma @@ -98,7 +98,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_idempotence: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. @@ -106,25 +106,24 @@ ntheorem prove_idempotence: ∀H0:eq Univ (negate (add a b)) (negate b). ∀H1:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X. ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)). -∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).∃X:Univ.eq Univ (add X X) X +∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).∃X:Univ.eq Univ (add X X) X) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#b. -#negate. -#H0. -#H1. -#H2. -#H3. -napply ex_intro[ -nid2: -nauto by H0,H1,H2,H3; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#b ##. +#negate ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2,H3 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/ROB008-1.ma b/helm/software/matita/contribs/ng_TPTP/ROB008-1.ma index d717a0325..86c734f3b 100644 --- a/helm/software/matita/contribs/ng_TPTP/ROB008-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/ROB008-1.ma @@ -90,7 +90,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_result: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. @@ -99,22 +99,22 @@ ntheorem prove_result: ∀H0:eq Univ (negate (add a (negate (add b c)))) (negate (add a (add b (negate c)))). ∀H1:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X. ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)). -∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add a b) a +∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add a b) a) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#b. -#c. -#negate. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#b ##. +#c ##. +#negate ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/ROB009-1.ma b/helm/software/matita/contribs/ng_TPTP/ROB009-1.ma index ee01fc637..e27abe286 100644 --- a/helm/software/matita/contribs/ng_TPTP/ROB009-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/ROB009-1.ma @@ -90,7 +90,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_result: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. @@ -99,22 +99,22 @@ ntheorem prove_result: ∀H0:eq Univ (negate (add a (negate (add b c)))) (negate (add b (negate (add a c)))). ∀H1:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X. ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)). -∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ a b +∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ a b) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#b. -#c. -#negate. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#b ##. +#c ##. +#negate ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/ROB010-1.ma b/helm/software/matita/contribs/ng_TPTP/ROB010-1.ma index 826fab990..314a7d9fa 100644 --- a/helm/software/matita/contribs/ng_TPTP/ROB010-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/ROB010-1.ma @@ -94,7 +94,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_result: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. @@ -103,22 +103,22 @@ ntheorem prove_result: ∀H0:eq Univ (negate (add a (negate b))) c. ∀H1:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X. ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)). -∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (negate (add c (negate (add b a)))) a +∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (negate (add c (negate (add b a)))) a) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#b. -#c. -#negate. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#b ##. +#c ##. +#negate ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/ROB013-1.ma b/helm/software/matita/contribs/ng_TPTP/ROB013-1.ma index aab351bdd..577a5fb60 100644 --- a/helm/software/matita/contribs/ng_TPTP/ROB013-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/ROB013-1.ma @@ -90,7 +90,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_result: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. @@ -99,22 +99,22 @@ ntheorem prove_result: ∀H0:eq Univ (negate (add a b)) c. ∀H1:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X. ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)). -∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (negate (add c (negate (add (negate b) a)))) a +∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (negate (add c (negate (add (negate b) a)))) a) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#b. -#c. -#negate. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#b ##. +#c ##. +#negate ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/ROB020-1.ma b/helm/software/matita/contribs/ng_TPTP/ROB020-1.ma index 22e28eeea..38a4cd42c 100644 --- a/helm/software/matita/contribs/ng_TPTP/ROB020-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/ROB020-1.ma @@ -98,7 +98,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_huntingtons_axiom: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. @@ -106,21 +106,21 @@ ntheorem prove_huntingtons_axiom: ∀H0:eq Univ (negate (add a (negate b))) b. ∀H1:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X. ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)). -∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b +∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#b. -#negate. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#b ##. +#negate ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/ROB020-2.ma b/helm/software/matita/contribs/ng_TPTP/ROB020-2.ma index 4a2cf5465..f670b4209 100644 --- a/helm/software/matita/contribs/ng_TPTP/ROB020-2.ma +++ b/helm/software/matita/contribs/ng_TPTP/ROB020-2.ma @@ -102,7 +102,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_idempotence: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. @@ -110,25 +110,24 @@ ntheorem prove_idempotence: ∀H0:eq Univ (negate (add a (negate b))) b. ∀H1:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X. ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)). -∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).∃X:Univ.eq Univ (add X X) X +∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).∃X:Univ.eq Univ (add X X) X) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#b. -#negate. -#H0. -#H1. -#H2. -#H3. -napply ex_intro[ -nid2: -nauto by H0,H1,H2,H3; -nid| -skip] +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#b ##. +#negate ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2,H3 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/ROB022-1.ma b/helm/software/matita/contribs/ng_TPTP/ROB022-1.ma index de2d007e3..48b53a3a8 100644 --- a/helm/software/matita/contribs/ng_TPTP/ROB022-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/ROB022-1.ma @@ -98,7 +98,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_huntingtons_axiom: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. @@ -107,22 +107,22 @@ ntheorem prove_huntingtons_axiom: ∀H0:eq Univ (add c (negate c)) c. ∀H1:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X. ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)). -∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b +∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#b. -#c. -#negate. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#b ##. +#c ##. +#negate ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/ROB023-1.ma b/helm/software/matita/contribs/ng_TPTP/ROB023-1.ma index 03691189e..8f10b8a86 100644 --- a/helm/software/matita/contribs/ng_TPTP/ROB023-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/ROB023-1.ma @@ -98,7 +98,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_huntingtons_axiom: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. @@ -106,21 +106,21 @@ ntheorem prove_huntingtons_axiom: ∀H0:∀X:Univ.eq Univ (add X X) X. ∀H1:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X. ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)). -∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b +∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#b. -#negate. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#b ##. +#negate ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/ROB024-1.ma b/helm/software/matita/contribs/ng_TPTP/ROB024-1.ma index 0d65e78d6..42848d7e8 100644 --- a/helm/software/matita/contribs/ng_TPTP/ROB024-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/ROB024-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_huntingtons_axiom: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. @@ -104,21 +104,21 @@ ntheorem prove_huntingtons_axiom: ∀H0:eq Univ (negate (add (negate (add a (add a b))) (negate (add a (negate b))))) a. ∀H1:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X. ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)). -∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b +∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#b. -#negate. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#b ##. +#negate ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/ROB026-1.ma b/helm/software/matita/contribs/ng_TPTP/ROB026-1.ma index b59420a6d..231f92e62 100644 --- a/helm/software/matita/contribs/ng_TPTP/ROB026-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/ROB026-1.ma @@ -100,7 +100,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_huntingtons_axiom: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. @@ -110,23 +110,23 @@ ntheorem prove_huntingtons_axiom: ∀H0:eq Univ (add c d) c. ∀H1:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X. ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)). -∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b +∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#b. -#c. -#d. -#negate. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#b ##. +#c ##. +#d ##. +#negate ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/ROB027-1.ma b/helm/software/matita/contribs/ng_TPTP/ROB027-1.ma index efba01858..b8189354d 100644 --- a/helm/software/matita/contribs/ng_TPTP/ROB027-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/ROB027-1.ma @@ -100,7 +100,7 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_huntingtons_axiom: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀b:Univ. @@ -109,22 +109,22 @@ ntheorem prove_huntingtons_axiom: ∀H0:eq Univ (negate (negate c)) c. ∀H1:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X. ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)). -∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b +∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b) . -#Univ. -#X. -#Y. -#Z. -#a. -#add. -#b. -#c. -#negate. -#H0. -#H1. -#H2. -#H3. -nauto by H0,H1,H2,H3; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#b ##. +#c ##. +#negate ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/ROB030-1.ma b/helm/software/matita/contribs/ng_TPTP/ROB030-1.ma index fb868fb1c..c96e41a02 100644 --- a/helm/software/matita/contribs/ng_TPTP/ROB030-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/ROB030-1.ma @@ -96,7 +96,7 @@ include "logic/equality.ma". (* ------------------------------------------------------------------------------ *) ntheorem prove_absorption_within_negation: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀c:Univ. ∀d:Univ. @@ -104,31 +104,29 @@ ntheorem prove_absorption_within_negation: ∀H0:eq Univ (add c d) d. ∀H1:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X. ∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)). -∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).∃A:Univ.∃B:Univ.eq Univ (negate (add A B)) (negate B) +∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).∃A:Univ.∃B:Univ.eq Univ (negate (add A B)) (negate B)) . -#Univ. -#A. -#B. -#X. -#Y. -#Z. -#add. -#c. -#d. -#negate. -#H0. -#H1. -#H2. -#H3. -napply ex_intro[ -nid2: -napply ex_intro[ -nid2: -nauto by H0,H1,H2,H3; -nid| -skip] -nid| -skip] +#Univ ##. +#A ##. +#B ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#c ##. +#d ##. +#negate ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2,H3 ##; +##| ##skip ##] +##| ##skip ##] nqed. (* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/ROB031-1.ma b/helm/software/matita/contribs/ng_TPTP/ROB031-1.ma index 2dac0a308..90b0758a6 100644 --- a/helm/software/matita/contribs/ng_TPTP/ROB031-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/ROB031-1.ma @@ -96,33 +96,31 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_absorption_within_negation: - ∀Univ:Type.∀A:Univ.∀B:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀A:Univ.∀B:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀negate:∀_:Univ.Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X. ∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)). -∀H2:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).∃A:Univ.∃B:Univ.eq Univ (negate (add A B)) (negate B) +∀H2:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).∃A:Univ.∃B:Univ.eq Univ (negate (add A B)) (negate B)) . -#Univ. -#A. -#B. -#X. -#Y. -#Z. -#add. -#negate. -#H0. -#H1. -#H2. -napply ex_intro[ -nid2: -napply ex_intro[ -nid2: -nauto by H0,H1,H2; -nid| -skip] -nid| -skip] +#Univ ##. +#A ##. +#B ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#negate ##. +#H0 ##. +#H1 ##. +#H2 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2 ##; +##| ##skip ##] +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/ROB032-1.ma b/helm/software/matita/contribs/ng_TPTP/ROB032-1.ma index 10130dfc7..72e2506aa 100644 --- a/helm/software/matita/contribs/ng_TPTP/ROB032-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/ROB032-1.ma @@ -98,33 +98,31 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_absorbtion: - ∀Univ:Type.∀C:Univ.∀D:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀C:Univ.∀D:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀add:∀_:Univ.∀_:Univ.Univ. ∀negate:∀_:Univ.Univ. ∀H0:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X. ∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)). -∀H2:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).∃C:Univ.∃D:Univ.eq Univ (add C D) D +∀H2:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).∃C:Univ.∃D:Univ.eq Univ (add C D) D) . -#Univ. -#C. -#D. -#X. -#Y. -#Z. -#add. -#negate. -#H0. -#H1. -#H2. -napply ex_intro[ -nid2: -napply ex_intro[ -nid2: -nauto by H0,H1,H2; -nid| -skip] -nid| -skip] +#Univ ##. +#C ##. +#D ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#negate ##. +#H0 ##. +#H1 ##. +#H2 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2 ##; +##| ##skip ##] +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/SYN080-1.ma b/helm/software/matita/contribs/ng_TPTP/SYN080-1.ma index c67b5a25a..c73ba7702 100644 --- a/helm/software/matita/contribs/ng_TPTP/SYN080-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/SYN080-1.ma @@ -42,22 +42,22 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_this: - ∀Univ:Type.∀X:Univ.∀Y:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ. ∀a:Univ. ∀b:Univ. ∀f:∀_:Univ.Univ. ∀g:∀_:Univ.Univ. -∀H0:∀X:Univ.∀Y:Univ.eq Univ (f X) (g Y).eq Univ (f (f a)) (f (g b)) +∀H0:∀X:Univ.∀Y:Univ.eq Univ (f X) (g Y).eq Univ (f (f a)) (f (g b))) . -#Univ. -#X. -#Y. -#a. -#b. -#f. -#g. -#H0. -nauto by H0; +#Univ ##. +#X ##. +#Y ##. +#a ##. +#b ##. +#f ##. +#g ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/SYN083-1.ma b/helm/software/matita/contribs/ng_TPTP/SYN083-1.ma index 6e2b48abe..75e2d93cf 100644 --- a/helm/software/matita/contribs/ng_TPTP/SYN083-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/SYN083-1.ma @@ -42,25 +42,25 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem prove_this: - ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. ∀a:Univ. ∀b:Univ. ∀c:Univ. ∀d:Univ. ∀f:∀_:Univ.∀_:Univ.Univ. -∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (f X (f Y Z)) (f (f X Y) Z).eq Univ (f a (f b (f c d))) (f (f (f a b) c) d) +∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (f X (f Y Z)) (f (f X Y) Z).eq Univ (f a (f b (f c d))) (f (f (f a b) c) d)) . -#Univ. -#X. -#Y. -#Z. -#a. -#b. -#c. -#d. -#f. -#H0. -nauto by H0; +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#f ##. +#H0 ##. +nauto by H0 ##; nqed. (* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/SYN305-1.ma b/helm/software/matita/contribs/ng_TPTP/SYN305-1.ma index 938dd75b7..bd361c182 100644 --- a/helm/software/matita/contribs/ng_TPTP/SYN305-1.ma +++ b/helm/software/matita/contribs/ng_TPTP/SYN305-1.ma @@ -42,25 +42,24 @@ include "logic/equality.ma". (* -------------------------------------------------------------------------- *) ntheorem clause3: - ∀Univ:Type.∀X:Univ. + (∀Univ:Type.∀X:Univ. ∀f:∀_:Univ.Univ. ∀g1:∀_:Univ.Univ. ∀g2:∀_:Univ.Univ. ∀H0:∀X:Univ.eq Univ (f (g2 X)) X. -∀H1:∀X:Univ.eq Univ (f (g1 X)) X.∃X:Univ.eq Univ (g1 X) (g2 X) +∀H1:∀X:Univ.eq Univ (f (g1 X)) X.∃X:Univ.eq Univ (g1 X) (g2 X)) . -#Univ. -#X. -#f. -#g1. -#g2. -#H0. -#H1. -napply ex_intro[ -nid2: -nauto by H0,H1; -nid| -skip] +#Univ ##. +#X ##. +#f ##. +#g1 ##. +#g2 ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] nqed. (* -------------------------------------------------------------------------- *) -- 2.39.2