From 3531d88e2a19cba027b4b882f8dd74bf37283b9c Mon Sep 17 00:00:00 2001 From: Ferruccio Guidi Date: Mon, 2 Mar 2009 12:03:37 +0000 Subject: [PATCH] some renaming to comply with new naming policy ... --- .../{LambdaDelta-1 => Basic-1}/A/defs.ma | 0 .../{LambdaDelta-1 => Basic-1}/C/defs.ma | 0 .../{LambdaDelta-1 => Basic-1}/C/props.ma | 0 .../{LambdaDelta-1 => Basic-1}/G/defs.ma | 0 .../{LambdaDelta-1 => Basic-1}/T/dec.ma | 0 .../{LambdaDelta-1 => Basic-1}/T/defs.ma | 0 .../{LambdaDelta-1 => Basic-1}/T/props.ma | 0 .../{LambdaDelta-1 => Basic-1}/aplus/defs.ma | 0 .../{LambdaDelta-1 => Basic-1}/aplus/props.ma | 0 .../{LambdaDelta-1 => Basic-1}/app/defs.ma | 0 .../{LambdaDelta-1 => Basic-1}/aprem/defs.ma | 0 .../{LambdaDelta-1 => Basic-1}/aprem/fwd.ma | 0 .../{LambdaDelta-1 => Basic-1}/aprem/props.ma | 0 .../{LambdaDelta-1 => Basic-1}/arity/aprem.ma | 0 .../{LambdaDelta-1 => Basic-1}/arity/cimp.ma | 0 .../{LambdaDelta-1 => Basic-1}/arity/defs.ma | 0 .../{LambdaDelta-1 => 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.../{LambdaDelta-2 => Basic-2}/pr3/fwd.mma | 0 .../{LambdaDelta-2 => Basic-2}/pr3/iso.mma | 0 .../{LambdaDelta-2 => Basic-2}/pr3/pr1.mma | 0 .../{LambdaDelta-2 => Basic-2}/pr3/pr3.mma | 0 .../{LambdaDelta-2 => Basic-2}/pr3/props.mma | 0 .../{LambdaDelta-2 => Basic-2}/pr3/subst1.mma | 0 .../{LambdaDelta-2 => Basic-2}/pr3/wcpr0.mma | 0 .../{LambdaDelta-2 => Basic-2}/preamble.ma | 0 .../{LambdaDelta-2 => Basic-2}/r/defs.mma | 0 .../{LambdaDelta-2 => Basic-2}/r/props.mma | 0 .../{LambdaDelta-2 => Basic-2}/s/defs.mma | 0 .../{LambdaDelta-2 => Basic-2}/s/props.mma | 0 .../{LambdaDelta-2 => Basic-2}/sc3/arity.mma | 0 .../{LambdaDelta-2 => Basic-2}/sc3/defs.mma | 0 .../{LambdaDelta-2 => Basic-2}/sc3/props.mma | 0 .../{LambdaDelta-2 => Basic-2}/sn3/defs.mma | 0 .../{LambdaDelta-2 => Basic-2}/sn3/fwd.mma | 0 .../{LambdaDelta-2 => Basic-2}/sn3/lift1.mma | 0 .../{LambdaDelta-2 => Basic-2}/sn3/nf2.mma | 0 .../{LambdaDelta-2 => Basic-2}/sn3/props.mma | 0 .../{LambdaDelta-2 => Basic-2}/sty0/defs.mma | 0 .../{LambdaDelta-2 => Basic-2}/sty0/fwd.mma | 0 .../{LambdaDelta-2 => Basic-2}/sty0/props.mma | 0 .../{LambdaDelta-2 => Basic-2}/sty1/cnt.mma | 0 .../{LambdaDelta-2 => Basic-2}/sty1/defs.mma | 0 .../{LambdaDelta-2 => Basic-2}/sty1/props.mma | 0 .../{LambdaDelta-2 => Basic-2}/subst/defs.mma | 0 .../{LambdaDelta-2 => Basic-2}/subst/fwd.mma | 0 .../subst/props.mma | 0 .../{LambdaDelta-2 => Basic-2}/subst0/dec.mma | 0 .../subst0/defs.mma | 0 .../{LambdaDelta-2 => Basic-2}/subst0/fwd.mma | 0 .../subst0/props.mma | 0 .../subst0/subst0.mma | 0 .../{LambdaDelta-2 => Basic-2}/subst0/tlt.mma | 0 .../subst1/defs.mma | 0 .../{LambdaDelta-2 => Basic-2}/subst1/fwd.mma | 0 .../subst1/props.mma | 0 .../subst1/subst1.mma | 0 .../{LambdaDelta-2 => Basic-2}/theory.ma | 0 .../{LambdaDelta-2 => Basic-2}/tlist/defs.mma | 0 .../tlist/props.mma | 0 .../{LambdaDelta-2 => Basic-2}/tlt/defs.mma | 0 .../{LambdaDelta-2 => Basic-2}/tlt/props.mma | 0 .../{LambdaDelta-2 => Basic-2}/ty3/arity.mma | 0 .../ty3/arity_props.mma | 0 .../{LambdaDelta-2 => Basic-2}/ty3/dec.mma | 0 .../{LambdaDelta-2 => Basic-2}/ty3/defs.mma | 0 .../ty3/fsubst0.mma | 0 .../{LambdaDelta-2 => Basic-2}/ty3/fwd.mma | 0 .../ty3/fwd_nf2.mma | 0 .../{LambdaDelta-2 => Basic-2}/ty3/nf2.mma | 0 .../{LambdaDelta-2 => Basic-2}/ty3/pr3.mma | 0 .../ty3/pr3_props.mma | 0 .../{LambdaDelta-2 => Basic-2}/ty3/props.mma | 0 .../{LambdaDelta-2 => Basic-2}/ty3/sty0.mma | 0 .../{LambdaDelta-2 => Basic-2}/ty3/subst1.mma | 0 .../{LambdaDelta-2 => Basic-2}/wcpr0/defs.mma | 0 .../{LambdaDelta-2 => Basic-2}/wcpr0/fwd.mma | 0 .../{LambdaDelta-2 => Basic-2}/wcpr0/getl.mma | 0 .../{LambdaDelta-2 => Basic-2}/wf3/clear.mma | 0 .../{LambdaDelta-2 => Basic-2}/wf3/defs.mma | 0 .../{LambdaDelta-2 => Basic-2}/wf3/fwd.mma | 0 .../{LambdaDelta-2 => Basic-2}/wf3/getl.mma | 0 .../{LambdaDelta-2 => Basic-2}/wf3/props.mma | 0 .../{LambdaDelta-2 => Basic-2}/wf3/ty3.mma | 0 .../{Base-1 => Ground-1}/blt/defs.ma | 0 .../{Base-1 => Ground-1}/blt/props.ma | 0 .../{Base-1 => Ground-1}/definitions.ma | 0 .../{Base-1 => Ground-1}/ext/arith.ma | 0 .../{Base-1 => Ground-1}/ext/tactics.ma | 0 .../{Base-1 => Ground-1}/plist/defs.ma | 0 .../{Base-1 => Ground-1}/plist/props.ma | 0 .../{Base-1 => Ground-1}/preamble.ma | 0 .../{Base-1 => Ground-1}/spare.ma | 0 .../{Base-1 => Ground-1}/theory.ma | 0 .../{Base-1 => Ground-1}/types/defs.ma | 0 .../{Base-1 => Ground-1}/types/props.ma | 0 .../{Base-2 => Ground-2}/blt/defs.mma | 0 .../{Base-2 => Ground-2}/blt/props.mma | 0 .../{Base-2 => Ground-2}/ext/arith.mma | 0 .../{Base-2 => Ground-2}/ext/tactics.mma | 0 .../{Base-2 => Ground-2}/plist/defs.mma | 0 .../{Base-2 => Ground-2}/plist/props.mma | 0 .../{Base-2 => Ground-2}/preamble.ma | 0 .../{Base-2 => Ground-2}/theory.ma | 0 .../{Base-2 => Ground-2}/types/defs.mma | 0 .../{Base-2 => Ground-2}/types/props.mma | 0 .../LAMBDA-TYPES/Legacy-1/coq/props.ma | 207 ++++++++++++++++++ 461 files changed, 207 insertions(+) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/A/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/C/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/C/props.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/G/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/T/dec.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/T/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/T/props.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/aplus/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/aplus/props.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/app/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/aprem/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/aprem/fwd.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/aprem/props.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/arity/aprem.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/arity/cimp.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/arity/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/arity/fwd.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/arity/lift1.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/arity/pr3.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/arity/props.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/arity/subst0.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/asucc/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/asucc/fwd.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/cimp/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/cimp/props.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/clear/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/clear/drop.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/clear/fwd.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/clear/props.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/clen/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/clen/getl.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/cnt/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/cnt/props.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csuba/arity.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csuba/clear.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csuba/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csuba/drop.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csuba/fwd.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csuba/getl.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csuba/props.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csubc/arity.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csubc/clear.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csubc/csuba.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csubc/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csubc/drop.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csubc/drop1.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csubc/fwd.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csubc/getl.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csubc/props.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csubst0/clear.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csubst0/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csubst0/drop.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csubst0/fwd.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csubst0/getl.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csubst0/props.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csubst1/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csubst1/fwd.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csubst1/getl.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csubst1/props.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csubt/clear.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csubt/csuba.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csubt/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csubt/drop.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csubt/fwd.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csubt/getl.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csubt/pc3.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csubt/props.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csubt/ty3.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csubv/clear.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csubv/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csubv/drop.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csubv/getl.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/csubv/props.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/definitions.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/drop/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/drop/fwd.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/drop/props.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/drop1/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/drop1/fwd.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/drop1/getl.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/drop1/props.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/ex0/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/ex0/props.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/ex1/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/ex1/props.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/ex2/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/ex2/props.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/flt/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/flt/props.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/fsubst0/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/fsubst0/fwd.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/getl/clear.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/getl/dec.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/getl/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/getl/drop.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/getl/flt.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/getl/fwd.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/getl/getl.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/getl/props.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/iso/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/iso/fwd.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/iso/props.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/leq/asucc.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/leq/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/leq/fwd.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/leq/props.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/lift/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/lift/fwd.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/lift/props.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/lift/tlt.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/lift1/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/lift1/fwd.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/lift1/props.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/llt/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/llt/props.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/next_plus/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/next_plus/props.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/nf2/arity.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/nf2/dec.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/nf2/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/nf2/fwd.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/nf2/iso.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/nf2/lift1.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/nf2/pr3.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/nf2/props.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/pc1/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/pc1/props.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/pc3/dec.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/pc3/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/pc3/fsubst0.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/pc3/fwd.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/pc3/left.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/pc3/nf2.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/pc3/pc1.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/pc3/props.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/pc3/subst1.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/pc3/wcpr0.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/pr0/dec.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/pr0/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/pr0/fwd.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/pr0/pr0.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/pr0/props.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/pr0/subst1.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/pr1/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/pr1/pr1.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/pr1/props.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/pr2/clen.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/pr2/defs.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/pr2/fwd.ma (100%) rename helm/software/matita/contribs/LAMBDA-TYPES/{LambdaDelta-1 => Basic-1}/pr2/pr2.ma (100%) rename 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rename to helm/software/matita/contribs/LAMBDA-TYPES/Ground-1/types/props.ma diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/blt/defs.mma b/helm/software/matita/contribs/LAMBDA-TYPES/Ground-2/blt/defs.mma similarity index 100% rename from helm/software/matita/contribs/LAMBDA-TYPES/Base-2/blt/defs.mma rename to helm/software/matita/contribs/LAMBDA-TYPES/Ground-2/blt/defs.mma diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/blt/props.mma b/helm/software/matita/contribs/LAMBDA-TYPES/Ground-2/blt/props.mma similarity index 100% rename from helm/software/matita/contribs/LAMBDA-TYPES/Base-2/blt/props.mma rename to helm/software/matita/contribs/LAMBDA-TYPES/Ground-2/blt/props.mma diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/ext/arith.mma b/helm/software/matita/contribs/LAMBDA-TYPES/Ground-2/ext/arith.mma similarity index 100% rename from helm/software/matita/contribs/LAMBDA-TYPES/Base-2/ext/arith.mma rename to 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helm/software/matita/contribs/LAMBDA-TYPES/Ground-2/plist/props.mma diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/preamble.ma b/helm/software/matita/contribs/LAMBDA-TYPES/Ground-2/preamble.ma similarity index 100% rename from helm/software/matita/contribs/LAMBDA-TYPES/Base-2/preamble.ma rename to helm/software/matita/contribs/LAMBDA-TYPES/Ground-2/preamble.ma diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/theory.ma b/helm/software/matita/contribs/LAMBDA-TYPES/Ground-2/theory.ma similarity index 100% rename from helm/software/matita/contribs/LAMBDA-TYPES/Base-2/theory.ma rename to helm/software/matita/contribs/LAMBDA-TYPES/Ground-2/theory.ma diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/types/defs.mma b/helm/software/matita/contribs/LAMBDA-TYPES/Ground-2/types/defs.mma similarity index 100% rename from helm/software/matita/contribs/LAMBDA-TYPES/Base-2/types/defs.mma rename to helm/software/matita/contribs/LAMBDA-TYPES/Ground-2/types/defs.mma diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/types/props.mma b/helm/software/matita/contribs/LAMBDA-TYPES/Ground-2/types/props.mma similarity index 100% rename from helm/software/matita/contribs/LAMBDA-TYPES/Base-2/types/props.mma rename to helm/software/matita/contribs/LAMBDA-TYPES/Ground-2/types/props.mma diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/Legacy-1/coq/props.ma b/helm/software/matita/contribs/LAMBDA-TYPES/Legacy-1/coq/props.ma index e9d29ff6d..0b9d97b42 100644 --- a/helm/software/matita/contribs/LAMBDA-TYPES/Legacy-1/coq/props.ma +++ b/helm/software/matita/contribs/LAMBDA-TYPES/Legacy-1/coq/props.ma @@ -23,6 +23,9 @@ A).(\forall (y: A).((eq A x y) \to (eq B (f x) (f y))))))) \lambda (A: Set).(\lambda (B: Set).(\lambda (f: ((A \to B))).(\lambda (x: A).(\lambda (y: A).(\lambda (H: (eq A x y)).(eq_ind A x (\lambda (a: A).(eq B (f x) (f a))) (refl_equal B (f x)) y H)))))). +(* COMMENTS +Initial nodes: 51 +END *) theorem f_equal2: \forall (A1: Set).(\forall (A2: Set).(\forall (B: Set).(\forall (f: ((A1 \to @@ -36,6 +39,9 @@ y2))))))))))) x2 y2) \to (eq B (f x1 x2) (f a y2)))) (\lambda (H0: (eq A2 x2 y2)).(eq_ind A2 x2 (\lambda (a: A2).(eq B (f x1 x2) (f x1 a))) (refl_equal B (f x1 x2)) y2 H0)) y1 H))))))))). +(* COMMENTS +Initial nodes: 109 +END *) theorem f_equal3: \forall (A1: Set).(\forall (A2: Set).(\forall (A3: Set).(\forall (B: @@ -53,6 +59,9 @@ A2 x2 y2)).(eq_ind A2 x2 (\lambda (a: A2).((eq A3 x3 y3) \to (eq B (f x1 x2 x3) (f x1 a y3)))) (\lambda (H1: (eq A3 x3 y3)).(eq_ind A3 x3 (\lambda (a: A3).(eq B (f x1 x2 x3) (f x1 x2 a))) (refl_equal B (f x1 x2 x3)) y3 H1)) y2 H0)) y1 H)))))))))))). +(* COMMENTS +Initial nodes: 183 +END *) theorem sym_eq: \forall (A: Set).(\forall (x: A).(\forall (y: A).((eq A x y) \to (eq A y @@ -60,6 +69,9 @@ x)))) \def \lambda (A: Set).(\lambda (x: A).(\lambda (y: A).(\lambda (H: (eq A x y)).(eq_ind A x (\lambda (a: A).(eq A a x)) (refl_equal A x) y H)))). +(* COMMENTS +Initial nodes: 39 +END *) theorem eq_ind_r: \forall (A: Set).(\forall (x: A).(\forall (P: ((A \to Prop))).((P x) \to @@ -69,6 +81,9 @@ theorem eq_ind_r: (P x)).(\lambda (y: A).(\lambda (H0: (eq A y x)).(match (sym_eq A y x H0) in eq return (\lambda (a: A).(\lambda (_: (eq ? ? a)).(P a))) with [refl_equal \Rightarrow H])))))). +(* COMMENTS +Initial nodes: 38 +END *) theorem trans_eq: \forall (A: Set).(\forall (x: A).(\forall (y: A).(\forall (z: A).((eq A x y) @@ -77,6 +92,9 @@ theorem trans_eq: \lambda (A: Set).(\lambda (x: A).(\lambda (y: A).(\lambda (z: A).(\lambda (H: (eq A x y)).(\lambda (H0: (eq A y z)).(eq_ind A y (\lambda (a: A).(eq A x a)) H z H0)))))). +(* COMMENTS +Initial nodes: 45 +END *) theorem sym_not_eq: \forall (A: Set).(\forall (x: A).(\forall (y: A).((not (eq A x y)) \to (not @@ -85,6 +103,9 @@ theorem sym_not_eq: \lambda (A: Set).(\lambda (x: A).(\lambda (y: A).(\lambda (h1: (not (eq A x y))).(\lambda (h2: (eq A y x)).(h1 (eq_ind A y (\lambda (a: A).(eq A a y)) (refl_equal A y) x h2)))))). +(* COMMENTS +Initial nodes: 51 +END *) theorem nat_double_ind: \forall (R: ((nat \to (nat \to Prop)))).(((\forall (n: nat).(R O n))) \to @@ -99,18 +120,27 @@ nat).(nat_ind (\lambda (n0: nat).(\forall (m: nat).(R n0 m))) H (\lambda (n0: nat).(\lambda (H2: ((\forall (m: nat).(R n0 m)))).(\lambda (m: nat).(nat_ind (\lambda (n1: nat).(R (S n0) n1)) (H0 n0) (\lambda (n1: nat).(\lambda (_: (R (S n0) n1)).(H1 n0 n1 (H2 n1)))) m)))) n))))). +(* COMMENTS +Initial nodes: 111 +END *) theorem eq_add_S: \forall (n: nat).(\forall (m: nat).((eq nat (S n) (S m)) \to (eq nat n m))) \def \lambda (n: nat).(\lambda (m: nat).(\lambda (H: (eq nat (S n) (S m))).(f_equal nat nat pred (S n) (S m) H))). +(* COMMENTS +Initial nodes: 33 +END *) theorem O_S: \forall (n: nat).(not (eq nat O (S n))) \def \lambda (n: nat).(\lambda (H: (eq nat O (S n))).(eq_ind nat (S n) (\lambda (n0: nat).(IsSucc n0)) I O (sym_eq nat O (S n) H))). +(* COMMENTS +Initial nodes: 41 +END *) theorem not_eq_S: \forall (n: nat).(\forall (m: nat).((not (eq nat n m)) \to (not (eq nat (S @@ -118,11 +148,17 @@ n) (S m))))) \def \lambda (n: nat).(\lambda (m: nat).(\lambda (H: (not (eq nat n m))).(\lambda (H0: (eq nat (S n) (S m))).(H (eq_add_S n m H0))))). +(* COMMENTS +Initial nodes: 35 +END *) theorem pred_Sn: \forall (m: nat).(eq nat m (pred (S m))) \def \lambda (m: nat).(refl_equal nat (pred (S m))). +(* COMMENTS +Initial nodes: 11 +END *) theorem S_pred: \forall (n: nat).(\forall (m: nat).((lt m n) \to (eq nat n (S (pred n))))) @@ -131,6 +167,9 @@ theorem S_pred: (\lambda (n0: nat).(eq nat n0 (S (pred n0)))) (refl_equal nat (S (pred (S m)))) (\lambda (m0: nat).(\lambda (_: (le (S m) m0)).(\lambda (_: (eq nat m0 (S (pred m0)))).(refl_equal nat (S (pred (S m0))))))) n H))). +(* COMMENTS +Initial nodes: 79 +END *) theorem le_trans: \forall (n: nat).(\forall (m: nat).(\forall (p: nat).((le n m) \to ((le m p) @@ -140,12 +179,18 @@ theorem le_trans: m)).(\lambda (H0: (le m p)).(le_ind m (\lambda (n0: nat).(le n n0)) H (\lambda (m0: nat).(\lambda (_: (le m m0)).(\lambda (IHle: (le n m0)).(le_S n m0 IHle)))) p H0))))). +(* COMMENTS +Initial nodes: 57 +END *) theorem le_trans_S: \forall (n: nat).(\forall (m: nat).((le (S n) m) \to (le n m))) \def \lambda (n: nat).(\lambda (m: nat).(\lambda (H: (le (S n) m)).(le_trans n (S n) m (le_S n n (le_n n)) H))). +(* COMMENTS +Initial nodes: 33 +END *) theorem le_n_S: \forall (n: nat).(\forall (m: nat).((le n m) \to (le (S n) (S m)))) @@ -153,12 +198,18 @@ theorem le_n_S: \lambda (n: nat).(\lambda (m: nat).(\lambda (H: (le n m)).(le_ind n (\lambda (n0: nat).(le (S n) (S n0))) (le_n (S n)) (\lambda (m0: nat).(\lambda (_: (le n m0)).(\lambda (IHle: (le (S n) (S m0))).(le_S (S n) (S m0) IHle)))) m H))). +(* COMMENTS +Initial nodes: 65 +END *) theorem le_O_n: \forall (n: nat).(le O n) \def \lambda (n: nat).(nat_ind (\lambda (n0: nat).(le O n0)) (le_n O) (\lambda (n0: nat).(\lambda (IHn: (le O n0)).(le_S O n0 IHn))) n). +(* COMMENTS +Initial nodes: 33 +END *) theorem le_S_n: \forall (n: nat).(\forall (m: nat).((le (S n) (S m)) \to (le n m))) @@ -167,6 +218,9 @@ theorem le_S_n: n) (\lambda (n0: nat).(le (pred (S n)) (pred n0))) (le_n n) (\lambda (m0: nat).(\lambda (H0: (le (S n) m0)).(\lambda (_: (le n (pred m0))).(le_trans_S n m0 H0)))) (S m) H))). +(* COMMENTS +Initial nodes: 69 +END *) theorem le_Sn_O: \forall (n: nat).(not (le (S n) O)) @@ -174,6 +228,9 @@ theorem le_Sn_O: \lambda (n: nat).(\lambda (H: (le (S n) O)).(le_ind (S n) (\lambda (n0: nat).(IsSucc n0)) I (\lambda (m: nat).(\lambda (_: (le (S n) m)).(\lambda (_: (IsSucc m)).I))) O H)). +(* COMMENTS +Initial nodes: 43 +END *) theorem le_Sn_n: \forall (n: nat).(not (le (S n) n)) @@ -181,6 +238,9 @@ theorem le_Sn_n: \lambda (n: nat).(nat_ind (\lambda (n0: nat).(not (le (S n0) n0))) (le_Sn_O O) (\lambda (n0: nat).(\lambda (IHn: (not (le (S n0) n0))).(\lambda (H: (le (S (S n0)) (S n0))).(IHn (le_S_n (S n0) n0 H))))) n). +(* COMMENTS +Initial nodes: 57 +END *) theorem le_antisym: \forall (n: nat).(\forall (m: nat).((le n m) \to ((le m n) \to (eq nat n @@ -192,11 +252,17 @@ nat n)) (\lambda (m0: nat).(\lambda (H: (le n m0)).(\lambda (_: (((le m0 n) \to (eq nat n m0)))).(\lambda (H1: (le (S m0) n)).(False_ind (eq nat n (S m0)) (let H2 \def (le_trans (S m0) n m0 H1 H) in ((let H3 \def (le_Sn_n m0) in (\lambda (H4: (le (S m0) m0)).(H3 H4))) H2))))))) m h))). +(* COMMENTS +Initial nodes: 119 +END *) theorem le_n_O_eq: \forall (n: nat).((le n O) \to (eq nat O n)) \def \lambda (n: nat).(\lambda (H: (le n O)).(le_antisym O n (le_O_n n) H)). +(* COMMENTS +Initial nodes: 19 +END *) theorem le_elim_rel: \forall (P: ((nat \to (nat \to Prop)))).(((\forall (p: nat).(P O p))) \to @@ -213,33 +279,51 @@ m)).(le_ind (S n0) (\lambda (n1: nat).(P (S n0) n1)) (H0 n0 n0 (le_n n0) (IHn n0 (le_n n0))) (\lambda (m0: nat).(\lambda (H1: (le (S n0) m0)).(\lambda (_: (P (S n0) m0)).(H0 n0 m0 (le_trans_S n0 m0 H1) (IHn m0 (le_trans_S n0 m0 H1)))))) m Le))))) n)))). +(* COMMENTS +Initial nodes: 181 +END *) theorem lt_n_n: \forall (n: nat).(not (lt n n)) \def le_Sn_n. +(* COMMENTS +Initial nodes: 1 +END *) theorem lt_n_S: \forall (n: nat).(\forall (m: nat).((lt n m) \to (lt (S n) (S m)))) \def \lambda (n: nat).(\lambda (m: nat).(\lambda (H: (lt n m)).(le_n_S (S n) m H))). +(* COMMENTS +Initial nodes: 19 +END *) theorem lt_n_Sn: \forall (n: nat).(lt n (S n)) \def \lambda (n: nat).(le_n (S n)). +(* COMMENTS +Initial nodes: 7 +END *) theorem lt_S_n: \forall (n: nat).(\forall (m: nat).((lt (S n) (S m)) \to (lt n m))) \def \lambda (n: nat).(\lambda (m: nat).(\lambda (H: (lt (S n) (S m))).(le_S_n (S n) m H))). +(* COMMENTS +Initial nodes: 23 +END *) theorem lt_n_O: \forall (n: nat).(not (lt n O)) \def le_Sn_O. +(* COMMENTS +Initial nodes: 1 +END *) theorem lt_trans: \forall (n: nat).(\forall (m: nat).(\forall (p: nat).((lt n m) \to ((lt m p) @@ -249,16 +333,25 @@ theorem lt_trans: m)).(\lambda (H0: (lt m p)).(le_ind (S m) (\lambda (n0: nat).(lt n n0)) (le_S (S n) m H) (\lambda (m0: nat).(\lambda (_: (le (S m) m0)).(\lambda (IHle: (lt n m0)).(le_S (S n) m0 IHle)))) p H0))))). +(* COMMENTS +Initial nodes: 71 +END *) theorem lt_O_Sn: \forall (n: nat).(lt O (S n)) \def \lambda (n: nat).(le_n_S O n (le_O_n n)). +(* COMMENTS +Initial nodes: 11 +END *) theorem lt_le_S: \forall (n: nat).(\forall (p: nat).((lt n p) \to (le (S n) p))) \def \lambda (n: nat).(\lambda (p: nat).(\lambda (H: (lt n p)).H)). +(* COMMENTS +Initial nodes: 11 +END *) theorem le_not_lt: \forall (n: nat).(\forall (m: nat).((le n m) \to (not (lt m n)))) @@ -267,11 +360,17 @@ theorem le_not_lt: (n0: nat).(not (lt n0 n))) (lt_n_n n) (\lambda (m0: nat).(\lambda (_: (le n m0)).(\lambda (IHle: (not (lt m0 n))).(\lambda (H1: (lt (S m0) n)).(IHle (le_trans_S (S m0) n H1)))))) m H))). +(* COMMENTS +Initial nodes: 67 +END *) theorem le_lt_n_Sm: \forall (n: nat).(\forall (m: nat).((le n m) \to (lt n (S m)))) \def \lambda (n: nat).(\lambda (m: nat).(\lambda (H: (le n m)).(le_n_S n m H))). +(* COMMENTS +Initial nodes: 17 +END *) theorem le_lt_trans: \forall (n: nat).(\forall (m: nat).(\forall (p: nat).((le n m) \to ((lt m p) @@ -281,6 +380,9 @@ theorem le_lt_trans: m)).(\lambda (H0: (lt m p)).(le_ind (S m) (\lambda (n0: nat).(lt n n0)) (le_n_S n m H) (\lambda (m0: nat).(\lambda (_: (le (S m) m0)).(\lambda (IHle: (lt n m0)).(le_S (S n) m0 IHle)))) p H0))))). +(* COMMENTS +Initial nodes: 69 +END *) theorem lt_le_trans: \forall (n: nat).(\forall (m: nat).(\forall (p: nat).((lt n m) \to ((le m p) @@ -290,18 +392,27 @@ theorem lt_le_trans: m)).(\lambda (H0: (le m p)).(le_ind m (\lambda (n0: nat).(lt n n0)) H (\lambda (m0: nat).(\lambda (_: (le m m0)).(\lambda (IHle: (lt n m0)).(le_S (S n) m0 IHle)))) p H0))))). +(* COMMENTS +Initial nodes: 59 +END *) theorem lt_le_weak: \forall (n: nat).(\forall (m: nat).((lt n m) \to (le n m))) \def \lambda (n: nat).(\lambda (m: nat).(\lambda (H: (lt n m)).(le_trans_S n m H))). +(* COMMENTS +Initial nodes: 17 +END *) theorem lt_n_Sm_le: \forall (n: nat).(\forall (m: nat).((lt n (S m)) \to (le n m))) \def \lambda (n: nat).(\lambda (m: nat).(\lambda (H: (lt n (S m))).(le_S_n n m H))). +(* COMMENTS +Initial nodes: 19 +END *) theorem le_lt_or_eq: \forall (n: nat).(\forall (m: nat).((le n m) \to (or (lt n m) (eq nat n m)))) @@ -311,6 +422,9 @@ theorem le_lt_or_eq: (refl_equal nat n)) (\lambda (m0: nat).(\lambda (H0: (le n m0)).(\lambda (_: (or (lt n m0) (eq nat n m0))).(or_introl (lt n (S m0)) (eq nat n (S m0)) (le_n_S n m0 H0))))) m H))). +(* COMMENTS +Initial nodes: 109 +END *) theorem le_or_lt: \forall (n: nat).(\forall (m: nat).(or (le n m) (lt m n))) @@ -324,6 +438,9 @@ n0))).(or_ind (le n0 m0) (lt m0 n0) (or (le (S n0) (S m0)) (lt (S m0) (S n0))) (\lambda (H0: (le n0 m0)).(or_introl (le (S n0) (S m0)) (lt (S m0) (S n0)) (le_n_S n0 m0 H0))) (\lambda (H0: (lt m0 n0)).(or_intror (le (S n0) (S m0)) (lt (S m0) (S n0)) (le_n_S (S m0) n0 H0))) H)))) n m)). +(* COMMENTS +Initial nodes: 209 +END *) theorem plus_n_O: \forall (n: nat).(eq nat n (plus n O)) @@ -331,6 +448,9 @@ theorem plus_n_O: \lambda (n: nat).(nat_ind (\lambda (n0: nat).(eq nat n0 (plus n0 O))) (refl_equal nat O) (\lambda (n0: nat).(\lambda (H: (eq nat n0 (plus n0 O))).(f_equal nat nat S n0 (plus n0 O) H))) n). +(* COMMENTS +Initial nodes: 57 +END *) theorem plus_n_Sm: \forall (n: nat).(\forall (m: nat).(eq nat (S (plus n m)) (plus n (S m)))) @@ -339,6 +459,9 @@ theorem plus_n_Sm: (plus n0 n)) (plus n0 (S n)))) (refl_equal nat (S n)) (\lambda (n0: nat).(\lambda (H: (eq nat (S (plus n0 n)) (plus n0 (S n)))).(f_equal nat nat S (S (plus n0 n)) (plus n0 (S n)) H))) m)). +(* COMMENTS +Initial nodes: 85 +END *) theorem plus_sym: \forall (n: nat).(\forall (m: nat).(eq nat (plus n m) (plus m n))) @@ -348,6 +471,9 @@ n0 m) (plus m n0))) (plus_n_O m) (\lambda (y: nat).(\lambda (H: (eq nat (plus y m) (plus m y))).(eq_ind nat (S (plus m y)) (\lambda (n0: nat).(eq nat (S (plus y m)) n0)) (f_equal nat nat S (plus y m) (plus m y) H) (plus m (S y)) (plus_n_Sm m y)))) n)). +(* COMMENTS +Initial nodes: 111 +END *) theorem plus_Snm_nSm: \forall (n: nat).(\forall (m: nat).(eq nat (plus (S n) m) (plus n (S m)))) @@ -356,6 +482,9 @@ theorem plus_Snm_nSm: nat).(eq nat (S n0) (plus n (S m)))) (eq_ind_r nat (plus (S m) n) (\lambda (n0: nat).(eq nat (S (plus m n)) n0)) (refl_equal nat (plus (S m) n)) (plus n (S m)) (plus_sym n (S m))) (plus n m) (plus_sym n m))). +(* COMMENTS +Initial nodes: 99 +END *) theorem plus_assoc_l: \forall (n: nat).(\forall (m: nat).(\forall (p: nat).(eq nat (plus n (plus m @@ -366,6 +495,9 @@ nat).(eq nat (plus n0 (plus m p)) (plus (plus n0 m) p))) (refl_equal nat (plus m p)) (\lambda (n0: nat).(\lambda (H: (eq nat (plus n0 (plus m p)) (plus (plus n0 m) p))).(f_equal nat nat S (plus n0 (plus m p)) (plus (plus n0 m) p) H))) n))). +(* COMMENTS +Initial nodes: 101 +END *) theorem plus_assoc_r: \forall (n: nat).(\forall (m: nat).(\forall (p: nat).(eq nat (plus (plus n @@ -373,6 +505,9 @@ m) p) (plus n (plus m p))))) \def \lambda (n: nat).(\lambda (m: nat).(\lambda (p: nat).(sym_eq nat (plus n (plus m p)) (plus (plus n m) p) (plus_assoc_l n m p)))). +(* COMMENTS +Initial nodes: 37 +END *) theorem simpl_plus_l: \forall (n: nat).(\forall (m: nat).(\forall (p: nat).((eq nat (plus n m) @@ -386,6 +521,9 @@ nat).(\lambda (IHn: ((\forall (m: nat).(\forall (p: nat).((eq nat (plus n0 m) nat).(\lambda (H: (eq nat (S (plus n0 m)) (S (plus n0 p)))).(IHn m p (IHn (plus n0 m) (plus n0 p) (f_equal nat nat (plus n0) (plus n0 m) (plus n0 p) (eq_add_S (plus n0 m) (plus n0 p) H))))))))) n). +(* COMMENTS +Initial nodes: 161 +END *) theorem minus_n_O: \forall (n: nat).(eq nat n (minus n O)) @@ -393,6 +531,9 @@ theorem minus_n_O: \lambda (n: nat).(nat_ind (\lambda (n0: nat).(eq nat n0 (minus n0 O))) (refl_equal nat O) (\lambda (n0: nat).(\lambda (_: (eq nat n0 (minus n0 O))).(refl_equal nat (S n0)))) n). +(* COMMENTS +Initial nodes: 47 +END *) theorem minus_n_n: \forall (n: nat).(eq nat O (minus n n)) @@ -400,6 +541,9 @@ theorem minus_n_n: \lambda (n: nat).(nat_ind (\lambda (n0: nat).(eq nat O (minus n0 n0))) (refl_equal nat O) (\lambda (n0: nat).(\lambda (IHn: (eq nat O (minus n0 n0))).IHn)) n). +(* COMMENTS +Initial nodes: 41 +END *) theorem minus_Sn_m: \forall (n: nat).(\forall (m: nat).((le m n) \to (eq nat (S (minus n m)) @@ -411,6 +555,9 @@ n0)))) (\lambda (p: nat).(f_equal nat nat S (minus p O) p (sym_eq nat p (minus p O) (minus_n_O p)))) (\lambda (p: nat).(\lambda (q: nat).(\lambda (_: (le p q)).(\lambda (H0: (eq nat (S (minus q p)) (match p with [O \Rightarrow (S q) | (S l) \Rightarrow (minus q l)]))).H0)))) m n Le))). +(* COMMENTS +Initial nodes: 111 +END *) theorem plus_minus: \forall (n: nat).(\forall (m: nat).(\forall (p: nat).((eq nat n (plus m p)) @@ -426,12 +573,18 @@ p)) in (\lambda (H2: (eq nat O (S (plus n0 p)))).(H1 H2))) H0))))) (\lambda (n0: nat).(\lambda (m0: nat).(\lambda (H: (((eq nat m0 (plus n0 p)) \to (eq nat p (minus m0 n0))))).(\lambda (H0: (eq nat (S m0) (S (plus n0 p)))).(H (eq_add_S m0 (plus n0 p) H0)))))) m n))). +(* COMMENTS +Initial nodes: 199 +END *) theorem minus_plus: \forall (n: nat).(\forall (m: nat).(eq nat (minus (plus n m) n) m)) \def \lambda (n: nat).(\lambda (m: nat).(sym_eq nat m (minus (plus n m) n) (plus_minus (plus n m) n m (refl_equal nat (plus n m))))). +(* COMMENTS +Initial nodes: 41 +END *) theorem le_pred_n: \forall (n: nat).(le (pred n) n) @@ -439,6 +592,9 @@ theorem le_pred_n: \lambda (n: nat).(nat_ind (\lambda (n0: nat).(le (pred n0) n0)) (le_n O) (\lambda (n0: nat).(\lambda (_: (le (pred n0) n0)).(le_S (pred (S n0)) n0 (le_n n0)))) n). +(* COMMENTS +Initial nodes: 43 +END *) theorem le_plus_l: \forall (n: nat).(\forall (m: nat).(le n (plus n m))) @@ -447,6 +603,9 @@ theorem le_plus_l: n0 m)))) (\lambda (m: nat).(le_O_n m)) (\lambda (n0: nat).(\lambda (IHn: ((\forall (m: nat).(le n0 (plus n0 m))))).(\lambda (m: nat).(le_n_S n0 (plus n0 m) (IHn m))))) n). +(* COMMENTS +Initial nodes: 55 +END *) theorem le_plus_r: \forall (n: nat).(\forall (m: nat).(le m (plus n m))) @@ -454,6 +613,9 @@ theorem le_plus_r: \lambda (n: nat).(\lambda (m: nat).(nat_ind (\lambda (n0: nat).(le m (plus n0 m))) (le_n m) (\lambda (n0: nat).(\lambda (H: (le m (plus n0 m))).(le_S m (plus n0 m) H))) n)). +(* COMMENTS +Initial nodes: 47 +END *) theorem simpl_le_plus_l: \forall (p: nat).(\forall (n: nat).(\forall (m: nat).((le (plus p n) (plus p @@ -466,6 +628,9 @@ nat).(\lambda (IHp: ((\forall (n: nat).(\forall (m: nat).((le (plus p0 n) (plus p0 m)) \to (le n m)))))).(\lambda (n: nat).(\lambda (m: nat).(\lambda (H: (le (S (plus p0 n)) (S (plus p0 m)))).(IHp n m (le_S_n (plus p0 n) (plus p0 m) H))))))) p). +(* COMMENTS +Initial nodes: 113 +END *) theorem le_plus_trans: \forall (n: nat).(\forall (m: nat).(\forall (p: nat).((le n m) \to (le n @@ -473,6 +638,9 @@ theorem le_plus_trans: \def \lambda (n: nat).(\lambda (m: nat).(\lambda (p: nat).(\lambda (H: (le n m)).(le_trans n m (plus m p) H (le_plus_l m p))))). +(* COMMENTS +Initial nodes: 31 +END *) theorem le_reg_l: \forall (n: nat).(\forall (m: nat).(\forall (p: nat).((le n m) \to (le (plus @@ -483,6 +651,9 @@ nat).((le n m) \to (le (plus n0 n) (plus n0 m)))) (\lambda (H: (le n m)).H) (\lambda (p0: nat).(\lambda (IHp: (((le n m) \to (le (plus p0 n) (plus p0 m))))).(\lambda (H: (le n m)).(le_n_S (plus p0 n) (plus p0 m) (IHp H))))) p))). +(* COMMENTS +Initial nodes: 85 +END *) theorem le_plus_plus: \forall (n: nat).(\forall (m: nat).(\forall (p: nat).(\forall (q: nat).((le @@ -493,6 +664,9 @@ nat).(\lambda (H: (le n m)).(\lambda (H0: (le p q)).(le_ind n (\lambda (n0: nat).(le (plus n p) (plus n0 q))) (le_reg_l p q n H0) (\lambda (m0: nat).(\lambda (_: (le n m0)).(\lambda (H2: (le (plus n p) (plus m0 q))).(le_S (plus n p) (plus m0 q) H2)))) m H)))))). +(* COMMENTS +Initial nodes: 91 +END *) theorem le_plus_minus: \forall (n: nat).(\forall (m: nat).((le n m) \to (eq nat m (plus n (minus m @@ -503,6 +677,9 @@ n))))) (\lambda (p: nat).(minus_n_O p)) (\lambda (p: nat).(\lambda (q: nat).(\lambda (_: (le p q)).(\lambda (H0: (eq nat q (plus p (minus q p)))).(f_equal nat nat S q (plus p (minus q p)) H0))))) n m Le))). +(* COMMENTS +Initial nodes: 91 +END *) theorem le_plus_minus_r: \forall (n: nat).(\forall (m: nat).((le n m) \to (eq nat (plus n (minus m @@ -510,6 +687,9 @@ n)) m))) \def \lambda (n: nat).(\lambda (m: nat).(\lambda (H: (le n m)).(sym_eq nat m (plus n (minus m n)) (le_plus_minus n m H)))). +(* COMMENTS +Initial nodes: 33 +END *) theorem simpl_lt_plus_l: \forall (n: nat).(\forall (m: nat).(\forall (p: nat).((lt (plus p n) (plus p @@ -520,6 +700,9 @@ nat).((lt (plus n0 n) (plus n0 m)) \to (lt n m))) (\lambda (H: (lt n m)).H) (\lambda (p0: nat).(\lambda (IHp: (((lt (plus p0 n) (plus p0 m)) \to (lt n m)))).(\lambda (H: (lt (S (plus p0 n)) (S (plus p0 m)))).(IHp (le_S_n (S (plus p0 n)) (plus p0 m) H))))) p))). +(* COMMENTS +Initial nodes: 99 +END *) theorem lt_reg_l: \forall (n: nat).(\forall (m: nat).(\forall (p: nat).((lt n m) \to (lt (plus @@ -530,6 +713,9 @@ nat).((lt n m) \to (lt (plus n0 n) (plus n0 m)))) (\lambda (H: (lt n m)).H) (\lambda (p0: nat).(\lambda (IHp: (((lt n m) \to (lt (plus p0 n) (plus p0 m))))).(\lambda (H: (lt n m)).(lt_n_S (plus p0 n) (plus p0 m) (IHp H))))) p))). +(* COMMENTS +Initial nodes: 85 +END *) theorem lt_reg_r: \forall (n: nat).(\forall (m: nat).(\forall (p: nat).((lt n m) \to (lt (plus @@ -541,6 +727,9 @@ nat (plus p m) (\lambda (n0: nat).(lt (plus p n) n0)) (nat_ind (\lambda (n0: nat).(lt (plus n0 n) (plus n0 m))) H (\lambda (n0: nat).(\lambda (_: (lt (plus n0 n) (plus n0 m))).(lt_reg_l n m (S n0) H))) p) (plus m p) (plus_sym m p)) (plus n p) (plus_sym n p))))). +(* COMMENTS +Initial nodes: 129 +END *) theorem le_lt_plus_plus: \forall (n: nat).(\forall (m: nat).(\forall (p: nat).(\forall (q: nat).((le @@ -550,6 +739,9 @@ n m) \to ((lt p q) \to (lt (plus n p) (plus m q))))))) nat).(\lambda (H: (le n m)).(\lambda (H0: (le (S p) q)).(eq_ind_r nat (plus n (S p)) (\lambda (n0: nat).(le n0 (plus m q))) (le_plus_plus n m (S p) q H H0) (plus (S n) p) (plus_Snm_nSm n p))))))). +(* COMMENTS +Initial nodes: 75 +END *) theorem lt_le_plus_plus: \forall (n: nat).(\forall (m: nat).(\forall (p: nat).(\forall (q: nat).((lt @@ -558,6 +750,9 @@ n m) \to ((le p q) \to (lt (plus n p) (plus m q))))))) \lambda (n: nat).(\lambda (m: nat).(\lambda (p: nat).(\lambda (q: nat).(\lambda (H: (le (S n) m)).(\lambda (H0: (le p q)).(le_plus_plus (S n) m p q H H0)))))). +(* COMMENTS +Initial nodes: 37 +END *) theorem lt_plus_plus: \forall (n: nat).(\forall (m: nat).(\forall (p: nat).(\forall (q: nat).((lt @@ -566,6 +761,9 @@ n m) \to ((lt p q) \to (lt (plus n p) (plus m q))))))) \lambda (n: nat).(\lambda (m: nat).(\lambda (p: nat).(\lambda (q: nat).(\lambda (H: (lt n m)).(\lambda (H0: (lt p q)).(lt_le_plus_plus n m p q H (lt_le_weak p q H0))))))). +(* COMMENTS +Initial nodes: 39 +END *) theorem well_founded_ltof: \forall (A: Set).(\forall (f: ((A \to nat))).(well_founded A (ltof A f))) @@ -580,11 +778,17 @@ nat).(nat_ind (\lambda (n0: nat).(\forall (a: A).((lt (f a) n0) \to (Acc A (ltfafb: (lt (f b) (f a))).(IHn b (lt_le_trans (f b) (f a) n0 ltfafb (lt_n_Sm_le (f a) n0 ltSma)))))))))) n)) in (\lambda (a: A).(H (S (f a)) a (le_n (S (f a))))))). +(* COMMENTS +Initial nodes: 189 +END *) theorem lt_wf: well_founded nat lt \def well_founded_ltof nat (\lambda (m: nat).m). +(* COMMENTS +Initial nodes: 7 +END *) theorem lt_wf_ind: \forall (p: nat).(\forall (P: ((nat \to Prop))).(((\forall (n: @@ -595,4 +799,7 @@ nat).(((\forall (m: nat).((lt m n) \to (P m)))) \to (P n))))).(Acc_ind nat lt (\lambda (n: nat).(P n)) (\lambda (x: nat).(\lambda (_: ((\forall (y: nat).((lt y x) \to (Acc nat lt y))))).(\lambda (H1: ((\forall (y: nat).((lt y x) \to (P y))))).(H x H1)))) p (lt_wf p)))). +(* COMMENTS +Initial nodes: 77 +END *) -- 2.39.2