From a89360d64f1fcbba917ad743b97a2d973ecf6db2 Mon Sep 17 00:00:00 2001 From: Ferruccio Guidi Date: Sat, 23 Aug 2008 13:18:57 +0000 Subject: [PATCH] Procedural: explicit flavour specification for constants is now working procedural inlining of inductive types is now working fixup in the generation of comments grafiteAstPp: syntax fixup transcript: now generates explicit flavour for inlined constants so we distinguish between definitions and theorems :) [the attributes are not present when we inline from Coq's library] CoRN-Procedural: mma files regenerated with explicit flavours --- .../acic_procedural/acic2Procedural.ml | 76 ++-- .../acic_procedural/proceduralTypes.ml | 64 +++- .../acic_procedural/proceduralTypes.mli | 3 + .../components/binaries/transcript/engine.ml | 4 +- .../components/binaries/transcript/grafite.ml | 8 +- .../components/binaries/transcript/types.ml | 4 +- .../binaries/transcript/v8Parser.mly | 86 +++-- .../components/grafite/grafiteAstPp.ml | 16 +- .../CoRN-Procedural/algebra/Basics.mma | 84 ++--- .../CoRN-Procedural/algebra/CAbGroups.mma | 80 ++-- .../CoRN-Procedural/algebra/CAbMonoids.mma | 14 +- .../CoRN-Procedural/algebra/CFields.mma | 140 +++---- .../CoRN-Procedural/algebra/CGroups.mma | 106 +++--- .../CoRN-Procedural/algebra/CLogic.mma | 210 +++++------ .../CoRN-Procedural/algebra/CMonoids.mma | 28 +- .../CoRN-Procedural/algebra/COrdAbs.mma | 58 +-- .../CoRN-Procedural/algebra/COrdCauchy.mma | 82 ++--- .../CoRN-Procedural/algebra/COrdFields.mma | 270 +++++++------- .../CoRN-Procedural/algebra/COrdFields2.mma | 170 ++++----- .../CoRN-Procedural/algebra/CPoly_ApZero.mma | 50 +-- .../CoRN-Procedural/algebra/CPoly_Degree.mma | 96 ++--- .../algebra/CPoly_NthCoeff.mma | 60 +-- .../CoRN-Procedural/algebra/CPolynomials.mma | 342 +++++++++--------- .../CoRN-Procedural/algebra/CRings.mma | 248 ++++++------- .../CoRN-Procedural/algebra/CSemiGroups.mma | 26 +- .../CoRN-Procedural/algebra/CSetoidFun.mma | 108 +++--- .../CoRN-Procedural/algebra/CSetoidInc.mma | 26 +- .../CoRN-Procedural/algebra/CSetoids.mma | 258 ++++++------- .../CoRN-Procedural/algebra/CSums.mma | 94 ++--- .../CoRN-Procedural/algebra/CVectorSpace.mma | 20 +- .../CoRN-Procedural/algebra/Cauchy_COF.mma | 114 +++--- .../CoRN-Procedural/algebra/Expon.mma | 84 ++--- .../CoRN-Procedural/algebra/ListType.mma | 56 +-- .../CoRN-Procedural/complex/AbsCC.mma | 64 ++-- .../CoRN-Procedural/complex/CComplex.mma | 166 ++++----- .../complex/Complex_Exponential.mma | 32 +- .../CoRN-Procedural/complex/NRootCC.mma | 172 ++++----- .../CoRN-Procedural/devel/loeb/IDA/Ch6.mma | 252 ++++++------- .../devel/loeb/per/csetfun.mma | 46 +-- .../devel/loeb/per/lst2fun.mma | 20 +- .../contribs/CoRN-Procedural/fta/CC_Props.mma | 46 +-- .../CoRN-Procedural/fta/CPoly_Contin1.mma | 10 +- .../CoRN-Procedural/fta/CPoly_Rev.mma | 50 +-- .../CoRN-Procedural/fta/CPoly_Shift.mma | 14 +- .../contribs/CoRN-Procedural/fta/FTA.mma | 18 +- .../contribs/CoRN-Procedural/fta/FTAreg.mma | 52 +-- .../contribs/CoRN-Procedural/fta/KeyLemma.mma | 68 ++-- .../CoRN-Procedural/fta/KneserLemma.mma | 48 +-- .../CoRN-Procedural/fta/MainLemma.mma | 28 +- .../CoRN-Procedural/ftc/COrdLemmas.mma | 30 +- .../CoRN-Procedural/ftc/CalculusTheorems.mma | 32 +- .../CoRN-Procedural/ftc/Composition.mma | 60 +-- .../CoRN-Procedural/ftc/Continuity.mma | 110 +++--- .../CoRN-Procedural/ftc/Derivative.mma | 38 +- .../CoRN-Procedural/ftc/DerivativeOps.mma | 42 +-- .../CoRN-Procedural/ftc/Differentiability.mma | 50 +-- .../contribs/CoRN-Procedural/ftc/FTC.mma | 38 +- .../CoRN-Procedural/ftc/FunctSequence.mma | 128 +++---- .../CoRN-Procedural/ftc/FunctSeries.mma | 74 ++-- .../CoRN-Procedural/ftc/FunctSums.mma | 70 ++-- .../contribs/CoRN-Procedural/ftc/Integral.mma | 100 ++--- .../CoRN-Procedural/ftc/IntervalFunct.mma | 50 +-- .../CoRN-Procedural/ftc/MoreFunSeries.mma | 148 ++++---- .../CoRN-Procedural/ftc/MoreFunctions.mma | 196 +++++----- .../CoRN-Procedural/ftc/MoreIntegrals.mma | 90 ++--- .../CoRN-Procedural/ftc/MoreIntervals.mma | 158 ++++---- .../CoRN-Procedural/ftc/NthDerivative.mma | 76 ++-- .../CoRN-Procedural/ftc/PartFunEquality.mma | 78 ++-- .../CoRN-Procedural/ftc/PartInterval.mma | 34 +- .../CoRN-Procedural/ftc/Partitions.mma | 88 ++--- .../contribs/CoRN-Procedural/ftc/RefLemma.mma | 138 +++---- .../CoRN-Procedural/ftc/RefSepRef.mma | 88 ++--- .../CoRN-Procedural/ftc/RefSeparated.mma | 80 ++-- .../CoRN-Procedural/ftc/RefSeparating.mma | 96 ++--- .../contribs/CoRN-Procedural/ftc/Rolle.mma | 96 ++--- .../CoRN-Procedural/ftc/StrongIVT.mma | 64 ++-- .../contribs/CoRN-Procedural/ftc/Taylor.mma | 28 +- .../CoRN-Procedural/ftc/TaylorLemma.mma | 80 ++-- .../contribs/CoRN-Procedural/ftc/WeakIVT.mma | 60 +-- .../CoRN-Procedural/metrics/CMetricSpaces.mma | 72 ++-- .../CoRN-Procedural/metrics/CPMSTheory.mma | 62 ++-- .../metrics/CPseudoMSpaces.mma | 48 +-- .../CoRN-Procedural/metrics/ContFunctions.mma | 64 ++-- .../CoRN-Procedural/metrics/Equiv.mma | 18 +- .../CoRN-Procedural/metrics/IR_CPMSpace.mma | 34 +- .../CoRN-Procedural/metrics/Prod_Sub.mma | 42 +-- .../model/abgroups/QSposabgroup.mma | 4 +- .../model/abgroups/Qabgroup.mma | 4 +- .../model/abgroups/Qposabgroup.mma | 4 +- .../model/abgroups/Zabgroup.mma | 4 +- .../CoRN-Procedural/model/fields/Qfield.mma | 4 +- .../model/groups/QSposgroup.mma | 4 +- .../CoRN-Procedural/model/groups/Qgroup.mma | 4 +- .../model/groups/Qposgroup.mma | 4 +- .../CoRN-Procedural/model/groups/Zgroup.mma | 4 +- .../CoRN-Procedural/model/monoids/Nmonoid.mma | 8 +- .../model/monoids/Nposmonoid.mma | 8 +- .../model/monoids/QSposmonoid.mma | 8 +- .../CoRN-Procedural/model/monoids/Qmonoid.mma | 16 +- .../model/monoids/Qposmonoid.mma | 8 +- .../CoRN-Procedural/model/monoids/Zmonoid.mma | 16 +- .../model/non_examples/N_no_group.mma | 4 +- .../model/non_examples/Npos_no_group.mma | 4 +- .../model/non_examples/Npos_no_monoid.mma | 4 +- .../model/ordfields/Qordfield.mma | 8 +- .../CoRN-Procedural/model/reals/Cauchy_IR.mma | 2 +- .../CoRN-Procedural/model/rings/Qring.mma | 12 +- .../CoRN-Procedural/model/rings/Zring.mma | 6 +- .../model/semigroups/Npossemigroup.mma | 6 +- .../model/semigroups/Nsemigroup.mma | 2 +- .../model/semigroups/QSpossemigroup.mma | 2 +- .../model/semigroups/Qpossemigroup.mma | 2 +- .../model/semigroups/Qsemigroup.mma | 4 +- .../model/semigroups/Zsemigroup.mma | 4 +- .../model/setoids/Npossetoid.mma | 20 +- .../CoRN-Procedural/model/setoids/Nsetoid.mma | 26 +- .../model/setoids/Qpossetoid.mma | 36 +- .../CoRN-Procedural/model/setoids/Qsetoid.mma | 42 +-- .../CoRN-Procedural/model/setoids/Zsetoid.mma | 38 +- .../model/structures/Npossec.mma | 6 +- .../CoRN-Procedural/model/structures/Nsec.mma | 18 +- .../model/structures/Qpossec.mma | 18 +- .../CoRN-Procedural/model/structures/Qsec.mma | 110 +++--- .../CoRN-Procedural/model/structures/Zsec.mma | 40 +- .../CoRN-Procedural/reals/Bridges_LUB.mma | 118 +++--- .../CoRN-Procedural/reals/Bridges_iso.mma | 136 +++---- .../CoRN-Procedural/reals/CMetricFields.mma | 12 +- .../CoRN-Procedural/reals/CPoly_Contin.mma | 8 +- .../contribs/CoRN-Procedural/reals/CReals.mma | 2 +- .../CoRN-Procedural/reals/CReals1.mma | 40 +- .../CoRN-Procedural/reals/CSumsReals.mma | 28 +- .../CoRN-Procedural/reals/CauchySeq.mma | 126 +++---- .../CoRN-Procedural/reals/Cauchy_CReals.mma | 62 ++-- .../contribs/CoRN-Procedural/reals/IVT.mma | 64 ++-- .../CoRN-Procedural/reals/Intervals.mma | 78 ++-- .../CoRN-Procedural/reals/Max_AbsIR.mma | 204 +++++------ .../CoRN-Procedural/reals/NRootIR.mma | 98 ++--- .../CoRN-Procedural/reals/OddPolyRootIR.mma | 44 +-- .../CoRN-Procedural/reals/Q_dense.mma | 78 ++-- .../CoRN-Procedural/reals/Q_in_CReals.mma | 58 +-- .../CoRN-Procedural/reals/R_morphism.mma | 82 ++--- .../CoRN-Procedural/reals/RealFuncts.mma | 36 +- .../CoRN-Procedural/reals/RealLists.mma | 36 +- .../contribs/CoRN-Procedural/reals/Series.mma | 110 +++--- .../CoRN-Procedural/reals/iso_CReals.mma | 74 ++-- .../CoRN-Procedural/tactics/AlgReflection.mma | 78 ++-- .../CoRN-Procedural/tactics/DiffTactics2.mma | 12 +- .../CoRN-Procedural/tactics/DiffTactics3.mma | 4 +- .../tactics/FieldReflection.mma | 62 ++-- .../tactics/GroupReflection.mma | 52 +-- .../tactics/RingReflection.mma | 50 +-- .../CoRN-Procedural/transc/Exponential.mma | 114 +++--- .../CoRN-Procedural/transc/InvTrigonom.mma | 126 +++---- .../contribs/CoRN-Procedural/transc/Pi.mma | 118 +++--- .../CoRN-Procedural/transc/PowerSeries.mma | 78 ++-- .../CoRN-Procedural/transc/RealPowers.mma | 50 +-- .../CoRN-Procedural/transc/SinCos.mma | 48 +-- .../CoRN-Procedural/transc/TaylorSeries.mma | 38 +- .../CoRN-Procedural/transc/TrigMon.mma | 36 +- .../CoRN-Procedural/transc/Trigonometric.mma | 42 +-- 160 files changed, 4973 insertions(+), 4874 deletions(-) diff --git a/helm/software/components/acic_procedural/acic2Procedural.ml b/helm/software/components/acic_procedural/acic2Procedural.ml index 4d5e3a668..1660df50d 100644 --- a/helm/software/components/acic_procedural/acic2Procedural.ml +++ b/helm/software/components/acic_procedural/acic2Procedural.ml @@ -38,6 +38,7 @@ module Pp = CicPp module PEH = ProofEngineHelpers module HEL = HExtlib module DTI = DoubleTypeInference +module NU = CicNotationUtil module Cl = ProceduralClassify module T = ProceduralTypes @@ -431,16 +432,15 @@ and proc_proof st t = and proc_bkd_proofs st synth names classes ts = try - let get_note = - let names = ref (names, push st) in - fun f -> - match !names with - | [], st -> fun _ -> f st - | "" :: tl, st -> names := tl, st; fun _ -> f st - | hd :: tl, st -> - let note = case st hd in - names := tl, inc st; - fun b -> if b then T.Note note :: f st else f st + let get_names b = ref (names, if b then push st else st) in + let get_note f b names = + match !names with + | [], st -> f st + | "" :: tl, st -> names := tl, st; f st + | hd :: tl, st -> + let note = case st hd in + names := tl, inc st; + if b then T.Note note :: f st else f st in let _, dtext = test_depth st in let aux (inv, _) v = @@ -450,32 +450,46 @@ try in let ps = T.list_map2_filter aux classes ts in let b = List.length ps > 1 in - List.rev_map (fun f -> f b) ps + let names = get_names b in + List.rev_map (fun f -> f b names) ps with Invalid_argument s -> failwith ("A2P.proc_bkd_proofs: " ^ s) (* object costruction *******************************************************) -let is_theorem pars = - pars = [] || - List.mem (`Flavour `Theorem) pars || List.mem (`Flavour `Fact) pars || - List.mem (`Flavour `Remark) pars || List.mem (`Flavour `Lemma) pars - -let is_definition pars = - List.mem (`Flavour `Definition) pars - -let proc_obj st = function - | C.AConstant (_, _, s, Some v, t, [], pars) when is_theorem pars -> - let ast = proc_proof st v in - let steps, nodes = T.count_steps 0 ast, T.count_nodes 0 ast in - let text = Printf.sprintf "tactics: %u\nnodes: %u" steps nodes in - T.Statement (`Theorem, Some s, t, None, "") :: ast @ [T.Qed text] - | C.AConstant (_, _, s, Some v, t, [], pars) when is_definition pars -> - [T.Statement (`Definition, Some s, t, Some v, "")] - | C.AConstant (_, _, s, None, t, [], pars) -> +let th_flavours = [`Theorem; `Lemma; `Remark; `Fact] + +let def_flavours = [`Definition] + +let get_flavour ?flavour attrs = + let rec aux = function + | [] -> List.hd th_flavours + | `Flavour fl :: _ -> fl + | _ :: tl -> aux tl + in + match flavour with + | Some fl -> fl + | None -> aux attrs + +let proc_obj ?flavour st = function + | C.AConstant (_, _, s, Some v, t, [], attrs) -> + begin match get_flavour ?flavour attrs with + | flavour when List.mem flavour th_flavours -> + let ast = proc_proof st v in + let steps, nodes = T.count_steps 0 ast, T.count_nodes 0 ast in + let text = Printf.sprintf "tactics: %u\nnodes: %u" steps nodes in + T.Statement (flavour, Some s, t, None, "") :: ast @ [T.Qed text] + | flavour when List.mem flavour def_flavours -> + [T.Statement (flavour, Some s, t, Some v, "")] + | _ -> + failwith "not a theorem, definition, axiom or inductive type" + end + | C.AConstant (_, _, s, None, t, [], attrs) -> [T.Statement (`Axiom, Some s, t, None, "")] - | _ -> - failwith "not a theorem, definition, axiom" + | C.AInductiveDefinition (_, types, [], lpsno, attrs) -> + [T.Inductive (types, lpsno, "")] + | _ -> + failwith "not a theorem, definition, axiom or inductive type" (* interface functions ******************************************************) @@ -490,7 +504,7 @@ let procedural_of_acic_object ~ids_to_inner_sorts ~ids_to_inner_types ?depth case = [] } in HLog.debug "Procedural: level 2 transformation"; - let steps = proc_obj st anobj in + let steps = proc_obj st ?flavour anobj in HLog.debug "Procedural: grafite rendering"; List.rev (T.render_steps [] steps) diff --git a/helm/software/components/acic_procedural/proceduralTypes.ml b/helm/software/components/acic_procedural/proceduralTypes.ml index d505a8b15..b194fbfa9 100644 --- a/helm/software/components/acic_procedural/proceduralTypes.ml +++ b/helm/software/components/acic_procedural/proceduralTypes.ml @@ -54,21 +54,24 @@ let list_init f i = (****************************************************************************) -type flavour = Cic.object_flavour +type flavour = C.object_flavour type name = string option type hyp = string -type what = Cic.annterm +type what = C.annterm type how = bool -type using = Cic.annterm +type using = C.annterm type count = int type note = string type where = (hyp * name) option -type inferred = Cic.annterm -type pattern = Cic.annterm -type body = Cic.annterm option +type inferred = C.annterm +type pattern = C.annterm +type body = C.annterm option +type types = C.anninductiveType list +type lpsno = int type step = Note of note - | Statement of flavour * name * what * body * note + | Inductive of types * lpsno * note + | Statement of flavour * name * what * body * note | Qed of note | Id of note | Intros of count option * name list * note @@ -84,7 +87,34 @@ type step = Note of note (* annterm constructors *****************************************************) -let mk_arel i b = Cic.ARel ("", "", i, b) +let mk_arel i b = C.ARel ("", "", i, b) + +(* FG: this is really awful !! *) +let arel_of_name = function + | C.Name s -> mk_arel 0 s + | C.Anonymous -> mk_arel 0 "_" + +(* helper functions on left params for use with inductive types *************) + +let strip_lps lpsno arity = + let rec aux no lps = function + | C.AProd (_, name, w, t) when no > 0 -> + let lp = name, Some w in + aux (pred no) (lp :: lps) t + | t -> lps, t + in + aux lpsno [] arity + +let merge_lps lps1 lps2 = + let map (n1, w1) (n2, _) = + let n = match n1, n2 with + | C.Name _, _ -> n1 + | _ -> n2 + in + n, w1 + in + if lps1 = [] then lps2 else + List.map2 map lps1 lps2 (* grafite ast constructors *************************************************) @@ -101,6 +131,22 @@ let mk_notenote str a = let mk_thnote str a = if str = "" then a else mk_note "" :: mk_note str :: a +let mk_inductive types lpsno = + let map1 (lps1, cons) (name, arity) = + let lps2, arity = strip_lps lpsno arity in + merge_lps lps1 lps2, (name, arity) :: cons + in + let map2 (lps1, types) (_, name, kind, arity, cons) = + let lps2, arity = strip_lps lpsno arity in + let lps1, rev_cons = List.fold_left map1 (lps1, []) cons in + merge_lps lps1 lps2, (name, kind, arity, List.rev rev_cons) :: types + in + let map3 (name, xw) = arel_of_name name, xw in + let rev_lps, rev_types = List.fold_left map2 ([], []) types in + let lpars, types = List.rev_map map3 rev_lps, List.rev rev_types in + let obj = N.Inductive (lpars, types) in + G.Executable (floc, G.Command (floc, G.Obj (floc, obj))) + let mk_statement flavour name t v = let name = match name with Some name -> name | None -> assert false in let obj = N.Theorem (flavour, name, t, v) in @@ -185,6 +231,7 @@ let mk_vb = G.Shift floc let rec render_step sep a = function | Note s -> mk_notenote s a | Statement (f, n, t, v, s) -> mk_statement f n t v :: mk_thnote s a + | Inductive (lps, ts, s) -> mk_inductive lps ts :: mk_thnote s a | Qed s -> mk_qed :: mk_tacnote s a | Id s -> mk_id sep :: mk_tacnote s a | Intros (c, ns, s) -> mk_intros c ns sep :: mk_tacnote s a @@ -228,6 +275,7 @@ and count_steps a = List.fold_left count_step a let rec count_node a = function | Note _ + | Inductive _ | Statement _ | Qed _ | Id _ diff --git a/helm/software/components/acic_procedural/proceduralTypes.mli b/helm/software/components/acic_procedural/proceduralTypes.mli index b750688a6..3cc482a8c 100644 --- a/helm/software/components/acic_procedural/proceduralTypes.mli +++ b/helm/software/components/acic_procedural/proceduralTypes.mli @@ -45,8 +45,11 @@ type where = (hyp * name) option type inferred = Cic.annterm type pattern = Cic.annterm type body = Cic.annterm option +type types = Cic.anninductiveType list +type lpsno = int type step = Note of note + | Inductive of types * lpsno * note | Statement of flavour * name * what * body * note | Qed of note | Id of note diff --git a/helm/software/components/binaries/transcript/engine.ml b/helm/software/components/binaries/transcript/engine.ml index f4b0c1e37..8009483f1 100644 --- a/helm/software/components/binaries/transcript/engine.ml +++ b/helm/software/components/binaries/transcript/engine.ml @@ -189,13 +189,13 @@ let produce st = let in_base_uri = Filename.concat st.input_base_uri name in let out_base_uri = Filename.concat st.output_base_uri name in let filter path = function - | T.Inline (b, k, obj, p) -> + | T.Inline (b, k, obj, p, f) -> let obj, p = if b then Filename.concat (make_path path) obj, make_prefix path else obj, p in let s = obj ^ G.string_of_inline_kind k in - path, Some (T.Inline (b, k, Filename.concat in_base_uri s, p)) + path, Some (T.Inline (b, k, Filename.concat in_base_uri s, p, f)) | T.Include s -> begin try path, Some (T.Include (List.assoc s st.requires)) diff --git a/helm/software/components/binaries/transcript/grafite.ml b/helm/software/components/binaries/transcript/grafite.ml index 83b745980..9e634d655 100644 --- a/helm/software/components/binaries/transcript/grafite.ml +++ b/helm/software/components/binaries/transcript/grafite.ml @@ -78,26 +78,26 @@ let require value = let coercion value = command_of_obj (G.Coercion (floc, UM.uri_of_string value, true, 0, 0)) -let inline (kind, uri, prefix) = +let inline (kind, uri, prefix, flavour) = let kind = match kind with | T.Declarative -> G.Declarative | T.Procedural -> G.Procedural None in - command_of_macro (G.Inline (floc, kind, uri, prefix, None)) + command_of_macro (G.Inline (floc, kind, uri, prefix, flavour)) let out_alias och name uri = Printf.fprintf och "alias id \"%s\" = \"%s\".\n\n" name uri let commit kind och items = let trd (_, _, x) = x in - let trd_rth kind (_, _, x, y) = kind, x, y in + let trd_rth kind (_, _, x, y, z) = kind, x, y, z in let commit = function | T.Heading heading -> out_preamble och heading | T.Line line -> out_line_comment och line | T.Include script -> out_command och (require script) | T.Coercion specs -> out_unexported och "COERCION" (snd specs) | T.Notation specs -> out_unexported och "NOTATION" (snd specs) (**) - | T.Inline (_, T.Var, src, _) -> out_alias och (UriManager.name_of_uri (UriManager.uri_of_string src)) src + | T.Inline (_, T.Var, src, _, _) -> out_alias och (UriManager.name_of_uri (UriManager.uri_of_string src)) src | T.Inline specs -> out_command och (inline (trd_rth kind specs)) | T.Section specs -> out_unexported och "UNEXPORTED" (trd specs) | T.Comment comment -> out_comment och comment diff --git a/helm/software/components/binaries/transcript/types.ml b/helm/software/components/binaries/transcript/types.ml index 2eb25a103..fbe112a83 100644 --- a/helm/software/components/binaries/transcript/types.ml +++ b/helm/software/components/binaries/transcript/types.ml @@ -33,6 +33,8 @@ type source = string type prefix = string +type flavour = Cic.object_flavour option + type item = Heading of (string * int) | Line of string | Comment of string @@ -41,7 +43,7 @@ type item = Heading of (string * int) | Coercion of (local * string) | Notation of (local * string) | Section of (local * string * string) - | Inline of (local * inline_kind * source * prefix) + | Inline of (local * inline_kind * source * prefix * flavour) | Verbatim of string | Discard of string diff --git a/helm/software/components/binaries/transcript/v8Parser.mly b/helm/software/components/binaries/transcript/v8Parser.mly index ff70df713..969524d22 100644 --- a/helm/software/components/binaries/transcript/v8Parser.mly +++ b/helm/software/components/binaries/transcript/v8Parser.mly @@ -35,7 +35,7 @@ let cat x = String.concat " " x let mk_vars local idents = - let map ident = T.Inline (local, T.Var, trim ident, "") in + let map ident = T.Inline (local, T.Var, trim ident, "", None) in List.map map idents let strip2 s = @@ -49,6 +49,16 @@ let notation str = [T.Notation (false, str); T.Notation (true, str)] + + let mk_flavour str = + match trim str with + | "Remark" -> Some `Remark + | "Lemma" -> Some `Lemma + | "Theorem" -> Some `Theorem + | "Definition" -> Some `Definition + | "Fixpoint" -> Some `Definition + | "Let" -> Some `Definition + | _ -> assert false %} %token SPC STR IDENT INT EXTRA AC OP CP OC CC OQ CQ DEF FS COE CN SC %token ABBR IN LET TH PROOF QED VAR AX IND SEC END UNX REQ XP IP SET NOT LOAD ID COERC @@ -277,59 +287,81 @@ macro_step: | th ident restricts fs proof FS steps qed FS - { out "TH" $2; $7 @ [T.Inline (false, T.Con, trim $2, "")] } + { out "TH" $2; + $7 @ [T.Inline (false, T.Con, trim $2, "", mk_flavour $1)] + } | th ident restricts fs proof restricts FS - { out "TH" $2; [T.Inline (false, T.Con, trim $2, "")] } + { out "TH" $2; + [T.Inline (false, T.Con, trim $2, "", mk_flavour $1)] + } | th ident restricts fs steps qed FS - { out "TH" $2; $5 @ [T.Inline (false, T.Con, trim $2, "")] } + { out "TH" $2; + $5 @ [T.Inline (false, T.Con, trim $2, "", mk_flavour $1)] + } | th ident restricts def restricts FS - { out "TH" $2; [T.Inline (false, T.Con, trim $2, "")] } + { out "TH" $2; + [T.Inline (false, T.Con, trim $2, "", mk_flavour $1)] + } | th ident def restricts FS - { out "TH" $2; [T.Inline (false, T.Con, trim $2, "")] } + { out "TH" $2; + [T.Inline (false, T.Con, trim $2, "", mk_flavour $1)] + } | xlet ident restricts fs proof FS steps qed FS - { out "LET" $2; $7 @ [T.Inline (true, T.Con, trim $2, "")] } + { out "LET" $2; + $7 @ [T.Inline (true, T.Con, trim $2, "", mk_flavour $1)] + } | xlet ident restricts fs proof restricts FS - { out "LET" $2; [T.Inline (true, T.Con, trim $2, "")] } + { out "LET" $2; + [T.Inline (true, T.Con, trim $2, "", mk_flavour $1)] + } | xlet ident restricts fs steps qed FS - { out "LET" $2; $5 @ [T.Inline (true, T.Con, trim $2, "")] } + { out "LET" $2; + $5 @ [T.Inline (true, T.Con, trim $2, "", mk_flavour $1)] + } | xlet ident restricts def restricts FS - { out "LET" $2; [T.Inline (true, T.Con, trim $2, "")] } + { out "LET" $2; + [T.Inline (true, T.Con, trim $2, "", mk_flavour $1)] + } | xlet ident def restricts FS - { out "LET" $2; [T.Inline (true, T.Con, trim $2, "")] } + { out "LET" $2; + [T.Inline (true, T.Con, trim $2, "", mk_flavour $1)] + } | var idents xres FS - { out "VAR" (cat $2); mk_vars true $2 } + { out "VAR" (cat $2); mk_vars true $2 } | ax idents xres FS - { out "AX" (cat $2); mk_vars false $2 } + { out "AX" (cat $2); mk_vars false $2 } | ind ident unexports FS - { out "IND" $2; T.Inline (false, T.Ind, trim $2, "") :: snd $3 } + { out "IND" $2; + T.Inline (false, T.Ind, trim $2, "", None) :: snd $3 + } | sec ident FS - { out "SEC" $2; [T.Section (true, trim $2, $1 ^ $2)] } + { out "SEC" $2; [T.Section (true, trim $2, $1 ^ $2)] } | xend ident FS - { out "END" $2; [T.Section (false, trim $2, $1 ^ $2)] } + { out "END" $2; [T.Section (false, trim $2, $1 ^ $2)] } | unx unexports FS - { out "UNX" (fst $2); [T.Unexport ($1 ^ fst $2 ^ trim $3)] } + { out "UNX" (fst $2); [T.Unexport ($1 ^ fst $2 ^ trim $3)] } | req xp ident FS - { out "REQ" $3; [T.Include (trim $3)] } + { out "REQ" $3; [T.Include (trim $3)] } | req ip ident FS - { out "REQ" $3; [T.Include (trim $3)] } + { out "REQ" $3; [T.Include (trim $3)] } | req ident FS - { out "REQ" $2; [T.Include (trim $2)] } + { out "REQ" $2; [T.Include (trim $2)] } | load str FS - { out "REQ" $2; [T.Include (strip2 (trim $2))] } + { out "REQ" $2; [T.Include (strip2 (trim $2))] } | coerc qid spcs cn unexports FS - { out "COERCE" (hd $2); coercion (hd $2) } + { out "COERCE" (hd $2); coercion (hd $2) } | id coerc qid spcs cn unexports FS - { out "COERCE" (hd $3); coercion (hd $3) } + { out "COERCE" (hd $3); coercion (hd $3) } | th ident error - { out "ERROR" $2; failwith ("macro_step " ^ $2) } + { out "ERROR" $2; failwith ("macro_step " ^ $2) } | ind ident error - { out "ERROR" $2; failwith ("macro_step " ^ $2) } + { out "ERROR" $2; failwith ("macro_step " ^ $2) } | var idents error { let vs = cat $2 in - out "ERROR" vs; failwith ("macro_step " ^ vs) } + out "ERROR" vs; failwith ("macro_step " ^ vs) } | ax idents error { let vs = cat $2 in - out "ERROR" vs; failwith ("macro_step " ^ vs) } + out "ERROR" vs; failwith ("macro_step " ^ vs) } ; item: | OQ verbatims CQ { [T.Comment $2] } diff --git a/helm/software/components/grafite/grafiteAstPp.ml b/helm/software/components/grafite/grafiteAstPp.ml index df436e709..189d172f8 100644 --- a/helm/software/components/grafite/grafiteAstPp.ml +++ b/helm/software/components/grafite/grafiteAstPp.ml @@ -260,14 +260,14 @@ let pp_macro ~term_pp = in let flavour_pp = function | None -> "" - | Some `Definition -> "as definition" - | Some `MutualDefinition -> "as mutual" - | Some `Fact -> "as fact" - | Some `Lemma -> "as lemma" - | Some `Remark -> "as remark" - | Some `Theorem -> "as theorem" - | Some `Variant -> "as variant" - | Some `Axiom -> "as axiom" + | Some `Definition -> " as definition" + | Some `MutualDefinition -> " as mutual" + | Some `Fact -> " as fact" + | Some `Lemma -> " as lemma" + | Some `Remark -> " as remark" + | Some `Theorem -> " as theorem" + | Some `Variant -> " as variant" + | Some `Axiom -> " as axiom" in function (* Whelp *) diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/Basics.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/Basics.mma index 598f294a1..5e862ff9f 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/Basics.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/Basics.mma @@ -42,26 +42,26 @@ include "algebra/ListType.ma". This is random stuff that should be in the Coq basic library. *) -inline procedural "cic:/CoRN/algebra/Basics/lt_le_dec.con". +inline procedural "cic:/CoRN/algebra/Basics/lt_le_dec.con" as lemma. -inline procedural "cic:/CoRN/algebra/Basics/lt_z_two.con". +inline procedural "cic:/CoRN/algebra/Basics/lt_z_two.con" as lemma. -inline procedural "cic:/CoRN/algebra/Basics/le_pred.con". +inline procedural "cic:/CoRN/algebra/Basics/le_pred.con" as lemma. -inline procedural "cic:/CoRN/algebra/Basics/lt_mult_right.con". +inline procedural "cic:/CoRN/algebra/Basics/lt_mult_right.con" as lemma. -inline procedural "cic:/CoRN/algebra/Basics/le_mult_right.con". +inline procedural "cic:/CoRN/algebra/Basics/le_mult_right.con" as lemma. (*#* The power function does not exist in the standard library *) -inline procedural "cic:/CoRN/algebra/Basics/power.con". +inline procedural "cic:/CoRN/algebra/Basics/power.con" as definition. (*#* Factorial function. Does not exist in Arith. Needed for special operations on polynomials. *) -inline procedural "cic:/CoRN/algebra/Basics/fac.con". +inline procedural "cic:/CoRN/algebra/Basics/fac.con" as definition. -inline procedural "cic:/CoRN/algebra/Basics/nat_fac_gtzero.con". +inline procedural "cic:/CoRN/algebra/Basics/nat_fac_gtzero.con" as lemma. (* needed for computational behavior of "Inversion" tactic *) @@ -119,9 +119,9 @@ Intros. Right. Reflexivity. Qed. *) -inline procedural "cic:/CoRN/algebra/Basics/not_r_sumbool_rec.con". +inline procedural "cic:/CoRN/algebra/Basics/not_r_sumbool_rec.con" as lemma. -inline procedural "cic:/CoRN/algebra/Basics/not_l_sumbool_rec.con". +inline procedural "cic:/CoRN/algebra/Basics/not_l_sumbool_rec.con" as lemma. (* begin hide *) @@ -148,31 +148,31 @@ cic:/Coq/ZArith/BinInt/Z_of_nat.con (* end hide *) -inline procedural "cic:/CoRN/algebra/Basics/POS_anti_convert.con". +inline procedural "cic:/CoRN/algebra/Basics/POS_anti_convert.con" as lemma. -inline procedural "cic:/CoRN/algebra/Basics/NEG_anti_convert.con". +inline procedural "cic:/CoRN/algebra/Basics/NEG_anti_convert.con" as lemma. -inline procedural "cic:/CoRN/algebra/Basics/lt_O_positive_to_nat.con". +inline procedural "cic:/CoRN/algebra/Basics/lt_O_positive_to_nat.con" as lemma. -inline procedural "cic:/CoRN/algebra/Basics/anti_convert_pred_convert.con". +inline procedural "cic:/CoRN/algebra/Basics/anti_convert_pred_convert.con" as lemma. -inline procedural "cic:/CoRN/algebra/Basics/p_is_some_anti_convert.con". +inline procedural "cic:/CoRN/algebra/Basics/p_is_some_anti_convert.con" as lemma. -inline procedural "cic:/CoRN/algebra/Basics/convert_is_POS.con". +inline procedural "cic:/CoRN/algebra/Basics/convert_is_POS.con" as lemma. -inline procedural "cic:/CoRN/algebra/Basics/min_convert_is_NEG.con". +inline procedural "cic:/CoRN/algebra/Basics/min_convert_is_NEG.con" as lemma. -inline procedural "cic:/CoRN/algebra/Basics/inject_nat_convert.con". +inline procedural "cic:/CoRN/algebra/Basics/inject_nat_convert.con" as lemma. -inline procedural "cic:/CoRN/algebra/Basics/Z_exh.con". +inline procedural "cic:/CoRN/algebra/Basics/Z_exh.con" as lemma. -inline procedural "cic:/CoRN/algebra/Basics/nats_Z_ind.con". +inline procedural "cic:/CoRN/algebra/Basics/nats_Z_ind.con" as lemma. -inline procedural "cic:/CoRN/algebra/Basics/pred_succ_Z_ind.con". +inline procedural "cic:/CoRN/algebra/Basics/pred_succ_Z_ind.con" as lemma. -inline procedural "cic:/CoRN/algebra/Basics/Zmult_minus_distr_r.con". +inline procedural "cic:/CoRN/algebra/Basics/Zmult_minus_distr_r.con" as lemma. -inline procedural "cic:/CoRN/algebra/Basics/Zodd_Zeven_min1.con". +inline procedural "cic:/CoRN/algebra/Basics/Zodd_Zeven_min1.con" as lemma. (* begin hide *) @@ -186,7 +186,7 @@ Unset Strict Implicit. (* end hide *) -inline procedural "cic:/CoRN/algebra/Basics/caseZ_diff.con". +inline procedural "cic:/CoRN/algebra/Basics/caseZ_diff.con" as definition. (* begin hide *) @@ -200,25 +200,25 @@ Unset Implicit Arguments. (* end hide *) -inline procedural "cic:/CoRN/algebra/Basics/caseZ_diff_O.con". +inline procedural "cic:/CoRN/algebra/Basics/caseZ_diff_O.con" as lemma. -inline procedural "cic:/CoRN/algebra/Basics/caseZ_diff_Pos.con". +inline procedural "cic:/CoRN/algebra/Basics/caseZ_diff_Pos.con" as lemma. -inline procedural "cic:/CoRN/algebra/Basics/caseZ_diff_Neg.con". +inline procedural "cic:/CoRN/algebra/Basics/caseZ_diff_Neg.con" as lemma. -inline procedural "cic:/CoRN/algebra/Basics/proper_caseZ_diff.con". +inline procedural "cic:/CoRN/algebra/Basics/proper_caseZ_diff.con" as lemma. -inline procedural "cic:/CoRN/algebra/Basics/diff_Z_ind.con". +inline procedural "cic:/CoRN/algebra/Basics/diff_Z_ind.con" as lemma. -inline procedural "cic:/CoRN/algebra/Basics/Zlt_reg_mult_l.con". +inline procedural "cic:/CoRN/algebra/Basics/Zlt_reg_mult_l.con" as lemma. -inline procedural "cic:/CoRN/algebra/Basics/Zlt_opp.con". +inline procedural "cic:/CoRN/algebra/Basics/Zlt_opp.con" as lemma. -inline procedural "cic:/CoRN/algebra/Basics/Zlt_conv_mult_l.con". +inline procedural "cic:/CoRN/algebra/Basics/Zlt_conv_mult_l.con" as lemma. -inline procedural "cic:/CoRN/algebra/Basics/Zgt_not_eq.con". +inline procedural "cic:/CoRN/algebra/Basics/Zgt_not_eq.con" as lemma. -inline procedural "cic:/CoRN/algebra/Basics/Zmult_absorb.con". +inline procedural "cic:/CoRN/algebra/Basics/Zmult_absorb.con" as lemma. (* UNEXPORTED Section Well_foundedT @@ -242,7 +242,7 @@ Section AccT alias id "A" = "cic:/CoRN/algebra/Basics/AccT/A.var". -inline procedural "cic:/CoRN/algebra/Basics/well_founded.con". +inline procedural "cic:/CoRN/algebra/Basics/well_founded.con" as definition. (* UNEXPORTED End AccT @@ -268,9 +268,9 @@ alias id "P" = "cic:/CoRN/algebra/Basics/IndT/AccIter/P.var". alias id "F" = "cic:/CoRN/algebra/Basics/IndT/AccIter/F.var". -inline procedural "cic:/CoRN/algebra/Basics/Acc_inv.con". +inline procedural "cic:/CoRN/algebra/Basics/Acc_inv.con" as lemma. -inline procedural "cic:/CoRN/algebra/Basics/Acc_iter.con". +inline procedural "cic:/CoRN/algebra/Basics/Acc_iter.con" as definition. (* UNEXPORTED End AccIter @@ -278,7 +278,7 @@ End AccIter alias id "Rwf" = "cic:/CoRN/algebra/Basics/IndT/Rwf.var". -inline procedural "cic:/CoRN/algebra/Basics/well_founded_induction_type.con". +inline procedural "cic:/CoRN/algebra/Basics/well_founded_induction_type.con" as theorem. (* UNEXPORTED End IndT @@ -292,11 +292,11 @@ alias id "A" = "cic:/CoRN/algebra/Basics/InductionT/A.var". alias id "f" = "cic:/CoRN/algebra/Basics/InductionT/f.var". -inline procedural "cic:/CoRN/algebra/Basics/ltof.con". +inline procedural "cic:/CoRN/algebra/Basics/ltof.con" as definition. -inline procedural "cic:/CoRN/algebra/Basics/well_founded_ltof.con". +inline procedural "cic:/CoRN/algebra/Basics/well_founded_ltof.con" as theorem. -inline procedural "cic:/CoRN/algebra/Basics/induction_ltof2T.con". +inline procedural "cic:/CoRN/algebra/Basics/induction_ltof2T.con" as theorem. (* UNEXPORTED End InductionT @@ -306,7 +306,7 @@ End InductionT Section InductionTT *) -inline procedural "cic:/CoRN/algebra/Basics/lt_wf_rect.con". +inline procedural "cic:/CoRN/algebra/Basics/lt_wf_rect.con" as lemma. (* UNEXPORTED End InductionTT diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/CAbGroups.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/CAbGroups.mma index 82bc6a265..a18d0e3e4 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/CAbGroups.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/CAbGroups.mma @@ -27,7 +27,7 @@ Section Abelian_Groups Now we introduce commutativity and add some results. *) -inline procedural "cic:/CoRN/algebra/CAbGroups/is_CAbGroup.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/is_CAbGroup.con" as definition. inline procedural "cic:/CoRN/algebra/CAbGroups/CAbGroup.ind". @@ -46,11 +46,11 @@ alias id "G" = "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/AbGroup_Axioms/G.var" %\end{convention}% *) -inline procedural "cic:/CoRN/algebra/CAbGroups/CAbGroup_is_CAbGroup.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/CAbGroup_is_CAbGroup.con" as lemma. -inline procedural "cic:/CoRN/algebra/CAbGroups/cag_commutes.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/cag_commutes.con" as lemma. -inline procedural "cic:/CoRN/algebra/CAbGroups/cag_commutes_unfolded.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/cag_commutes_unfolded.con" as lemma. (* UNEXPORTED End AbGroup_Axioms @@ -81,11 +81,11 @@ that contains [Zero] and is closed under [[+]] and [[--]]. %\end{convention}% *) -inline procedural "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/subcrr.con" "Abelian_Groups__SubCAbGroups__". +inline procedural "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/subcrr.con" "Abelian_Groups__SubCAbGroups__" as definition. -inline procedural "cic:/CoRN/algebra/CAbGroups/isabgrp_scrr.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/isabgrp_scrr.con" as lemma. -inline procedural "cic:/CoRN/algebra/CAbGroups/Build_SubCAbGroup.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/Build_SubCAbGroup.con" as definition. (* UNEXPORTED End SubCAbGroups @@ -110,21 +110,21 @@ alias id "G" = "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/Various/G.var". %\end{convention}% *) -inline procedural "cic:/CoRN/algebra/CAbGroups/cag_op_inv.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/cag_op_inv.con" as lemma. (* UNEXPORTED Hint Resolve cag_op_inv: algebra. *) -inline procedural "cic:/CoRN/algebra/CAbGroups/assoc_1.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/assoc_1.con" as lemma. -inline procedural "cic:/CoRN/algebra/CAbGroups/minus_plus.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/minus_plus.con" as lemma. -inline procedural "cic:/CoRN/algebra/CAbGroups/op_lft_resp_ap.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/op_lft_resp_ap.con" as lemma. -inline procedural "cic:/CoRN/algebra/CAbGroups/cag_ap_cancel_lft.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/cag_ap_cancel_lft.con" as lemma. -inline procedural "cic:/CoRN/algebra/CAbGroups/plus_cancel_ap_lft.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/plus_cancel_ap_lft.con" as lemma. (* UNEXPORTED End Various @@ -191,23 +191,23 @@ alias id "inv" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/inv.var". alias id "inv_inv" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/inv_inv.var". -inline procedural "cic:/CoRN/algebra/CAbGroups/plus_rext.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/plus_rext.con" as lemma. -inline procedural "cic:/CoRN/algebra/CAbGroups/plus_runit.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/plus_runit.con" as lemma. -inline procedural "cic:/CoRN/algebra/CAbGroups/plus_is_fun.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/plus_is_fun.con" as lemma. -inline procedural "cic:/CoRN/algebra/CAbGroups/inv_inv'.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/inv_inv'.con" as lemma. -inline procedural "cic:/CoRN/algebra/CAbGroups/plus_fun.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/plus_fun.con" as definition. -inline procedural "cic:/CoRN/algebra/CAbGroups/Build_CSemiGroup'.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/Build_CSemiGroup'.con" as definition. -inline procedural "cic:/CoRN/algebra/CAbGroups/Build_CMonoid'.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/Build_CMonoid'.con" as definition. -inline procedural "cic:/CoRN/algebra/CAbGroups/Build_CGroup'.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/Build_CGroup'.con" as definition. -inline procedural "cic:/CoRN/algebra/CAbGroups/Build_CAbGroup'.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/Build_CAbGroup'.con" as definition. (* UNEXPORTED End Nice_Char @@ -224,27 +224,27 @@ Section Group_Extras alias id "G" = "cic:/CoRN/algebra/CAbGroups/Group_Extras/G.var". -inline procedural "cic:/CoRN/algebra/CAbGroups/nmult.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/nmult.con" as definition. -inline procedural "cic:/CoRN/algebra/CAbGroups/nmult_wd.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/nmult_wd.con" as lemma. -inline procedural "cic:/CoRN/algebra/CAbGroups/nmult_one.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/nmult_one.con" as lemma. -inline procedural "cic:/CoRN/algebra/CAbGroups/nmult_Zero.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/nmult_Zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CAbGroups/nmult_plus.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/nmult_plus.con" as lemma. -inline procedural "cic:/CoRN/algebra/CAbGroups/nmult_mult.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/nmult_mult.con" as lemma. -inline procedural "cic:/CoRN/algebra/CAbGroups/nmult_inv.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/nmult_inv.con" as lemma. -inline procedural "cic:/CoRN/algebra/CAbGroups/nmult_plus'.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/nmult_plus'.con" as lemma. (* UNEXPORTED Hint Resolve nmult_wd nmult_Zero nmult_inv nmult_plus nmult_plus': algebra. *) -inline procedural "cic:/CoRN/algebra/CAbGroups/zmult.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/zmult.con" as definition. (* Lemma Zeq_imp_nat_eq : forall m n:nat, m = n -> m = n. @@ -262,27 +262,27 @@ auto with zarith. Qed. *) -inline procedural "cic:/CoRN/algebra/CAbGroups/zmult_char.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/zmult_char.con" as lemma. -inline procedural "cic:/CoRN/algebra/CAbGroups/zmult_wd.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/zmult_wd.con" as lemma. -inline procedural "cic:/CoRN/algebra/CAbGroups/zmult_one.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/zmult_one.con" as lemma. -inline procedural "cic:/CoRN/algebra/CAbGroups/zmult_min_one.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/zmult_min_one.con" as lemma. -inline procedural "cic:/CoRN/algebra/CAbGroups/zmult_zero.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/zmult_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CAbGroups/zmult_Zero.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/zmult_Zero.con" as lemma. (* UNEXPORTED Hint Resolve zmult_zero: algebra. *) -inline procedural "cic:/CoRN/algebra/CAbGroups/zmult_plus.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/zmult_plus.con" as lemma. -inline procedural "cic:/CoRN/algebra/CAbGroups/zmult_mult.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/zmult_mult.con" as lemma. -inline procedural "cic:/CoRN/algebra/CAbGroups/zmult_plus'.con". +inline procedural "cic:/CoRN/algebra/CAbGroups/zmult_plus'.con" as lemma. (* UNEXPORTED End Group_Extras diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/CAbMonoids.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/CAbMonoids.mma index b639df6cc..eada9abc4 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/CAbMonoids.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/CAbMonoids.mma @@ -27,7 +27,7 @@ Section Abelian_Monoids Now we introduce commutativity and add some results. *) -inline procedural "cic:/CoRN/algebra/CAbMonoids/is_CAbMonoid.con". +inline procedural "cic:/CoRN/algebra/CAbMonoids/is_CAbMonoid.con" as definition. inline procedural "cic:/CoRN/algebra/CAbMonoids/CAbMonoid.ind". @@ -46,11 +46,11 @@ alias id "M" = "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/AbMonoid_Axioms/M.v %\end{convention}% *) -inline procedural "cic:/CoRN/algebra/CAbMonoids/CAbMonoid_is_CAbMonoid.con". +inline procedural "cic:/CoRN/algebra/CAbMonoids/CAbMonoid_is_CAbMonoid.con" as lemma. -inline procedural "cic:/CoRN/algebra/CAbMonoids/cam_commutes.con". +inline procedural "cic:/CoRN/algebra/CAbMonoids/cam_commutes.con" as lemma. -inline procedural "cic:/CoRN/algebra/CAbMonoids/cam_commutes_unfolded.con". +inline procedural "cic:/CoRN/algebra/CAbMonoids/cam_commutes_unfolded.con" as lemma. (* UNEXPORTED End AbMonoid_Axioms @@ -79,11 +79,11 @@ that contains [Zero] and is closed under [[+]] and [[--]]. %\end{convention}% *) -inline procedural "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/subcrr.con" "Abelian_Monoids__SubCAbMonoids__". +inline procedural "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/subcrr.con" "Abelian_Monoids__SubCAbMonoids__" as definition. -inline procedural "cic:/CoRN/algebra/CAbMonoids/isabgrp_scrr.con". +inline procedural "cic:/CoRN/algebra/CAbMonoids/isabgrp_scrr.con" as lemma. -inline procedural "cic:/CoRN/algebra/CAbMonoids/Build_SubCAbMonoid.con". +inline procedural "cic:/CoRN/algebra/CAbMonoids/Build_SubCAbMonoid.con" as definition. (* UNEXPORTED End SubCAbMonoids diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/CFields.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/CFields.mma index 5e6aeb87e..9d1245aa9 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/CFields.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/CFields.mma @@ -119,7 +119,7 @@ Transparent nexp_op. ** Definition of the notion Field *) -inline procedural "cic:/CoRN/algebra/CFields/is_CField.con". +inline procedural "cic:/CoRN/algebra/CFields/is_CField.con" as definition. inline procedural "cic:/CoRN/algebra/CFields/CField.ind". @@ -129,9 +129,9 @@ cic:/matita/CoRN-Procedural/algebra/CFields/cf_crr.con (* End_SpecReals *) -inline procedural "cic:/CoRN/algebra/CFields/f_rcpcl'.con". +inline procedural "cic:/CoRN/algebra/CFields/f_rcpcl'.con" as definition. -inline procedural "cic:/CoRN/algebra/CFields/f_rcpcl.con". +inline procedural "cic:/CoRN/algebra/CFields/f_rcpcl.con" as definition. (* UNEXPORTED Implicit Arguments f_rcpcl [F]. @@ -143,7 +143,7 @@ multiplication and the reciprocal. [x[/]y] is only defined if we have a proof of [y [#] Zero]. *) -inline procedural "cic:/CoRN/algebra/CFields/cf_div.con". +inline procedural "cic:/CoRN/algebra/CFields/cf_div.con" as definition. (* UNEXPORTED Implicit Arguments cf_div [F]. @@ -190,9 +190,9 @@ Section Field_axioms alias id "F" = "cic:/CoRN/algebra/CFields/Field_axioms/F.var". -inline procedural "cic:/CoRN/algebra/CFields/CField_is_CField.con". +inline procedural "cic:/CoRN/algebra/CFields/CField_is_CField.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/rcpcl_is_inverse.con". +inline procedural "cic:/CoRN/algebra/CFields/rcpcl_is_inverse.con" as lemma. (* UNEXPORTED End Field_axioms @@ -209,15 +209,15 @@ Section Field_basics alias id "F" = "cic:/CoRN/algebra/CFields/Field_basics/F.var". -inline procedural "cic:/CoRN/algebra/CFields/rcpcl_is_inverse_unfolded.con". +inline procedural "cic:/CoRN/algebra/CFields/rcpcl_is_inverse_unfolded.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/field_mult_inv.con". +inline procedural "cic:/CoRN/algebra/CFields/field_mult_inv.con" as lemma. (* UNEXPORTED Hint Resolve field_mult_inv: algebra. *) -inline procedural "cic:/CoRN/algebra/CFields/field_mult_inv_op.con". +inline procedural "cic:/CoRN/algebra/CFields/field_mult_inv_op.con" as lemma. (* UNEXPORTED End Field_basics @@ -239,27 +239,27 @@ Section Field_multiplication alias id "F" = "cic:/CoRN/algebra/CFields/Field_multiplication/F.var". -inline procedural "cic:/CoRN/algebra/CFields/mult_resp_ap_zero.con". +inline procedural "cic:/CoRN/algebra/CFields/mult_resp_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/mult_lft_resp_ap.con". +inline procedural "cic:/CoRN/algebra/CFields/mult_lft_resp_ap.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/mult_rht_resp_ap.con". +inline procedural "cic:/CoRN/algebra/CFields/mult_rht_resp_ap.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/mult_resp_neq_zero.con". +inline procedural "cic:/CoRN/algebra/CFields/mult_resp_neq_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/mult_resp_neq.con". +inline procedural "cic:/CoRN/algebra/CFields/mult_resp_neq.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/mult_eq_zero.con". +inline procedural "cic:/CoRN/algebra/CFields/mult_eq_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/mult_cancel_lft.con". +inline procedural "cic:/CoRN/algebra/CFields/mult_cancel_lft.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/mult_cancel_rht.con". +inline procedural "cic:/CoRN/algebra/CFields/mult_cancel_rht.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/square_eq_aux.con". +inline procedural "cic:/CoRN/algebra/CFields/square_eq_aux.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/square_eq_weak.con". +inline procedural "cic:/CoRN/algebra/CFields/square_eq_weak.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/cond_square_eq.con". +inline procedural "cic:/CoRN/algebra/CFields/cond_square_eq.con" as lemma. (* UNEXPORTED End Field_multiplication @@ -269,9 +269,9 @@ End Field_multiplication Section x_square *) -inline procedural "cic:/CoRN/algebra/CFields/x_xminone.con". +inline procedural "cic:/CoRN/algebra/CFields/x_xminone.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/square_id.con". +inline procedural "cic:/CoRN/algebra/CFields/square_id.con" as lemma. (* UNEXPORTED End x_square @@ -293,15 +293,15 @@ Section Rcpcl_properties alias id "F" = "cic:/CoRN/algebra/CFields/Rcpcl_properties/F.var". -inline procedural "cic:/CoRN/algebra/CFields/inv_one.con". +inline procedural "cic:/CoRN/algebra/CFields/inv_one.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/f_rcpcl_wd.con". +inline procedural "cic:/CoRN/algebra/CFields/f_rcpcl_wd.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/f_rcpcl_mult.con". +inline procedural "cic:/CoRN/algebra/CFields/f_rcpcl_mult.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/f_rcpcl_resp_ap_zero.con". +inline procedural "cic:/CoRN/algebra/CFields/f_rcpcl_resp_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/f_rcpcl_f_rcpcl.con". +inline procedural "cic:/CoRN/algebra/CFields/f_rcpcl_f_rcpcl.con" as lemma. (* UNEXPORTED End Rcpcl_properties @@ -323,13 +323,13 @@ alias id "F" = "cic:/CoRN/algebra/CFields/MultipGroup/F.var". The multiplicative monoid of NonZeros. *) -inline procedural "cic:/CoRN/algebra/CFields/NonZeroMonoid.con". +inline procedural "cic:/CoRN/algebra/CFields/NonZeroMonoid.con" as definition. -inline procedural "cic:/CoRN/algebra/CFields/fmg_cs_inv.con". +inline procedural "cic:/CoRN/algebra/CFields/fmg_cs_inv.con" as definition. -inline procedural "cic:/CoRN/algebra/CFields/plus_nonzeros_eq_mult_dom.con". +inline procedural "cic:/CoRN/algebra/CFields/plus_nonzeros_eq_mult_dom.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/cfield_to_mult_cgroup.con". +inline procedural "cic:/CoRN/algebra/CFields/cfield_to_mult_cgroup.con" as lemma. (* UNEXPORTED End MultipGroup @@ -352,38 +352,38 @@ In the names of lemmas, we denote [[/]] by [div], and alias id "F" = "cic:/CoRN/algebra/CFields/Div_properties/F.var". -inline procedural "cic:/CoRN/algebra/CFields/div_prop.con". +inline procedural "cic:/CoRN/algebra/CFields/div_prop.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/div_1.con". +inline procedural "cic:/CoRN/algebra/CFields/div_1.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/div_1'.con". +inline procedural "cic:/CoRN/algebra/CFields/div_1'.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/div_1''.con". +inline procedural "cic:/CoRN/algebra/CFields/div_1''.con" as lemma. (* UNEXPORTED Hint Resolve div_1: algebra. *) -inline procedural "cic:/CoRN/algebra/CFields/x_div_x.con". +inline procedural "cic:/CoRN/algebra/CFields/x_div_x.con" as lemma. (* UNEXPORTED Hint Resolve x_div_x: algebra. *) -inline procedural "cic:/CoRN/algebra/CFields/x_div_one.con". +inline procedural "cic:/CoRN/algebra/CFields/x_div_one.con" as lemma. (*#* The next lemma says $x\cdot\frac{y}{z} = \frac{x\cdot y}{z}$ #x.(y/z) = (x.y)/z#. *) -inline procedural "cic:/CoRN/algebra/CFields/x_mult_y_div_z.con". +inline procedural "cic:/CoRN/algebra/CFields/x_mult_y_div_z.con" as lemma. (* UNEXPORTED Hint Resolve x_mult_y_div_z: algebra. *) -inline procedural "cic:/CoRN/algebra/CFields/div_wd.con". +inline procedural "cic:/CoRN/algebra/CFields/div_wd.con" as lemma. (* UNEXPORTED Hint Resolve div_wd: algebra_c. @@ -394,39 +394,39 @@ The next lemma says $\frac{\frac{x}{y}}{z} = \frac{x}{y\cdot z}$ #[(x/y)/z = x/(y.z)]# *) -inline procedural "cic:/CoRN/algebra/CFields/div_div.con". +inline procedural "cic:/CoRN/algebra/CFields/div_div.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/div_resp_ap_zero_rev.con". +inline procedural "cic:/CoRN/algebra/CFields/div_resp_ap_zero_rev.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/div_resp_ap_zero.con". +inline procedural "cic:/CoRN/algebra/CFields/div_resp_ap_zero.con" as lemma. (*#* The next lemma says $\frac{x}{\frac{y}{z}} = \frac{x\cdot z}{y}$ #[x/(y/z) = (x.z)/y]# *) -inline procedural "cic:/CoRN/algebra/CFields/div_div2.con". +inline procedural "cic:/CoRN/algebra/CFields/div_div2.con" as lemma. (*#* The next lemma says $\frac{x\cdot p}{y\cdot q} = \frac{x}{y}\cdot \frac{p}{q}$ #[(x.p)/(y.q) = (x/y).(p/q)]# *) -inline procedural "cic:/CoRN/algebra/CFields/mult_of_divs.con". +inline procedural "cic:/CoRN/algebra/CFields/mult_of_divs.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/div_dist.con". +inline procedural "cic:/CoRN/algebra/CFields/div_dist.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/div_dist'.con". +inline procedural "cic:/CoRN/algebra/CFields/div_dist'.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/div_semi_sym.con". +inline procedural "cic:/CoRN/algebra/CFields/div_semi_sym.con" as lemma. (* UNEXPORTED Hint Resolve div_semi_sym: algebra. *) -inline procedural "cic:/CoRN/algebra/CFields/eq_div.con". +inline procedural "cic:/CoRN/algebra/CFields/eq_div.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/div_strext.con". +inline procedural "cic:/CoRN/algebra/CFields/div_strext.con" as lemma. (* UNEXPORTED End Div_properties @@ -450,13 +450,13 @@ Section Mult_Cancel_Ap_Zero alias id "F" = "cic:/CoRN/algebra/CFields/Mult_Cancel_Ap_Zero/F.var". -inline procedural "cic:/CoRN/algebra/CFields/mult_cancel_ap_zero_lft.con". +inline procedural "cic:/CoRN/algebra/CFields/mult_cancel_ap_zero_lft.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/mult_cancel_ap_zero_rht.con". +inline procedural "cic:/CoRN/algebra/CFields/mult_cancel_ap_zero_rht.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/recip_ap_zero.con". +inline procedural "cic:/CoRN/algebra/CFields/recip_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/recip_resp_ap.con". +inline procedural "cic:/CoRN/algebra/CFields/recip_resp_ap.con" as lemma. (* UNEXPORTED End Mult_Cancel_Ap_Zero @@ -488,9 +488,9 @@ alias id "G" = "cic:/CoRN/algebra/CFields/CField_Ops/G.var". (* begin hide *) -inline procedural "cic:/CoRN/algebra/CFields/CField_Ops/P.con" "CField_Ops__". +inline procedural "cic:/CoRN/algebra/CFields/CField_Ops/P.con" "CField_Ops__" as definition. -inline procedural "cic:/CoRN/algebra/CFields/CField_Ops/Q.con" "CField_Ops__". +inline procedural "cic:/CoRN/algebra/CFields/CField_Ops/Q.con" "CField_Ops__" as definition. (* end hide *) @@ -502,15 +502,15 @@ Section Part_Function_Recip Some auxiliary notions are helpful in defining the domain. *) -inline procedural "cic:/CoRN/algebra/CFields/CField_Ops/Part_Function_Recip/R.con" "CField_Ops__Part_Function_Recip__". +inline procedural "cic:/CoRN/algebra/CFields/CField_Ops/Part_Function_Recip/R.con" "CField_Ops__Part_Function_Recip__" as definition. -inline procedural "cic:/CoRN/algebra/CFields/CField_Ops/Part_Function_Recip/Ext2R.con" "CField_Ops__Part_Function_Recip__". +inline procedural "cic:/CoRN/algebra/CFields/CField_Ops/Part_Function_Recip/Ext2R.con" "CField_Ops__Part_Function_Recip__" as definition. -inline procedural "cic:/CoRN/algebra/CFields/part_function_recip_strext.con". +inline procedural "cic:/CoRN/algebra/CFields/part_function_recip_strext.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/part_function_recip_pred_wd.con". +inline procedural "cic:/CoRN/algebra/CFields/part_function_recip_pred_wd.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/Frecip.con". +inline procedural "cic:/CoRN/algebra/CFields/Frecip.con" as definition. (* UNEXPORTED End Part_Function_Recip @@ -524,15 +524,15 @@ Section Part_Function_Div For division things work out almost in the same way. *) -inline procedural "cic:/CoRN/algebra/CFields/CField_Ops/Part_Function_Div/R.con" "CField_Ops__Part_Function_Div__". +inline procedural "cic:/CoRN/algebra/CFields/CField_Ops/Part_Function_Div/R.con" "CField_Ops__Part_Function_Div__" as definition. -inline procedural "cic:/CoRN/algebra/CFields/CField_Ops/Part_Function_Div/Ext2R.con" "CField_Ops__Part_Function_Div__". +inline procedural "cic:/CoRN/algebra/CFields/CField_Ops/Part_Function_Div/Ext2R.con" "CField_Ops__Part_Function_Div__" as definition. -inline procedural "cic:/CoRN/algebra/CFields/part_function_div_strext.con". +inline procedural "cic:/CoRN/algebra/CFields/part_function_div_strext.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/part_function_div_pred_wd.con". +inline procedural "cic:/CoRN/algebra/CFields/part_function_div_pred_wd.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/Fdiv.con". +inline procedural "cic:/CoRN/algebra/CFields/Fdiv.con" as definition. (* UNEXPORTED End Part_Function_Div @@ -545,15 +545,15 @@ End Part_Function_Div alias id "R" = "cic:/CoRN/algebra/CFields/CField_Ops/R.var". -inline procedural "cic:/CoRN/algebra/CFields/included_FRecip.con". +inline procedural "cic:/CoRN/algebra/CFields/included_FRecip.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/included_FRecip'.con". +inline procedural "cic:/CoRN/algebra/CFields/included_FRecip'.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/included_FDiv.con". +inline procedural "cic:/CoRN/algebra/CFields/included_FDiv.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/included_FDiv'.con". +inline procedural "cic:/CoRN/algebra/CFields/included_FDiv'.con" as lemma. -inline procedural "cic:/CoRN/algebra/CFields/included_FDiv''.con". +inline procedural "cic:/CoRN/algebra/CFields/included_FDiv''.con" as lemma. (* UNEXPORTED End CField_Ops diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/CGroups.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/CGroups.mma index 82ca16f2a..12594f975 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/CGroups.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/CGroups.mma @@ -35,13 +35,13 @@ include "algebra/CMonoids.ma". ** Definition of the notion of Group *) -inline procedural "cic:/CoRN/algebra/CGroups/is_inverse.con". +inline procedural "cic:/CoRN/algebra/CGroups/is_inverse.con" as definition. (* UNEXPORTED Implicit Arguments is_inverse [S]. *) -inline procedural "cic:/CoRN/algebra/CGroups/is_CGroup.con". +inline procedural "cic:/CoRN/algebra/CGroups/is_CGroup.con" as definition. inline procedural "cic:/CoRN/algebra/CGroups/CGroup.ind". @@ -61,7 +61,7 @@ Implicit Arguments cg_inv [c]. Notation "[--] x" := (cg_inv x) (at level 2, right associativity). *) -inline procedural "cic:/CoRN/algebra/CGroups/cg_minus.con". +inline procedural "cic:/CoRN/algebra/CGroups/cg_minus.con" as definition. (*#* %\begin{nameconvention}% @@ -92,7 +92,7 @@ Section CGroup_axioms alias id "G" = "cic:/CoRN/algebra/CGroups/CGroup_axioms/G.var". -inline procedural "cic:/CoRN/algebra/CGroups/cg_inverse.con". +inline procedural "cic:/CoRN/algebra/CGroups/cg_inverse.con" as lemma. (* UNEXPORTED End CGroup_axioms @@ -111,74 +111,74 @@ Section CGroup_basics alias id "G" = "cic:/CoRN/algebra/CGroups/CGroup_basics/G.var". -inline procedural "cic:/CoRN/algebra/CGroups/cg_rht_inv_unfolded.con". +inline procedural "cic:/CoRN/algebra/CGroups/cg_rht_inv_unfolded.con" as lemma. -inline procedural "cic:/CoRN/algebra/CGroups/cg_lft_inv_unfolded.con". +inline procedural "cic:/CoRN/algebra/CGroups/cg_lft_inv_unfolded.con" as lemma. -inline procedural "cic:/CoRN/algebra/CGroups/cg_minus_correct.con". +inline procedural "cic:/CoRN/algebra/CGroups/cg_minus_correct.con" as lemma. (* UNEXPORTED Hint Resolve cg_rht_inv_unfolded cg_lft_inv_unfolded cg_minus_correct: algebra. *) -inline procedural "cic:/CoRN/algebra/CGroups/cg_inverse'.con". +inline procedural "cic:/CoRN/algebra/CGroups/cg_inverse'.con" as lemma. (* Hints for Auto *) -inline procedural "cic:/CoRN/algebra/CGroups/cg_minus_unfolded.con". +inline procedural "cic:/CoRN/algebra/CGroups/cg_minus_unfolded.con" as lemma. (* UNEXPORTED Hint Resolve cg_minus_unfolded: algebra. *) -inline procedural "cic:/CoRN/algebra/CGroups/cg_minus_wd.con". +inline procedural "cic:/CoRN/algebra/CGroups/cg_minus_wd.con" as lemma. (* UNEXPORTED Hint Resolve cg_minus_wd: algebra_c. *) -inline procedural "cic:/CoRN/algebra/CGroups/cg_minus_strext.con". +inline procedural "cic:/CoRN/algebra/CGroups/cg_minus_strext.con" as lemma. -inline procedural "cic:/CoRN/algebra/CGroups/cg_minus_is_csetoid_bin_op.con". +inline procedural "cic:/CoRN/algebra/CGroups/cg_minus_is_csetoid_bin_op.con" as definition. -inline procedural "cic:/CoRN/algebra/CGroups/grp_inv_assoc.con". +inline procedural "cic:/CoRN/algebra/CGroups/grp_inv_assoc.con" as lemma. (* UNEXPORTED Hint Resolve grp_inv_assoc: algebra. *) -inline procedural "cic:/CoRN/algebra/CGroups/cg_inv_unique.con". +inline procedural "cic:/CoRN/algebra/CGroups/cg_inv_unique.con" as lemma. -inline procedural "cic:/CoRN/algebra/CGroups/cg_inv_inv.con". +inline procedural "cic:/CoRN/algebra/CGroups/cg_inv_inv.con" as lemma. (* UNEXPORTED Hint Resolve cg_inv_inv: algebra. *) -inline procedural "cic:/CoRN/algebra/CGroups/cg_cancel_lft.con". +inline procedural "cic:/CoRN/algebra/CGroups/cg_cancel_lft.con" as lemma. -inline procedural "cic:/CoRN/algebra/CGroups/cg_cancel_rht.con". +inline procedural "cic:/CoRN/algebra/CGroups/cg_cancel_rht.con" as lemma. -inline procedural "cic:/CoRN/algebra/CGroups/cg_inv_unique'.con". +inline procedural "cic:/CoRN/algebra/CGroups/cg_inv_unique'.con" as lemma. -inline procedural "cic:/CoRN/algebra/CGroups/cg_inv_unique_2.con". +inline procedural "cic:/CoRN/algebra/CGroups/cg_inv_unique_2.con" as lemma. -inline procedural "cic:/CoRN/algebra/CGroups/cg_zero_inv.con". +inline procedural "cic:/CoRN/algebra/CGroups/cg_zero_inv.con" as lemma. (* UNEXPORTED Hint Resolve cg_zero_inv: algebra. *) -inline procedural "cic:/CoRN/algebra/CGroups/cg_inv_zero.con". +inline procedural "cic:/CoRN/algebra/CGroups/cg_inv_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CGroups/cg_inv_op.con". +inline procedural "cic:/CoRN/algebra/CGroups/cg_inv_op.con" as lemma. (*#* Useful for interactive proof development. *) -inline procedural "cic:/CoRN/algebra/CGroups/x_minus_x.con". +inline procedural "cic:/CoRN/algebra/CGroups/x_minus_x.con" as lemma. (*#* ** Sub-groups @@ -199,13 +199,13 @@ alias id "op_pres_P" = "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/op_pr alias id "inv_pres_P" = "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/inv_pres_P.var". -inline procedural "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/subcrr.con" "CGroup_basics__SubCGroups__". +inline procedural "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/subcrr.con" "CGroup_basics__SubCGroups__" as definition. -inline procedural "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/subinv.con" "CGroup_basics__SubCGroups__". +inline procedural "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/subinv.con" "CGroup_basics__SubCGroups__" as definition. -inline procedural "cic:/CoRN/algebra/CGroups/isgrp_scrr.con". +inline procedural "cic:/CoRN/algebra/CGroups/isgrp_scrr.con" as lemma. -inline procedural "cic:/CoRN/algebra/CGroups/Build_SubCGroup.con". +inline procedural "cic:/CoRN/algebra/CGroups/Build_SubCGroup.con" as definition. (* UNEXPORTED End SubCGroups @@ -243,13 +243,13 @@ Section Assoc_properties alias id "G" = "cic:/CoRN/algebra/CGroups/Assoc_properties/G.var". -inline procedural "cic:/CoRN/algebra/CGroups/assoc_2.con". +inline procedural "cic:/CoRN/algebra/CGroups/assoc_2.con" as lemma. -inline procedural "cic:/CoRN/algebra/CGroups/zero_minus.con". +inline procedural "cic:/CoRN/algebra/CGroups/zero_minus.con" as lemma. -inline procedural "cic:/CoRN/algebra/CGroups/cg_cancel_mixed.con". +inline procedural "cic:/CoRN/algebra/CGroups/cg_cancel_mixed.con" as lemma. -inline procedural "cic:/CoRN/algebra/CGroups/plus_resp_eq.con". +inline procedural "cic:/CoRN/algebra/CGroups/plus_resp_eq.con" as lemma. (* UNEXPORTED End Assoc_properties @@ -273,27 +273,27 @@ Section cgroups_apartness alias id "G" = "cic:/CoRN/algebra/CGroups/cgroups_apartness/G.var". -inline procedural "cic:/CoRN/algebra/CGroups/cg_add_ap_zero.con". +inline procedural "cic:/CoRN/algebra/CGroups/cg_add_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CGroups/op_rht_resp_ap.con". +inline procedural "cic:/CoRN/algebra/CGroups/op_rht_resp_ap.con" as lemma. -inline procedural "cic:/CoRN/algebra/CGroups/cg_ap_cancel_rht.con". +inline procedural "cic:/CoRN/algebra/CGroups/cg_ap_cancel_rht.con" as lemma. -inline procedural "cic:/CoRN/algebra/CGroups/plus_cancel_ap_rht.con". +inline procedural "cic:/CoRN/algebra/CGroups/plus_cancel_ap_rht.con" as lemma. -inline procedural "cic:/CoRN/algebra/CGroups/minus_ap_zero.con". +inline procedural "cic:/CoRN/algebra/CGroups/minus_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CGroups/zero_minus_apart.con". +inline procedural "cic:/CoRN/algebra/CGroups/zero_minus_apart.con" as lemma. -inline procedural "cic:/CoRN/algebra/CGroups/inv_resp_ap_zero.con". +inline procedural "cic:/CoRN/algebra/CGroups/inv_resp_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CGroups/inv_resp_ap.con". +inline procedural "cic:/CoRN/algebra/CGroups/inv_resp_ap.con" as lemma. -inline procedural "cic:/CoRN/algebra/CGroups/minus_resp_ap_rht.con". +inline procedural "cic:/CoRN/algebra/CGroups/minus_resp_ap_rht.con" as lemma. -inline procedural "cic:/CoRN/algebra/CGroups/minus_resp_ap_lft.con". +inline procedural "cic:/CoRN/algebra/CGroups/minus_resp_ap_lft.con" as lemma. -inline procedural "cic:/CoRN/algebra/CGroups/minus_cancel_ap_rht.con". +inline procedural "cic:/CoRN/algebra/CGroups/minus_cancel_ap_rht.con" as lemma. (* UNEXPORTED End cgroups_apartness @@ -330,9 +330,9 @@ alias id "F'" = "cic:/CoRN/algebra/CGroups/CGroup_Ops/F'.var". (* begin hide *) -inline procedural "cic:/CoRN/algebra/CGroups/CGroup_Ops/P.con" "CGroup_Ops__". +inline procedural "cic:/CoRN/algebra/CGroups/CGroup_Ops/P.con" "CGroup_Ops__" as definition. -inline procedural "cic:/CoRN/algebra/CGroups/CGroup_Ops/Q.con" "CGroup_Ops__". +inline procedural "cic:/CoRN/algebra/CGroups/CGroup_Ops/Q.con" "CGroup_Ops__" as definition. (* end hide *) @@ -340,9 +340,9 @@ inline procedural "cic:/CoRN/algebra/CGroups/CGroup_Ops/Q.con" "CGroup_Ops__". Section Part_Function_Inv *) -inline procedural "cic:/CoRN/algebra/CGroups/part_function_inv_strext.con". +inline procedural "cic:/CoRN/algebra/CGroups/part_function_inv_strext.con" as lemma. -inline procedural "cic:/CoRN/algebra/CGroups/Finv.con". +inline procedural "cic:/CoRN/algebra/CGroups/Finv.con" as definition. (* UNEXPORTED End Part_Function_Inv @@ -352,9 +352,9 @@ End Part_Function_Inv Section Part_Function_Minus *) -inline procedural "cic:/CoRN/algebra/CGroups/part_function_minus_strext.con". +inline procedural "cic:/CoRN/algebra/CGroups/part_function_minus_strext.con" as lemma. -inline procedural "cic:/CoRN/algebra/CGroups/Fminus.con". +inline procedural "cic:/CoRN/algebra/CGroups/Fminus.con" as definition. (* UNEXPORTED End Part_Function_Minus @@ -367,15 +367,15 @@ End Part_Function_Minus alias id "R" = "cic:/CoRN/algebra/CGroups/CGroup_Ops/R.var". -inline procedural "cic:/CoRN/algebra/CGroups/included_FInv.con". +inline procedural "cic:/CoRN/algebra/CGroups/included_FInv.con" as lemma. -inline procedural "cic:/CoRN/algebra/CGroups/included_FInv'.con". +inline procedural "cic:/CoRN/algebra/CGroups/included_FInv'.con" as lemma. -inline procedural "cic:/CoRN/algebra/CGroups/included_FMinus.con". +inline procedural "cic:/CoRN/algebra/CGroups/included_FMinus.con" as lemma. -inline procedural "cic:/CoRN/algebra/CGroups/included_FMinus'.con". +inline procedural "cic:/CoRN/algebra/CGroups/included_FMinus'.con" as lemma. -inline procedural "cic:/CoRN/algebra/CGroups/included_FMinus''.con". +inline procedural "cic:/CoRN/algebra/CGroups/included_FMinus''.con" as lemma. (* UNEXPORTED End CGroup_Ops diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/CLogic.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/CLogic.mma index 27c279377..09a03a9f5 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/CLogic.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/CLogic.mma @@ -76,7 +76,7 @@ propositions, such as [(le m n)], we have to introduce a [CProp]-valued version. *) -inline procedural "cic:/CoRN/algebra/CLogic/CProp.con". +inline procedural "cic:/CoRN/algebra/CLogic/CProp.con" as definition. (* UNEXPORTED Section Basics @@ -87,35 +87,35 @@ Here we treat conversion from [Prop] to [CProp] and vice versa, and some basic connectives in [CProp]. *) -inline procedural "cic:/CoRN/algebra/CLogic/Not.con". +inline procedural "cic:/CoRN/algebra/CLogic/Not.con" as definition. inline procedural "cic:/CoRN/algebra/CLogic/CAnd.ind". -inline procedural "cic:/CoRN/algebra/CLogic/Iff.con". +inline procedural "cic:/CoRN/algebra/CLogic/Iff.con" as definition. inline procedural "cic:/CoRN/algebra/CLogic/CFalse.ind". inline procedural "cic:/CoRN/algebra/CLogic/CTrue.ind". -inline procedural "cic:/CoRN/algebra/CLogic/proj1_sigT.con". +inline procedural "cic:/CoRN/algebra/CLogic/proj1_sigT.con" as definition. -inline procedural "cic:/CoRN/algebra/CLogic/proj2_sigT.con". +inline procedural "cic:/CoRN/algebra/CLogic/proj2_sigT.con" as definition. inline procedural "cic:/CoRN/algebra/CLogic/sig2T.ind". -inline procedural "cic:/CoRN/algebra/CLogic/proj1_sig2T.con". +inline procedural "cic:/CoRN/algebra/CLogic/proj1_sig2T.con" as definition. -inline procedural "cic:/CoRN/algebra/CLogic/proj2a_sig2T.con". +inline procedural "cic:/CoRN/algebra/CLogic/proj2a_sig2T.con" as definition. -inline procedural "cic:/CoRN/algebra/CLogic/proj2b_sig2T.con". +inline procedural "cic:/CoRN/algebra/CLogic/proj2b_sig2T.con" as definition. inline procedural "cic:/CoRN/algebra/CLogic/toCProp.ind". -inline procedural "cic:/CoRN/algebra/CLogic/toCProp_e.con". +inline procedural "cic:/CoRN/algebra/CLogic/toCProp_e.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/CNot.con". +inline procedural "cic:/CoRN/algebra/CLogic/CNot.con" as definition. -inline procedural "cic:/CoRN/algebra/CLogic/Ccontrapos'.con". +inline procedural "cic:/CoRN/algebra/CLogic/Ccontrapos'.con" as lemma. inline procedural "cic:/CoRN/algebra/CLogic/COr.ind". @@ -127,17 +127,17 @@ biimplications.*) Infix "IFF" := Iff (at level 60, right associativity). *) -inline procedural "cic:/CoRN/algebra/CLogic/Iff_left.con". +inline procedural "cic:/CoRN/algebra/CLogic/Iff_left.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/Iff_right.con". +inline procedural "cic:/CoRN/algebra/CLogic/Iff_right.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/Iff_refl.con". +inline procedural "cic:/CoRN/algebra/CLogic/Iff_refl.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/Iff_sym.con". +inline procedural "cic:/CoRN/algebra/CLogic/Iff_sym.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/Iff_trans.con". +inline procedural "cic:/CoRN/algebra/CLogic/Iff_trans.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/Iff_imp_imp.con". +inline procedural "cic:/CoRN/algebra/CLogic/Iff_imp_imp.con" as lemma. (* UNEXPORTED Declare Right Step Iff_right. @@ -167,9 +167,9 @@ Infix "and" := CAnd (at level 80, right associativity). (* end hide *) -inline procedural "cic:/CoRN/algebra/CLogic/not_r_cor_rect.con". +inline procedural "cic:/CoRN/algebra/CLogic/not_r_cor_rect.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/not_l_cor_rect.con". +inline procedural "cic:/CoRN/algebra/CLogic/not_l_cor_rect.con" as lemma. (* begin hide *) @@ -217,7 +217,7 @@ Let [P] be a predicate on $\NN^2$#N times N#. alias id "P" = "cic:/CoRN/algebra/CLogic/Choice/P.var". -inline procedural "cic:/CoRN/algebra/CLogic/choice.con". +inline procedural "cic:/CoRN/algebra/CLogic/choice.con" as lemma. (* UNEXPORTED End Choice @@ -231,9 +231,9 @@ Section Logical_Remarks when [A], [B] and [C] are non trivial. *) -inline procedural "cic:/CoRN/algebra/CLogic/CNot_Not_or.con". +inline procedural "cic:/CoRN/algebra/CLogic/CNot_Not_or.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/CdeMorgan_ex_all.con". +inline procedural "cic:/CoRN/algebra/CLogic/CdeMorgan_ex_all.con" as lemma. (* UNEXPORTED End Logical_Remarks @@ -252,17 +252,17 @@ Similar to Relations.v in Coq's standard library. alias id "A" = "cic:/CoRN/algebra/CLogic/CRelation_Definition/A.var". -inline procedural "cic:/CoRN/algebra/CLogic/Crelation.con". +inline procedural "cic:/CoRN/algebra/CLogic/Crelation.con" as definition. alias id "R" = "cic:/CoRN/algebra/CLogic/CRelation_Definition/R.var". -inline procedural "cic:/CoRN/algebra/CLogic/Creflexive.con". +inline procedural "cic:/CoRN/algebra/CLogic/Creflexive.con" as definition. -inline procedural "cic:/CoRN/algebra/CLogic/Ctransitive.con". +inline procedural "cic:/CoRN/algebra/CLogic/Ctransitive.con" as definition. -inline procedural "cic:/CoRN/algebra/CLogic/Csymmetric.con". +inline procedural "cic:/CoRN/algebra/CLogic/Csymmetric.con" as definition. -inline procedural "cic:/CoRN/algebra/CLogic/Cequiv.con". +inline procedural "cic:/CoRN/algebra/CLogic/Cequiv.con" as definition. (* UNEXPORTED End CRelation_Definition @@ -281,17 +281,17 @@ Analogous. alias id "A" = "cic:/CoRN/algebra/CLogic/TRelation_Definition/A.var". -inline procedural "cic:/CoRN/algebra/CLogic/Trelation.con". +inline procedural "cic:/CoRN/algebra/CLogic/Trelation.con" as definition. alias id "R" = "cic:/CoRN/algebra/CLogic/TRelation_Definition/R.var". -inline procedural "cic:/CoRN/algebra/CLogic/Treflexive.con". +inline procedural "cic:/CoRN/algebra/CLogic/Treflexive.con" as definition. -inline procedural "cic:/CoRN/algebra/CLogic/Ttransitive.con". +inline procedural "cic:/CoRN/algebra/CLogic/Ttransitive.con" as definition. -inline procedural "cic:/CoRN/algebra/CLogic/Tsymmetric.con". +inline procedural "cic:/CoRN/algebra/CLogic/Tsymmetric.con" as definition. -inline procedural "cic:/CoRN/algebra/CLogic/Tequiv.con". +inline procedural "cic:/CoRN/algebra/CLogic/Tequiv.con" as definition. (* UNEXPORTED End TRelation_Definition @@ -308,43 +308,43 @@ Section le_odd inline procedural "cic:/CoRN/algebra/CLogic/Cle.ind". -inline procedural "cic:/CoRN/algebra/CLogic/Cnat_double_ind.con". +inline procedural "cic:/CoRN/algebra/CLogic/Cnat_double_ind.con" as theorem. -inline procedural "cic:/CoRN/algebra/CLogic/my_Cle_ind.con". +inline procedural "cic:/CoRN/algebra/CLogic/my_Cle_ind.con" as theorem. -inline procedural "cic:/CoRN/algebra/CLogic/Cle_n_S.con". +inline procedural "cic:/CoRN/algebra/CLogic/Cle_n_S.con" as theorem. -inline procedural "cic:/CoRN/algebra/CLogic/toCle.con". +inline procedural "cic:/CoRN/algebra/CLogic/toCle.con" as lemma. (* UNEXPORTED Hint Resolve toCle. *) -inline procedural "cic:/CoRN/algebra/CLogic/Cle_to.con". +inline procedural "cic:/CoRN/algebra/CLogic/Cle_to.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/Clt.con". +inline procedural "cic:/CoRN/algebra/CLogic/Clt.con" as definition. -inline procedural "cic:/CoRN/algebra/CLogic/toCProp_lt.con". +inline procedural "cic:/CoRN/algebra/CLogic/toCProp_lt.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/Clt_to.con". +inline procedural "cic:/CoRN/algebra/CLogic/Clt_to.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/Cle_le_S_eq.con". +inline procedural "cic:/CoRN/algebra/CLogic/Cle_le_S_eq.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/Cnat_total_order.con". +inline procedural "cic:/CoRN/algebra/CLogic/Cnat_total_order.con" as lemma. inline procedural "cic:/CoRN/algebra/CLogic/Codd.ind". -inline procedural "cic:/CoRN/algebra/CLogic/Codd_even_to.con". +inline procedural "cic:/CoRN/algebra/CLogic/Codd_even_to.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/Codd_to.con". +inline procedural "cic:/CoRN/algebra/CLogic/Codd_to.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/Ceven_to.con". +inline procedural "cic:/CoRN/algebra/CLogic/Ceven_to.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/to_Codd_even.con". +inline procedural "cic:/CoRN/algebra/CLogic/to_Codd_even.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/to_Codd.con". +inline procedural "cic:/CoRN/algebra/CLogic/to_Codd.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/to_Ceven.con". +inline procedural "cic:/CoRN/algebra/CLogic/to_Ceven.con" as lemma. (* UNEXPORTED End le_odd @@ -357,17 +357,17 @@ Section Misc (*#* **Miscellaneous *) -inline procedural "cic:/CoRN/algebra/CLogic/CZ_exh.con". +inline procedural "cic:/CoRN/algebra/CLogic/CZ_exh.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/Cnats_Z_ind.con". +inline procedural "cic:/CoRN/algebra/CLogic/Cnats_Z_ind.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/Cdiff_Z_ind.con". +inline procedural "cic:/CoRN/algebra/CLogic/Cdiff_Z_ind.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/Cpred_succ_Z_ind.con". +inline procedural "cic:/CoRN/algebra/CLogic/Cpred_succ_Z_ind.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/not_r_sum_rec.con". +inline procedural "cic:/CoRN/algebra/CLogic/not_r_sum_rec.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/not_l_sum_rec.con". +inline procedural "cic:/CoRN/algebra/CLogic/not_l_sum_rec.con" as lemma. (* UNEXPORTED End Misc @@ -382,9 +382,9 @@ write them in that form but we will single out the preservation of the setoid equality. *) -inline procedural "cic:/CoRN/algebra/CLogic/nat_less_n_pred.con". +inline procedural "cic:/CoRN/algebra/CLogic/nat_less_n_pred.con" as definition. -inline procedural "cic:/CoRN/algebra/CLogic/nat_less_n_pred'.con". +inline procedural "cic:/CoRN/algebra/CLogic/nat_less_n_pred'.con" as definition. (* UNEXPORTED Implicit Arguments nat_less_n_pred [n]. @@ -404,14 +404,14 @@ We begin by proving that this case distinction is decidable. Next, we prove the usual results about sums of even and odd numbers: *) -inline procedural "cic:/CoRN/algebra/CLogic/even_plus_n_n.con". +inline procedural "cic:/CoRN/algebra/CLogic/even_plus_n_n.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/even_or_odd_plus.con". +inline procedural "cic:/CoRN/algebra/CLogic/even_or_odd_plus.con" as lemma. (*#* Finally, we prove that an arbitrary natural number can be written in some canonical way. *) -inline procedural "cic:/CoRN/algebra/CLogic/even_or_odd_plus_gt.con". +inline procedural "cic:/CoRN/algebra/CLogic/even_or_odd_plus_gt.con" as lemma. (* UNEXPORTED End Odd_and_Even @@ -437,27 +437,27 @@ definitions. Giving a name to these results allows us to use them in definitions keeping conciseness. *) -inline procedural "cic:/CoRN/algebra/CLogic/Clt_le_weak.con". +inline procedural "cic:/CoRN/algebra/CLogic/Clt_le_weak.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/lt_5.con". +inline procedural "cic:/CoRN/algebra/CLogic/lt_5.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/lt_8.con". +inline procedural "cic:/CoRN/algebra/CLogic/lt_8.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/pred_lt.con". +inline procedural "cic:/CoRN/algebra/CLogic/pred_lt.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/lt_10.con". +inline procedural "cic:/CoRN/algebra/CLogic/lt_10.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/lt_pred'.con". +inline procedural "cic:/CoRN/algebra/CLogic/lt_pred'.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/le_1.con". +inline procedural "cic:/CoRN/algebra/CLogic/le_1.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/le_2.con". +inline procedural "cic:/CoRN/algebra/CLogic/le_2.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/plus_eq_one_imp_eq_zero.con". +inline procedural "cic:/CoRN/algebra/CLogic/plus_eq_one_imp_eq_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/not_not_lt.con". +inline procedural "cic:/CoRN/algebra/CLogic/not_not_lt.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/plus_pred_pred_plus.con". +inline procedural "cic:/CoRN/algebra/CLogic/plus_pred_pred_plus.con" as lemma. (*#* We now prove some properties of functions on the natural numbers. @@ -473,17 +473,17 @@ for every natural number [n] then [h] is monotonous. An analogous result holds for weak monotonicity. *) -inline procedural "cic:/CoRN/algebra/CLogic/nat_local_mon_imp_mon.con". +inline procedural "cic:/CoRN/algebra/CLogic/nat_local_mon_imp_mon.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/nat_local_mon_imp_mon_le.con". +inline procedural "cic:/CoRN/algebra/CLogic/nat_local_mon_imp_mon_le.con" as lemma. (*#* A strictly increasing function is injective: *) -inline procedural "cic:/CoRN/algebra/CLogic/nat_mon_imp_inj.con". +inline procedural "cic:/CoRN/algebra/CLogic/nat_mon_imp_inj.con" as lemma. (*#* And (not completely trivial) a function that preserves [lt] also preserves [le]. *) -inline procedural "cic:/CoRN/algebra/CLogic/nat_mon_imp_mon'.con". +inline procedural "cic:/CoRN/algebra/CLogic/nat_mon_imp_mon'.con" as lemma. (*#* The last lemmas in this section state that a monotonous function in the @@ -492,9 +492,9 @@ natural number [n] there is an [i] such that [h(i) <= n<(n+1) <= h(i+1)]. These are useful for integration. *) -inline procedural "cic:/CoRN/algebra/CLogic/mon_fun_covers.con". +inline procedural "cic:/CoRN/algebra/CLogic/mon_fun_covers.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/weird_mon_covers.con". +inline procedural "cic:/CoRN/algebra/CLogic/weird_mon_covers.con" as lemma. (* UNEXPORTED End Natural_Numbers @@ -504,7 +504,7 @@ End Natural_Numbers Useful for the Fundamental Theorem of Algebra. *) -inline procedural "cic:/CoRN/algebra/CLogic/kseq_prop.con". +inline procedural "cic:/CoRN/algebra/CLogic/kseq_prop.con" as lemma. (* UNEXPORTED Section Predicates_to_CProp @@ -518,23 +518,23 @@ for [CProp]- and [Prop]-valued predicates. We begin by presenting the results for [CProp]-valued predicates: *) -inline procedural "cic:/CoRN/algebra/CLogic/even_induction.con". +inline procedural "cic:/CoRN/algebra/CLogic/even_induction.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/odd_induction.con". +inline procedural "cic:/CoRN/algebra/CLogic/odd_induction.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/four_induction.con". +inline procedural "cic:/CoRN/algebra/CLogic/four_induction.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/nat_complete_double_induction.con". +inline procedural "cic:/CoRN/algebra/CLogic/nat_complete_double_induction.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/odd_double_ind.con". +inline procedural "cic:/CoRN/algebra/CLogic/odd_double_ind.con" as lemma. (*#* For subsetoid predicates in the natural numbers we can eliminate disjunction (and existential quantification) as follows. *) -inline procedural "cic:/CoRN/algebra/CLogic/finite_or_elim.con". +inline procedural "cic:/CoRN/algebra/CLogic/finite_or_elim.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/str_finite_or_elim.con". +inline procedural "cic:/CoRN/algebra/CLogic/str_finite_or_elim.con" as lemma. (* UNEXPORTED End Predicates_to_CProp @@ -548,13 +548,13 @@ Section Predicates_to_Prop completeness's sake. *) -inline procedural "cic:/CoRN/algebra/CLogic/even_ind.con". +inline procedural "cic:/CoRN/algebra/CLogic/even_ind.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/odd_ind.con". +inline procedural "cic:/CoRN/algebra/CLogic/odd_ind.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/nat_complete_double_ind.con". +inline procedural "cic:/CoRN/algebra/CLogic/nat_complete_double_ind.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/four_ind.con". +inline procedural "cic:/CoRN/algebra/CLogic/four_ind.con" as lemma. (* UNEXPORTED End Predicates_to_Prop @@ -573,43 +573,43 @@ Tactic Notation "ElimCompare" constr(c) constr(d) := elim_compare c d. (* end hide *) -inline procedural "cic:/CoRN/algebra/CLogic/Zlts.con". +inline procedural "cic:/CoRN/algebra/CLogic/Zlts.con" as definition. -inline procedural "cic:/CoRN/algebra/CLogic/toCProp_Zlt.con". +inline procedural "cic:/CoRN/algebra/CLogic/toCProp_Zlt.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/CZlt_to.con". +inline procedural "cic:/CoRN/algebra/CLogic/CZlt_to.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/Zsgn_1.con". +inline procedural "cic:/CoRN/algebra/CLogic/Zsgn_1.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/Zsgn_2.con". +inline procedural "cic:/CoRN/algebra/CLogic/Zsgn_2.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/Zsgn_3.con". +inline procedural "cic:/CoRN/algebra/CLogic/Zsgn_3.con" as lemma. (*#* The following have unusual names, in line with the series of lemmata in fast_integers.v. *) -inline procedural "cic:/CoRN/algebra/CLogic/ZL4'.con". +inline procedural "cic:/CoRN/algebra/CLogic/ZL4'.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/ZL9.con". +inline procedural "cic:/CoRN/algebra/CLogic/ZL9.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/Zsgn_4.con". +inline procedural "cic:/CoRN/algebra/CLogic/Zsgn_4.con" as theorem. -inline procedural "cic:/CoRN/algebra/CLogic/Zsgn_5.con". +inline procedural "cic:/CoRN/algebra/CLogic/Zsgn_5.con" as theorem. -inline procedural "cic:/CoRN/algebra/CLogic/nat_nat_pos.con". +inline procedural "cic:/CoRN/algebra/CLogic/nat_nat_pos.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/S_predn.con". +inline procedural "cic:/CoRN/algebra/CLogic/S_predn.con" as theorem. -inline procedural "cic:/CoRN/algebra/CLogic/absolu_1.con". +inline procedural "cic:/CoRN/algebra/CLogic/absolu_1.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/absolu_2.con". +inline procedural "cic:/CoRN/algebra/CLogic/absolu_2.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/Zgt_mult_conv_absorb_l.con". +inline procedural "cic:/CoRN/algebra/CLogic/Zgt_mult_conv_absorb_l.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/Zgt_mult_reg_absorb_l.con". +inline procedural "cic:/CoRN/algebra/CLogic/Zgt_mult_reg_absorb_l.con" as lemma. -inline procedural "cic:/CoRN/algebra/CLogic/Zmult_Sm_Sn.con". +inline procedural "cic:/CoRN/algebra/CLogic/Zmult_Sm_Sn.con" as lemma. (* NOTATION Notation ProjT1 := (proj1_sigT _ _). diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/CMonoids.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/CMonoids.mma index 7ce31a35a..6d13c1b52 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/CMonoids.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/CMonoids.mma @@ -29,11 +29,11 @@ include "algebra/CSemiGroups.ma". ** Definition of monoids *) -inline procedural "cic:/CoRN/algebra/CMonoids/is_rht_unit.con". +inline procedural "cic:/CoRN/algebra/CMonoids/is_rht_unit.con" as definition. (* End_SpecReals *) -inline procedural "cic:/CoRN/algebra/CMonoids/is_lft_unit.con". +inline procedural "cic:/CoRN/algebra/CMonoids/is_lft_unit.con" as definition. (* UNEXPORTED Implicit Arguments is_lft_unit [S]. @@ -74,7 +74,7 @@ e.g. for the setoid of non-zeros. Notation Zero := (cm_unit _). *) -inline procedural "cic:/CoRN/algebra/CMonoids/nonZeroP.con". +inline procedural "cic:/CoRN/algebra/CMonoids/nonZeroP.con" as definition. (* End_SpecReals *) @@ -94,11 +94,11 @@ Section CMonoid_axioms alias id "M" = "cic:/CoRN/algebra/CMonoids/CMonoid_axioms/M.var". -inline procedural "cic:/CoRN/algebra/CMonoids/CMonoid_is_CMonoid.con". +inline procedural "cic:/CoRN/algebra/CMonoids/CMonoid_is_CMonoid.con" as lemma. -inline procedural "cic:/CoRN/algebra/CMonoids/cm_rht_unit.con". +inline procedural "cic:/CoRN/algebra/CMonoids/cm_rht_unit.con" as lemma. -inline procedural "cic:/CoRN/algebra/CMonoids/cm_lft_unit.con". +inline procedural "cic:/CoRN/algebra/CMonoids/cm_lft_unit.con" as lemma. (* UNEXPORTED End CMonoid_axioms @@ -116,17 +116,17 @@ Section CMonoid_basics alias id "M" = "cic:/CoRN/algebra/CMonoids/CMonoid_basics/M.var". -inline procedural "cic:/CoRN/algebra/CMonoids/cm_rht_unit_unfolded.con". +inline procedural "cic:/CoRN/algebra/CMonoids/cm_rht_unit_unfolded.con" as lemma. -inline procedural "cic:/CoRN/algebra/CMonoids/cm_lft_unit_unfolded.con". +inline procedural "cic:/CoRN/algebra/CMonoids/cm_lft_unit_unfolded.con" as lemma. (* UNEXPORTED Hint Resolve cm_rht_unit_unfolded cm_lft_unit_unfolded: algebra. *) -inline procedural "cic:/CoRN/algebra/CMonoids/cm_unit_unique_lft.con". +inline procedural "cic:/CoRN/algebra/CMonoids/cm_unit_unique_lft.con" as lemma. -inline procedural "cic:/CoRN/algebra/CMonoids/cm_unit_unique_rht.con". +inline procedural "cic:/CoRN/algebra/CMonoids/cm_unit_unique_rht.con" as lemma. (* Begin_SpecReals *) @@ -134,7 +134,7 @@ inline procedural "cic:/CoRN/algebra/CMonoids/cm_unit_unique_rht.con". The proof component of the monoid is irrelevant. *) -inline procedural "cic:/CoRN/algebra/CMonoids/is_CMonoid_proof_irr.con". +inline procedural "cic:/CoRN/algebra/CMonoids/is_CMonoid_proof_irr.con" as lemma. (* End_SpecReals *) @@ -155,11 +155,11 @@ alias id "Punit" = "cic:/CoRN/algebra/CMonoids/CMonoid_basics/SubCMonoids/Punit. alias id "op_pres_P" = "cic:/CoRN/algebra/CMonoids/CMonoid_basics/SubCMonoids/op_pres_P.var". -inline procedural "cic:/CoRN/algebra/CMonoids/CMonoid_basics/SubCMonoids/subcrr.con" "CMonoid_basics__SubCMonoids__". +inline procedural "cic:/CoRN/algebra/CMonoids/CMonoid_basics/SubCMonoids/subcrr.con" "CMonoid_basics__SubCMonoids__" as definition. -inline procedural "cic:/CoRN/algebra/CMonoids/ismon_scrr.con". +inline procedural "cic:/CoRN/algebra/CMonoids/ismon_scrr.con" as lemma. -inline procedural "cic:/CoRN/algebra/CMonoids/Build_SubCMonoid.con". +inline procedural "cic:/CoRN/algebra/CMonoids/Build_SubCMonoid.con" as definition. (* UNEXPORTED End SubCMonoids diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/COrdAbs.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/COrdAbs.mma index cf2ee34e5..e3b9709c7 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/COrdAbs.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/COrdAbs.mma @@ -24,7 +24,7 @@ include "algebra/COrdFields2.ma". (* Begin_SpecReals *) -inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall.con". +inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall.con" as definition. (* UNEXPORTED Implicit Arguments AbsSmall [R]. @@ -43,13 +43,13 @@ Section AbsSmall_properties alias id "R" = "cic:/CoRN/algebra/COrdAbs/AbsSmall_properties/R.var". -inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_wdr.con". +inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_wdr.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_wdr_unfolded.con". +inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_wdr_unfolded.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_wdl.con". +inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_wdl.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_wdl_unfolded.con". +inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_wdl_unfolded.con" as lemma. (* UNEXPORTED Declare Left Step AbsSmall_wdl_unfolded. @@ -67,41 +67,41 @@ Notation ZeroR := (Zero:R). (* end hide *) -inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_leEq_trans.con". +inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_leEq_trans.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdAbs/zero_AbsSmall.con". +inline procedural "cic:/CoRN/algebra/COrdAbs/zero_AbsSmall.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_trans.con". +inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_trans.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdAbs/leEq_imp_AbsSmall.con". +inline procedural "cic:/CoRN/algebra/COrdAbs/leEq_imp_AbsSmall.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdAbs/inv_resp_AbsSmall.con". +inline procedural "cic:/CoRN/algebra/COrdAbs/inv_resp_AbsSmall.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_minus.con". +inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_minus.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_plus.con". +inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_plus.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_eps_div_two.con". +inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_eps_div_two.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_x_plus_delta.con". +inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_x_plus_delta.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_x_minus_delta.con". +inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_x_minus_delta.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_x_plus_eps_div2.con". +inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_x_plus_eps_div2.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_x_minus_eps_div2.con". +inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_x_minus_eps_div2.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_intermediate.con". +inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_intermediate.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_eps_div2.con". +inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_eps_div2.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_nonneg.con". +inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_nonneg.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_mult.con". +inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_mult.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_cancel_mult.con". +inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_cancel_mult.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_approach_zero.con". +inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_approach_zero.con" as lemma. (* UNEXPORTED End AbsSmall_properties @@ -117,13 +117,13 @@ Declare Right Step AbsSmall_wdr_unfolded. (*#* ** Properties of [AbsBig] *) -inline procedural "cic:/CoRN/algebra/COrdAbs/absBig.con". +inline procedural "cic:/CoRN/algebra/COrdAbs/absBig.con" as definition. (* NOTATION Notation AbsBig := (absBig _). *) -inline procedural "cic:/CoRN/algebra/COrdAbs/AbsBigSmall_minus.con". +inline procedural "cic:/CoRN/algebra/COrdAbs/AbsBigSmall_minus.con" as lemma. (* UNEXPORTED Section absBig_wd_properties @@ -136,13 +136,13 @@ Section absBig_wd_properties alias id "R" = "cic:/CoRN/algebra/COrdAbs/absBig_wd_properties/R.var". -inline procedural "cic:/CoRN/algebra/COrdAbs/AbsBig_wdr.con". +inline procedural "cic:/CoRN/algebra/COrdAbs/AbsBig_wdr.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdAbs/AbsBig_wdl.con". +inline procedural "cic:/CoRN/algebra/COrdAbs/AbsBig_wdl.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdAbs/AbsBig_wdr_unfolded.con". +inline procedural "cic:/CoRN/algebra/COrdAbs/AbsBig_wdr_unfolded.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdAbs/AbsBig_wdl_unfolded.con". +inline procedural "cic:/CoRN/algebra/COrdAbs/AbsBig_wdl_unfolded.con" as lemma. (* UNEXPORTED End absBig_wd_properties diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/COrdCauchy.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/COrdCauchy.mma index a77326c63..c9dc0e0cd 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/COrdCauchy.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/COrdCauchy.mma @@ -43,7 +43,7 @@ Unset Strict Implicit. (* end hide *) -inline procedural "cic:/CoRN/algebra/COrdCauchy/Cauchy_prop.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/Cauchy_prop.con" as definition. (* begin hide *) @@ -72,7 +72,7 @@ inline procedural "cic:/CoRN/algebra/COrdCauchy/CauchySeq.ind". cic:/matita/CoRN-Procedural/algebra/COrdCauchy/CS_seq.con *) -inline procedural "cic:/CoRN/algebra/COrdCauchy/SeqLimit.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/SeqLimit.con" as definition. (* End_SpecReals *) @@ -86,9 +86,9 @@ hold). %\end{convention}% *) -inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_bounded.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_bounded.con" as theorem. -inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_const.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_const.con" as lemma. (*#* %\begin{convention}% Assume [f] and [g] are Cauchy sequences on [R]. @@ -103,11 +103,11 @@ alias id "Hf" = "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/Hf.var". alias id "Hg" = "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/Hg.var". -inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_plus.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_plus.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_inv.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_inv.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_mult.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_mult.con" as lemma. (*#* We now assume that [f] is, from some point onwards, greater than @@ -129,11 +129,11 @@ alias id "N" = "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/N.var". alias id "f_bnd" = "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/f_bnd.var". -inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_recip_def.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_recip_def.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_recip_seq.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_recip_seq.con" as definition. -inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_recip.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_recip.con" as lemma. (* UNEXPORTED End OrdField_Cauchy @@ -148,7 +148,7 @@ The following lemma does not require the sequence to be Cauchy, but it fits well here anyway. *) -inline procedural "cic:/CoRN/algebra/COrdCauchy/maj_upto_eps.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/maj_upto_eps.con" as lemma. (* UNEXPORTED Section Mult_AbsSmall @@ -162,13 +162,13 @@ alias id "R" = "cic:/CoRN/algebra/COrdCauchy/Mult_AbsSmall/R.var". %\end{convention}% *) -inline procedural "cic:/CoRN/algebra/COrdCauchy/mult_AbsSmall'_rht.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/mult_AbsSmall'_rht.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdCauchy/mult_AbsSmall_rht.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/mult_AbsSmall_rht.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdCauchy/mult_AbsSmall_lft.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/mult_AbsSmall_lft.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdCauchy/mult_AbsSmall.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/mult_AbsSmall.con" as lemma. (* UNEXPORTED End Mult_AbsSmall @@ -186,15 +186,15 @@ alias id "R" = "cic:/CoRN/algebra/COrdCauchy/Mult_Continuous/R.var". %\end{convention}% *) -inline procedural "cic:/CoRN/algebra/COrdCauchy/smaller.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/smaller.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdCauchy/estimate_abs.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/estimate_abs.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdCauchy/mult_contin.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/mult_contin.con" as lemma. (*#* Addition is also continuous. *) -inline procedural "cic:/CoRN/algebra/COrdCauchy/plus_contin.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/plus_contin.con" as lemma. (* UNEXPORTED End Mult_Continuous @@ -221,13 +221,13 @@ We begin by characterizing the preservation of less (less or equal) in terms of preservation of less or equal (less). *) -inline procedural "cic:/CoRN/algebra/COrdCauchy/resp_less_char'.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/resp_less_char'.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdCauchy/resp_less_char.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/resp_less_char.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdCauchy/resp_leEq_char'.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/resp_leEq_char'.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdCauchy/resp_leEq_char.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/resp_leEq_char.con" as lemma. (*#* Next, we see different characterizations of monotonous functions from @@ -238,45 +238,45 @@ is monotonous iff [f(i) [<] f(i+1)] for every [i]. Also, strictly monotonous functions are injective. *) -inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon_imp_mon.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon_imp_mon.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon_imp_mon'.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon_imp_mon'.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon'_imp_mon'.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon'_imp_mon'.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdCauchy/mon_imp_mon'.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/mon_imp_mon'.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdCauchy/mon_imp_inj.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/mon_imp_inj.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon_imp_mon_lt.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon_imp_mon_lt.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon_imp_mon'_lt.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon_imp_mon'_lt.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon'_imp_mon'_lt.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon'_imp_mon'_lt.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon'_imp_mon'2_lt.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon'_imp_mon'2_lt.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdCauchy/mon_imp_mon'_lt.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/mon_imp_mon'_lt.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdCauchy/mon_imp_inj_lt.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/mon_imp_inj_lt.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon_imp_mon_le.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon_imp_mon_le.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon_imp_mon'_le.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon_imp_mon'_le.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon'_imp_mon'_le.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon'_imp_mon'_le.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon'_imp_mon'2_le.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon'_imp_mon'2_le.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdCauchy/mon_imp_mon'_le.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/mon_imp_mon'_le.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdCauchy/mon_imp_inj_le.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/mon_imp_inj_le.con" as lemma. (*#* A similar result for %{\em %partial%}% functions. *) -inline procedural "cic:/CoRN/algebra/COrdCauchy/part_mon_imp_mon'.con". +inline procedural "cic:/CoRN/algebra/COrdCauchy/part_mon_imp_mon'.con" as lemma. (* UNEXPORTED End Monotonous_functions diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/COrdFields.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/COrdFields.mma index b0bb26b26..44e978614 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/COrdFields.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/COrdFields.mma @@ -100,7 +100,7 @@ Implicit Arguments cof_less [c]. Infix "[<]" := cof_less (at level 70, no associativity). *) -inline procedural "cic:/CoRN/algebra/COrdFields/greater.con". +inline procedural "cic:/CoRN/algebra/COrdFields/greater.con" as definition. (* UNEXPORTED Implicit Arguments greater [F]. @@ -116,7 +116,7 @@ Infix "[>]" := greater (at level 70, no associativity). Less or equal is defined as ``not greater than''. *) -inline procedural "cic:/CoRN/algebra/COrdFields/leEq.con". +inline procedural "cic:/CoRN/algebra/COrdFields/leEq.con" as definition. (*#* %\begin{nameconvention}% @@ -146,27 +146,27 @@ Let [F] be a field. alias id "F" = "cic:/CoRN/algebra/COrdFields/COrdField_axioms/F.var". -inline procedural "cic:/CoRN/algebra/COrdFields/COrdField_is_COrdField.con". +inline procedural "cic:/CoRN/algebra/COrdFields/COrdField_is_COrdField.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/less_strorder.con". +inline procedural "cic:/CoRN/algebra/COrdFields/less_strorder.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/less_transitive_unfolded.con". +inline procedural "cic:/CoRN/algebra/COrdFields/less_transitive_unfolded.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/less_antisymmetric_unfolded.con". +inline procedural "cic:/CoRN/algebra/COrdFields/less_antisymmetric_unfolded.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/less_irreflexive.con". +inline procedural "cic:/CoRN/algebra/COrdFields/less_irreflexive.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/less_irreflexive_unfolded.con". +inline procedural "cic:/CoRN/algebra/COrdFields/less_irreflexive_unfolded.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/plus_resp_less_rht.con". +inline procedural "cic:/CoRN/algebra/COrdFields/plus_resp_less_rht.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/mult_resp_pos.con". +inline procedural "cic:/CoRN/algebra/COrdFields/mult_resp_pos.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/less_conf_ap.con". +inline procedural "cic:/CoRN/algebra/COrdFields/less_conf_ap.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/less_wdr.con". +inline procedural "cic:/CoRN/algebra/COrdFields/less_wdr.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/less_wdl.con". +inline procedural "cic:/CoRN/algebra/COrdFields/less_wdl.con" as lemma. (* UNEXPORTED End COrdField_axioms @@ -197,25 +197,25 @@ Let in the rest of this section (and all subsections) alias id "R" = "cic:/CoRN/algebra/COrdFields/OrdField_basics/R.var". -inline procedural "cic:/CoRN/algebra/COrdFields/less_imp_ap.con". +inline procedural "cic:/CoRN/algebra/COrdFields/less_imp_ap.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/Greater_imp_ap.con". +inline procedural "cic:/CoRN/algebra/COrdFields/Greater_imp_ap.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/ap_imp_less.con". +inline procedural "cic:/CoRN/algebra/COrdFields/ap_imp_less.con" as lemma. (*#* Now properties which can be derived. *) -inline procedural "cic:/CoRN/algebra/COrdFields/less_cotransitive.con". +inline procedural "cic:/CoRN/algebra/COrdFields/less_cotransitive.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/less_cotransitive_unfolded.con". +inline procedural "cic:/CoRN/algebra/COrdFields/less_cotransitive_unfolded.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/pos_ap_zero.con". +inline procedural "cic:/CoRN/algebra/COrdFields/pos_ap_zero.con" as lemma. (* Main characterization of less *) -inline procedural "cic:/CoRN/algebra/COrdFields/leEq_not_eq.con". +inline procedural "cic:/CoRN/algebra/COrdFields/leEq_not_eq.con" as lemma. (* UNEXPORTED End OrdField_basics @@ -234,11 +234,11 @@ Section Basic_Properties_of_leEq alias id "R" = "cic:/CoRN/algebra/COrdFields/Basic_Properties_of_leEq/R.var". -inline procedural "cic:/CoRN/algebra/COrdFields/leEq_wdr.con". +inline procedural "cic:/CoRN/algebra/COrdFields/leEq_wdr.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/leEq_wdl.con". +inline procedural "cic:/CoRN/algebra/COrdFields/leEq_wdl.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/leEq_reflexive.con". +inline procedural "cic:/CoRN/algebra/COrdFields/leEq_reflexive.con" as lemma. (* UNEXPORTED Declare Left Step leEq_wdl. @@ -248,19 +248,19 @@ Declare Left Step leEq_wdl. Declare Right Step leEq_wdr. *) -inline procedural "cic:/CoRN/algebra/COrdFields/eq_imp_leEq.con". +inline procedural "cic:/CoRN/algebra/COrdFields/eq_imp_leEq.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/leEq_imp_eq.con". +inline procedural "cic:/CoRN/algebra/COrdFields/leEq_imp_eq.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/lt_equiv_imp_eq.con". +inline procedural "cic:/CoRN/algebra/COrdFields/lt_equiv_imp_eq.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/less_leEq_trans.con". +inline procedural "cic:/CoRN/algebra/COrdFields/less_leEq_trans.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/leEq_less_trans.con". +inline procedural "cic:/CoRN/algebra/COrdFields/leEq_less_trans.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/leEq_transitive.con". +inline procedural "cic:/CoRN/algebra/COrdFields/leEq_transitive.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/less_leEq.con". +inline procedural "cic:/CoRN/algebra/COrdFields/less_leEq.con" as lemma. (* UNEXPORTED End Basic_Properties_of_leEq @@ -290,31 +290,31 @@ e.g.%\% [x[/]TwoNZ]. alias id "R" = "cic:/CoRN/algebra/COrdFields/infinity_of_cordfields/R.var". -inline procedural "cic:/CoRN/algebra/COrdFields/pos_one.con". +inline procedural "cic:/CoRN/algebra/COrdFields/pos_one.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/nring_less_succ.con". +inline procedural "cic:/CoRN/algebra/COrdFields/nring_less_succ.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/nring_less.con". +inline procedural "cic:/CoRN/algebra/COrdFields/nring_less.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/nring_leEq.con". +inline procedural "cic:/CoRN/algebra/COrdFields/nring_leEq.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/nring_apart.con". +inline procedural "cic:/CoRN/algebra/COrdFields/nring_apart.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/nring_ap_zero.con". +inline procedural "cic:/CoRN/algebra/COrdFields/nring_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/nring_ap_zero'.con". +inline procedural "cic:/CoRN/algebra/COrdFields/nring_ap_zero'.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/nring_ap_zero_imp.con". +inline procedural "cic:/CoRN/algebra/COrdFields/nring_ap_zero_imp.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/Snring.con". +inline procedural "cic:/CoRN/algebra/COrdFields/Snring.con" as definition. include "tactics/Transparent_algebra.ma". -inline procedural "cic:/CoRN/algebra/COrdFields/pos_Snring.con". +inline procedural "cic:/CoRN/algebra/COrdFields/pos_Snring.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/nringS_ap_zero.con". +inline procedural "cic:/CoRN/algebra/COrdFields/nringS_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/nring_fac_ap_zero.con". +inline procedural "cic:/CoRN/algebra/COrdFields/nring_fac_ap_zero.con" as lemma. include "tactics/Opaque_algebra.ma". @@ -330,35 +330,35 @@ In the names of lemmas, we denote the numbers 0,1,2,3,4 and so on, by %\end{nameconvention}% *) -inline procedural "cic:/CoRN/algebra/COrdFields/less_plusOne.con". +inline procedural "cic:/CoRN/algebra/COrdFields/less_plusOne.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/zero_lt_posplus1.con". +inline procedural "cic:/CoRN/algebra/COrdFields/zero_lt_posplus1.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/plus_one_ext_less.con". +inline procedural "cic:/CoRN/algebra/COrdFields/plus_one_ext_less.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/one_less_two.con". +inline procedural "cic:/CoRN/algebra/COrdFields/one_less_two.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/two_less_three.con". +inline procedural "cic:/CoRN/algebra/COrdFields/two_less_three.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/three_less_four.con". +inline procedural "cic:/CoRN/algebra/COrdFields/three_less_four.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/pos_two.con". +inline procedural "cic:/CoRN/algebra/COrdFields/pos_two.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/one_less_three.con". +inline procedural "cic:/CoRN/algebra/COrdFields/one_less_three.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/two_less_four.con". +inline procedural "cic:/CoRN/algebra/COrdFields/two_less_four.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/pos_three.con". +inline procedural "cic:/CoRN/algebra/COrdFields/pos_three.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/one_less_four.con". +inline procedural "cic:/CoRN/algebra/COrdFields/one_less_four.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/pos_four.con". +inline procedural "cic:/CoRN/algebra/COrdFields/pos_four.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/two_ap_zero.con". +inline procedural "cic:/CoRN/algebra/COrdFields/two_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/three_ap_zero.con". +inline procedural "cic:/CoRN/algebra/COrdFields/three_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/four_ap_zero.con". +inline procedural "cic:/CoRN/algebra/COrdFields/four_ap_zero.con" as lemma. (* UNEXPORTED End up_to_four @@ -370,37 +370,37 @@ Section More_than_four (*#* *** Properties of some other numbers *) -inline procedural "cic:/CoRN/algebra/COrdFields/pos_six.con". +inline procedural "cic:/CoRN/algebra/COrdFields/pos_six.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/pos_eight.con". +inline procedural "cic:/CoRN/algebra/COrdFields/pos_eight.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/pos_nine.con". +inline procedural "cic:/CoRN/algebra/COrdFields/pos_nine.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/pos_twelve.con". +inline procedural "cic:/CoRN/algebra/COrdFields/pos_twelve.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/pos_sixteen.con". +inline procedural "cic:/CoRN/algebra/COrdFields/pos_sixteen.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/pos_eighteen.con". +inline procedural "cic:/CoRN/algebra/COrdFields/pos_eighteen.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/pos_twentyfour.con". +inline procedural "cic:/CoRN/algebra/COrdFields/pos_twentyfour.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/pos_fortyeight.con". +inline procedural "cic:/CoRN/algebra/COrdFields/pos_fortyeight.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/six_ap_zero.con". +inline procedural "cic:/CoRN/algebra/COrdFields/six_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/eight_ap_zero.con". +inline procedural "cic:/CoRN/algebra/COrdFields/eight_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/nine_ap_zero.con". +inline procedural "cic:/CoRN/algebra/COrdFields/nine_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/twelve_ap_zero.con". +inline procedural "cic:/CoRN/algebra/COrdFields/twelve_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/sixteen_ap_zero.con". +inline procedural "cic:/CoRN/algebra/COrdFields/sixteen_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/eighteen_ap_zero.con". +inline procedural "cic:/CoRN/algebra/COrdFields/eighteen_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/twentyfour_ap_zero.con". +inline procedural "cic:/CoRN/algebra/COrdFields/twentyfour_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/fortyeight_ap_zero.con". +inline procedural "cic:/CoRN/algebra/COrdFields/fortyeight_ap_zero.con" as lemma. (* UNEXPORTED End More_than_four @@ -476,13 +476,13 @@ Section consequences_of_infinity alias id "F" = "cic:/CoRN/algebra/COrdFields/consequences_of_infinity/F.var". -inline procedural "cic:/CoRN/algebra/COrdFields/square_eq.con". +inline procedural "cic:/CoRN/algebra/COrdFields/square_eq.con" as lemma. (*#* Ordered fields have characteristic zero. *) -inline procedural "cic:/CoRN/algebra/COrdFields/char0_OrdField.con". +inline procedural "cic:/CoRN/algebra/COrdFields/char0_OrdField.con" as lemma. (* UNEXPORTED End consequences_of_infinity @@ -519,23 +519,23 @@ Section addition *) -inline procedural "cic:/CoRN/algebra/COrdFields/plus_resp_less_lft.con". +inline procedural "cic:/CoRN/algebra/COrdFields/plus_resp_less_lft.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/inv_resp_less.con". +inline procedural "cic:/CoRN/algebra/COrdFields/inv_resp_less.con" as lemma. (* UNEXPORTED Transparent cg_minus. *) -inline procedural "cic:/CoRN/algebra/COrdFields/minus_resp_less.con". +inline procedural "cic:/CoRN/algebra/COrdFields/minus_resp_less.con" as lemma. (* UNEXPORTED Transparent cg_minus. *) -inline procedural "cic:/CoRN/algebra/COrdFields/minus_resp_less_rht.con". +inline procedural "cic:/CoRN/algebra/COrdFields/minus_resp_less_rht.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/plus_resp_less_both.con". +inline procedural "cic:/CoRN/algebra/COrdFields/plus_resp_less_both.con" as lemma. (*#* For versions of [plus_resp_less_both] where one [ [<] ] in the @@ -545,9 +545,9 @@ Section~\ref{section:leEq-plus-minus}%. Cancellation laws *) -inline procedural "cic:/CoRN/algebra/COrdFields/plus_cancel_less.con". +inline procedural "cic:/CoRN/algebra/COrdFields/plus_cancel_less.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/inv_cancel_less.con". +inline procedural "cic:/CoRN/algebra/COrdFields/inv_cancel_less.con" as lemma. (*#* @@ -566,31 +566,31 @@ However, it is impractical to use these in Coq%(see the Coq shortcoming in Section~\ref{section:setoid-basics})%. *) -inline procedural "cic:/CoRN/algebra/COrdFields/shift_less_plus.con". +inline procedural "cic:/CoRN/algebra/COrdFields/shift_less_plus.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/shift_less_plus'.con". +inline procedural "cic:/CoRN/algebra/COrdFields/shift_less_plus'.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/shift_less_minus.con". +inline procedural "cic:/CoRN/algebra/COrdFields/shift_less_minus.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/shift_less_minus'.con". +inline procedural "cic:/CoRN/algebra/COrdFields/shift_less_minus'.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/shift_plus_less.con". +inline procedural "cic:/CoRN/algebra/COrdFields/shift_plus_less.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/shift_plus_less'.con". +inline procedural "cic:/CoRN/algebra/COrdFields/shift_plus_less'.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/shift_minus_less.con". +inline procedural "cic:/CoRN/algebra/COrdFields/shift_minus_less.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/shift_minus_less'.con". +inline procedural "cic:/CoRN/algebra/COrdFields/shift_minus_less'.con" as lemma. (*#* Some special cases of laws for shifting. *) -inline procedural "cic:/CoRN/algebra/COrdFields/shift_zero_less_minus.con". +inline procedural "cic:/CoRN/algebra/COrdFields/shift_zero_less_minus.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/shift_zero_less_minus'.con". +inline procedural "cic:/CoRN/algebra/COrdFields/shift_zero_less_minus'.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/qltone.con". +inline procedural "cic:/CoRN/algebra/COrdFields/qltone.con" as lemma. (* UNEXPORTED End addition @@ -615,26 +615,26 @@ We do this to keep it easy to use such lemmas. *) -inline procedural "cic:/CoRN/algebra/COrdFields/mult_resp_less.con". +inline procedural "cic:/CoRN/algebra/COrdFields/mult_resp_less.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/recip_resp_pos.con". +inline procedural "cic:/CoRN/algebra/COrdFields/recip_resp_pos.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/div_resp_less_rht.con". +inline procedural "cic:/CoRN/algebra/COrdFields/div_resp_less_rht.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/div_resp_pos.con". +inline procedural "cic:/CoRN/algebra/COrdFields/div_resp_pos.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/mult_resp_less_lft.con". +inline procedural "cic:/CoRN/algebra/COrdFields/mult_resp_less_lft.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/mult_resp_less_both.con". +inline procedural "cic:/CoRN/algebra/COrdFields/mult_resp_less_both.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/recip_resp_less.con". +inline procedural "cic:/CoRN/algebra/COrdFields/recip_resp_less.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/div_resp_less.con". +inline procedural "cic:/CoRN/algebra/COrdFields/div_resp_less.con" as lemma. (*#* Cancellation laws *) -inline procedural "cic:/CoRN/algebra/COrdFields/mult_cancel_less.con". +inline procedural "cic:/CoRN/algebra/COrdFields/mult_cancel_less.con" as lemma. (*#* Laws for shifting @@ -643,30 +643,30 @@ Laws for shifting on plus and minus.% *) -inline procedural "cic:/CoRN/algebra/COrdFields/shift_div_less.con". +inline procedural "cic:/CoRN/algebra/COrdFields/shift_div_less.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/shift_div_less'.con". +inline procedural "cic:/CoRN/algebra/COrdFields/shift_div_less'.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/shift_less_div.con". +inline procedural "cic:/CoRN/algebra/COrdFields/shift_less_div.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/shift_less_mult.con". +inline procedural "cic:/CoRN/algebra/COrdFields/shift_less_mult.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/shift_less_mult'.con". +inline procedural "cic:/CoRN/algebra/COrdFields/shift_less_mult'.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/shift_mult_less.con". +inline procedural "cic:/CoRN/algebra/COrdFields/shift_mult_less.con" as lemma. (*#* Other properties of multiplication and division *) -inline procedural "cic:/CoRN/algebra/COrdFields/minusOne_less.con". +inline procedural "cic:/CoRN/algebra/COrdFields/minusOne_less.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/swap_div.con". +inline procedural "cic:/CoRN/algebra/COrdFields/swap_div.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/eps_div_less_eps.con". +inline procedural "cic:/CoRN/algebra/COrdFields/eps_div_less_eps.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_two.con". +inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_two.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_two'.con". +inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_two'.con" as lemma. (* Apply mult_cancel_less with (Two::R). @@ -677,29 +677,29 @@ Auto. Qed. *) -inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_three.con". +inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_three.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_three'.con". +inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_three'.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_four.con". +inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_four.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_four'.con". +inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_four'.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_six.con". +inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_six.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_eight.con". +inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_eight.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_nine.con". +inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_nine.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_twelve.con". +inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_twelve.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_sixteen.con". +inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_sixteen.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_eighteen.con". +inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_eighteen.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_twentyfour.con". +inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_twentyfour.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_fortyeight.con". +inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_fortyeight.con" as lemma. (* UNEXPORTED End multiplication @@ -713,25 +713,25 @@ Section misc *** Miscellaneous properties *) -inline procedural "cic:/CoRN/algebra/COrdFields/nring_pos.con". +inline procedural "cic:/CoRN/algebra/COrdFields/nring_pos.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/less_nring.con". +inline procedural "cic:/CoRN/algebra/COrdFields/less_nring.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/pos_nring_fac.con". +inline procedural "cic:/CoRN/algebra/COrdFields/pos_nring_fac.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/Smallest_less_Average.con". +inline procedural "cic:/CoRN/algebra/COrdFields/Smallest_less_Average.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/Average_less_Greatest.con". +inline procedural "cic:/CoRN/algebra/COrdFields/Average_less_Greatest.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/Sum_resp_less.con". +inline procedural "cic:/CoRN/algebra/COrdFields/Sum_resp_less.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/Sumx_resp_less.con". +inline procedural "cic:/CoRN/algebra/COrdFields/Sumx_resp_less.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/positive_Sum_two.con". +inline procedural "cic:/CoRN/algebra/COrdFields/positive_Sum_two.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/positive_Sumx.con". +inline procedural "cic:/CoRN/algebra/COrdFields/positive_Sumx.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields/negative_Sumx.con". +inline procedural "cic:/CoRN/algebra/COrdFields/negative_Sumx.con" as lemma. (* UNEXPORTED End misc diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/COrdFields2.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/COrdFields2.mma index 3e39c77f0..595d7ef8b 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/COrdFields2.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/COrdFields2.mma @@ -46,61 +46,61 @@ Section addition *** Addition and subtraction%\label{section:leEq-plus-minus}% *) -inline procedural "cic:/CoRN/algebra/COrdFields2/plus_resp_leEq.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/plus_resp_leEq.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/plus_resp_leEq_lft.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/plus_resp_leEq_lft.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/minus_resp_leEq.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/minus_resp_leEq.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/inv_resp_leEq.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/inv_resp_leEq.con" as lemma. (* UNEXPORTED Transparent cg_minus. *) -inline procedural "cic:/CoRN/algebra/COrdFields2/minus_resp_leEq_rht.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/minus_resp_leEq_rht.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/plus_resp_leEq_both.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/plus_resp_leEq_both.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/plus_resp_less_leEq.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/plus_resp_less_leEq.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/plus_resp_leEq_less.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/plus_resp_leEq_less.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/minus_resp_less_leEq.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/minus_resp_less_leEq.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/minus_resp_leEq_both.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/minus_resp_leEq_both.con" as lemma. (*#* Cancellation properties *) -inline procedural "cic:/CoRN/algebra/COrdFields2/plus_cancel_leEq_rht.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/plus_cancel_leEq_rht.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/inv_cancel_leEq.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/inv_cancel_leEq.con" as lemma. (*#* Laws for shifting *) -inline procedural "cic:/CoRN/algebra/COrdFields2/shift_plus_leEq.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/shift_plus_leEq.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/shift_leEq_plus.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/shift_leEq_plus.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/shift_plus_leEq'.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/shift_plus_leEq'.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/shift_leEq_plus'.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/shift_leEq_plus'.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/shift_leEq_rht.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/shift_leEq_rht.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/shift_leEq_lft.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/shift_leEq_lft.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/shift_minus_leEq.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/shift_minus_leEq.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/shift_leEq_minus.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/shift_leEq_minus.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/shift_leEq_minus'.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/shift_leEq_minus'.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/shift_zero_leEq_minus.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/shift_zero_leEq_minus.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/shift_zero_leEq_minus'.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/shift_zero_leEq_minus'.con" as lemma. (* UNEXPORTED End addition @@ -116,15 +116,15 @@ Section multiplication Multiplication and division respect [[<=]] *) -inline procedural "cic:/CoRN/algebra/COrdFields2/mult_resp_leEq_rht.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/mult_resp_leEq_rht.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/mult_resp_leEq_lft.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/mult_resp_leEq_lft.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/mult_resp_leEq_both.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/mult_resp_leEq_both.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/recip_resp_leEq.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/recip_resp_leEq.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/div_resp_leEq.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/div_resp_leEq.con" as lemma. (* UNEXPORTED Hint Resolve recip_resp_leEq: algebra. @@ -133,40 +133,40 @@ Hint Resolve recip_resp_leEq: algebra. (*#* Cancellation properties *) -inline procedural "cic:/CoRN/algebra/COrdFields2/mult_cancel_leEq.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/mult_cancel_leEq.con" as lemma. (*#* Laws for shifting *) -inline procedural "cic:/CoRN/algebra/COrdFields2/shift_mult_leEq.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/shift_mult_leEq.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/shift_mult_leEq'.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/shift_mult_leEq'.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/shift_leEq_mult'.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/shift_leEq_mult'.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/shift_div_leEq.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/shift_div_leEq.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/shift_div_leEq'.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/shift_div_leEq'.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/shift_leEq_div.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/shift_leEq_div.con" as lemma. (* UNEXPORTED Hint Resolve shift_leEq_div: algebra. *) -inline procedural "cic:/CoRN/algebra/COrdFields2/eps_div_leEq_eps.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/eps_div_leEq_eps.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/nonneg_div_two.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/nonneg_div_two.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/nonneg_div_two'.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/nonneg_div_two'.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/nonneg_div_three.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/nonneg_div_three.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/nonneg_div_three'.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/nonneg_div_three'.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/nonneg_div_four.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/nonneg_div_four.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/nonneg_div_four'.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/nonneg_div_four'.con" as lemma. (* UNEXPORTED End multiplication @@ -180,53 +180,53 @@ Section misc *** Miscellaneous Properties *) -inline procedural "cic:/CoRN/algebra/COrdFields2/sqr_nonneg.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/sqr_nonneg.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/nring_nonneg.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/nring_nonneg.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/suc_leEq_dub.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/suc_leEq_dub.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/leEq_nring.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/leEq_nring.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/cc_abs_aid.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/cc_abs_aid.con" as lemma. include "tactics/Transparent_algebra.ma". -inline procedural "cic:/CoRN/algebra/COrdFields2/nexp_resp_pos.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/nexp_resp_pos.con" as lemma. include "tactics/Opaque_algebra.ma". -inline procedural "cic:/CoRN/algebra/COrdFields2/mult_resp_nonneg.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/mult_resp_nonneg.con" as lemma. include "tactics/Transparent_algebra.ma". -inline procedural "cic:/CoRN/algebra/COrdFields2/nexp_resp_nonneg.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/nexp_resp_nonneg.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/power_resp_leEq.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/power_resp_leEq.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/nexp_resp_less.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/nexp_resp_less.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/power_cancel_leEq.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/power_cancel_leEq.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/power_cancel_less.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/power_cancel_less.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/nat_less_bin_nexp.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/nat_less_bin_nexp.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/Sum_resp_leEq.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/Sum_resp_leEq.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/Sumx_resp_leEq.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/Sumx_resp_leEq.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/Sum2_resp_leEq.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/Sum2_resp_leEq.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/approach_zero.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/approach_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/approach_zero_weak.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/approach_zero_weak.con" as lemma. (* UNEXPORTED End misc *) -inline procedural "cic:/CoRN/algebra/COrdFields2/equal_less_leEq.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/equal_less_leEq.con" as lemma. (* UNEXPORTED End Properties_of_leEq @@ -260,31 +260,31 @@ Notation OneR := (One:R). (* end hide *) -inline procedural "cic:/CoRN/algebra/COrdFields2/mult_pos_imp.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/mult_pos_imp.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/plus_resp_pos_nonneg.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/plus_resp_pos_nonneg.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/plus_resp_nonneg_pos.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/plus_resp_nonneg_pos.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/pos_square.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/pos_square.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/mult_cancel_pos_rht.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/mult_cancel_pos_rht.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/mult_cancel_pos_lft.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/mult_cancel_pos_lft.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/pos_wd.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/pos_wd.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/even_power_pos.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/even_power_pos.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/odd_power_cancel_pos.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/odd_power_cancel_pos.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/plus_resp_pos.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/plus_resp_pos.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/pos_nring_S.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/pos_nring_S.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/square_eq_pos.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/square_eq_pos.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/square_eq_neg.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/square_eq_neg.con" as lemma. (* UNEXPORTED End PosP_properties @@ -300,7 +300,7 @@ Hint Resolve mult_resp_nonneg. %\end{convention}% *) -inline procedural "cic:/CoRN/algebra/COrdFields2/one_div_succ.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/one_div_succ.con" as definition. (* UNEXPORTED Implicit Arguments one_div_succ [R]. @@ -312,11 +312,11 @@ Section One_div_succ_properties alias id "R" = "cic:/CoRN/algebra/COrdFields2/One_div_succ_properties/R.var". -inline procedural "cic:/CoRN/algebra/COrdFields2/one_div_succ_resp_leEq.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/one_div_succ_resp_leEq.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/one_div_succ_pos.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/one_div_succ_pos.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/one_div_succ_resp_less.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/one_div_succ_resp_less.con" as lemma. (* UNEXPORTED End One_div_succ_properties @@ -326,7 +326,7 @@ End One_div_succ_properties ** Properties of [Half] *) -inline procedural "cic:/CoRN/algebra/COrdFields2/Half.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/Half.con" as definition. (* UNEXPORTED Implicit Arguments Half [R]. @@ -344,21 +344,21 @@ Let [R] be an ordered field. alias id "R" = "cic:/CoRN/algebra/COrdFields2/Half_properties/R.var". -inline procedural "cic:/CoRN/algebra/COrdFields2/half_1.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/half_1.con" as lemma. (* UNEXPORTED Hint Resolve half_1: algebra. *) -inline procedural "cic:/CoRN/algebra/COrdFields2/pos_half.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/pos_half.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/half_1'.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/half_1'.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/half_2.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/half_2.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/half_lt1.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/half_lt1.con" as lemma. -inline procedural "cic:/CoRN/algebra/COrdFields2/half_3.con". +inline procedural "cic:/CoRN/algebra/COrdFields2/half_3.con" as lemma. (* UNEXPORTED End Half_properties diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/CPoly_ApZero.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/CPoly_ApZero.mma index adb08299d..362c9e91b 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/CPoly_ApZero.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/CPoly_ApZero.mma @@ -24,7 +24,7 @@ include "algebra/COrdFields2.ma". (*#* * Polynomials apart from zero *) -inline procedural "cic:/CoRN/algebra/CPoly_ApZero/distinct1.con". +inline procedural "cic:/CoRN/algebra/CPoly_ApZero/distinct1.con" as definition. (* UNEXPORTED Implicit Arguments distinct1 [A]. @@ -65,65 +65,65 @@ Notation RX := (cpoly_cring R). include "tactics/Transparent_algebra.ma". -inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_linear_shifted.con". +inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_linear_shifted.con" as lemma. include "tactics/Opaque_algebra.ma". -inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_linear_factor.con". +inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_linear_factor.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_ApZero/zero_poly.con". +inline procedural "cic:/CoRN/algebra/CPoly_ApZero/zero_poly.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_ApZero/identical_poly.con". +inline procedural "cic:/CoRN/algebra/CPoly_ApZero/identical_poly.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor'.con". +inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor'.con" as definition. -inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor'_degree.con". +inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor'_degree.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor'_zero.con". +inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor'_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor'_apzero.con". +inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor'_apzero.con" as lemma. (* UNEXPORTED Hint Resolve poly_01_factor'_zero. *) -inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor.con". +inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor.con" as definition. -inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor_degree.con". +inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor_degree.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor_zero.con". +inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor_one.con". +inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor_one.con" as lemma. (* UNEXPORTED Hint Resolve poly_01_factor_zero poly_01_factor_one: algebra. *) -inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01.con". +inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01.con" as definition. -inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_degree'.con". +inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_degree'.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_degree.con". +inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_degree.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_zero.con". +inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_one.con". +inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_one.con" as lemma. (* UNEXPORTED Hint Resolve poly_01_zero poly_01_one: algebra. *) -inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_representation''.con". +inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_representation''.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_representation'.con". +inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_representation'.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_representation.con". +inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_representation.con" as lemma. (* UNEXPORTED Hint Resolve poly_representation: algebra. *) -inline procedural "cic:/CoRN/algebra/CPoly_ApZero/Cpoly_choose_apzero.con". +inline procedural "cic:/CoRN/algebra/CPoly_ApZero/Cpoly_choose_apzero.con" as lemma. (* UNEXPORTED End Poly_Representation @@ -154,13 +154,13 @@ Notation RX := (cpoly_cring R). (* end hide *) -inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_apzero.con". +inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_apzero.con" as lemma. (*#* Also, in this situation polynomials are extensional functions. *) -inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_extensional.con". +inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_extensional.con" as lemma. (* UNEXPORTED End Characteristic_zero @@ -184,7 +184,7 @@ Notation RX := (cpoly_cring R). (* end hide *) -inline procedural "cic:/CoRN/algebra/CPoly_ApZero/Cpoly_apzero_interval.con". +inline procedural "cic:/CoRN/algebra/CPoly_ApZero/Cpoly_apzero_interval.con" as lemma. (* UNEXPORTED End Poly_ApZero_Interval diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/CPoly_Degree.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/CPoly_Degree.mma index 5b8104be8..52272b28e 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/CPoly_Degree.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/CPoly_Degree.mma @@ -53,7 +53,7 @@ is always [1] higher than the `degree' (assuming that the highest coefficient is [[#]Zero])! *) -inline procedural "cic:/CoRN/algebra/CPoly_Degree/lth_of_poly.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/lth_of_poly.con" as definition. (*#* When dealing with constructive polynomials, notably over the reals or @@ -70,17 +70,17 @@ X^(n-1)#, if $p_i \mathrel{\#}0$#pi apart from 0#, we can say that the that the `degree is at most [j]'. *) -inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le.con" as definition. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree.con" as definition. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic.con" as definition. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/odd_cpoly.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/odd_cpoly.con" as definition. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/even_cpoly.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/even_cpoly.con" as definition. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/regular.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/regular.con" as definition. (* UNEXPORTED End Degree_def @@ -116,87 +116,87 @@ Notation RX := (cpoly_cring R). (* end hide *) -inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_wd.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_wd.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_wd.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_wd.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_wd.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_wd.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_imp_degree_le.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_imp_degree_le.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_c_.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_c_.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_c_.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_c_.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_c_one.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_c_one.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_x_.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_x_.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_x_.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_x_.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_x_.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_x_.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_mon.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_mon.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_inv.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_inv.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_plus.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_plus.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_minus.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_minus.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/Sum_degree_le.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/Sum_degree_le.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_inv.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_inv.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_plus_rht.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_plus_rht.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_minus_lft.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_minus_lft.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_plus.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_plus.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_minus.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_minus.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_mult.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_mult.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_mult_aux.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_mult_aux.con" as lemma. (* UNEXPORTED Hint Resolve degree_mult_aux: algebra. *) -inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_mult.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_mult.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_nexp.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_nexp.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_nexp.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_nexp.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/lt_i_lth_of_poly.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/lt_i_lth_of_poly.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/poly_degree_lth.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/poly_degree_lth.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/Cpoly_ex_degree.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/Cpoly_ex_degree.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/poly_as_sum''.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/poly_as_sum''.con" as lemma. (* UNEXPORTED Hint Resolve poly_as_sum'': algebra. *) -inline procedural "cic:/CoRN/algebra/CPoly_Degree/poly_as_sum'.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/poly_as_sum'.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/poly_as_sum.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/poly_as_sum.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_zero.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_1_imp.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_1_imp.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_cpoly_linear.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_cpoly_linear.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_cpoly_linear.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_cpoly_linear.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_one.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_one.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_apzero.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_apzero.con" as lemma. (* UNEXPORTED End Degree_props @@ -230,13 +230,13 @@ Notation FX := (cpoly_cring F). (* end hide *) -inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_mult.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_mult.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_nexp.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_nexp.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_mult_imp.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_mult_imp.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_mult_imp.con". +inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_mult_imp.con" as lemma. (* UNEXPORTED End degree_props_Field diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/CPoly_NthCoeff.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/CPoly_NthCoeff.mma index 81ddb6ab6..b198a9f80 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/CPoly_NthCoeff.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/CPoly_NthCoeff.mma @@ -50,13 +50,13 @@ polynomial $a_0 +a_1 X +a_2 X^2 + \cdots + a_n X^n$ #a0 +a1 X +a2 X^2 + ... + an X^n#, the [Zero]-th coefficient is $a_0$#a0#, the first is $a_1$#a1# etcetera. *) -inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff.con". +inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff.con" as definition. -inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_strext.con". +inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_strext.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_wd.con". +inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_wd.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_fun.con". +inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_fun.con" as definition. (*#* %\begin{shortcoming}% @@ -72,24 +72,24 @@ to [((nth_coeff_fun n) p)]. %\end{shortcoming}% *) -inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nonConst.con". +inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nonConst.con" as definition. (*#* The following is probably NOT needed. These functions are NOT extensional, that is, they are not CSetoid functions. *) -inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_ok.con". +inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_ok.con" as definition. (* The in_coeff predicate*) -inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/in_coeff.con". +inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/in_coeff.con" as definition. (*#* The [cpoly_zero] case should be [c [=] Zero] in order to be extensional. *) -inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_S.con". +inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_S.con" as lemma. (* UNEXPORTED End NthCoeff_def @@ -123,66 +123,66 @@ Notation RX := (cpoly_cring R). (* end hide *) -inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_zero.con". +inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/coeff_O_lin.con". +inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/coeff_O_lin.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/coeff_Sm_lin.con". +inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/coeff_Sm_lin.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/coeff_O_c_.con". +inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/coeff_O_c_.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/coeff_O_x_mult.con". +inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/coeff_O_x_mult.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/coeff_Sm_x_mult.con". +inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/coeff_Sm_x_mult.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/coeff_Sm_mult_x_.con". +inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/coeff_Sm_mult_x_.con" as lemma. (* UNEXPORTED Hint Resolve nth_coeff_zero coeff_O_lin coeff_Sm_lin coeff_O_c_ coeff_O_x_mult coeff_Sm_x_mult coeff_Sm_mult_x_: algebra. *) -inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_ap_zero_imp.con". +inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_ap_zero_imp.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_plus.con". +inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_plus.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_inv.con". +inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_inv.con" as lemma. (* UNEXPORTED Hint Resolve nth_coeff_inv: algebra. *) -inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_c_mult_p.con". +inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_c_mult_p.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_p_mult_c_.con". +inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_p_mult_c_.con" as lemma. (* UNEXPORTED Hint Resolve nth_coeff_c_mult_p nth_coeff_p_mult_c_ nth_coeff_plus: algebra. *) -inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_complicated.con". +inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_complicated.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/all_nth_coeff_eq_imp.con". +inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/all_nth_coeff_eq_imp.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/poly_at_zero.con". +inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/poly_at_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_inv'.con". +inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_inv'.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_minus.con". +inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_minus.con" as lemma. (* UNEXPORTED Hint Resolve nth_coeff_minus: algebra. *) -inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_sum0.con". +inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_sum0.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_sum.con". +inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_sum.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_nexp_eq.con". +inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_nexp_eq.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_nexp_neq.con". +inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_nexp_neq.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_mult.con". +inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_mult.con" as lemma. (* UNEXPORTED End NthCoeff_props diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/CPolynomials.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/CPolynomials.mma index 25155ca72..99b2465aa 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/CPolynomials.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/CPolynomials.mma @@ -60,52 +60,52 @@ The intuition behind the type [cpoly] is the following inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly.ind". -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_constant.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_constant.con" as definition. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_one.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_one.con" as definition. (*#* Some useful induction lemmas for doubly quantified propositions. *) -inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_double_ind0.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_double_ind0.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_double_sym_ind0.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_double_sym_ind0.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_double_ind0'.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_double_ind0'.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_double_ind0.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_double_ind0.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_double_sym_ind0.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_double_sym_ind0.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_double_ind0'.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_double_ind0'.con" as lemma. (*#* *** The polynomials form a setoid *) -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_eq_zero.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_eq_zero.con" as definition. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_eq.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_eq.con" as definition. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_eq_p_zero.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_eq_p_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_ap_zero.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_ap_zero.con" as definition. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_ap.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_ap.con" as definition. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_ap_p_zero.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_ap_p_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/irreflexive_cpoly_ap.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/irreflexive_cpoly_ap.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/symmetric_cpoly_ap.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/symmetric_cpoly_ap.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cotransitive_cpoly_ap.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cotransitive_cpoly_ap.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/tight_apart_cpoly_ap.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/tight_apart_cpoly_ap.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_is_CSetoid.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_is_CSetoid.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_csetoid.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_csetoid.con" as definition. (*#* Now that we know that the polynomials form a setoid, we can use the @@ -117,203 +117,203 @@ the most basic properties of equality and apartness in terms of these generators. *) -inline procedural "cic:/CoRN/algebra/CPolynomials/CPoly_CRing/cpoly_zero_cs.con" "CPoly_CRing__". +inline procedural "cic:/CoRN/algebra/CPolynomials/CPoly_CRing/cpoly_zero_cs.con" "CPoly_CRing__" as definition. -inline procedural "cic:/CoRN/algebra/CPolynomials/CPoly_CRing/cpoly_linear_cs.con" "CPoly_CRing__". +inline procedural "cic:/CoRN/algebra/CPolynomials/CPoly_CRing/cpoly_linear_cs.con" "CPoly_CRing__" as definition. -inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_ind_cs.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_ind_cs.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_double_ind0_cs.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_double_ind0_cs.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_double_sym_ind0_cs.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_double_sym_ind0_cs.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_ind_cs.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_ind_cs.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_double_ind0_cs.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_double_ind0_cs.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_double_sym_ind0_cs.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_double_sym_ind0_cs.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin_eq_zero_.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin_eq_zero_.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/_cpoly_lin_eq_zero.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/_cpoly_lin_eq_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_zero_eq_lin_.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_zero_eq_lin_.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/_cpoly_zero_eq_lin.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/_cpoly_zero_eq_lin.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin_eq_lin_.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin_eq_lin_.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/_cpoly_lin_eq_lin.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/_cpoly_lin_eq_lin.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin_ap_zero_.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin_ap_zero_.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/_cpoly_lin_ap_zero.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/_cpoly_lin_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin_ap_zero.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_zero_ap_lin_.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_zero_ap_lin_.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/_cpoly_zero_ap_lin.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/_cpoly_zero_ap_lin.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_zero_ap_lin.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_zero_ap_lin.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin_ap_lin_.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin_ap_lin_.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/_cpoly_lin_ap_lin.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/_cpoly_lin_ap_lin.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin_ap_lin.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin_ap_lin.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_linear_strext.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_linear_strext.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_linear_wd.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_linear_wd.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_linear_fun.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_linear_fun.con" as definition. -inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_double_comp_ind.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_double_comp_ind.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_triple_comp_ind.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_triple_comp_ind.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_double_comp_ind.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_double_comp_ind.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_triple_comp_ind.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_triple_comp_ind.con" as lemma. (*#* *** The polynomials form a semi-group and a monoid *) -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_plus.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_plus.con" as definition. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_plus_cs.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_plus_cs.con" as definition. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_zero_plus.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_zero_plus.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_plus_zero.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_plus_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin_plus_lin.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin_plus_lin.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_plus_commutative.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_plus_commutative.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_plus_q_ap_q.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_plus_q_ap_q.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_p_plus_ap_p.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_p_plus_ap_p.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_ap_zero_plus.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_ap_zero_plus.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_plus_op_strext.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_plus_op_strext.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_plus_op_wd.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_plus_op_wd.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_plus_op.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_plus_op.con" as definition. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_plus_associative.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_plus_associative.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_csemi_grp.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_csemi_grp.con" as definition. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_cm_proof.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_cm_proof.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_cmonoid.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_cmonoid.con" as definition. (*#* *** The polynomials form a group *) -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_inv.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_inv.con" as definition. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_inv_cs.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_inv_cs.con" as definition. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_inv_zero.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_inv_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_inv_lin.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_inv_lin.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_inv_op_strext.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_inv_op_strext.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_inv_op_wd.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_inv_op_wd.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_inv_op.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_inv_op.con" as definition. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_cg_proof.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_cg_proof.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_cgroup.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_cgroup.con" as definition. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_cag_proof.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_cag_proof.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_cabgroup.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_cabgroup.con" as definition. (*#* *** The polynomials form a ring *) -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr.con" as definition. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult.con" as definition. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_cs.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_cs.con" as definition. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_zero_mult_cr.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_zero_mult_cr.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin_mult_cr.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin_mult_cr.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_zero.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_strext.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_strext.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_wd.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_wd.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cs.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cs.con" as definition. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_zero_mult.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_zero_mult.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin_mult.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin_mult.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_op_strext.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_op_strext.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_op_wd.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_op_wd.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_op.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_op.con" as definition. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_dist.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_dist.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_cr_dist.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_cr_dist.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_assoc_mult_cr.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_assoc_mult_cr.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_assoc_mult.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_assoc_mult.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_zero.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_lin.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_lin.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_commutative.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_commutative.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_dist_rht.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_dist_rht.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_assoc.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_assoc.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_one.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_one.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_one_mult.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_one_mult.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_one.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_one.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_monoid.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_monoid.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_cr_non_triv.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_cr_non_triv.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_is_CRing.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_is_CRing.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_cring.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_cring.con" as definition. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_constant_strext.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_constant_strext.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_constant_wd.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_constant_wd.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/_C_.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/_C_.con" as definition. -inline procedural "cic:/CoRN/algebra/CPolynomials/_X_.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/_X_.con" as definition. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_x_minus_c.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_x_minus_c.con" as definition. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_x_minus_c_strext.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_x_minus_c_strext.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_x_minus_c_wd.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_x_minus_c_wd.con" as lemma. (* UNEXPORTED End CPoly_CRing @@ -327,7 +327,7 @@ Implicit Arguments _C_ [CR]. Implicit Arguments _X_ [CR]. *) -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_linear_fun'.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_linear_fun'.con" as definition. (* UNEXPORTED Implicit Arguments cpoly_linear_fun' [CR]. @@ -370,55 +370,55 @@ alias id "c" = "cic:/CoRN/algebra/CPolynomials/CPoly_CRing_ctd/helpful_section/c alias id "d" = "cic:/CoRN/algebra/CPolynomials/CPoly_CRing_ctd/helpful_section/d.var". -inline procedural "cic:/CoRN/algebra/CPolynomials/linear_eq_zero_.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/linear_eq_zero_.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/_linear_eq_zero.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/_linear_eq_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/zero_eq_linear_.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/zero_eq_linear_.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/_zero_eq_linear.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/_zero_eq_linear.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/linear_eq_linear_.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/linear_eq_linear_.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/_linear_eq_linear.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/_linear_eq_linear.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/linear_ap_zero_.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/linear_ap_zero_.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/_linear_ap_zero.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/_linear_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/linear_ap_zero.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/linear_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/zero_ap_linear_.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/zero_ap_linear_.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/_zero_ap_linear.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/_zero_ap_linear.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/zero_ap_linear.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/zero_ap_linear.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/linear_ap_linear_.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/linear_ap_linear_.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/_linear_ap_linear.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/_linear_ap_linear.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/linear_ap_linear.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/linear_ap_linear.con" as lemma. (* UNEXPORTED End helpful_section *) -inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_induc.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_induc.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_double_sym_ind.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_double_sym_ind.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/Cpoly_double_comp_ind.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/Cpoly_double_comp_ind.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/Cpoly_triple_comp_ind.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/Cpoly_triple_comp_ind.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_induc.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_induc.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_double_sym_ind.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_double_sym_ind.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/poly_double_comp_ind.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/poly_double_comp_ind.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/poly_triple_comp_ind.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/poly_triple_comp_ind.con" as lemma. (* UNEXPORTED Transparent cpoly_cring. @@ -432,13 +432,13 @@ Transparent cpoly_cgroup. Transparent cpoly_csetoid. *) -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_apply.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_apply.con" as definition. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_apply_strext.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_apply_strext.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_apply_wd.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_apply_wd.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_apply_fun.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_apply_fun.con" as definition. (* UNEXPORTED End CPoly_CRing_ctd @@ -482,23 +482,23 @@ Notation RX := (cpoly_cring R). *** Constant and identity *) -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_X_.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_X_.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_C_.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_C_.con" as lemma. (* UNEXPORTED Hint Resolve cpoly_X_ cpoly_C_: algebra. *) -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_const_eq.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_const_eq.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/_c_zero.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/_c_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/_c_one.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/_c_one.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/_c_mult.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/_c_mult.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin.con" as lemma. (* UNEXPORTED Hint Resolve cpoly_lin: algebra. @@ -506,19 +506,19 @@ Hint Resolve cpoly_lin: algebra. (* SUPERFLUOUS *) -inline procedural "cic:/CoRN/algebra/CPolynomials/poly_linear.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/poly_linear.con" as lemma. (* UNEXPORTED Hint Resolve _c_zero: algebra. *) -inline procedural "cic:/CoRN/algebra/CPolynomials/poly_c_apzero.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/poly_c_apzero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/_c_mult_lin.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/_c_mult_lin.con" as lemma. (* SUPERFLUOUS ? *) -inline procedural "cic:/CoRN/algebra/CPolynomials/lin_mult.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/lin_mult.con" as lemma. (* UNEXPORTED Hint Resolve lin_mult: algebra. @@ -527,57 +527,57 @@ Hint Resolve lin_mult: algebra. (*#* *** Application of polynomials *) -inline procedural "cic:/CoRN/algebra/CPolynomials/poly_eq_zero.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/poly_eq_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/apply_wd.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/apply_wd.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpolyap_pres_eq.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpolyap_pres_eq.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpolyap_strext.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpolyap_strext.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_csetoid_op.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_csetoid_op.con" as definition. -inline procedural "cic:/CoRN/algebra/CPolynomials/_c_apply.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/_c_apply.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/_x_apply.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/_x_apply.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/plus_apply.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/plus_apply.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/inv_apply.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/inv_apply.con" as lemma. (* UNEXPORTED Hint Resolve plus_apply inv_apply: algebra. *) -inline procedural "cic:/CoRN/algebra/CPolynomials/minus_apply.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/minus_apply.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/_c_mult_apply.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/_c_mult_apply.con" as lemma. (* UNEXPORTED Hint Resolve _c_mult_apply: algebra. *) -inline procedural "cic:/CoRN/algebra/CPolynomials/mult_apply.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/mult_apply.con" as lemma. (* UNEXPORTED Hint Resolve mult_apply: algebra. *) -inline procedural "cic:/CoRN/algebra/CPolynomials/one_apply.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/one_apply.con" as lemma. (* UNEXPORTED Hint Resolve one_apply: algebra. *) -inline procedural "cic:/CoRN/algebra/CPolynomials/nexp_apply.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/nexp_apply.con" as lemma. (* SUPERFLUOUS *) -inline procedural "cic:/CoRN/algebra/CPolynomials/poly_inv_apply.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/poly_inv_apply.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/Sum0_cpoly_ap.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/Sum0_cpoly_ap.con" as lemma. -inline procedural "cic:/CoRN/algebra/CPolynomials/Sum_cpoly_ap.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/Sum_cpoly_ap.con" as lemma. (* UNEXPORTED End Poly_properties @@ -608,7 +608,7 @@ Notation Cpoly_linear := (cpoly_linear CR). Notation Cpoly_cring := (cpoly_cring CR). *) -inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_double_ind.con". +inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_double_ind.con" as lemma. (* UNEXPORTED End Poly_Prop_Induction diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/CRings.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/CRings.mma index 88764d191..96435df75 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/CRings.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/CRings.mma @@ -71,7 +71,7 @@ We actually define commutative rings with identity. ** Definition of the notion of Ring *) -inline procedural "cic:/CoRN/algebra/CRings/distributive.con". +inline procedural "cic:/CoRN/algebra/CRings/distributive.con" as definition. (* UNEXPORTED Implicit Arguments distributive [S]. @@ -85,11 +85,11 @@ inline procedural "cic:/CoRN/algebra/CRings/CRing.ind". cic:/matita/CoRN-Procedural/algebra/CRings/cr_crr.con *) -inline procedural "cic:/CoRN/algebra/CRings/cr_plus.con". +inline procedural "cic:/CoRN/algebra/CRings/cr_plus.con" as definition. -inline procedural "cic:/CoRN/algebra/CRings/cr_inv.con". +inline procedural "cic:/CoRN/algebra/CRings/cr_inv.con" as definition. -inline procedural "cic:/CoRN/algebra/CRings/cr_minus.con". +inline procedural "cic:/CoRN/algebra/CRings/cr_minus.con" as definition. (* NOTATION Notation One := (cr_one _). @@ -126,25 +126,25 @@ Section CRing_axioms alias id "R" = "cic:/CoRN/algebra/CRings/CRing_axioms/R.var". -inline procedural "cic:/CoRN/algebra/CRings/CRing_is_CRing.con". +inline procedural "cic:/CoRN/algebra/CRings/CRing_is_CRing.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/mult_assoc.con". +inline procedural "cic:/CoRN/algebra/CRings/mult_assoc.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/mult_commutes.con". +inline procedural "cic:/CoRN/algebra/CRings/mult_commutes.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/mult_mon.con". +inline procedural "cic:/CoRN/algebra/CRings/mult_mon.con" as lemma. (* End_SpecReals *) -inline procedural "cic:/CoRN/algebra/CRings/dist.con". +inline procedural "cic:/CoRN/algebra/CRings/dist.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/ring_non_triv.con". +inline procedural "cic:/CoRN/algebra/CRings/ring_non_triv.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/mult_wd.con". +inline procedural "cic:/CoRN/algebra/CRings/mult_wd.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/mult_wdl.con". +inline procedural "cic:/CoRN/algebra/CRings/mult_wdl.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/mult_wdr.con". +inline procedural "cic:/CoRN/algebra/CRings/mult_wdr.con" as lemma. (* Begin_SpecReals *) @@ -169,7 +169,7 @@ alias id "R" = "cic:/CoRN/algebra/CRings/Ring_constructions/R.var". The multiplicative monoid of a ring is defined as follows. *) -inline procedural "cic:/CoRN/algebra/CRings/Build_multCMonoid.con". +inline procedural "cic:/CoRN/algebra/CRings/Build_multCMonoid.con" as definition. (* UNEXPORTED End Ring_constructions @@ -191,29 +191,29 @@ alias id "R" = "cic:/CoRN/algebra/CRings/Ring_unfolded/R.var". (* begin hide *) -inline procedural "cic:/CoRN/algebra/CRings/Ring_unfolded/mmR.con" "Ring_unfolded__". +inline procedural "cic:/CoRN/algebra/CRings/Ring_unfolded/mmR.con" "Ring_unfolded__" as definition. (* end hide *) -inline procedural "cic:/CoRN/algebra/CRings/mult_assoc_unfolded.con". +inline procedural "cic:/CoRN/algebra/CRings/mult_assoc_unfolded.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/mult_commut_unfolded.con". +inline procedural "cic:/CoRN/algebra/CRings/mult_commut_unfolded.con" as lemma. (* UNEXPORTED Hint Resolve mult_commut_unfolded: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/mult_one.con". +inline procedural "cic:/CoRN/algebra/CRings/mult_one.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/one_mult.con". +inline procedural "cic:/CoRN/algebra/CRings/one_mult.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/ring_dist_unfolded.con". +inline procedural "cic:/CoRN/algebra/CRings/ring_dist_unfolded.con" as lemma. (* UNEXPORTED Hint Resolve ring_dist_unfolded: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/ring_distl_unfolded.con". +inline procedural "cic:/CoRN/algebra/CRings/ring_distl_unfolded.con" as lemma. (* UNEXPORTED End Ring_unfolded @@ -243,11 +243,11 @@ Section Ring_basics alias id "R" = "cic:/CoRN/algebra/CRings/Ring_basics/R.var". -inline procedural "cic:/CoRN/algebra/CRings/one_ap_zero.con". +inline procedural "cic:/CoRN/algebra/CRings/one_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/is_zero_rht.con". +inline procedural "cic:/CoRN/algebra/CRings/is_zero_rht.con" as definition. -inline procedural "cic:/CoRN/algebra/CRings/is_zero_lft.con". +inline procedural "cic:/CoRN/algebra/CRings/is_zero_lft.con" as definition. (* UNEXPORTED Implicit Arguments is_zero_rht [S]. @@ -257,45 +257,45 @@ Implicit Arguments is_zero_rht [S]. Implicit Arguments is_zero_lft [S]. *) -inline procedural "cic:/CoRN/algebra/CRings/cring_mult_zero.con". +inline procedural "cic:/CoRN/algebra/CRings/cring_mult_zero.con" as lemma. (* UNEXPORTED Hint Resolve cring_mult_zero: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/x_mult_zero.con". +inline procedural "cic:/CoRN/algebra/CRings/x_mult_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/cring_mult_zero_op.con". +inline procedural "cic:/CoRN/algebra/CRings/cring_mult_zero_op.con" as lemma. (* UNEXPORTED Hint Resolve cring_mult_zero_op: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/cring_inv_mult_lft.con". +inline procedural "cic:/CoRN/algebra/CRings/cring_inv_mult_lft.con" as lemma. (* UNEXPORTED Hint Resolve cring_inv_mult_lft: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/cring_inv_mult_rht.con". +inline procedural "cic:/CoRN/algebra/CRings/cring_inv_mult_rht.con" as lemma. (* UNEXPORTED Hint Resolve cring_inv_mult_rht: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/cring_mult_ap_zero.con". +inline procedural "cic:/CoRN/algebra/CRings/cring_mult_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/cring_mult_ap_zero_op.con". +inline procedural "cic:/CoRN/algebra/CRings/cring_mult_ap_zero_op.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/inv_mult_invol.con". +inline procedural "cic:/CoRN/algebra/CRings/inv_mult_invol.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/ring_dist_minus.con". +inline procedural "cic:/CoRN/algebra/CRings/ring_dist_minus.con" as lemma. (* UNEXPORTED Hint Resolve ring_dist_minus: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/ring_distl_minus.con". +inline procedural "cic:/CoRN/algebra/CRings/ring_distl_minus.con" as lemma. (* UNEXPORTED Hint Resolve ring_distl_minus: algebra. @@ -348,13 +348,13 @@ alias id "R" = "cic:/CoRN/algebra/CRings/exponentiation/R.var". (* End_SpecReals *) -inline procedural "cic:/CoRN/algebra/CRings/nexp.con". +inline procedural "cic:/CoRN/algebra/CRings/nexp.con" as definition. -inline procedural "cic:/CoRN/algebra/CRings/nexp_well_def.con". +inline procedural "cic:/CoRN/algebra/CRings/nexp_well_def.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/nexp_strong_ext.con". +inline procedural "cic:/CoRN/algebra/CRings/nexp_strong_ext.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/nexp_op.con". +inline procedural "cic:/CoRN/algebra/CRings/nexp_op.con" as definition. (* Begin_SpecReals *) @@ -392,15 +392,15 @@ Note that this need not really be an injection; when it is, the ring is said to have characteristic [0]. *) -inline procedural "cic:/CoRN/algebra/CRings/nring.con". +inline procedural "cic:/CoRN/algebra/CRings/nring.con" as definition. -inline procedural "cic:/CoRN/algebra/CRings/Char0.con". +inline procedural "cic:/CoRN/algebra/CRings/Char0.con" as definition. (* End_SpecReals *) -inline procedural "cic:/CoRN/algebra/CRings/nring_comm_plus.con". +inline procedural "cic:/CoRN/algebra/CRings/nring_comm_plus.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/nring_comm_mult.con". +inline procedural "cic:/CoRN/algebra/CRings/nring_comm_mult.con" as lemma. (* Begin_SpecReals *) @@ -466,9 +466,9 @@ Notation TwentyFour := (nring 24). Notation FortyEight := (nring 48). *) -inline procedural "cic:/CoRN/algebra/CRings/one_plus_one.con". +inline procedural "cic:/CoRN/algebra/CRings/one_plus_one.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/x_plus_x.con". +inline procedural "cic:/CoRN/algebra/CRings/x_plus_x.con" as lemma. (* UNEXPORTED Hint Resolve one_plus_one x_plus_x: algebra. @@ -478,7 +478,7 @@ Hint Resolve one_plus_one x_plus_x: algebra. In a ring of characteristic zero, [nring] is really an injection. *) -inline procedural "cic:/CoRN/algebra/CRings/nring_different.con". +inline procedural "cic:/CoRN/algebra/CRings/nring_different.con" as lemma. (* UNEXPORTED Section int_injection @@ -501,27 +501,27 @@ The first definition is now obsolete, having been replaced by a more efficient one. It is kept to avoid having to redo all the proofs. *) -inline procedural "cic:/CoRN/algebra/CRings/zring_old.con". +inline procedural "cic:/CoRN/algebra/CRings/zring_old.con" as definition. -inline procedural "cic:/CoRN/algebra/CRings/zring_old_zero.con". +inline procedural "cic:/CoRN/algebra/CRings/zring_old_zero.con" as lemma. (* UNEXPORTED Hint Resolve zring_old_zero: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/zring_old_diff.con". +inline procedural "cic:/CoRN/algebra/CRings/zring_old_diff.con" as lemma. (* UNEXPORTED Hint Resolve zring_old_diff. *) -inline procedural "cic:/CoRN/algebra/CRings/zring_old_plus_nat.con". +inline procedural "cic:/CoRN/algebra/CRings/zring_old_plus_nat.con" as lemma. (* UNEXPORTED Hint Resolve zring_old_plus_nat: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/zring_old_inv_nat.con". +inline procedural "cic:/CoRN/algebra/CRings/zring_old_inv_nat.con" as lemma. (* UNEXPORTED Hint Resolve zring_old_inv_nat: algebra. @@ -531,94 +531,94 @@ Hint Resolve zring_old_inv_nat: algebra. Hint Resolve zring_old_diff: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/zring_old_plus.con". +inline procedural "cic:/CoRN/algebra/CRings/zring_old_plus.con" as lemma. (* UNEXPORTED Hint Resolve zring_old_plus: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/zring_old_inv.con". +inline procedural "cic:/CoRN/algebra/CRings/zring_old_inv.con" as lemma. (* UNEXPORTED Hint Resolve zring_old_inv: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/zring_old_minus.con". +inline procedural "cic:/CoRN/algebra/CRings/zring_old_minus.con" as lemma. (* UNEXPORTED Hint Resolve zring_old_minus: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/zring_old_mult.con". +inline procedural "cic:/CoRN/algebra/CRings/zring_old_mult.con" as lemma. (* UNEXPORTED Hint Resolve zring_old_mult: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/zring_old_one.con". +inline procedural "cic:/CoRN/algebra/CRings/zring_old_one.con" as lemma. (* UNEXPORTED Hint Resolve zring_old_one: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/zring_old_inv_one.con". +inline procedural "cic:/CoRN/algebra/CRings/zring_old_inv_one.con" as lemma. (*#************** new def of zring. ***********************) (*#* The [zring] function can be defined directly. This is done here. *) -inline procedural "cic:/CoRN/algebra/CRings/pring_aux.con". +inline procedural "cic:/CoRN/algebra/CRings/pring_aux.con" as definition. -inline procedural "cic:/CoRN/algebra/CRings/pring.con". +inline procedural "cic:/CoRN/algebra/CRings/pring.con" as definition. -inline procedural "cic:/CoRN/algebra/CRings/zring.con". +inline procedural "cic:/CoRN/algebra/CRings/zring.con" as definition. -inline procedural "cic:/CoRN/algebra/CRings/pring_aux_lemma.con". +inline procedural "cic:/CoRN/algebra/CRings/pring_aux_lemma.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/double_nring.con". +inline procedural "cic:/CoRN/algebra/CRings/double_nring.con" as lemma. (* UNEXPORTED Hint Resolve pring_aux_lemma double_nring: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/pring_aux_nring.con". +inline procedural "cic:/CoRN/algebra/CRings/pring_aux_nring.con" as lemma. (* UNEXPORTED Hint Resolve pring_aux_nring: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/pring_convert.con". +inline procedural "cic:/CoRN/algebra/CRings/pring_convert.con" as lemma. (* UNEXPORTED Hint Resolve pring_convert: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/zring_zring_old.con". +inline procedural "cic:/CoRN/algebra/CRings/zring_zring_old.con" as lemma. (* UNEXPORTED Hint Resolve zring_zring_old: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/zring_zero.con". +inline procedural "cic:/CoRN/algebra/CRings/zring_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/zring_diff.con". +inline procedural "cic:/CoRN/algebra/CRings/zring_diff.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/zring_plus_nat.con". +inline procedural "cic:/CoRN/algebra/CRings/zring_plus_nat.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/zring_inv_nat.con". +inline procedural "cic:/CoRN/algebra/CRings/zring_inv_nat.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/zring_plus.con". +inline procedural "cic:/CoRN/algebra/CRings/zring_plus.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/zring_inv.con". +inline procedural "cic:/CoRN/algebra/CRings/zring_inv.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/zring_minus.con". +inline procedural "cic:/CoRN/algebra/CRings/zring_minus.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/zring_mult.con". +inline procedural "cic:/CoRN/algebra/CRings/zring_mult.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/zring_one.con". +inline procedural "cic:/CoRN/algebra/CRings/zring_one.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/zring_inv_one.con". +inline procedural "cic:/CoRN/algebra/CRings/zring_inv_one.con" as lemma. (* UNEXPORTED End int_injection @@ -654,20 +654,20 @@ alias id "R" = "cic:/CoRN/algebra/CRings/Ring_sums/R.var". Section infinite_ring_sums *) -inline procedural "cic:/CoRN/algebra/CRings/Sum_upto.con". +inline procedural "cic:/CoRN/algebra/CRings/Sum_upto.con" as definition. -inline procedural "cic:/CoRN/algebra/CRings/sum_upto_O.con". +inline procedural "cic:/CoRN/algebra/CRings/sum_upto_O.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/Sum_from_upto.con". +inline procedural "cic:/CoRN/algebra/CRings/Sum_from_upto.con" as definition. (*#* Here's an alternative def of [Sum_from_upto], with a lemma that it's equivalent to the original. *) -inline procedural "cic:/CoRN/algebra/CRings/seq_from.con". +inline procedural "cic:/CoRN/algebra/CRings/seq_from.con" as definition. -inline procedural "cic:/CoRN/algebra/CRings/Sum_from_upto_alt.con". +inline procedural "cic:/CoRN/algebra/CRings/Sum_from_upto_alt.con" as definition. (* UNEXPORTED End infinite_ring_sums @@ -680,13 +680,13 @@ Section ring_sums_over_lists (*#* *** Ring Sums over Lists *) -inline procedural "cic:/CoRN/algebra/CRings/RList_Mem.con". +inline procedural "cic:/CoRN/algebra/CRings/RList_Mem.con" as definition. -inline procedural "cic:/CoRN/algebra/CRings/List_Sum_upto.con". +inline procedural "cic:/CoRN/algebra/CRings/List_Sum_upto.con" as definition. -inline procedural "cic:/CoRN/algebra/CRings/list_sum_upto_O.con". +inline procedural "cic:/CoRN/algebra/CRings/list_sum_upto_O.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/List_Sum_from_upto.con". +inline procedural "cic:/CoRN/algebra/CRings/List_Sum_from_upto.con" as definition. (* UNEXPORTED End ring_sums_over_lists @@ -709,39 +709,39 @@ Section Dist_properties alias id "R" = "cic:/CoRN/algebra/CRings/Dist_properties/R.var". -inline procedural "cic:/CoRN/algebra/CRings/dist_1b.con". +inline procedural "cic:/CoRN/algebra/CRings/dist_1b.con" as lemma. (* UNEXPORTED Hint Resolve dist_1b: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/dist_2a.con". +inline procedural "cic:/CoRN/algebra/CRings/dist_2a.con" as lemma. (* UNEXPORTED Hint Resolve dist_2a: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/dist_2b.con". +inline procedural "cic:/CoRN/algebra/CRings/dist_2b.con" as lemma. (* UNEXPORTED Hint Resolve dist_2b: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/mult_distr_sum0_lft.con". +inline procedural "cic:/CoRN/algebra/CRings/mult_distr_sum0_lft.con" as lemma. (* UNEXPORTED Hint Resolve mult_distr_sum0_lft. *) -inline procedural "cic:/CoRN/algebra/CRings/mult_distr_sum_lft.con". +inline procedural "cic:/CoRN/algebra/CRings/mult_distr_sum_lft.con" as lemma. (* UNEXPORTED Hint Resolve mult_distr_sum_lft: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/mult_distr_sum_rht.con". +inline procedural "cic:/CoRN/algebra/CRings/mult_distr_sum_rht.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/sumx_const.con". +inline procedural "cic:/CoRN/algebra/CRings/sumx_const.con" as lemma. (* UNEXPORTED End Dist_properties @@ -765,99 +765,99 @@ Section NExp_properties alias id "R" = "cic:/CoRN/algebra/CRings/NExp_properties/R.var". -inline procedural "cic:/CoRN/algebra/CRings/nexp_wd.con". +inline procedural "cic:/CoRN/algebra/CRings/nexp_wd.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/nexp_strext.con". +inline procedural "cic:/CoRN/algebra/CRings/nexp_strext.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/nexp_Sn.con". +inline procedural "cic:/CoRN/algebra/CRings/nexp_Sn.con" as lemma. (* UNEXPORTED Hint Resolve nexp_wd nexp_Sn: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/nexp_plus.con". +inline procedural "cic:/CoRN/algebra/CRings/nexp_plus.con" as lemma. (* UNEXPORTED Hint Resolve nexp_plus: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/one_nexp.con". +inline procedural "cic:/CoRN/algebra/CRings/one_nexp.con" as lemma. (* UNEXPORTED Hint Resolve one_nexp: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/mult_nexp.con". +inline procedural "cic:/CoRN/algebra/CRings/mult_nexp.con" as lemma. (* UNEXPORTED Hint Resolve mult_nexp: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/nexp_mult.con". +inline procedural "cic:/CoRN/algebra/CRings/nexp_mult.con" as lemma. (* UNEXPORTED Hint Resolve nexp_mult: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/zero_nexp.con". +inline procedural "cic:/CoRN/algebra/CRings/zero_nexp.con" as lemma. (* UNEXPORTED Hint Resolve zero_nexp: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/inv_nexp_even.con". +inline procedural "cic:/CoRN/algebra/CRings/inv_nexp_even.con" as lemma. (* UNEXPORTED Hint Resolve inv_nexp_even: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/inv_nexp_two.con". +inline procedural "cic:/CoRN/algebra/CRings/inv_nexp_two.con" as lemma. (* UNEXPORTED Hint Resolve inv_nexp_two: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/inv_nexp_odd.con". +inline procedural "cic:/CoRN/algebra/CRings/inv_nexp_odd.con" as lemma. (* UNEXPORTED Hint Resolve inv_nexp_odd: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/nexp_one.con". +inline procedural "cic:/CoRN/algebra/CRings/nexp_one.con" as lemma. (* UNEXPORTED Hint Resolve nexp_one: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/nexp_two.con". +inline procedural "cic:/CoRN/algebra/CRings/nexp_two.con" as lemma. (* UNEXPORTED Hint Resolve nexp_two: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/inv_one_even_nexp.con". +inline procedural "cic:/CoRN/algebra/CRings/inv_one_even_nexp.con" as lemma. (* UNEXPORTED Hint Resolve inv_one_even_nexp: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/inv_one_odd_nexp.con". +inline procedural "cic:/CoRN/algebra/CRings/inv_one_odd_nexp.con" as lemma. (* UNEXPORTED Hint Resolve inv_one_odd_nexp: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/square_plus.con". +inline procedural "cic:/CoRN/algebra/CRings/square_plus.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/square_minus.con". +inline procedural "cic:/CoRN/algebra/CRings/square_minus.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/nexp_funny.con". +inline procedural "cic:/CoRN/algebra/CRings/nexp_funny.con" as lemma. (* UNEXPORTED Hint Resolve nexp_funny: algebra. *) -inline procedural "cic:/CoRN/algebra/CRings/nexp_funny'.con". +inline procedural "cic:/CoRN/algebra/CRings/nexp_funny'.con" as lemma. (* UNEXPORTED Hint Resolve nexp_funny': algebra. @@ -897,9 +897,9 @@ alias id "G" = "cic:/CoRN/algebra/CRings/CRing_Ops/G.var". (* begin hide *) -inline procedural "cic:/CoRN/algebra/CRings/CRing_Ops/P.con" "CRing_Ops__". +inline procedural "cic:/CoRN/algebra/CRings/CRing_Ops/P.con" "CRing_Ops__" as definition. -inline procedural "cic:/CoRN/algebra/CRings/CRing_Ops/Q.con" "CRing_Ops__". +inline procedural "cic:/CoRN/algebra/CRings/CRing_Ops/Q.con" "CRing_Ops__" as definition. (* end hide *) @@ -907,9 +907,9 @@ inline procedural "cic:/CoRN/algebra/CRings/CRing_Ops/Q.con" "CRing_Ops__". Section Part_Function_Mult *) -inline procedural "cic:/CoRN/algebra/CRings/part_function_mult_strext.con". +inline procedural "cic:/CoRN/algebra/CRings/part_function_mult_strext.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/Fmult.con". +inline procedural "cic:/CoRN/algebra/CRings/Fmult.con" as definition. (* UNEXPORTED End Part_Function_Mult @@ -921,9 +921,9 @@ Section Part_Function_Nth_Power alias id "n" = "cic:/CoRN/algebra/CRings/CRing_Ops/Part_Function_Nth_Power/n.var". -inline procedural "cic:/CoRN/algebra/CRings/part_function_nth_strext.con". +inline procedural "cic:/CoRN/algebra/CRings/part_function_nth_strext.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/Fnth.con". +inline procedural "cic:/CoRN/algebra/CRings/Fnth.con" as definition. (* UNEXPORTED End Part_Function_Nth_Power @@ -936,23 +936,23 @@ End Part_Function_Nth_Power alias id "R'" = "cic:/CoRN/algebra/CRings/CRing_Ops/R'.var". -inline procedural "cic:/CoRN/algebra/CRings/included_FMult.con". +inline procedural "cic:/CoRN/algebra/CRings/included_FMult.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/included_FMult'.con". +inline procedural "cic:/CoRN/algebra/CRings/included_FMult'.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/included_FMult''.con". +inline procedural "cic:/CoRN/algebra/CRings/included_FMult''.con" as lemma. alias id "n" = "cic:/CoRN/algebra/CRings/CRing_Ops/n.var". -inline procedural "cic:/CoRN/algebra/CRings/included_FNth.con". +inline procedural "cic:/CoRN/algebra/CRings/included_FNth.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/included_FNth'.con". +inline procedural "cic:/CoRN/algebra/CRings/included_FNth'.con" as lemma. (* UNEXPORTED End CRing_Ops *) -inline procedural "cic:/CoRN/algebra/CRings/Fscalmult.con". +inline procedural "cic:/CoRN/algebra/CRings/Fscalmult.con" as definition. (* UNEXPORTED Implicit Arguments Fmult [R]. @@ -988,15 +988,15 @@ alias id "F" = "cic:/CoRN/algebra/CRings/ScalarMultiplication/F.var". (* begin hide *) -inline procedural "cic:/CoRN/algebra/CRings/ScalarMultiplication/P.con" "ScalarMultiplication__". +inline procedural "cic:/CoRN/algebra/CRings/ScalarMultiplication/P.con" "ScalarMultiplication__" as definition. (* end hide *) alias id "R'" = "cic:/CoRN/algebra/CRings/ScalarMultiplication/R'.var". -inline procedural "cic:/CoRN/algebra/CRings/included_FScalMult.con". +inline procedural "cic:/CoRN/algebra/CRings/included_FScalMult.con" as lemma. -inline procedural "cic:/CoRN/algebra/CRings/included_FScalMult'.con". +inline procedural "cic:/CoRN/algebra/CRings/included_FScalMult'.con" as lemma. (* UNEXPORTED End ScalarMultiplication diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/CSemiGroups.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/CSemiGroups.mma index 001974e55..dbbe3f12a 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/CSemiGroups.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/CSemiGroups.mma @@ -31,7 +31,7 @@ include "algebra/CSetoidInc.ma". **Definition of the notion of semigroup *) -inline procedural "cic:/CoRN/algebra/CSemiGroups/is_CSemiGroup.con". +inline procedural "cic:/CoRN/algebra/CSemiGroups/is_CSemiGroup.con" as definition. inline procedural "cic:/CoRN/algebra/CSemiGroups/CSemiGroup.ind". @@ -68,9 +68,9 @@ Section CSemiGroup_axioms alias id "G" = "cic:/CoRN/algebra/CSemiGroups/CSemiGroup_axioms/G.var". -inline procedural "cic:/CoRN/algebra/CSemiGroups/CSemiGroup_is_CSemiGroup.con". +inline procedural "cic:/CoRN/algebra/CSemiGroups/CSemiGroup_is_CSemiGroup.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSemiGroups/plus_assoc.con". +inline procedural "cic:/CoRN/algebra/CSemiGroups/plus_assoc.con" as lemma. (* UNEXPORTED End CSemiGroup_axioms @@ -93,7 +93,7 @@ alias id "G" = "cic:/CoRN/algebra/CSemiGroups/CSemiGroup_basics/G.var". (* End_SpecReals *) -inline procedural "cic:/CoRN/algebra/CSemiGroups/plus_assoc_unfolded.con". +inline procedural "cic:/CoRN/algebra/CSemiGroups/plus_assoc_unfolded.con" as lemma. (* UNEXPORTED End CSemiGroup_basics @@ -129,15 +129,15 @@ alias id "F'" = "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/F'.var". (* begin hide *) -inline procedural "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/P.con" "Part_Function_Plus__". +inline procedural "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/P.con" "Part_Function_Plus__" as definition. -inline procedural "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/Q.con" "Part_Function_Plus__". +inline procedural "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/Q.con" "Part_Function_Plus__" as definition. (* end hide *) -inline procedural "cic:/CoRN/algebra/CSemiGroups/part_function_plus_strext.con". +inline procedural "cic:/CoRN/algebra/CSemiGroups/part_function_plus_strext.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSemiGroups/Fplus.con". +inline procedural "cic:/CoRN/algebra/CSemiGroups/Fplus.con" as definition. (*#* %\begin{convention}% Let [R:G->CProp]. @@ -146,11 +146,11 @@ inline procedural "cic:/CoRN/algebra/CSemiGroups/Fplus.con". alias id "R" = "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/R.var". -inline procedural "cic:/CoRN/algebra/CSemiGroups/included_FPlus.con". +inline procedural "cic:/CoRN/algebra/CSemiGroups/included_FPlus.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSemiGroups/included_FPlus'.con". +inline procedural "cic:/CoRN/algebra/CSemiGroups/included_FPlus'.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSemiGroups/included_FPlus''.con". +inline procedural "cic:/CoRN/algebra/CSemiGroups/included_FPlus''.con" as lemma. (* UNEXPORTED End Part_Function_Plus @@ -189,9 +189,9 @@ alias id "P" = "cic:/CoRN/algebra/CSemiGroups/SubCSemiGroups/P.var". alias id "op_pres_P" = "cic:/CoRN/algebra/CSemiGroups/SubCSemiGroups/op_pres_P.var". -inline procedural "cic:/CoRN/algebra/CSemiGroups/SubCSemiGroups/subcrr.con" "SubCSemiGroups__". +inline procedural "cic:/CoRN/algebra/CSemiGroups/SubCSemiGroups/subcrr.con" "SubCSemiGroups__" as definition. -inline procedural "cic:/CoRN/algebra/CSemiGroups/Build_SubCSemiGroup.con". +inline procedural "cic:/CoRN/algebra/CSemiGroups/Build_SubCSemiGroup.con" as definition. (* UNEXPORTED End SubCSemiGroups diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/CSetoidFun.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/CSetoidFun.mma index 89a477fde..3ec367947 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/CSetoidFun.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/CSetoidFun.mma @@ -40,7 +40,7 @@ alias id "f" = "cic:/CoRN/algebra/CSetoidFun/unary_function_composition/f.var". alias id "g" = "cic:/CoRN/algebra/CSetoidFun/unary_function_composition/g.var". -inline procedural "cic:/CoRN/algebra/CSetoidFun/compose_CSetoid_fun.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/compose_CSetoid_fun.con" as definition. (* UNEXPORTED End unary_function_composition @@ -50,11 +50,11 @@ End unary_function_composition Section unary_and_binary_function_composition *) -inline procedural "cic:/CoRN/algebra/CSetoidFun/compose_CSetoid_bin_un_fun.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/compose_CSetoid_bin_un_fun.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoidFun/compose_CSetoid_bin_fun.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/compose_CSetoid_bin_fun.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoidFun/compose_CSetoid_un_bin_fun.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/compose_CSetoid_un_bin_fun.con" as definition. (* UNEXPORTED End unary_and_binary_function_composition @@ -67,9 +67,9 @@ End unary_and_binary_function_composition Section function_projection *) -inline procedural "cic:/CoRN/algebra/CSetoidFun/proj_bin_fun.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/proj_bin_fun.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoidFun/projected_bin_fun.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/projected_bin_fun.con" as definition. (* UNEXPORTED End function_projection @@ -81,11 +81,11 @@ Section BinProj alias id "S" = "cic:/CoRN/algebra/CSetoidFun/BinProj/S.var". -inline procedural "cic:/CoRN/algebra/CSetoidFun/binproj1.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/binproj1.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoidFun/binproj1_strext.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/binproj1_strext.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoidFun/cs_binproj1.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/cs_binproj1.con" as definition. (* UNEXPORTED End BinProj @@ -120,7 +120,7 @@ alias id "f" = "cic:/CoRN/algebra/CSetoidFun/CombiningOperations/CombiningUnaryO alias id "op" = "cic:/CoRN/algebra/CSetoidFun/CombiningOperations/CombiningUnaryOperations/op.var". -inline procedural "cic:/CoRN/algebra/CSetoidFun/opOnFun.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/opOnFun.con" as definition. (* UNEXPORTED End CombiningUnaryOperations @@ -181,13 +181,13 @@ alias id "P" = "cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Conjunction/P.var". alias id "Q" = "cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Conjunction/Q.var". -inline procedural "cic:/CoRN/algebra/CSetoidFun/conjP.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/conjP.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoidFun/prj1.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/prj1.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoidFun/prj2.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/prj2.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoidFun/conj_wd.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/conj_wd.con" as lemma. (* UNEXPORTED End Conjunction @@ -205,13 +205,13 @@ alias id "Q" = "cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Disjunction/Q.var". Although at this stage we never use it, for completeness's sake we also treat disjunction (corresponding to union of subsets). *) -inline procedural "cic:/CoRN/algebra/CSetoidFun/disj.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/disj.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoidFun/inj1.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/inj1.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoidFun/inj2.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/inj2.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoidFun/disj_wd.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/disj_wd.con" as lemma. (* UNEXPORTED End Disjunction @@ -229,15 +229,15 @@ alias id "P" = "cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Extension/P.var". alias id "R" = "cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Extension/R.var". -inline procedural "cic:/CoRN/algebra/CSetoidFun/extend.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/extend.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoidFun/ext1.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/ext1.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoidFun/ext2_a.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/ext2_a.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoidFun/ext2.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/ext2.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoidFun/extension_wd.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/extension_wd.con" as lemma. (* UNEXPORTED End Extension @@ -290,7 +290,7 @@ Implicit Arguments bpfpfun [S1 S2]. The next lemma states that every partial function is well defined. *) -inline procedural "cic:/CoRN/algebra/CSetoidFun/bpfwdef.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/bpfwdef.con" as lemma. (*#* Similar for automorphisms. *) @@ -316,7 +316,7 @@ Implicit Arguments pfpfun [S]. The next lemma states that every partial function is well defined. *) -inline procedural "cic:/CoRN/algebra/CSetoidFun/pfwdef.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/pfwdef.con" as lemma. (*#* A few characteristics of this definition should be explained: @@ -376,7 +376,7 @@ alias id "S" = "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/S.var". To begin with, we want to be able to ``see'' each total function as a partial function. *) -inline procedural "cic:/CoRN/algebra/CSetoidFun/total_eq_part.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/total_eq_part.con" as definition. (* UNEXPORTED Section Part_Function_Const @@ -391,7 +391,7 @@ In any setoid we can also define constant functions (one for each element of the alias id "c" = "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Const/c.var". -inline procedural "cic:/CoRN/algebra/CSetoidFun/Fconst.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/Fconst.con" as definition. (* UNEXPORTED End Part_Function_Const @@ -401,7 +401,7 @@ End Part_Function_Const Section Part_Function_Id *) -inline procedural "cic:/CoRN/algebra/CSetoidFun/Fid.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/Fid.con" as definition. (* UNEXPORTED End Part_Function_Id @@ -426,19 +426,19 @@ alias id "F" = "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Compositi (* begin hide *) -inline procedural "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Composition/P.con" "CSetoid_Ops__Part_Function_Composition__". +inline procedural "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Composition/P.con" "CSetoid_Ops__Part_Function_Composition__" as definition. -inline procedural "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Composition/Q.con" "CSetoid_Ops__Part_Function_Composition__". +inline procedural "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Composition/Q.con" "CSetoid_Ops__Part_Function_Composition__" as definition. (* end hide *) -inline procedural "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Composition/R.con" "CSetoid_Ops__Part_Function_Composition__". +inline procedural "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Composition/R.con" "CSetoid_Ops__Part_Function_Composition__" as definition. -inline procedural "cic:/CoRN/algebra/CSetoidFun/part_function_comp_strext.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/part_function_comp_strext.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoidFun/part_function_comp_dom_wd.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/part_function_comp_dom_wd.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoidFun/Fcomp.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/Fcomp.con" as definition. (* UNEXPORTED End Part_Function_Composition @@ -469,19 +469,19 @@ alias id "F" = "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/F.var" (* begin hide *) -inline procedural "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/P.con" "BinPart_Function_Composition__". +inline procedural "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/P.con" "BinPart_Function_Composition__" as definition. -inline procedural "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/Q.con" "BinPart_Function_Composition__". +inline procedural "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/Q.con" "BinPart_Function_Composition__" as definition. (* end hide *) -inline procedural "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/R.con" "BinPart_Function_Composition__". +inline procedural "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/R.con" "BinPart_Function_Composition__" as definition. -inline procedural "cic:/CoRN/algebra/CSetoidFun/bin_part_function_comp_strext.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/bin_part_function_comp_strext.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoidFun/bin_part_function_comp_dom_wd.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/bin_part_function_comp_dom_wd.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoidFun/BinFcomp.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/BinFcomp.con" as definition. (* UNEXPORTED End BinPart_Function_Composition @@ -519,11 +519,11 @@ Section bijections (*#* **Bijections *) -inline procedural "cic:/CoRN/algebra/CSetoidFun/injective.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/injective.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoidFun/injective_weak.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/injective_weak.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoidFun/surjective.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/surjective.con" as definition. (* UNEXPORTED Implicit Arguments injective [A B]. @@ -537,43 +537,43 @@ Implicit Arguments injective_weak [A B]. Implicit Arguments surjective [A B]. *) -inline procedural "cic:/CoRN/algebra/CSetoidFun/injective_imp_injective_weak.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/injective_imp_injective_weak.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoidFun/bijective.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/bijective.con" as definition. (* UNEXPORTED Implicit Arguments bijective [A B]. *) -inline procedural "cic:/CoRN/algebra/CSetoidFun/id_is_bij.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/id_is_bij.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoidFun/comp_resp_bij.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/comp_resp_bij.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoidFun/inv.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/inv.con" as lemma. (* UNEXPORTED Implicit Arguments inv [A B]. *) -inline procedural "cic:/CoRN/algebra/CSetoidFun/invfun.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/invfun.con" as definition. (* UNEXPORTED Implicit Arguments invfun [A B]. *) -inline procedural "cic:/CoRN/algebra/CSetoidFun/inv1.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/inv1.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoidFun/inv2.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/inv2.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoidFun/inv_strext.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/inv_strext.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoidFun/Inv.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/Inv.con" as definition. (* UNEXPORTED Implicit Arguments Inv [A B]. *) -inline procedural "cic:/CoRN/algebra/CSetoidFun/Inv_bij.con". +inline procedural "cic:/CoRN/algebra/CSetoidFun/Inv_bij.con" as definition. (* UNEXPORTED End bijections diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/CSetoidInc.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/CSetoidInc.mma index c90a2d06a..ed961f468 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/CSetoidInc.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/CSetoidInc.mma @@ -32,7 +32,7 @@ Let [S] be a setoid, and [P], [Q], [R] be predicates on [S]. *) alias id "S" = "cic:/CoRN/algebra/CSetoidInc/inclusion/S.var". -inline procedural "cic:/CoRN/algebra/CSetoidInc/included.con". +inline procedural "cic:/CoRN/algebra/CSetoidInc/included.con" as definition. (* UNEXPORTED Section Basics @@ -44,21 +44,21 @@ alias id "Q" = "cic:/CoRN/algebra/CSetoidInc/inclusion/Basics/Q.var". alias id "R" = "cic:/CoRN/algebra/CSetoidInc/inclusion/Basics/R.var". -inline procedural "cic:/CoRN/algebra/CSetoidInc/included_refl.con". +inline procedural "cic:/CoRN/algebra/CSetoidInc/included_refl.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoidInc/included_trans.con". +inline procedural "cic:/CoRN/algebra/CSetoidInc/included_trans.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoidInc/included_conj.con". +inline procedural "cic:/CoRN/algebra/CSetoidInc/included_conj.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoidInc/included_conj'.con". +inline procedural "cic:/CoRN/algebra/CSetoidInc/included_conj'.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoidInc/included_conj''.con". +inline procedural "cic:/CoRN/algebra/CSetoidInc/included_conj''.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoidInc/included_conj_lft.con". +inline procedural "cic:/CoRN/algebra/CSetoidInc/included_conj_lft.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoidInc/included_conj_rht.con". +inline procedural "cic:/CoRN/algebra/CSetoidInc/included_conj_rht.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoidInc/included_extend.con". +inline procedural "cic:/CoRN/algebra/CSetoidInc/included_extend.con" as lemma. (* UNEXPORTED End Basics @@ -76,17 +76,17 @@ alias id "G" = "cic:/CoRN/algebra/CSetoidInc/inclusion/G.var". (* begin hide *) -inline procedural "cic:/CoRN/algebra/CSetoidInc/inclusion/P.con" "inclusion__". +inline procedural "cic:/CoRN/algebra/CSetoidInc/inclusion/P.con" "inclusion__" as definition. -inline procedural "cic:/CoRN/algebra/CSetoidInc/inclusion/Q.con" "inclusion__". +inline procedural "cic:/CoRN/algebra/CSetoidInc/inclusion/Q.con" "inclusion__" as definition. (* end hide *) alias id "R" = "cic:/CoRN/algebra/CSetoidInc/inclusion/R.var". -inline procedural "cic:/CoRN/algebra/CSetoidInc/included_FComp.con". +inline procedural "cic:/CoRN/algebra/CSetoidInc/included_FComp.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoidInc/included_FComp'.con". +inline procedural "cic:/CoRN/algebra/CSetoidInc/included_FComp'.con" as lemma. (* UNEXPORTED End inclusion diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/CSetoids.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/CSetoids.mma index 7a2e9a0f0..23107d94a 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/CSetoids.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/CSetoids.mma @@ -41,7 +41,7 @@ include "algebra/CLogic.ma". include "tactics/Step.ma". -inline procedural "cic:/CoRN/algebra/CSetoids/Relation.con". +inline procedural "cic:/CoRN/algebra/CSetoids/Relation.con" as definition. (* End_SpecReals *) @@ -96,13 +96,13 @@ Section Properties_of_relations alias id "A" = "cic:/CoRN/algebra/CSetoids/Properties_of_relations/A.var". -inline procedural "cic:/CoRN/algebra/CSetoids/irreflexive.con". +inline procedural "cic:/CoRN/algebra/CSetoids/irreflexive.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/cotransitive.con". +inline procedural "cic:/CoRN/algebra/CSetoids/cotransitive.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/tight_apart.con". +inline procedural "cic:/CoRN/algebra/CSetoids/tight_apart.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/antisymmetric.con". +inline procedural "cic:/CoRN/algebra/CSetoids/antisymmetric.con" as definition. (* UNEXPORTED End Properties_of_relations @@ -151,7 +151,7 @@ Infix "[#]" := cs_ap (at level 70, no associativity). (* End_SpecReals *) -inline procedural "cic:/CoRN/algebra/CSetoids/cs_neq.con". +inline procedural "cic:/CoRN/algebra/CSetoids/cs_neq.con" as definition. (* UNEXPORTED Implicit Arguments cs_neq [S]. @@ -182,15 +182,15 @@ Section CSetoid_axioms alias id "S" = "cic:/CoRN/algebra/CSetoids/CSetoid_axioms/S.var". -inline procedural "cic:/CoRN/algebra/CSetoids/CSetoid_is_CSetoid.con". +inline procedural "cic:/CoRN/algebra/CSetoids/CSetoid_is_CSetoid.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/ap_irreflexive.con". +inline procedural "cic:/CoRN/algebra/CSetoids/ap_irreflexive.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/ap_symmetric.con". +inline procedural "cic:/CoRN/algebra/CSetoids/ap_symmetric.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/ap_cotransitive.con". +inline procedural "cic:/CoRN/algebra/CSetoids/ap_cotransitive.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/ap_tight.con". +inline procedural "cic:/CoRN/algebra/CSetoids/ap_tight.con" as lemma. (* UNEXPORTED End CSetoid_axioms @@ -217,13 +217,13 @@ alias id "S" = "cic:/CoRN/algebra/CSetoids/CSetoid_basics/S.var". In `there exists a unique [a:S] such that %\ldots%#...#', we now mean unique with respect to the setoid equality. We use [ex_unq] to denote unique existence. *) -inline procedural "cic:/CoRN/algebra/CSetoids/ex_unq.con". +inline procedural "cic:/CoRN/algebra/CSetoids/ex_unq.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/eq_reflexive.con". +inline procedural "cic:/CoRN/algebra/CSetoids/eq_reflexive.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/eq_symmetric.con". +inline procedural "cic:/CoRN/algebra/CSetoids/eq_symmetric.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/eq_transitive.con". +inline procedural "cic:/CoRN/algebra/CSetoids/eq_transitive.con" as lemma. (*#* %\begin{shortcoming}% @@ -239,23 +239,23 @@ If lemma [a] is just an unfolding of lemma [b], the name of [a] is the name %\end{nameconvention}% *) -inline procedural "cic:/CoRN/algebra/CSetoids/eq_reflexive_unfolded.con". +inline procedural "cic:/CoRN/algebra/CSetoids/eq_reflexive_unfolded.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/eq_symmetric_unfolded.con". +inline procedural "cic:/CoRN/algebra/CSetoids/eq_symmetric_unfolded.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/eq_transitive_unfolded.con". +inline procedural "cic:/CoRN/algebra/CSetoids/eq_transitive_unfolded.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/eq_wdl.con". +inline procedural "cic:/CoRN/algebra/CSetoids/eq_wdl.con" as lemma. (* Begin_SpecReals *) -inline procedural "cic:/CoRN/algebra/CSetoids/ap_irreflexive_unfolded.con". +inline procedural "cic:/CoRN/algebra/CSetoids/ap_irreflexive_unfolded.con" as lemma. (* End_SpecReals *) -inline procedural "cic:/CoRN/algebra/CSetoids/ap_cotransitive_unfolded.con". +inline procedural "cic:/CoRN/algebra/CSetoids/ap_cotransitive_unfolded.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/ap_symmetric_unfolded.con". +inline procedural "cic:/CoRN/algebra/CSetoids/ap_symmetric_unfolded.con" as lemma. (*#* %\begin{shortcoming}% @@ -268,19 +268,19 @@ Therefore we have to split the lemma into the following two lemmas [eq_imp_not_a %\end{shortcoming}% *) -inline procedural "cic:/CoRN/algebra/CSetoids/eq_imp_not_ap.con". +inline procedural "cic:/CoRN/algebra/CSetoids/eq_imp_not_ap.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/not_ap_imp_eq.con". +inline procedural "cic:/CoRN/algebra/CSetoids/not_ap_imp_eq.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/neq_imp_notnot_ap.con". +inline procedural "cic:/CoRN/algebra/CSetoids/neq_imp_notnot_ap.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/notnot_ap_imp_neq.con". +inline procedural "cic:/CoRN/algebra/CSetoids/notnot_ap_imp_neq.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/ap_imp_neq.con". +inline procedural "cic:/CoRN/algebra/CSetoids/ap_imp_neq.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/not_neq_imp_eq.con". +inline procedural "cic:/CoRN/algebra/CSetoids/not_neq_imp_eq.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/eq_imp_not_neq.con". +inline procedural "cic:/CoRN/algebra/CSetoids/eq_imp_not_neq.con" as lemma. (* Begin_SpecReals *) @@ -296,13 +296,13 @@ Section product_csetoid (*#* **The product of setoids *) -inline procedural "cic:/CoRN/algebra/CSetoids/prod_ap.con". +inline procedural "cic:/CoRN/algebra/CSetoids/prod_ap.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/prod_eq.con". +inline procedural "cic:/CoRN/algebra/CSetoids/prod_eq.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/prodcsetoid_is_CSetoid.con". +inline procedural "cic:/CoRN/algebra/CSetoids/prodcsetoid_is_CSetoid.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/ProdCSetoid.con". +inline procedural "cic:/CoRN/algebra/CSetoids/ProdCSetoid.con" as definition. (* UNEXPORTED End product_csetoid @@ -366,9 +366,9 @@ Section CSetoidPredicates alias id "P" = "cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/CSetoidPredicates/P.var". -inline procedural "cic:/CoRN/algebra/CSetoids/pred_strong_ext.con". +inline procedural "cic:/CoRN/algebra/CSetoids/pred_strong_ext.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/pred_wd.con". +inline procedural "cic:/CoRN/algebra/CSetoids/pred_wd.con" as definition. (* UNEXPORTED End CSetoidPredicates @@ -380,7 +380,7 @@ inline procedural "cic:/CoRN/algebra/CSetoids/CSetoid_predicate.ind". cic:/matita/CoRN-Procedural/algebra/CSetoids/csp_pred.con *) -inline procedural "cic:/CoRN/algebra/CSetoids/csp_wd.con". +inline procedural "cic:/CoRN/algebra/CSetoids/csp_wd.con" as lemma. (*#* Similar, with [Prop] instead of [CProp]. *) @@ -390,9 +390,9 @@ Section CSetoidPPredicates alias id "P" = "cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/CSetoidPPredicates/P.var". -inline procedural "cic:/CoRN/algebra/CSetoids/pred_strong_ext'.con". +inline procedural "cic:/CoRN/algebra/CSetoids/pred_strong_ext'.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/pred_wd'.con". +inline procedural "cic:/CoRN/algebra/CSetoids/pred_wd'.con" as definition. (* UNEXPORTED End CSetoidPPredicates @@ -406,7 +406,7 @@ inline procedural "cic:/CoRN/algebra/CSetoids/CSetoid_predicate'.ind". cic:/matita/CoRN-Procedural/algebra/CSetoids/csp'_pred.con *) -inline procedural "cic:/CoRN/algebra/CSetoids/csp'_wd.con". +inline procedural "cic:/CoRN/algebra/CSetoids/csp'_wd.con" as lemma. (* Begin_SpecReals *) @@ -421,23 +421,23 @@ Section CsetoidRelations alias id "R" = "cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/CsetoidRelations/R.var". -inline procedural "cic:/CoRN/algebra/CSetoids/rel_wdr.con". +inline procedural "cic:/CoRN/algebra/CSetoids/rel_wdr.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/rel_wdl.con". +inline procedural "cic:/CoRN/algebra/CSetoids/rel_wdl.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/rel_strext.con". +inline procedural "cic:/CoRN/algebra/CSetoids/rel_strext.con" as definition. (* End_SpecReals *) -inline procedural "cic:/CoRN/algebra/CSetoids/rel_strext_lft.con". +inline procedural "cic:/CoRN/algebra/CSetoids/rel_strext_lft.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/rel_strext_rht.con". +inline procedural "cic:/CoRN/algebra/CSetoids/rel_strext_rht.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/rel_strext_imp_lftarg.con". +inline procedural "cic:/CoRN/algebra/CSetoids/rel_strext_imp_lftarg.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/rel_strext_imp_rhtarg.con". +inline procedural "cic:/CoRN/algebra/CSetoids/rel_strext_imp_rhtarg.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/rel_strextarg_imp_strext.con". +inline procedural "cic:/CoRN/algebra/CSetoids/rel_strextarg_imp_strext.con" as lemma. (* Begin_SpecReals *) @@ -466,23 +466,23 @@ Section CCsetoidRelations alias id "R" = "cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/CCsetoidRelations/R.var". -inline procedural "cic:/CoRN/algebra/CSetoids/Crel_wdr.con". +inline procedural "cic:/CoRN/algebra/CSetoids/Crel_wdr.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/Crel_wdl.con". +inline procedural "cic:/CoRN/algebra/CSetoids/Crel_wdl.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/Crel_strext.con". +inline procedural "cic:/CoRN/algebra/CSetoids/Crel_strext.con" as definition. (* End_SpecReals *) -inline procedural "cic:/CoRN/algebra/CSetoids/Crel_strext_lft.con". +inline procedural "cic:/CoRN/algebra/CSetoids/Crel_strext_lft.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/Crel_strext_rht.con". +inline procedural "cic:/CoRN/algebra/CSetoids/Crel_strext_rht.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/Crel_strext_imp_lftarg.con". +inline procedural "cic:/CoRN/algebra/CSetoids/Crel_strext_imp_lftarg.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/Crel_strext_imp_rhtarg.con". +inline procedural "cic:/CoRN/algebra/CSetoids/Crel_strext_imp_rhtarg.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/Crel_strextarg_imp_strext.con". +inline procedural "cic:/CoRN/algebra/CSetoids/Crel_strextarg_imp_strext.con" as lemma. (* Begin_SpecReals *) @@ -500,23 +500,23 @@ inline procedural "cic:/CoRN/algebra/CSetoids/CCSetoid_relation.ind". cic:/matita/CoRN-Procedural/algebra/CSetoids/Ccsr_rel.con *) -inline procedural "cic:/CoRN/algebra/CSetoids/Ccsr_wdr.con". +inline procedural "cic:/CoRN/algebra/CSetoids/Ccsr_wdr.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/Ccsr_wdl.con". +inline procedural "cic:/CoRN/algebra/CSetoids/Ccsr_wdl.con" as lemma. (* End_SpecReals *) -inline procedural "cic:/CoRN/algebra/CSetoids/ap_wdr.con". +inline procedural "cic:/CoRN/algebra/CSetoids/ap_wdr.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/ap_wdl.con". +inline procedural "cic:/CoRN/algebra/CSetoids/ap_wdl.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/ap_wdr_unfolded.con". +inline procedural "cic:/CoRN/algebra/CSetoids/ap_wdr_unfolded.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/ap_wdl_unfolded.con". +inline procedural "cic:/CoRN/algebra/CSetoids/ap_wdl_unfolded.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/ap_strext.con". +inline procedural "cic:/CoRN/algebra/CSetoids/ap_strext.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/predS_well_def.con". +inline procedural "cic:/CoRN/algebra/CSetoids/predS_well_def.con" as definition. (* Begin_SpecReals *) @@ -568,13 +568,13 @@ In the following two definitions, alias id "f" = "cic:/CoRN/algebra/CSetoids/CSetoid_functions/unary_functions/f.var". -inline procedural "cic:/CoRN/algebra/CSetoids/fun_wd.con". +inline procedural "cic:/CoRN/algebra/CSetoids/fun_wd.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/fun_strext.con". +inline procedural "cic:/CoRN/algebra/CSetoids/fun_strext.con" as definition. (* End_SpecReals *) -inline procedural "cic:/CoRN/algebra/CSetoids/fun_strext_imp_wd.con". +inline procedural "cic:/CoRN/algebra/CSetoids/fun_strext_imp_wd.con" as lemma. (* Begin_SpecReals *) @@ -588,11 +588,11 @@ inline procedural "cic:/CoRN/algebra/CSetoids/CSetoid_fun.ind". cic:/matita/CoRN-Procedural/algebra/CSetoids/csf_fun.con *) -inline procedural "cic:/CoRN/algebra/CSetoids/csf_wd.con". +inline procedural "cic:/CoRN/algebra/CSetoids/csf_wd.con" as lemma. (* End_SpecReals *) -inline procedural "cic:/CoRN/algebra/CSetoids/Const_CSetoid_fun.con". +inline procedural "cic:/CoRN/algebra/CSetoids/Const_CSetoid_fun.con" as definition. (* Begin_SpecReals *) @@ -608,13 +608,13 @@ In the following two definitions, alias id "f" = "cic:/CoRN/algebra/CSetoids/CSetoid_functions/binary_functions/f.var". -inline procedural "cic:/CoRN/algebra/CSetoids/bin_fun_wd.con". +inline procedural "cic:/CoRN/algebra/CSetoids/bin_fun_wd.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/bin_fun_strext.con". +inline procedural "cic:/CoRN/algebra/CSetoids/bin_fun_strext.con" as definition. (* End_SpecReals *) -inline procedural "cic:/CoRN/algebra/CSetoids/bin_fun_strext_imp_wd.con". +inline procedural "cic:/CoRN/algebra/CSetoids/bin_fun_strext_imp_wd.con" as lemma. (* Begin_SpecReals *) @@ -628,13 +628,13 @@ inline procedural "cic:/CoRN/algebra/CSetoids/CSetoid_bin_fun.ind". cic:/matita/CoRN-Procedural/algebra/CSetoids/csbf_fun.con *) -inline procedural "cic:/CoRN/algebra/CSetoids/csbf_wd.con". +inline procedural "cic:/CoRN/algebra/CSetoids/csbf_wd.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/csf_wd_unfolded.con". +inline procedural "cic:/CoRN/algebra/CSetoids/csf_wd_unfolded.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/csf_strext_unfolded.con". +inline procedural "cic:/CoRN/algebra/CSetoids/csf_strext_unfolded.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/csbf_wd_unfolded.con". +inline procedural "cic:/CoRN/algebra/CSetoids/csbf_wd_unfolded.con" as lemma. (* UNEXPORTED End CSetoid_functions @@ -677,27 +677,27 @@ alias id "S" = "cic:/CoRN/algebra/CSetoids/csetoid_inner_ops/S.var". (*#* Properties of binary operations *) -inline procedural "cic:/CoRN/algebra/CSetoids/commutes.con". +inline procedural "cic:/CoRN/algebra/CSetoids/commutes.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/associative.con". +inline procedural "cic:/CoRN/algebra/CSetoids/associative.con" as definition. (*#* Well-defined unary operations on a setoid. *) -inline procedural "cic:/CoRN/algebra/CSetoids/un_op_wd.con". +inline procedural "cic:/CoRN/algebra/CSetoids/un_op_wd.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/un_op_strext.con". +inline procedural "cic:/CoRN/algebra/CSetoids/un_op_strext.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/CSetoid_un_op.con". +inline procedural "cic:/CoRN/algebra/CSetoids/CSetoid_un_op.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/Build_CSetoid_un_op.con". +inline procedural "cic:/CoRN/algebra/CSetoids/Build_CSetoid_un_op.con" as definition. (* End_SpecReals *) -inline procedural "cic:/CoRN/algebra/CSetoids/id_strext.con". +inline procedural "cic:/CoRN/algebra/CSetoids/id_strext.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/id_pres_eq.con". +inline procedural "cic:/CoRN/algebra/CSetoids/id_pres_eq.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/id_un_op.con". +inline procedural "cic:/CoRN/algebra/CSetoids/id_un_op.con" as definition. (* begin hide *) @@ -709,31 +709,31 @@ cic:/matita/CoRN-Procedural/algebra/CSetoids/un_op_fun.con (* Begin_SpecReals *) -inline procedural "cic:/CoRN/algebra/CSetoids/cs_un_op_strext.con". +inline procedural "cic:/CoRN/algebra/CSetoids/cs_un_op_strext.con" as definition. (* End_SpecReals *) -inline procedural "cic:/CoRN/algebra/CSetoids/un_op_wd_unfolded.con". +inline procedural "cic:/CoRN/algebra/CSetoids/un_op_wd_unfolded.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/un_op_strext_unfolded.con". +inline procedural "cic:/CoRN/algebra/CSetoids/un_op_strext_unfolded.con" as lemma. (*#* Well-defined binary operations on a setoid. *) -inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_wd.con". +inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_wd.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_strext.con". +inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_strext.con" as definition. (* Begin_SpecReals *) -inline procedural "cic:/CoRN/algebra/CSetoids/CSetoid_bin_op.con". +inline procedural "cic:/CoRN/algebra/CSetoids/CSetoid_bin_op.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/Build_CSetoid_bin_op.con". +inline procedural "cic:/CoRN/algebra/CSetoids/Build_CSetoid_bin_op.con" as definition. (* End_SpecReals *) -inline procedural "cic:/CoRN/algebra/CSetoids/cs_bin_op_wd.con". +inline procedural "cic:/CoRN/algebra/CSetoids/cs_bin_op_wd.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/cs_bin_op_strext.con". +inline procedural "cic:/CoRN/algebra/CSetoids/cs_bin_op_strext.con" as definition. (* Begin_SpecReals *) @@ -747,21 +747,21 @@ cic:/matita/CoRN-Procedural/algebra/CSetoids/bin_op_bin_fun.con (* End_SpecReals *) -inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_wd_unfolded.con". +inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_wd_unfolded.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_strext_unfolded.con". +inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_strext_unfolded.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_is_wd_un_op_lft.con". +inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_is_wd_un_op_lft.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_is_wd_un_op_rht.con". +inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_is_wd_un_op_rht.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_is_strext_un_op_lft.con". +inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_is_strext_un_op_lft.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_is_strext_un_op_rht.con". +inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_is_strext_un_op_rht.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/bin_op2un_op_rht.con". +inline procedural "cic:/CoRN/algebra/CSetoids/bin_op2un_op_rht.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/bin_op2un_op_lft.con". +inline procedural "cic:/CoRN/algebra/CSetoids/bin_op2un_op_lft.con" as definition. (* Begin_SpecReals *) @@ -805,17 +805,17 @@ alias id "S2" = "cic:/CoRN/algebra/CSetoids/csetoid_outer_ops/S2.var". Well-defined outer operations on a setoid. *) -inline procedural "cic:/CoRN/algebra/CSetoids/outer_op_well_def.con". +inline procedural "cic:/CoRN/algebra/CSetoids/outer_op_well_def.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/outer_op_strext.con". +inline procedural "cic:/CoRN/algebra/CSetoids/outer_op_strext.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/CSetoid_outer_op.con". +inline procedural "cic:/CoRN/algebra/CSetoids/CSetoid_outer_op.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/Build_CSetoid_outer_op.con". +inline procedural "cic:/CoRN/algebra/CSetoids/Build_CSetoid_outer_op.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/csoo_wd.con". +inline procedural "cic:/CoRN/algebra/CSetoids/csoo_wd.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/csoo_strext.con". +inline procedural "cic:/CoRN/algebra/CSetoids/csoo_strext.con" as definition. (* begin hide *) @@ -825,7 +825,7 @@ cic:/matita/CoRN-Procedural/algebra/CSetoids/outer_op_bin_fun.con (* end hide *) -inline procedural "cic:/CoRN/algebra/CSetoids/csoo_wd_unfolded.con". +inline procedural "cic:/CoRN/algebra/CSetoids/csoo_wd_unfolded.con" as lemma. (* UNEXPORTED End csetoid_outer_ops @@ -862,23 +862,23 @@ uniform inheritance condition and will not be inserted. However it will also not be printed, which is handy. *) -inline procedural "cic:/CoRN/algebra/CSetoids/restrict_relation.con". +inline procedural "cic:/CoRN/algebra/CSetoids/restrict_relation.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/Crestrict_relation.con". +inline procedural "cic:/CoRN/algebra/CSetoids/Crestrict_relation.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/subcsetoid_eq.con". +inline procedural "cic:/CoRN/algebra/CSetoids/subcsetoid_eq.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/subcsetoid_ap.con". +inline procedural "cic:/CoRN/algebra/CSetoids/subcsetoid_ap.con" as definition. (* End_SpecReals *) -inline procedural "cic:/CoRN/algebra/CSetoids/subcsetoid_equiv.con". +inline procedural "cic:/CoRN/algebra/CSetoids/subcsetoid_equiv.con" as remark. (* Begin_SpecReals *) -inline procedural "cic:/CoRN/algebra/CSetoids/subcsetoid_is_CSetoid.con". +inline procedural "cic:/CoRN/algebra/CSetoids/subcsetoid_is_CSetoid.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/Build_SubCSetoid.con". +inline procedural "cic:/CoRN/algebra/CSetoids/Build_SubCSetoid.con" as definition. (* End_SpecReals *) @@ -894,7 +894,7 @@ Section SubCSetoid_unary_operations alias id "f" = "cic:/CoRN/algebra/CSetoids/SubCSetoids/SubCSetoid_unary_operations/f.var". -inline procedural "cic:/CoRN/algebra/CSetoids/un_op_pres_pred.con". +inline procedural "cic:/CoRN/algebra/CSetoids/un_op_pres_pred.con" as definition. (*#* %\begin{convention}% @@ -903,13 +903,13 @@ Assume [pr:un_op_pres_pred]. alias id "pr" = "cic:/CoRN/algebra/CSetoids/SubCSetoids/SubCSetoid_unary_operations/pr.var". -inline procedural "cic:/CoRN/algebra/CSetoids/restr_un_op.con". +inline procedural "cic:/CoRN/algebra/CSetoids/restr_un_op.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/restr_un_op_wd.con". +inline procedural "cic:/CoRN/algebra/CSetoids/restr_un_op_wd.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/restr_un_op_strext.con". +inline procedural "cic:/CoRN/algebra/CSetoids/restr_un_op_strext.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/Build_SubCSetoid_un_op.con". +inline procedural "cic:/CoRN/algebra/CSetoids/Build_SubCSetoid_un_op.con" as definition. (* UNEXPORTED End SubCSetoid_unary_operations @@ -927,7 +927,7 @@ Section SubCSetoid_binary_operations alias id "f" = "cic:/CoRN/algebra/CSetoids/SubCSetoids/SubCSetoid_binary_operations/f.var". -inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_pres_pred.con". +inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_pres_pred.con" as definition. (*#* %\begin{convention}% @@ -937,15 +937,15 @@ Assume [bin_op_pres_pred]. alias id "pr" = "cic:/CoRN/algebra/CSetoids/SubCSetoids/SubCSetoid_binary_operations/pr.var". -inline procedural "cic:/CoRN/algebra/CSetoids/restr_bin_op.con". +inline procedural "cic:/CoRN/algebra/CSetoids/restr_bin_op.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/restr_bin_op_well_def.con". +inline procedural "cic:/CoRN/algebra/CSetoids/restr_bin_op_well_def.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/restr_bin_op_strext.con". +inline procedural "cic:/CoRN/algebra/CSetoids/restr_bin_op_strext.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSetoids/Build_SubCSetoid_bin_op.con". +inline procedural "cic:/CoRN/algebra/CSetoids/Build_SubCSetoid_bin_op.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/restr_f_assoc.con". +inline procedural "cic:/CoRN/algebra/CSetoids/restr_f_assoc.con" as lemma. (* UNEXPORTED End SubCSetoid_binary_operations @@ -974,15 +974,15 @@ Tactic Notation "Step_final" constr(c) := Step_final c. (*#* **Miscellaneous *) -inline procedural "cic:/CoRN/algebra/CSetoids/proper_caseZ_diff_CS.con". +inline procedural "cic:/CoRN/algebra/CSetoids/proper_caseZ_diff_CS.con" as lemma. (*#* Finally, we characterize functions defined on the natural numbers also as setoid functions, similarly to what we already did for predicates. *) -inline procedural "cic:/CoRN/algebra/CSetoids/nat_less_n_fun.con". +inline procedural "cic:/CoRN/algebra/CSetoids/nat_less_n_fun.con" as definition. -inline procedural "cic:/CoRN/algebra/CSetoids/nat_less_n_fun'.con". +inline procedural "cic:/CoRN/algebra/CSetoids/nat_less_n_fun'.con" as definition. (* UNEXPORTED Implicit Arguments nat_less_n_fun [S n]. diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/CSums.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/CSums.mma index 5bb30914e..57ece830d 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/CSums.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/CSums.mma @@ -44,9 +44,9 @@ alias id "G" = "cic:/CoRN/algebra/CSums/Sums/G.var". (* Sum1 and Sum use subtraction *) -inline procedural "cic:/CoRN/algebra/CSums/Sumlist.con". +inline procedural "cic:/CoRN/algebra/CSums/Sumlist.con" as definition. -inline procedural "cic:/CoRN/algebra/CSums/Sumx.con". +inline procedural "cic:/CoRN/algebra/CSums/Sumx.con" as definition. (*#* It is sometimes useful to view a function defined on $\{0,\ldots,i-1\}$ @@ -54,137 +54,137 @@ It is sometimes useful to view a function defined on $\{0,\ldots,i-1\}$ [Zero] when the input is greater than or equal to [i]. *) -inline procedural "cic:/CoRN/algebra/CSums/part_tot_nat_fun.con". +inline procedural "cic:/CoRN/algebra/CSums/part_tot_nat_fun.con" as definition. -inline procedural "cic:/CoRN/algebra/CSums/part_tot_nat_fun_ch1.con". +inline procedural "cic:/CoRN/algebra/CSums/part_tot_nat_fun_ch1.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSums/part_tot_nat_fun_ch2.con". +inline procedural "cic:/CoRN/algebra/CSums/part_tot_nat_fun_ch2.con" as lemma. (*#* [Sum0] defines the sum for [i=0..(n-1)] *) -inline procedural "cic:/CoRN/algebra/CSums/Sum0.con". +inline procedural "cic:/CoRN/algebra/CSums/Sum0.con" as definition. (*#* [Sum1] defines the sum for [i=m..(n-1)] *) -inline procedural "cic:/CoRN/algebra/CSums/Sum1.con". +inline procedural "cic:/CoRN/algebra/CSums/Sum1.con" as definition. -inline procedural "cic:/CoRN/algebra/CSums/Sum.con". +inline procedural "cic:/CoRN/algebra/CSums/Sum.con" as definition. (* Sum i=m..n *) (*#* [Sum2] is similar to [Sum1], but does not require the summand to be defined outside where it is being added. *) -inline procedural "cic:/CoRN/algebra/CSums/Sum2.con". +inline procedural "cic:/CoRN/algebra/CSums/Sum2.con" as definition. -inline procedural "cic:/CoRN/algebra/CSums/Sum_one.con". +inline procedural "cic:/CoRN/algebra/CSums/Sum_one.con" as lemma. (* UNEXPORTED Hint Resolve Sum_one: algebra. *) -inline procedural "cic:/CoRN/algebra/CSums/Sum_empty.con". +inline procedural "cic:/CoRN/algebra/CSums/Sum_empty.con" as lemma. (* UNEXPORTED Hint Resolve Sum_empty: algebra. *) -inline procedural "cic:/CoRN/algebra/CSums/Sum_Sum.con". +inline procedural "cic:/CoRN/algebra/CSums/Sum_Sum.con" as lemma. (* UNEXPORTED Hint Resolve Sum_Sum: algebra. *) -inline procedural "cic:/CoRN/algebra/CSums/Sum_first.con". +inline procedural "cic:/CoRN/algebra/CSums/Sum_first.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSums/Sum_last.con". +inline procedural "cic:/CoRN/algebra/CSums/Sum_last.con" as lemma. (* UNEXPORTED Hint Resolve Sum_last: algebra. *) -inline procedural "cic:/CoRN/algebra/CSums/Sum_last'.con". +inline procedural "cic:/CoRN/algebra/CSums/Sum_last'.con" as lemma. (*#* We add some extensionality results which will be quite useful when working with integration. *) -inline procedural "cic:/CoRN/algebra/CSums/Sum0_strext.con". +inline procedural "cic:/CoRN/algebra/CSums/Sum0_strext.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSums/Sum_strext.con". +inline procedural "cic:/CoRN/algebra/CSums/Sum_strext.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSums/Sumx_strext.con". +inline procedural "cic:/CoRN/algebra/CSums/Sumx_strext.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSums/Sum0_strext'.con". +inline procedural "cic:/CoRN/algebra/CSums/Sum0_strext'.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSums/Sum_strext'.con". +inline procedural "cic:/CoRN/algebra/CSums/Sum_strext'.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSums/Sum0_wd.con". +inline procedural "cic:/CoRN/algebra/CSums/Sum0_wd.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSums/Sum_wd.con". +inline procedural "cic:/CoRN/algebra/CSums/Sum_wd.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSums/Sumx_wd.con". +inline procedural "cic:/CoRN/algebra/CSums/Sumx_wd.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSums/Sum_wd'.con". +inline procedural "cic:/CoRN/algebra/CSums/Sum_wd'.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSums/Sum2_wd.con". +inline procedural "cic:/CoRN/algebra/CSums/Sum2_wd.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSums/Sum0_plus_Sum0.con". +inline procedural "cic:/CoRN/algebra/CSums/Sum0_plus_Sum0.con" as lemma. (* UNEXPORTED Hint Resolve Sum0_plus_Sum0: algebra. *) -inline procedural "cic:/CoRN/algebra/CSums/Sum_plus_Sum.con". +inline procedural "cic:/CoRN/algebra/CSums/Sum_plus_Sum.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSums/Sumx_plus_Sumx.con". +inline procedural "cic:/CoRN/algebra/CSums/Sumx_plus_Sumx.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSums/Sum2_plus_Sum2.con". +inline procedural "cic:/CoRN/algebra/CSums/Sum2_plus_Sum2.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSums/inv_Sum0.con". +inline procedural "cic:/CoRN/algebra/CSums/inv_Sum0.con" as lemma. (* UNEXPORTED Hint Resolve inv_Sum0: algebra. *) -inline procedural "cic:/CoRN/algebra/CSums/inv_Sum.con". +inline procedural "cic:/CoRN/algebra/CSums/inv_Sum.con" as lemma. (* UNEXPORTED Hint Resolve inv_Sum: algebra. *) -inline procedural "cic:/CoRN/algebra/CSums/inv_Sumx.con". +inline procedural "cic:/CoRN/algebra/CSums/inv_Sumx.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSums/inv_Sum2.con". +inline procedural "cic:/CoRN/algebra/CSums/inv_Sum2.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSums/Sum_minus_Sum.con". +inline procedural "cic:/CoRN/algebra/CSums/Sum_minus_Sum.con" as lemma. (* UNEXPORTED Hint Resolve Sum_minus_Sum: algebra. *) -inline procedural "cic:/CoRN/algebra/CSums/Sumx_minus_Sumx.con". +inline procedural "cic:/CoRN/algebra/CSums/Sumx_minus_Sumx.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSums/Sum2_minus_Sum2.con". +inline procedural "cic:/CoRN/algebra/CSums/Sum2_minus_Sum2.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSums/Sum_apzero.con". +inline procedural "cic:/CoRN/algebra/CSums/Sum_apzero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSums/Sum_zero.con". +inline procedural "cic:/CoRN/algebra/CSums/Sum_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSums/Sum_term.con". +inline procedural "cic:/CoRN/algebra/CSums/Sum_term.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSums/Sum0_shift.con". +inline procedural "cic:/CoRN/algebra/CSums/Sum0_shift.con" as lemma. (* UNEXPORTED Hint Resolve Sum0_shift: algebra. *) -inline procedural "cic:/CoRN/algebra/CSums/Sum_shift.con". +inline procedural "cic:/CoRN/algebra/CSums/Sum_shift.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSums/Sum_big_shift.con". +inline procedural "cic:/CoRN/algebra/CSums/Sum_big_shift.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSums/Sumx_Sum0.con". +inline procedural "cic:/CoRN/algebra/CSums/Sumx_Sum0.con" as lemma. (* UNEXPORTED End Sums @@ -219,13 +219,13 @@ Section More_Sums alias id "G" = "cic:/CoRN/algebra/CSums/More_Sums/G.var". -inline procedural "cic:/CoRN/algebra/CSums/Mengolli_Sum.con". +inline procedural "cic:/CoRN/algebra/CSums/Mengolli_Sum.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSums/Mengolli_Sum_gen.con". +inline procedural "cic:/CoRN/algebra/CSums/Mengolli_Sum_gen.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSums/str_Mengolli_Sum_gen.con". +inline procedural "cic:/CoRN/algebra/CSums/str_Mengolli_Sum_gen.con" as lemma. -inline procedural "cic:/CoRN/algebra/CSums/Sumx_to_Sum.con". +inline procedural "cic:/CoRN/algebra/CSums/Sumx_to_Sum.con" as lemma. (* UNEXPORTED End More_Sums diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/CVectorSpace.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/CVectorSpace.mma index 0d983cca9..93515c59d 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/CVectorSpace.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/CVectorSpace.mma @@ -84,39 +84,39 @@ alias id "F" = "cic:/CoRN/algebra/CVectorSpace/VS_basics/F.var". alias id "V" = "cic:/CoRN/algebra/CVectorSpace/VS_basics/V.var". -inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_op_zero.con". +inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_op_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CVectorSpace/zero_vs_op.con". +inline procedural "cic:/CoRN/algebra/CVectorSpace/zero_vs_op.con" as lemma. (* UNEXPORTED Hint Resolve vs_op_zero zero_vs_op: algebra. *) -inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_op_inv_V.con". +inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_op_inv_V.con" as lemma. -inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_op_inv_S.con". +inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_op_inv_S.con" as lemma. (* UNEXPORTED Hint Resolve vs_op_inv_V vs_op_inv_S: algebra. *) -inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_inv_assoc.con". +inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_inv_assoc.con" as lemma. (* UNEXPORTED Hint Resolve vs_inv_assoc: algebra. *) -inline procedural "cic:/CoRN/algebra/CVectorSpace/ap_zero_vs_op_l.con". +inline procedural "cic:/CoRN/algebra/CVectorSpace/ap_zero_vs_op_l.con" as lemma. -inline procedural "cic:/CoRN/algebra/CVectorSpace/ap_zero_vs_op_r.con". +inline procedural "cic:/CoRN/algebra/CVectorSpace/ap_zero_vs_op_r.con" as lemma. (* note this is the same proof as mult_resp_ap_zero *) -inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_op_resp_ap_rht.con". +inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_op_resp_ap_rht.con" as lemma. -inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_op_resp_ap_zero.con". +inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_op_resp_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_op_resp_ap_lft.con". +inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_op_resp_ap_lft.con" as lemma. (* UNEXPORTED End VS_basics diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/Cauchy_COF.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/Cauchy_COF.mma index 2ee126f6f..e0beb5018 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/Cauchy_COF.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/Cauchy_COF.mma @@ -48,31 +48,31 @@ onwards [(y n) [-] (x n)] is greater than some fixed, positive than the other, equality is the negation of the apartness. *) -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_Set.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_Set.con" as definition. (* UNEXPORTED Section CSetoid_Structure *) -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_lt.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_lt.con" as definition. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_ap.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_ap.con" as definition. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_eq.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_eq.con" as definition. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_lt_cotrans.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_lt_cotrans.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_ap_cotrans.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_ap_cotrans.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_ap_symmetric.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_ap_symmetric.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_lt_irreflexive.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_lt_irreflexive.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_ap_irreflexive.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_ap_irreflexive.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_ap_eq_tight.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_ap_eq_tight.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_CSetoid.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_CSetoid.con" as definition. (* UNEXPORTED End CSetoid_Structure @@ -88,27 +88,27 @@ The group structure is just the expected one; the lemmas which are specifically proved are just the necessary ones to get the group axioms. *) -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_plus.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_plus.con" as definition. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_zero.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_zero.con" as definition. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_plus_lft_ext.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_plus_lft_ext.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_plus_assoc.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_plus_assoc.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_zero_lft_unit.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_zero_lft_unit.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_plus_comm.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_plus_comm.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_inv.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_inv.con" as definition. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_inv_is_inv.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_inv_is_inv.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_inv_ext.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_inv_ext.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/Rinv.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/Rinv.con" as definition. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_CAbGroup.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_CAbGroup.con" as definition. (* UNEXPORTED End Group_Structure @@ -122,35 +122,35 @@ Section Ring_Structure Same comments as previously. *) -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult.con" as definition. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_one.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_one.con" as definition. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_one_ap_zero.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_one_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult_dist_plus.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult_dist_plus.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult_dist_minus.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult_dist_minus.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_one_rht_unit.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_one_rht_unit.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult_comm.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult_comm.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult_ap_zero'.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult_ap_zero'.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult_lft_ext.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult_lft_ext.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult_rht_ext.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult_rht_ext.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult_strext.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult_strext.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/Rmult.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/Rmult.con" as definition. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult_assoc.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult_assoc.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_one_lft_unit.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_one_lft_unit.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_CRing.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_CRing.con" as definition. (* UNEXPORTED End Ring_Structure @@ -166,17 +166,17 @@ that our ring is actually an integral domain. The rest then follows quite straightforwardly. *) -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_integral_domain.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_integral_domain.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_recip.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_recip.con" as definition. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_recip_inverse.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_recip_inverse.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_recip_strext.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_recip_strext.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_recip_inverse'.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_recip_inverse'.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_CField.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_CField.con" as definition. (* UNEXPORTED End Field_Structure @@ -191,19 +191,19 @@ Finally, we extend the field structure with the ordering we defined at the beginning. *) -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_lt_strext.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_lt_strext.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/Rlt.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/Rlt.con" as definition. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/Rlt_transitive.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/Rlt_transitive.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/Rlt_strict.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/Rlt_strict.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_plus_resp_lt.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_plus_resp_lt.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult_resp_lt.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult_resp_lt.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_COrdField.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_COrdField.con" as definition. (* UNEXPORTED End Order @@ -218,19 +218,19 @@ Auxiliary characterizations of the main relations on [R_Set]. Section Auxiliary *) -inline procedural "cic:/CoRN/algebra/Cauchy_COF/Rlt_alt_1.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/Rlt_alt_1.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/Rlt_alt_2.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/Rlt_alt_2.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_ap_alt_1.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_ap_alt_1.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/Eq_alt_1.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/Eq_alt_1.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_ap_alt_2.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_ap_alt_2.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/Eq_alt_2_1.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/Eq_alt_2_1.con" as lemma. -inline procedural "cic:/CoRN/algebra/Cauchy_COF/Eq_alt_2_2.con". +inline procedural "cic:/CoRN/algebra/Cauchy_COF/Eq_alt_2_2.con" as lemma. (* UNEXPORTED End Auxiliary diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/Expon.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/Expon.mma index cbdb42802..a0ed1a5f9 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/Expon.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/Expon.mma @@ -36,45 +36,45 @@ Section More_Nexp alias id "R" = "cic:/CoRN/algebra/Expon/More_Nexp/R.var". -inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_ap_zero.con". +inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_ap_zero.con" as lemma. (* UNEXPORTED Hint Resolve nexp_resp_ap_zero: algebra. *) -inline procedural "cic:/CoRN/algebra/Expon/nexp_distr_div.con". +inline procedural "cic:/CoRN/algebra/Expon/nexp_distr_div.con" as lemma. -inline procedural "cic:/CoRN/algebra/Expon/nexp_distr_div'.con". +inline procedural "cic:/CoRN/algebra/Expon/nexp_distr_div'.con" as lemma. -inline procedural "cic:/CoRN/algebra/Expon/small_nexp_resp_lt.con". +inline procedural "cic:/CoRN/algebra/Expon/small_nexp_resp_lt.con" as lemma. -inline procedural "cic:/CoRN/algebra/Expon/great_nexp_resp_lt.con". +inline procedural "cic:/CoRN/algebra/Expon/great_nexp_resp_lt.con" as lemma. -inline procedural "cic:/CoRN/algebra/Expon/small_nexp_resp_le.con". +inline procedural "cic:/CoRN/algebra/Expon/small_nexp_resp_le.con" as lemma. -inline procedural "cic:/CoRN/algebra/Expon/great_nexp_resp_le.con". +inline procedural "cic:/CoRN/algebra/Expon/great_nexp_resp_le.con" as lemma. -inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_leEq.con". +inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_leEq.con" as lemma. -inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_leEq_one.con". +inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_leEq_one.con" as lemma. -inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_leEq_neg_even.con". +inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_leEq_neg_even.con" as lemma. -inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_leEq_neg_odd.con". +inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_leEq_neg_odd.con" as lemma. -inline procedural "cic:/CoRN/algebra/Expon/nexp_distr_recip.con". +inline procedural "cic:/CoRN/algebra/Expon/nexp_distr_recip.con" as lemma. (* UNEXPORTED Hint Resolve nexp_distr_recip: algebra. *) -inline procedural "cic:/CoRN/algebra/Expon/nexp_even_nonneg.con". +inline procedural "cic:/CoRN/algebra/Expon/nexp_even_nonneg.con" as lemma. -inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_le'.con". +inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_le'.con" as lemma. -inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_le.con". +inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_le.con" as lemma. -inline procedural "cic:/CoRN/algebra/Expon/bin_less_un.con". +inline procedural "cic:/CoRN/algebra/Expon/bin_less_un.con" as lemma. (* UNEXPORTED End More_Nexp @@ -104,7 +104,7 @@ It would be nicer to define [zexp] using [caseZdiff], but we already have most properties now. *) -inline procedural "cic:/CoRN/algebra/Expon/zexp.con". +inline procedural "cic:/CoRN/algebra/Expon/zexp.con" as definition. (* UNEXPORTED End Zexp_def @@ -129,131 +129,131 @@ Section Zexp_properties alias id "R" = "cic:/CoRN/algebra/Expon/Zexp_properties/R.var". -inline procedural "cic:/CoRN/algebra/Expon/zexp_zero.con". +inline procedural "cic:/CoRN/algebra/Expon/zexp_zero.con" as lemma. (* UNEXPORTED Hint Resolve zexp_zero: algebra. *) -inline procedural "cic:/CoRN/algebra/Expon/zexp_nexp.con". +inline procedural "cic:/CoRN/algebra/Expon/zexp_nexp.con" as lemma. (* UNEXPORTED Hint Resolve zexp_nexp: algebra. *) -inline procedural "cic:/CoRN/algebra/Expon/zexp_inv_nexp.con". +inline procedural "cic:/CoRN/algebra/Expon/zexp_inv_nexp.con" as lemma. (* UNEXPORTED Hint Resolve zexp_inv_nexp: algebra. *) -inline procedural "cic:/CoRN/algebra/Expon/zexp_inv_nexp'.con". +inline procedural "cic:/CoRN/algebra/Expon/zexp_inv_nexp'.con" as lemma. (* UNEXPORTED Hint Resolve zexp_inv_nexp': algebra. *) -inline procedural "cic:/CoRN/algebra/Expon/zexp_strext.con". +inline procedural "cic:/CoRN/algebra/Expon/zexp_strext.con" as lemma. -inline procedural "cic:/CoRN/algebra/Expon/zexp_wd.con". +inline procedural "cic:/CoRN/algebra/Expon/zexp_wd.con" as lemma. (* UNEXPORTED Hint Resolve zexp_wd: algebra_c. *) -inline procedural "cic:/CoRN/algebra/Expon/zexp_plus1.con". +inline procedural "cic:/CoRN/algebra/Expon/zexp_plus1.con" as lemma. (* UNEXPORTED Hint Resolve zexp_plus1: algebra. *) -inline procedural "cic:/CoRN/algebra/Expon/zexp_resp_ap_zero.con". +inline procedural "cic:/CoRN/algebra/Expon/zexp_resp_ap_zero.con" as lemma. (* UNEXPORTED Hint Resolve zexp_resp_ap_zero: algebra. *) -inline procedural "cic:/CoRN/algebra/Expon/zexp_inv.con". +inline procedural "cic:/CoRN/algebra/Expon/zexp_inv.con" as lemma. (* UNEXPORTED Hint Resolve zexp_inv: algebra. *) -inline procedural "cic:/CoRN/algebra/Expon/zexp_inv1.con". +inline procedural "cic:/CoRN/algebra/Expon/zexp_inv1.con" as lemma. (* UNEXPORTED Hint Resolve zexp_inv1: algebra. *) -inline procedural "cic:/CoRN/algebra/Expon/zexp_plus.con". +inline procedural "cic:/CoRN/algebra/Expon/zexp_plus.con" as lemma. (* UNEXPORTED Hint Resolve zexp_plus: algebra. *) -inline procedural "cic:/CoRN/algebra/Expon/zexp_minus.con". +inline procedural "cic:/CoRN/algebra/Expon/zexp_minus.con" as lemma. (* UNEXPORTED Hint Resolve zexp_minus: algebra. *) -inline procedural "cic:/CoRN/algebra/Expon/one_zexp.con". +inline procedural "cic:/CoRN/algebra/Expon/one_zexp.con" as lemma. (* UNEXPORTED Hint Resolve one_zexp: algebra. *) -inline procedural "cic:/CoRN/algebra/Expon/mult_zexp.con". +inline procedural "cic:/CoRN/algebra/Expon/mult_zexp.con" as lemma. (* UNEXPORTED Hint Resolve mult_zexp: algebra. *) -inline procedural "cic:/CoRN/algebra/Expon/zexp_mult.con". +inline procedural "cic:/CoRN/algebra/Expon/zexp_mult.con" as lemma. (* UNEXPORTED Hint Resolve zexp_mult: algebra. *) -inline procedural "cic:/CoRN/algebra/Expon/zexp_two.con". +inline procedural "cic:/CoRN/algebra/Expon/zexp_two.con" as lemma. (* UNEXPORTED Hint Resolve zexp_two: algebra. *) -inline procedural "cic:/CoRN/algebra/Expon/inv_zexp_even.con". +inline procedural "cic:/CoRN/algebra/Expon/inv_zexp_even.con" as lemma. (* UNEXPORTED Hint Resolve inv_zexp_even: algebra. *) -inline procedural "cic:/CoRN/algebra/Expon/inv_zexp_two.con". +inline procedural "cic:/CoRN/algebra/Expon/inv_zexp_two.con" as lemma. (* UNEXPORTED Hint Resolve inv_zexp_two: algebra. *) -inline procedural "cic:/CoRN/algebra/Expon/inv_zexp_odd.con". +inline procedural "cic:/CoRN/algebra/Expon/inv_zexp_odd.con" as lemma. -inline procedural "cic:/CoRN/algebra/Expon/zexp_one.con". +inline procedural "cic:/CoRN/algebra/Expon/zexp_one.con" as lemma. (* UNEXPORTED Hint Resolve zexp_one: algebra. *) -inline procedural "cic:/CoRN/algebra/Expon/zexp_funny.con". +inline procedural "cic:/CoRN/algebra/Expon/zexp_funny.con" as lemma. (* UNEXPORTED Hint Resolve zexp_funny: algebra. *) -inline procedural "cic:/CoRN/algebra/Expon/zexp_funny'.con". +inline procedural "cic:/CoRN/algebra/Expon/zexp_funny'.con" as lemma. (* UNEXPORTED Hint Resolve zexp_funny': algebra. *) -inline procedural "cic:/CoRN/algebra/Expon/zexp_pos.con". +inline procedural "cic:/CoRN/algebra/Expon/zexp_pos.con" as lemma. (* UNEXPORTED End Zexp_properties @@ -276,9 +276,9 @@ Section Root_Unique alias id "R" = "cic:/CoRN/algebra/Expon/Root_Unique/R.var". -inline procedural "cic:/CoRN/algebra/Expon/root_unique.con". +inline procedural "cic:/CoRN/algebra/Expon/root_unique.con" as lemma. -inline procedural "cic:/CoRN/algebra/Expon/root_one.con". +inline procedural "cic:/CoRN/algebra/Expon/root_one.con" as lemma. (* UNEXPORTED End Root_Unique diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/ListType.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/ListType.mma index 51a20cf6e..9e83709f4 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/ListType.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/ListType.mma @@ -56,29 +56,29 @@ alias id "A" = "cic:/CoRN/algebra/ListType/List/A.var". inline procedural "cic:/CoRN/algebra/ListType/list.ind". -inline procedural "cic:/CoRN/algebra/ListType/app.con". +inline procedural "cic:/CoRN/algebra/ListType/app.con" as definition. -inline procedural "cic:/CoRN/algebra/ListType/app_nil_end.con". +inline procedural "cic:/CoRN/algebra/ListType/app_nil_end.con" as lemma. (* UNEXPORTED Hint Resolve app_nil_end: list v62. *) -inline procedural "cic:/CoRN/algebra/ListType/app_ass.con". +inline procedural "cic:/CoRN/algebra/ListType/app_ass.con" as lemma. (* UNEXPORTED Hint Resolve app_ass: list v62. *) -inline procedural "cic:/CoRN/algebra/ListType/ass_app.con". +inline procedural "cic:/CoRN/algebra/ListType/ass_app.con" as lemma. (* UNEXPORTED Hint Resolve ass_app: list v62. *) -inline procedural "cic:/CoRN/algebra/ListType/tail.con". +inline procedural "cic:/CoRN/algebra/ListType/tail.con" as definition. -inline procedural "cic:/CoRN/algebra/ListType/nil_cons.con". +inline procedural "cic:/CoRN/algebra/ListType/nil_cons.con" as lemma. (*#***************************************) @@ -86,7 +86,7 @@ inline procedural "cic:/CoRN/algebra/ListType/nil_cons.con". (*#***************************************) -inline procedural "cic:/CoRN/algebra/ListType/length.con". +inline procedural "cic:/CoRN/algebra/ListType/length.con" as definition. (*#*****************************) @@ -98,7 +98,7 @@ inline procedural "cic:/CoRN/algebra/ListType/length.con". Section length_order *) -inline procedural "cic:/CoRN/algebra/ListType/lel.con". +inline procedural "cic:/CoRN/algebra/ListType/lel.con" as definition. (* UNEXPORTED Hint Unfold lel: list. @@ -114,17 +114,17 @@ alias id "m" = "cic:/CoRN/algebra/ListType/List/length_order/m.var". alias id "n" = "cic:/CoRN/algebra/ListType/List/length_order/n.var". -inline procedural "cic:/CoRN/algebra/ListType/lel_refl.con". +inline procedural "cic:/CoRN/algebra/ListType/lel_refl.con" as lemma. -inline procedural "cic:/CoRN/algebra/ListType/lel_trans.con". +inline procedural "cic:/CoRN/algebra/ListType/lel_trans.con" as lemma. -inline procedural "cic:/CoRN/algebra/ListType/lel_cons_cons.con". +inline procedural "cic:/CoRN/algebra/ListType/lel_cons_cons.con" as lemma. -inline procedural "cic:/CoRN/algebra/ListType/lel_cons.con". +inline procedural "cic:/CoRN/algebra/ListType/lel_cons.con" as lemma. -inline procedural "cic:/CoRN/algebra/ListType/lel_tail.con". +inline procedural "cic:/CoRN/algebra/ListType/lel_tail.con" as lemma. -inline procedural "cic:/CoRN/algebra/ListType/lel_nil.con". +inline procedural "cic:/CoRN/algebra/ListType/lel_nil.con" as lemma. (* UNEXPORTED End length_order @@ -135,71 +135,71 @@ Hint Resolve lel_refl lel_cons_cons lel_cons lel_nil lel_nil nil_cons: list v62. *) -inline procedural "cic:/CoRN/algebra/ListType/In.con". +inline procedural "cic:/CoRN/algebra/ListType/In.con" as definition. -inline procedural "cic:/CoRN/algebra/ListType/in_eq.con". +inline procedural "cic:/CoRN/algebra/ListType/in_eq.con" as lemma. (* UNEXPORTED Hint Resolve in_eq: list v62. *) -inline procedural "cic:/CoRN/algebra/ListType/in_cons.con". +inline procedural "cic:/CoRN/algebra/ListType/in_cons.con" as lemma. (* UNEXPORTED Hint Resolve in_cons: list v62. *) -inline procedural "cic:/CoRN/algebra/ListType/in_app_or.con". +inline procedural "cic:/CoRN/algebra/ListType/in_app_or.con" as lemma. (* UNEXPORTED Hint Immediate in_app_or: list v62. *) -inline procedural "cic:/CoRN/algebra/ListType/in_or_app.con". +inline procedural "cic:/CoRN/algebra/ListType/in_or_app.con" as lemma. (* UNEXPORTED Hint Resolve in_or_app: list v62. *) -inline procedural "cic:/CoRN/algebra/ListType/incl.con". +inline procedural "cic:/CoRN/algebra/ListType/incl.con" as definition. (* UNEXPORTED Hint Unfold incl: list v62. *) -inline procedural "cic:/CoRN/algebra/ListType/incl_refl.con". +inline procedural "cic:/CoRN/algebra/ListType/incl_refl.con" as lemma. (* UNEXPORTED Hint Resolve incl_refl: list v62. *) -inline procedural "cic:/CoRN/algebra/ListType/incl_tl.con". +inline procedural "cic:/CoRN/algebra/ListType/incl_tl.con" as lemma. (* UNEXPORTED Hint Immediate incl_tl: list v62. *) -inline procedural "cic:/CoRN/algebra/ListType/incl_tran.con". +inline procedural "cic:/CoRN/algebra/ListType/incl_tran.con" as lemma. -inline procedural "cic:/CoRN/algebra/ListType/incl_appl.con". +inline procedural "cic:/CoRN/algebra/ListType/incl_appl.con" as lemma. (* UNEXPORTED Hint Immediate incl_appl: list v62. *) -inline procedural "cic:/CoRN/algebra/ListType/incl_appr.con". +inline procedural "cic:/CoRN/algebra/ListType/incl_appr.con" as lemma. (* UNEXPORTED Hint Immediate incl_appr: list v62. *) -inline procedural "cic:/CoRN/algebra/ListType/incl_cons.con". +inline procedural "cic:/CoRN/algebra/ListType/incl_cons.con" as lemma. (* UNEXPORTED Hint Resolve incl_cons: list v62. *) -inline procedural "cic:/CoRN/algebra/ListType/incl_app.con". +inline procedural "cic:/CoRN/algebra/ListType/incl_app.con" as lemma. (* UNEXPORTED End List @@ -227,7 +227,7 @@ alias id "B" = "cic:/CoRN/algebra/ListType/Map/B.var". alias id "f" = "cic:/CoRN/algebra/ListType/Map/f.var". -inline procedural "cic:/CoRN/algebra/ListType/map.con". +inline procedural "cic:/CoRN/algebra/ListType/map.con" as definition. (* UNEXPORTED End Map diff --git a/helm/software/matita/contribs/CoRN-Procedural/complex/AbsCC.mma b/helm/software/matita/contribs/CoRN-Procedural/complex/AbsCC.mma index 9a098c020..6ab364763 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/complex/AbsCC.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/complex/AbsCC.mma @@ -27,61 +27,61 @@ include "complex/CComplex.ma". Section AbsCC_properties *) -inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_nonneg.con". +inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_nonneg.con" as lemma. -inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_ap_zero_imp_pos.con". +inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_ap_zero_imp_pos.con" as lemma. -inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_wd.con". +inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_wd.con" as lemma. (* UNEXPORTED Hint Resolve AbsCC_wd: algebra_c. *) -inline procedural "cic:/CoRN/complex/AbsCC/cc_inv_abs.con". +inline procedural "cic:/CoRN/complex/AbsCC/cc_inv_abs.con" as lemma. (* UNEXPORTED Hint Resolve cc_inv_abs: algebra. *) -inline procedural "cic:/CoRN/complex/AbsCC/cc_minus_abs.con". +inline procedural "cic:/CoRN/complex/AbsCC/cc_minus_abs.con" as lemma. -inline procedural "cic:/CoRN/complex/AbsCC/cc_mult_abs.con". +inline procedural "cic:/CoRN/complex/AbsCC/cc_mult_abs.con" as lemma. (* UNEXPORTED Hint Resolve cc_mult_abs: algebra. *) -inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_minzero.con". +inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_minzero.con" as lemma. -inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_IR.con". +inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_IR.con" as lemma. (* UNEXPORTED Hint Resolve AbsCC_IR: algebra. *) -inline procedural "cic:/CoRN/complex/AbsCC/cc_div_abs.con". +inline procedural "cic:/CoRN/complex/AbsCC/cc_div_abs.con" as lemma. -inline procedural "cic:/CoRN/complex/AbsCC/cc_div_abs'.con". +inline procedural "cic:/CoRN/complex/AbsCC/cc_div_abs'.con" as lemma. -inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_zero.con". +inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_zero.con" as lemma. (* UNEXPORTED Hint Resolve AbsCC_zero: algebra. *) -inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_one.con". +inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_one.con" as lemma. -inline procedural "cic:/CoRN/complex/AbsCC/cc_pow_abs.con". +inline procedural "cic:/CoRN/complex/AbsCC/cc_pow_abs.con" as lemma. -inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_pos.con". +inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_pos.con" as lemma. -inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_ap_zero.con". +inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_small_imp_eq.con". +inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_small_imp_eq.con" as lemma. (* begin hide *) -inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_1_1_2.con" "AbsCC_properties__". +inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_1_1_2.con" "AbsCC_properties__" as definition. (* end hide *) @@ -89,7 +89,7 @@ inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_1_1_2.con" "AbsCC_ Hint Resolve l_1_1_2: algebra. *) -inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_square_Re_Im.con". +inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_square_Re_Im.con" as lemma. (* UNEXPORTED Hint Resolve AbsCC_square_Re_Im: algebra. @@ -97,7 +97,7 @@ Hint Resolve AbsCC_square_Re_Im: algebra. (* begin hide *) -inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_1_2_3_CC.con" "AbsCC_properties__". +inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_1_2_3_CC.con" "AbsCC_properties__" as definition. (* end hide *) @@ -105,7 +105,7 @@ inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_1_2_3_CC.con" "Abs Hint Resolve l_1_2_3_CC: algebra. *) -inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_mult_conj.con". +inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_mult_conj.con" as lemma. (* UNEXPORTED Hint Resolve CC_conj_mult: algebra. @@ -113,7 +113,7 @@ Hint Resolve CC_conj_mult: algebra. (* begin hide *) -inline procedural "cic:/CoRN/complex/AbsCC/l_2_1_2.con". +inline procedural "cic:/CoRN/complex/AbsCC/l_2_1_2.con" as lemma. (* UNEXPORTED Hint Resolve l_2_1_2: algebra. @@ -121,27 +121,27 @@ Hint Resolve l_2_1_2: algebra. (* end hide *) -inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_mult_square.con". +inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_mult_square.con" as lemma. -inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_square_ap_zero.con". +inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_square_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/complex/AbsCC/cc_recip_char.con". +inline procedural "cic:/CoRN/complex/AbsCC/cc_recip_char.con" as lemma. -inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_strext.con". +inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_strext.con" as lemma. -inline procedural "cic:/CoRN/complex/AbsCC/AbsSmallCC.con". +inline procedural "cic:/CoRN/complex/AbsCC/AbsSmallCC.con" as definition. -inline procedural "cic:/CoRN/complex/AbsCC/Cexis_AFS_CC.con". +inline procedural "cic:/CoRN/complex/AbsCC/Cexis_AFS_CC.con" as lemma. (* The following lemmas are just auxiliary results *) (* begin hide *) -inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_4_1_2.con" "AbsCC_properties__". +inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_4_1_2.con" "AbsCC_properties__" as definition. -inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_4_2_3.con" "AbsCC_properties__". +inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_4_2_3.con" "AbsCC_properties__" as definition. -inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_4_3_4.con" "AbsCC_properties__". +inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_4_3_4.con" "AbsCC_properties__" as definition. (* end hide *) @@ -161,7 +161,7 @@ Hint Resolve cc_inv_abs cc_mult_abs cc_div_abs cc_div_abs' cc_pow_abs (*#* ** The triangle inequality *) -inline procedural "cic:/CoRN/complex/AbsCC/triangle.con". +inline procedural "cic:/CoRN/complex/AbsCC/triangle.con" as lemma. -inline procedural "cic:/CoRN/complex/AbsCC/triangle_Sum.con". +inline procedural "cic:/CoRN/complex/AbsCC/triangle_Sum.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/complex/CComplex.mma b/helm/software/matita/contribs/CoRN-Procedural/complex/CComplex.mma index 27a1bd926..176a77d88 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/complex/CComplex.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/complex/CComplex.mma @@ -44,25 +44,25 @@ Section Complex_Numbers inline procedural "cic:/CoRN/complex/CComplex/CC_set.ind". -inline procedural "cic:/CoRN/complex/CComplex/cc_ap.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_ap.con" as definition. -inline procedural "cic:/CoRN/complex/CComplex/cc_eq.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_eq.con" as definition. -inline procedural "cic:/CoRN/complex/CComplex/cc_is_CSetoid.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_is_CSetoid.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/cc_csetoid.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_csetoid.con" as definition. -inline procedural "cic:/CoRN/complex/CComplex/cc_plus.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_plus.con" as definition. -inline procedural "cic:/CoRN/complex/CComplex/cc_mult.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_mult.con" as definition. -inline procedural "cic:/CoRN/complex/CComplex/cc_zero.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_zero.con" as definition. -inline procedural "cic:/CoRN/complex/CComplex/cc_one.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_one.con" as definition. -inline procedural "cic:/CoRN/complex/CComplex/cc_i.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_i.con" as definition. -inline procedural "cic:/CoRN/complex/CComplex/cc_inv.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_inv.con" as definition. (* not needed anymore Lemma cc_plus_op_proof : (bin_op_wd cc_csetoid cc_plus). @@ -90,56 +90,56 @@ Split; Algebra. Qed. *) -inline procedural "cic:/CoRN/complex/CComplex/cc_inv_strext.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_inv_strext.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/cc_plus_strext.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_plus_strext.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/cc_mult_strext.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_mult_strext.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/cc_inv_op.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_inv_op.con" as definition. -inline procedural "cic:/CoRN/complex/CComplex/cc_plus_op.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_plus_op.con" as definition. -inline procedural "cic:/CoRN/complex/CComplex/cc_mult_op.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_mult_op.con" as definition. -inline procedural "cic:/CoRN/complex/CComplex/cc_csg_associative.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_csg_associative.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/cc_cr_mult_associative.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_cr_mult_associative.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/cc_csemi_grp.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_csemi_grp.con" as definition. -inline procedural "cic:/CoRN/complex/CComplex/cc_cm_proof.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_cm_proof.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/cc_cmonoid.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_cmonoid.con" as definition. -inline procedural "cic:/CoRN/complex/CComplex/cc_cg_proof.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_cg_proof.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/cc_cr_dist.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_cr_dist.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/cc_cr_non_triv.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_cr_non_triv.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/cc_cgroup.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_cgroup.con" as definition. -inline procedural "cic:/CoRN/complex/CComplex/cc_cabgroup.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_cabgroup.con" as definition. -inline procedural "cic:/CoRN/complex/CComplex/cc_cr_mult_mon.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_cr_mult_mon.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/cc_mult_commutes.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_mult_commutes.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/cc_isCRing.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_isCRing.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/cc_cring.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_cring.con" as definition. -inline procedural "cic:/CoRN/complex/CComplex/cc_ap_zero.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/cc_inv_aid.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_inv_aid.con" as lemma. (*#* If [x [~=] Zero] or [y [~=] Zero], then [x [/] x[^]2 [+] y[^]2 [~=] Zero] or [[--]y[/]x[^]2[+]y[^]2 [~=] Zero]. *) -inline procedural "cic:/CoRN/complex/CComplex/cc_inv_aid2.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_inv_aid2.con" as lemma. (* REMARK KEPT FOR SENTIMENTAL REASONS... @@ -150,11 +150,11 @@ input (Re or Im) is NonZero (a Prop), we manage to construct the actual function. *) -inline procedural "cic:/CoRN/complex/CComplex/cc_recip.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_recip.con" as definition. -inline procedural "cic:/CoRN/complex/CComplex/cc_cfield_proof.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_cfield_proof.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/cc_Recip_proof.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_Recip_proof.con" as lemma. (* UNEXPORTED Opaque cc_recip. @@ -164,27 +164,27 @@ Opaque cc_recip. Opaque cc_inv. *) -inline procedural "cic:/CoRN/complex/CComplex/cc_cfield.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_cfield.con" as definition. -inline procedural "cic:/CoRN/complex/CComplex/CC.con". +inline procedural "cic:/CoRN/complex/CComplex/CC.con" as definition. (*#* Maps from reals to complex and vice-versa are defined, as well as conjugate, absolute value and the imaginary unit [I] *) -inline procedural "cic:/CoRN/complex/CComplex/cc_set_CC.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_set_CC.con" as definition. -inline procedural "cic:/CoRN/complex/CComplex/cc_IR.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_IR.con" as definition. -inline procedural "cic:/CoRN/complex/CComplex/CC_conj.con". +inline procedural "cic:/CoRN/complex/CComplex/CC_conj.con" as definition. (* old def Definition CC_conj' : CC->CC := [z:CC_set] (CC_set_rec [_:CC_set]CC_set [Re0,Im0:IR] (Build_CC_set Re0 [--]Im0) z). *) -inline procedural "cic:/CoRN/complex/CComplex/AbsCC.con". +inline procedural "cic:/CoRN/complex/CComplex/AbsCC.con" as definition. -inline procedural "cic:/CoRN/complex/CComplex/TwoCC_ap_zero.con". +inline procedural "cic:/CoRN/complex/CComplex/TwoCC_ap_zero.con" as lemma. (* UNEXPORTED End Complex_Numbers @@ -198,7 +198,7 @@ Notation CCX := (cpoly_cring CC). (* end hide *) -inline procedural "cic:/CoRN/complex/CComplex/II.con". +inline procedural "cic:/CoRN/complex/CComplex/II.con" as definition. (* NOTATION Infix "[+I*]" := cc_set_CC (at level 48, no associativity). @@ -210,43 +210,43 @@ Infix "[+I*]" := cc_set_CC (at level 48, no associativity). Section I_properties *) -inline procedural "cic:/CoRN/complex/CComplex/I_square.con". +inline procedural "cic:/CoRN/complex/CComplex/I_square.con" as lemma. (* UNEXPORTED Hint Resolve I_square: algebra. *) -inline procedural "cic:/CoRN/complex/CComplex/I_square'.con". +inline procedural "cic:/CoRN/complex/CComplex/I_square'.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/I_recip_lft.con". +inline procedural "cic:/CoRN/complex/CComplex/I_recip_lft.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/I_recip_rht.con". +inline procedural "cic:/CoRN/complex/CComplex/I_recip_rht.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/mult_I.con". +inline procedural "cic:/CoRN/complex/CComplex/mult_I.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/I_wd.con". +inline procedural "cic:/CoRN/complex/CComplex/I_wd.con" as lemma. (*#* ** Properties of [Re] and [Im] *) -inline procedural "cic:/CoRN/complex/CComplex/calculate_norm.con". +inline procedural "cic:/CoRN/complex/CComplex/calculate_norm.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/calculate_Re.con". +inline procedural "cic:/CoRN/complex/CComplex/calculate_Re.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/calculate_Im.con". +inline procedural "cic:/CoRN/complex/CComplex/calculate_Im.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/Re_wd.con". +inline procedural "cic:/CoRN/complex/CComplex/Re_wd.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/Im_wd.con". +inline procedural "cic:/CoRN/complex/CComplex/Im_wd.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/Re_resp_plus.con". +inline procedural "cic:/CoRN/complex/CComplex/Re_resp_plus.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/Re_resp_inv.con". +inline procedural "cic:/CoRN/complex/CComplex/Re_resp_inv.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/Im_resp_plus.con". +inline procedural "cic:/CoRN/complex/CComplex/Im_resp_plus.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/Im_resp_inv.con". +inline procedural "cic:/CoRN/complex/CComplex/Im_resp_inv.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/cc_calculate_square.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_calculate_square.con" as lemma. (* UNEXPORTED End I_properties @@ -267,27 +267,27 @@ Hint Resolve I_wd Re_wd Im_wd: algebra_c. Section Conj_properties *) -inline procedural "cic:/CoRN/complex/CComplex/CC_conj_plus.con". +inline procedural "cic:/CoRN/complex/CComplex/CC_conj_plus.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/CC_conj_mult.con". +inline procedural "cic:/CoRN/complex/CComplex/CC_conj_mult.con" as lemma. (* UNEXPORTED Hint Resolve CC_conj_mult: algebra. *) -inline procedural "cic:/CoRN/complex/CComplex/CC_conj_strext.con". +inline procedural "cic:/CoRN/complex/CComplex/CC_conj_strext.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/CC_conj_conj.con". +inline procedural "cic:/CoRN/complex/CComplex/CC_conj_conj.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/CC_conj_zero.con". +inline procedural "cic:/CoRN/complex/CComplex/CC_conj_zero.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/CC_conj_one.con". +inline procedural "cic:/CoRN/complex/CComplex/CC_conj_one.con" as lemma. (* UNEXPORTED Hint Resolve CC_conj_one: algebra. *) -inline procedural "cic:/CoRN/complex/CComplex/CC_conj_nexp.con". +inline procedural "cic:/CoRN/complex/CComplex/CC_conj_nexp.con" as lemma. (* UNEXPORTED End Conj_properties @@ -304,51 +304,51 @@ Hint Resolve CC_conj_plus CC_conj_mult CC_conj_nexp CC_conj_conj Section cc_IR_properties *) -inline procedural "cic:/CoRN/complex/CComplex/Re_cc_IR.con". +inline procedural "cic:/CoRN/complex/CComplex/Re_cc_IR.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/Im_cc_IR.con". +inline procedural "cic:/CoRN/complex/CComplex/Im_cc_IR.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/cc_IR_wd.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_IR_wd.con" as lemma. (* UNEXPORTED Hint Resolve cc_IR_wd: algebra_c. *) -inline procedural "cic:/CoRN/complex/CComplex/cc_IR_resp_ap.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_IR_resp_ap.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/cc_IR_mult.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_IR_mult.con" as lemma. (* UNEXPORTED Hint Resolve cc_IR_mult: algebra. *) -inline procedural "cic:/CoRN/complex/CComplex/cc_IR_mult_lft.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_IR_mult_lft.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/cc_IR_mult_rht.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_IR_mult_rht.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/cc_IR_plus.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_IR_plus.con" as lemma. (* UNEXPORTED Hint Resolve cc_IR_plus: algebra. *) -inline procedural "cic:/CoRN/complex/CComplex/cc_IR_minus.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_IR_minus.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/cc_IR_zero.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_IR_zero.con" as lemma. (* UNEXPORTED Hint Resolve cc_IR_zero: algebra. *) -inline procedural "cic:/CoRN/complex/CComplex/cc_IR_one.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_IR_one.con" as lemma. (* UNEXPORTED Hint Resolve cc_IR_one: algebra. *) -inline procedural "cic:/CoRN/complex/CComplex/cc_IR_nring.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_IR_nring.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/cc_IR_nexp.con". +inline procedural "cic:/CoRN/complex/CComplex/cc_IR_nexp.con" as lemma. (* UNEXPORTED End cc_IR_properties @@ -375,11 +375,11 @@ Hint Resolve cc_IR_nring cc_IR_zero: algebra. include "tactics/Transparent_algebra.ma". -inline procedural "cic:/CoRN/complex/CComplex/char0_CC.con". +inline procedural "cic:/CoRN/complex/CComplex/char0_CC.con" as lemma. include "tactics/Opaque_algebra.ma". -inline procedural "cic:/CoRN/complex/CComplex/poly_apzero_CC.con". +inline procedural "cic:/CoRN/complex/CComplex/poly_apzero_CC.con" as lemma. -inline procedural "cic:/CoRN/complex/CComplex/poly_CC_extensional.con". +inline procedural "cic:/CoRN/complex/CComplex/poly_CC_extensional.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/complex/Complex_Exponential.mma b/helm/software/matita/contribs/CoRN-Procedural/complex/Complex_Exponential.mma index b5cabd4a0..f48ca187c 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/complex/Complex_Exponential.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/complex/Complex_Exponential.mma @@ -28,67 +28,67 @@ include "transc/Pi.ma". (*#* ** The Complex Exponential *) -inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC.con". +inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC.con" as definition. -inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_wd.con". +inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_wd.con" as lemma. (* begin hide *) -inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_equation_aid_1.con". +inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_equation_aid_1.con" as lemma. -inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_equation_aid_2.con". +inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_equation_aid_2.con" as lemma. -inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_equation_aid_3.con". +inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_equation_aid_3.con" as lemma. -inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_equation_aid_4.con". +inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_equation_aid_4.con" as lemma. (* end hide *) -inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_plus.con". +inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_plus.con" as lemma. (* UNEXPORTED Hint Resolve ExpCC_plus: algebra. *) -inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_Zero.con". +inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_Zero.con" as lemma. (* UNEXPORTED Hint Resolve ExpCC_Zero: algebra. *) -inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_inv_aid.con". +inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_inv_aid.con" as lemma. (* UNEXPORTED Hint Resolve ExpCC_inv_aid: algebra. *) -inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_ap_zero.con". +inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_inv.con". +inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_inv.con" as lemma. (* UNEXPORTED Hint Resolve ExpCC_inv: algebra. *) -inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_pow.con". +inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_pow.con" as lemma. (* UNEXPORTED Hint Resolve ExpCC_pow: algebra. *) -inline procedural "cic:/CoRN/complex/Complex_Exponential/AbsCC_ExpCC.con". +inline procedural "cic:/CoRN/complex/Complex_Exponential/AbsCC_ExpCC.con" as lemma. (* UNEXPORTED Hint Resolve AbsCC_ExpCC: algebra. *) -inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_Periodic.con". +inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_Periodic.con" as lemma. (* UNEXPORTED Hint Resolve ExpCC_Periodic: algebra. *) -inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_Exp.con". +inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_Exp.con" as lemma. (* UNEXPORTED Hint Resolve ExpCC_Exp: algebra. @@ -98,5 +98,5 @@ Hint Resolve ExpCC_Exp: algebra. Opaque Sin Cos Exp. *) -inline procedural "cic:/CoRN/complex/Complex_Exponential/Euler.con". +inline procedural "cic:/CoRN/complex/Complex_Exponential/Euler.con" as theorem. diff --git a/helm/software/matita/contribs/CoRN-Procedural/complex/NRootCC.mma b/helm/software/matita/contribs/CoRN-Procedural/complex/NRootCC.mma index 57f1f1a91..ddd6b7350 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/complex/NRootCC.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/complex/NRootCC.mma @@ -37,9 +37,9 @@ Properties of non-zero complex numbers Section CC_ap_zero *) -inline procedural "cic:/CoRN/complex/NRootCC/cc_ap_zero.con". +inline procedural "cic:/CoRN/complex/NRootCC/cc_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/complex/NRootCC/C_cc_ap_zero.con". +inline procedural "cic:/CoRN/complex/NRootCC/C_cc_ap_zero.con" as lemma. (* UNEXPORTED End CC_ap_zero @@ -51,7 +51,7 @@ End CC_ap_zero Section Imag_to_Real *) -inline procedural "cic:/CoRN/complex/NRootCC/imag_to_real.con". +inline procedural "cic:/CoRN/complex/NRootCC/imag_to_real.con" as lemma. (* UNEXPORTED End Imag_to_Real @@ -63,25 +63,25 @@ End Imag_to_Real Section NRootI *) -inline procedural "cic:/CoRN/complex/NRootCC/sqrt_Half.con". +inline procedural "cic:/CoRN/complex/NRootCC/sqrt_Half.con" as definition. -inline procedural "cic:/CoRN/complex/NRootCC/sqrt_I.con". +inline procedural "cic:/CoRN/complex/NRootCC/sqrt_I.con" as definition. -inline procedural "cic:/CoRN/complex/NRootCC/sqrt_I_nexp.con". +inline procedural "cic:/CoRN/complex/NRootCC/sqrt_I_nexp.con" as lemma. -inline procedural "cic:/CoRN/complex/NRootCC/nroot_I_nexp_aux.con". +inline procedural "cic:/CoRN/complex/NRootCC/nroot_I_nexp_aux.con" as lemma. -inline procedural "cic:/CoRN/complex/NRootCC/nroot_I.con". +inline procedural "cic:/CoRN/complex/NRootCC/nroot_I.con" as definition. -inline procedural "cic:/CoRN/complex/NRootCC/nroot_I_nexp.con". +inline procedural "cic:/CoRN/complex/NRootCC/nroot_I_nexp.con" as lemma. (* UNEXPORTED Hint Resolve nroot_I_nexp: algebra. *) -inline procedural "cic:/CoRN/complex/NRootCC/nroot_minus_I.con". +inline procedural "cic:/CoRN/complex/NRootCC/nroot_minus_I.con" as definition. -inline procedural "cic:/CoRN/complex/NRootCC/nroot_minus_I_nexp.con". +inline procedural "cic:/CoRN/complex/NRootCC/nroot_minus_I_nexp.con" as lemma. (* UNEXPORTED End NRootI @@ -115,69 +115,69 @@ alias id "b_" = "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/b_.var". (* begin hide *) -inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/c2.con" "NRootCC_1__NRootCC_1_ap_real__". +inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/c2.con" "NRootCC_1__NRootCC_1_ap_real__" as definition. (* end hide *) -inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_c2pos.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_c2pos.con" as lemma. (* begin hide *) -inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/c.con" "NRootCC_1__NRootCC_1_ap_real__". +inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/c.con" "NRootCC_1__NRootCC_1_ap_real__" as definition. -inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/a'2.con" "NRootCC_1__NRootCC_1_ap_real__". +inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/a'2.con" "NRootCC_1__NRootCC_1_ap_real__" as definition. (* end hide *) -inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_a'2pos.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_a'2pos.con" as lemma. (* begin hide *) -inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/a'.con" "NRootCC_1__NRootCC_1_ap_real__". +inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/a'.con" "NRootCC_1__NRootCC_1_ap_real__" as definition. -inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/b'2.con" "NRootCC_1__NRootCC_1_ap_real__". +inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/b'2.con" "NRootCC_1__NRootCC_1_ap_real__" as definition. (* end hide *) -inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_b'2pos.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_b'2pos.con" as lemma. (* begin hide *) -inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/b'.con" "NRootCC_1__NRootCC_1_ap_real__". +inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/b'.con" "NRootCC_1__NRootCC_1_ap_real__" as definition. (* end hide *) -inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_a3.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_a3.con" as lemma. -inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_a4.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_a4.con" as lemma. (* UNEXPORTED Hint Resolve nrCC1_a4: algebra. *) -inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_a5.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_a5.con" as lemma. -inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_a6.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_a6.con" as lemma. -inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_a6'.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_a6'.con" as lemma. (* UNEXPORTED Hint Resolve nrCC1_a5: algebra. *) -inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_a7_upper.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_a7_upper.con" as lemma. -inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_a7_lower.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_a7_lower.con" as lemma. (* UNEXPORTED Hint Resolve nrCC1_a3 nrCC1_a7_upper nrCC1_a7_lower: algebra. *) -inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_1_upper.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_1_upper.con" as lemma. -inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_1_lower.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_1_lower.con" as lemma. -inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_1_ap_real.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_1_ap_real.con" as lemma. (* UNEXPORTED End NRootCC_1_ap_real @@ -204,11 +204,11 @@ alias id "a_" = "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/a_.var". (* begin hide *) -inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/c'.con" "NRootCC_1__NRootCC_1_ap_imag__". +inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/c'.con" "NRootCC_1__NRootCC_1_ap_imag__" as definition. -inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/a'.con" "NRootCC_1__NRootCC_1_ap_imag__". +inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/a'.con" "NRootCC_1__NRootCC_1_ap_imag__" as definition. -inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/b'.con" "NRootCC_1__NRootCC_1_ap_imag__". +inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/b'.con" "NRootCC_1__NRootCC_1_ap_imag__" as definition. (* end hide *) @@ -216,7 +216,7 @@ inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/b'.con" Hint Resolve sqrt_I_nexp: algebra. *) -inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_1_ap_imag.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_1_ap_imag.con" as lemma. (* UNEXPORTED End NRootCC_1_ap_imag @@ -224,7 +224,7 @@ End NRootCC_1_ap_imag (*#* We now define the roots of arbitrary non zero complex numbers. *) -inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_1.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_1.con" as lemma. (* UNEXPORTED End NRootCC_1 @@ -247,9 +247,9 @@ alias id "z" = "cic:/CoRN/complex/NRootCC/NRootCC_2/z.var". alias id "c_" = "cic:/CoRN/complex/NRootCC/NRootCC_2/c_.var". -inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_2'.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_2'.con" as lemma. -inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_2.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_2.con" as lemma. (* UNEXPORTED End NRootCC_2 @@ -259,11 +259,11 @@ End NRootCC_2 Section NRootCC_3 *) -inline procedural "cic:/CoRN/complex/NRootCC/Im_poly.con". +inline procedural "cic:/CoRN/complex/NRootCC/Im_poly.con" as definition. -inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a1.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a1.con" as lemma. -inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a2.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a2.con" as lemma. (*#* %\begin{convention}% Let [a,b : IR], [b_ : (b [#] Zero)] and [n : nat]. @@ -278,25 +278,25 @@ alias id "b_" = "cic:/CoRN/complex/NRootCC/NRootCC_3/b_.var". alias id "n" = "cic:/CoRN/complex/NRootCC/NRootCC_3/n.var". -inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_poly''.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_poly''.con" as definition. -inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a3.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a3.con" as lemma. -inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a4.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a4.con" as lemma. -inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a5.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a5.con" as lemma. -inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a6.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a6.con" as lemma. -inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_poly'.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_poly'.con" as definition. (* UNEXPORTED Hint Resolve nrCC3_a3: algebra. *) -inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a7.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a7.con" as lemma. -inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a8.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a8.con" as lemma. (* UNEXPORTED Hint Resolve nth_coeff_p_mult_c_: algebra. @@ -306,15 +306,15 @@ Hint Resolve nth_coeff_p_mult_c_: algebra. Hint Resolve nrCC3_a6: algebra. *) -inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a9.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a9.con" as lemma. -inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_3_poly.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_3_poly.con" as definition. (* UNEXPORTED Hint Resolve nrCC3_a1 nrCC3_a7: algebra. *) -inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_3_.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_3_.con" as lemma. (* UNEXPORTED Hint Resolve nrootCC_3_: algebra. @@ -324,7 +324,7 @@ Hint Resolve nrootCC_3_: algebra. Hint Resolve calculate_Im: algebra. *) -inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_3.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_3.con" as lemma. (* UNEXPORTED Hint Resolve nrCC3_a2: algebra. @@ -334,7 +334,7 @@ Hint Resolve nrCC3_a2: algebra. Hint Resolve nrCC3_a9: algebra. *) -inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_3_degree.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_3_degree.con" as lemma. (* UNEXPORTED End NRootCC_3 @@ -355,11 +355,11 @@ alias id "n" = "cic:/CoRN/complex/NRootCC/NRootCC_3'/n.var". alias id "n_" = "cic:/CoRN/complex/NRootCC/NRootCC_3'/n_.var". -inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_3'_poly.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_3'_poly.con" as definition. -inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_3'.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_3'.con" as lemma. -inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_3'_degree.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_3'_degree.con" as lemma. (* UNEXPORTED End NRootCC_3' @@ -391,7 +391,7 @@ alias id "n_" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/n_.var". (* begin hide *) -inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/c.con" "NRootCC_4__NRootCC_4_ap_real__". +inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/c.con" "NRootCC_4__NRootCC_4_ap_real__" as definition. (* end hide *) @@ -403,7 +403,7 @@ Section NRootCC_4_solutions Hint Resolve nrootCC_3: algebra. *) -inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a1.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a1.con" as lemma. (*#* %\begin{convention}% Let [r2',c2 : IR] and [r2'_ : (r2' [#] Zero)]. @@ -420,7 +420,7 @@ alias id "r2'_" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC Hint Resolve nrootCC_3': algebra. *) -inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a1'.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a1'.con" as lemma. (* UNEXPORTED End NRootCC_4_solutions @@ -445,45 +445,45 @@ alias id "y2" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4 alias id "y2_property" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/y2_property.var". -inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a2.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a2.con" as lemma. -inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a3.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a3.con" as lemma. -inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a4.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a4.con" as lemma. -inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_y.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_y.con" as definition. -inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/y.con" "NRootCC_4__NRootCC_4_ap_real__NRootCC_4_equations__". +inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/y.con" "NRootCC_4__NRootCC_4_ap_real__NRootCC_4_equations__" as definition. -inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_x.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_x.con" as definition. -inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/x.con" "NRootCC_4__NRootCC_4_ap_real__NRootCC_4_equations__". +inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/x.con" "NRootCC_4__NRootCC_4_ap_real__NRootCC_4_equations__" as definition. -inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a5.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a5.con" as lemma. -inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a6.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a6.con" as lemma. -inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_z.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_z.con" as definition. -inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/z.con" "NRootCC_4__NRootCC_4_ap_real__NRootCC_4_equations__". +inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/z.con" "NRootCC_4__NRootCC_4_ap_real__NRootCC_4_equations__" as definition. -inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a7.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a7.con" as lemma. (* UNEXPORTED Hint Resolve nrCC4_a6: algebra. *) -inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a8.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a8.con" as lemma. -inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a9.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a9.con" as lemma. (* UNEXPORTED End NRootCC_4_equations *) -inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a10.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a10.con" as lemma. -inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_4_ap_real.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_4_ap_real.con" as lemma. (* UNEXPORTED End NRootCC_4_ap_real @@ -511,27 +511,27 @@ alias id "n_" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/n_.var". (* begin hide *) -inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/c'.con" "NRootCC_4__NRootCC_4_ap_imag__". +inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/c'.con" "NRootCC_4__NRootCC_4_ap_imag__" as definition. -inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/a'.con" "NRootCC_4__NRootCC_4_ap_imag__". +inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/a'.con" "NRootCC_4__NRootCC_4_ap_imag__" as definition. -inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/b'.con" "NRootCC_4__NRootCC_4_ap_imag__". +inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/b'.con" "NRootCC_4__NRootCC_4_ap_imag__" as definition. (* end hide *) -inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_4_ap_real'.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_4_ap_real'.con" as lemma. (* UNEXPORTED Hint Resolve nroot_minus_I_nexp: algebra. *) -inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_4_ap_imag.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_4_ap_imag.con" as lemma. (* UNEXPORTED End NRootCC_4_ap_imag *) -inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_4.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_4.con" as lemma. (* UNEXPORTED End NRootCC_4 @@ -543,9 +543,9 @@ End NRootCC_4 Section NRootCC_5 *) -inline procedural "cic:/CoRN/complex/NRootCC/nrCC_5a2.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC_5a2.con" as lemma. -inline procedural "cic:/CoRN/complex/NRootCC/nrCC_5a3.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC_5a3.con" as lemma. (* UNEXPORTED Hint Resolve nrCC_5a3: algebra. @@ -560,9 +560,9 @@ alias id "c" = "cic:/CoRN/complex/NRootCC/NRootCC_5/c.var". alias id "c_" = "cic:/CoRN/complex/NRootCC/NRootCC_5/c_.var". -inline procedural "cic:/CoRN/complex/NRootCC/nrCC_5a4.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrCC_5a4.con" as lemma. -inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_5.con". +inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_5.con" as lemma. (* UNEXPORTED End NRootCC_5 @@ -570,5 +570,5 @@ End NRootCC_5 (*#* Final definition *) -inline procedural "cic:/CoRN/complex/NRootCC/CnrootCC.con". +inline procedural "cic:/CoRN/complex/NRootCC/CnrootCC.con" as definition. diff --git a/helm/software/matita/contribs/CoRN-Procedural/devel/loeb/IDA/Ch6.mma b/helm/software/matita/contribs/CoRN-Procedural/devel/loeb/IDA/Ch6.mma index 39953fa3b..4e7f837d7 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/devel/loeb/IDA/Ch6.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/devel/loeb/IDA/Ch6.mma @@ -20,33 +20,33 @@ include "algebra/CSemiGroups.ma". (* Remark blz 65 1 *) -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/is_nullary_operation.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/is_nullary_operation.con" as definition. include "model/setoids/Zsetoid.ma". -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/is_nullary_operation_Z_0.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/is_nullary_operation_Z_0.con" as lemma. (* Remark blz 65 2 *) include "devel/loeb/per/csetfun.ma". -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/n_ary_operation.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/n_ary_operation.con" as definition. include "model/setoids/Nsetoid.ma". -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/plus1.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/plus1.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/to_plus1_strext.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/to_plus1_strext.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/plus2.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/plus2.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/to_plus2_strext.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/to_plus2_strext.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/plus3.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/plus3.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/on.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/on.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/ex_3_ary.con" "__". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/ex_3_ary.con" "__" as definition. (* blz 65 Example 1 *) @@ -101,13 +101,13 @@ End p66E2 include "model/semigroups/Zsemigroup.ma". -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/Zplus_is_CSemiGroup.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/Zplus_is_CSemiGroup.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/Zmult_is_CSemiGroup.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/Zmult_is_CSemiGroup.con" as lemma. (* blz 66 Example % 3 *) -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/FS_is_CSemiGroup.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/FS_is_CSemiGroup.con" as lemma. (* blz 66 Example % 4 *) @@ -117,39 +117,39 @@ Section p66E2b4 alias id "A" = "cic:/CoRN/devel/loeb/IDA/Ch6/p66E2b4/A.var". -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/Astar.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/Astar.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/empty_word.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/empty_word.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/app.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/app.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/eq_fm.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/eq_fm.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/ap_fm.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/ap_fm.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/ap_fm_irreflexive.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/ap_fm_irreflexive.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/ap_fm_symmetric.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/ap_fm_symmetric.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/ap_fm_cotransitive.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/ap_fm_cotransitive.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/ap_fm_tight.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/ap_fm_tight.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/free_csetoid_is_CSetoid.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/free_csetoid_is_CSetoid.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/free_csetoid_as_csetoid.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/free_csetoid_as_csetoid.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/app_strext.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/app_strext.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/app_as_csb_fun.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/app_as_csb_fun.con" as definition. include "algebra/CSemiGroups.ma". -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/eq_fm_reflexive.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/eq_fm_reflexive.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/Astar_is_CSemiGroup.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/Astar_is_CSemiGroup.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/Astar_as_CSemiGroup.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/Astar_as_CSemiGroup.con" as definition. (* UNEXPORTED End p66E2b4 @@ -157,13 +157,13 @@ End p66E2b4 (* Definition 5 *) -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/is_unit.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/is_unit.con" as definition. (* blz 67 Remark 1 *) include "model/monoids/Zmonoid.ma". -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/is_unit_Z_0.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/is_unit_Z_0.con" as lemma. (* blz 67 Remark 2 *) @@ -173,7 +173,7 @@ Section p67R2 alias id "X" = "cic:/CoRN/devel/loeb/IDA/Ch6/p67R2/X.var". -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/is_unit_FS_id.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/is_unit_FS_id.con" as lemma. (* UNEXPORTED End p67R2 @@ -181,11 +181,11 @@ End p67R2 (* blz 67 Remark 3 *) -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/is_unit_Astar_empty_word.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/is_unit_Astar_empty_word.con" as lemma. (* Lemma 6 *) -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/unique_unit.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/unique_unit.con" as lemma. (* blz 67 Example 1 *) @@ -211,71 +211,71 @@ Section p68E1b1 inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1.ind". -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_eq.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_eq.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_ap.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_ap.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_ap_irreflexive.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_ap_irreflexive.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_ap_symmetric.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_ap_symmetric.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_ap_cotransitive.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_ap_cotransitive.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_eq_dec.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_eq_dec.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/is_e1.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/is_e1.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/not_M1_eq_e1_u.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/not_M1_eq_e1_u.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_ap_tight.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_ap_tight.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_is_CSetoid.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_is_CSetoid.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_as_CSetoid.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_as_CSetoid.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_mult.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_mult.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_CS_mult.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_CS_mult.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_CS_mult_strext.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_CS_mult_strext.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_mult_as_bin_fun.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_mult_as_bin_fun.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_is_CSemiGroup.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_is_CSemiGroup.con" as lemma. include "algebra/CMonoids.ma". -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/e1_is_lft_unit.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/e1_is_lft_unit.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/e1_is_rht_unit.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/e1_is_rht_unit.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_as_CSemiGroup.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_as_CSemiGroup.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_is_CMonoid.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_is_CMonoid.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_as_CMonoid.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_as_CMonoid.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M2_mult.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M2_mult.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M2_CS_mult.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M2_CS_mult.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M2_CS_mult_strext.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M2_CS_mult_strext.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M2_mult_as_bin_fun.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M2_mult_as_bin_fun.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M2_is_CSemiGroup.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M2_is_CSemiGroup.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M2_as_CSemiGroup.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M2_as_CSemiGroup.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/e1_is_lft_unit_M2.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/e1_is_lft_unit_M2.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/e1_is_rht_unit_M2.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/e1_is_rht_unit_M2.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M2_is_CMonoid.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M2_is_CMonoid.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M2_as_CMonoid.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M2_as_CMonoid.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/two_element_CMonoids.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/two_element_CMonoids.con" as lemma. (* UNEXPORTED End p68E1b1 @@ -303,15 +303,15 @@ alias id "M1" = "cic:/CoRN/devel/loeb/IDA/Ch6/D9S/M1.var". alias id "M2" = "cic:/CoRN/devel/loeb/IDA/Ch6/D9S/M2.var". -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/dprod.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/dprod.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/dprod_strext.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/dprod_strext.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/dprod_as_csb_fun.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/dprod_as_csb_fun.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/direct_product_is_CSemiGroup.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/direct_product_is_CSemiGroup.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/direct_product_as_CSemiGroup.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/direct_product_as_CSemiGroup.con" as definition. (* UNEXPORTED End D9S @@ -325,13 +325,13 @@ alias id "M1" = "cic:/CoRN/devel/loeb/IDA/Ch6/D9M/M1.var". alias id "M2" = "cic:/CoRN/devel/loeb/IDA/Ch6/D9M/M2.var". -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/e1e2_is_rht_unit.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/e1e2_is_rht_unit.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/e1e2_is_lft_unit.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/e1e2_is_lft_unit.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/direct_product_is_CMonoid.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/direct_product_is_CMonoid.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/direct_product_as_CMonoid.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/direct_product_as_CMonoid.con" as definition. (* UNEXPORTED End D9M @@ -343,13 +343,13 @@ End D9M Section p69E1 *) -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/p69E1/PM1M2.con" "p69E1__". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/p69E1/PM1M2.con" "p69E1__" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/p69E1/uu.con" "p69E1__". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/p69E1/uu.con" "p69E1__" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/p69E1/e1u.con" "p69E1__". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/p69E1/e1u.con" "p69E1__" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/ex_69.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/ex_69.con" as lemma. (* UNEXPORTED End p69E1 @@ -371,11 +371,11 @@ alias id "Cunit" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th11/Cunit.var". alias id "op_pres_C" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th11/op_pres_C.var". -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/K.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/K.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/op_pres_K.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/op_pres_K.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/K_is_Monoid.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/K_is_Monoid.con" as definition. (* UNEXPORTED End Th11 @@ -389,13 +389,13 @@ Section Th12 alias id "A" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th12/A.var". -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/nil_is_rht_unit.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/nil_is_rht_unit.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/nil_is_lft_unit.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/nil_is_lft_unit.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/free_monoid_is_CMonoid.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/free_monoid_is_CMonoid.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/free_monoid_as_CMonoid.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/free_monoid_as_CMonoid.con" as definition. (* UNEXPORTED End Th12 @@ -409,21 +409,21 @@ Section p70text include "devel/loeb/per/lst2fun.ma". -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/p70text/A.con" "p70text__". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/p70text/A.con" "p70text__" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/ZerolessOne.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/ZerolessOne.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/to_word.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/to_word.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/to_word'.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/to_word'.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/to_word'_strext.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/to_word'_strext.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/to_word_as_CSetoid_fun.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/to_word_as_CSetoid_fun.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/to_word_bijective.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/to_word_bijective.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/pres_plus_to_word.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/pres_plus_to_word.con" as lemma. (* UNEXPORTED End p70text @@ -439,9 +439,9 @@ alias id "M1" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th13/M1.var". alias id "M2" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th13/M2.var". -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/morphism.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/morphism.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/isomorphism.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/isomorphism.con" as definition. (* UNEXPORTED End Th13 @@ -457,19 +457,19 @@ alias id "M" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71E1/M.var". alias id "c" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71E1/c.var". -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/power_CMonoid.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/power_CMonoid.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/power_CMonoid_CSetoid.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/power_CMonoid_CSetoid.con" as definition. alias id "is_generated_by" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71E1/is_generated_by.var". -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/p71E1/f.con" "p71E1__". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/p71E1/f.con" "p71E1__" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/f_strext.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/f_strext.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/f_as_CSetoid_fun.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/f_as_CSetoid_fun.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/surjective_f.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/surjective_f.con" as lemma. (* UNEXPORTED End p71E1 @@ -479,9 +479,9 @@ End p71E1 Section p71E1' *) -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_is_generated_by_u.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_is_generated_by_u.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/not_injective_f.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/not_injective_f.con" as lemma. (* UNEXPORTED End p71E1' @@ -495,13 +495,13 @@ Section p71E2 alias id "A" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2/A.var". -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2/L.con" "p71E2__". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2/L.con" "p71E2__" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/L_strext.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/L_strext.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/L_as_CSetoid_fun.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/L_as_CSetoid_fun.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/L_is_morphism.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/L_is_morphism.con" as lemma. (* UNEXPORTED End p71E2 @@ -517,7 +517,7 @@ alias id "S1" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71R1/S1.var". alias id "S2" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71R1/S2.var". -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/morphism_of_CSemiGroups.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/morphism_of_CSemiGroups.con" as definition. (* UNEXPORTED End p71R1 @@ -529,7 +529,7 @@ Section p71R2 alias id "M" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71R2/M.var". -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/automorphism.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/automorphism.con" as definition. (* UNEXPORTED End p71R2 @@ -549,9 +549,9 @@ alias id "f" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th14/f.var". alias id "isof" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th14/isof.var". -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/iso_imp_bij.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/iso_imp_bij.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/iso_inv.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/iso_inv.con" as lemma. (* UNEXPORTED End Th14 @@ -563,9 +563,9 @@ End Th14 Section p71E2b1 *) -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/isomorphic.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/isomorphic.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/not_isomorphic_M1_M2.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/not_isomorphic_M1_M2.con" as lemma. (* UNEXPORTED End p71E2b1 @@ -579,13 +579,13 @@ alias id "M1" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2b2/M1.var". alias id "M2" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2b2/M2.var". -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2b2/f.con" "p71E2b2__". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2b2/f.con" "p71E2b2__" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/f_strext'.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/f_strext'.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/f_as_CSetoid_fun'.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/f_as_CSetoid_fun'.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/isomorphic_PM1M2_PM2M1.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/isomorphic_PM1M2_PM2M1.con" as lemma. (* UNEXPORTED End p71E2b2 @@ -597,27 +597,27 @@ Section Th15 alias id "M" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th15/M.var". -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/cm_Sum.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/cm_Sum.con" as definition. alias id "D" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th15/D.var". -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/member.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/member.con" as definition. (* UNEXPORTED Implicit Arguments member [A]. *) -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/Dbrack.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/Dbrack.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/Dbrack_unit.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/Dbrack_unit.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/member_app.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/member_app.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/cm_Sum_app.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/cm_Sum_app.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/op_pres_Dbrack.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/op_pres_Dbrack.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/Dbrack_as_CMonoid.con". +inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/Dbrack_as_CMonoid.con" as definition. (* UNEXPORTED End Th15 diff --git a/helm/software/matita/contribs/CoRN-Procedural/devel/loeb/per/csetfun.mma b/helm/software/matita/contribs/CoRN-Procedural/devel/loeb/per/csetfun.mma index d5827f8f4..16e84da38 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/devel/loeb/per/csetfun.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/devel/loeb/per/csetfun.mma @@ -20,53 +20,53 @@ include "algebra/CSetoids.ma". include "algebra/CSetoidFun.ma". -inline procedural "cic:/CoRN/devel/loeb/per/csetfun/ap_fun.con". +inline procedural "cic:/CoRN/devel/loeb/per/csetfun/ap_fun.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/per/csetfun/eq_fun.con". +inline procedural "cic:/CoRN/devel/loeb/per/csetfun/eq_fun.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/per/csetfun/irrefl_apfun.con". +inline procedural "cic:/CoRN/devel/loeb/per/csetfun/irrefl_apfun.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/per/csetfun/cotrans_apfun.con". +inline procedural "cic:/CoRN/devel/loeb/per/csetfun/cotrans_apfun.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/per/csetfun/ta_apfun.con". +inline procedural "cic:/CoRN/devel/loeb/per/csetfun/ta_apfun.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/per/csetfun/sym_apfun.con". +inline procedural "cic:/CoRN/devel/loeb/per/csetfun/sym_apfun.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/per/csetfun/FS_is_CSetoid.con". +inline procedural "cic:/CoRN/devel/loeb/per/csetfun/FS_is_CSetoid.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/per/csetfun/FS_as_CSetoid.con". +inline procedural "cic:/CoRN/devel/loeb/per/csetfun/FS_as_CSetoid.con" as definition. (* UNEXPORTED Print associative. *) -inline procedural "cic:/CoRN/devel/loeb/per/csetfun/comp.con". +inline procedural "cic:/CoRN/devel/loeb/per/csetfun/comp.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/per/csetfun/comp_as_bin_op.con". +inline procedural "cic:/CoRN/devel/loeb/per/csetfun/comp_as_bin_op.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/per/csetfun/assoc_comp.con". +inline procedural "cic:/CoRN/devel/loeb/per/csetfun/assoc_comp.con" as lemma. include "algebra/CSemiGroups.ma". -inline procedural "cic:/CoRN/devel/loeb/per/csetfun/FS_as_CSemiGroup.con". +inline procedural "cic:/CoRN/devel/loeb/per/csetfun/FS_as_CSemiGroup.con" as definition. include "algebra/CMonoids.ma". -inline procedural "cic:/CoRN/devel/loeb/per/csetfun/FS_id.con". +inline procedural "cic:/CoRN/devel/loeb/per/csetfun/FS_id.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/per/csetfun/id_is_rht_unit.con". +inline procedural "cic:/CoRN/devel/loeb/per/csetfun/id_is_rht_unit.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/per/csetfun/id_is_lft_unit.con". +inline procedural "cic:/CoRN/devel/loeb/per/csetfun/id_is_lft_unit.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/per/csetfun/FS_is_CMonoid.con". +inline procedural "cic:/CoRN/devel/loeb/per/csetfun/FS_is_CMonoid.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/per/csetfun/FS_as_CMonoid.con". +inline procedural "cic:/CoRN/devel/loeb/per/csetfun/FS_as_CMonoid.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/per/csetfun/PS_as_CMonoid.con". +inline procedural "cic:/CoRN/devel/loeb/per/csetfun/PS_as_CMonoid.con" as definition. include "algebra/CGroups.ma". -inline procedural "cic:/CoRN/devel/loeb/per/csetfun/Inv_is_bij.con". +inline procedural "cic:/CoRN/devel/loeb/per/csetfun/Inv_is_bij.con" as lemma. (* Lemma Inv_is_bij : forall (A B : CSetoid) (f : CSetoid_fun A B) (H : bijective f), @@ -120,13 +120,13 @@ set (H6 := ap_imp_neq B (f0 x) (f0 b) H4) in *. intuition. Qed.*) -inline procedural "cic:/CoRN/devel/loeb/per/csetfun/PS_Inv.con". +inline procedural "cic:/CoRN/devel/loeb/per/csetfun/PS_Inv.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/per/csetfun/Inv_as_un_op.con". +inline procedural "cic:/CoRN/devel/loeb/per/csetfun/Inv_as_un_op.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/per/csetfun/PS_is_CGroup.con". +inline procedural "cic:/CoRN/devel/loeb/per/csetfun/PS_is_CGroup.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/per/csetfun/PS_as_CGroup.con". +inline procedural "cic:/CoRN/devel/loeb/per/csetfun/PS_as_CGroup.con" as definition. (* In het algemeen niet Abels! *) diff --git a/helm/software/matita/contribs/CoRN-Procedural/devel/loeb/per/lst2fun.mma b/helm/software/matita/contribs/CoRN-Procedural/devel/loeb/per/lst2fun.mma index a859e2c18..087e44f82 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/devel/loeb/per/lst2fun.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/devel/loeb/per/lst2fun.mma @@ -16,7 +16,7 @@ include "CoRN.ma". -inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/F'.con". +inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/F'.con" as definition. inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/F.ind". @@ -24,7 +24,7 @@ inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/F.ind". cic:/matita/CoRN-Procedural/devel/loeb/per/lst2fun/F_crr.con *) -inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/to_nat.con". +inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/to_nat.con" as definition. (* UNEXPORTED Implicit Arguments to_nat [n]. @@ -36,19 +36,19 @@ cic:/matita/CoRN-Procedural/devel/loeb/per/lst2fun/to_nat.con include "algebra/CSetoids.ma". -inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/Feq.con". +inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/Feq.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/Fap.con". +inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/Fap.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/Fap_irreflexive.con". +inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/Fap_irreflexive.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/Fap_symmetric.con". +inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/Fap_symmetric.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/Fap_cotransitive.con". +inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/Fap_cotransitive.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/Fap_tight.con". +inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/Fap_tight.con" as lemma. -inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/less.con". +inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/less.con" as definition. -inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/CSetoid_of_less.con". +inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/CSetoid_of_less.con" as definition. diff --git a/helm/software/matita/contribs/CoRN-Procedural/fta/CC_Props.mma b/helm/software/matita/contribs/CoRN-Procedural/fta/CC_Props.mma index a9ca19cfe..9c273c863 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/fta/CC_Props.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/fta/CC_Props.mma @@ -27,15 +27,15 @@ include "complex/AbsCC.ma". Hint Resolve AbsIR_sqrt_sqr: algebra. *) -inline procedural "cic:/CoRN/fta/CC_Props/absCC_absIR_re.con". +inline procedural "cic:/CoRN/fta/CC_Props/absCC_absIR_re.con" as lemma. -inline procedural "cic:/CoRN/fta/CC_Props/absCC_absIR_im.con". +inline procedural "cic:/CoRN/fta/CC_Props/absCC_absIR_im.con" as lemma. -inline procedural "cic:/CoRN/fta/CC_Props/seq_re.con". +inline procedural "cic:/CoRN/fta/CC_Props/seq_re.con" as definition. -inline procedural "cic:/CoRN/fta/CC_Props/seq_im.con". +inline procedural "cic:/CoRN/fta/CC_Props/seq_im.con" as definition. -inline procedural "cic:/CoRN/fta/CC_Props/CC_Cauchy_prop.con". +inline procedural "cic:/CoRN/fta/CC_Props/CC_Cauchy_prop.con" as definition. inline procedural "cic:/CoRN/fta/CC_Props/CC_CauchySeq.ind". @@ -43,27 +43,27 @@ inline procedural "cic:/CoRN/fta/CC_Props/CC_CauchySeq.ind". cic:/matita/CoRN-Procedural/fta/CC_Props/CC_seq.con *) -inline procedural "cic:/CoRN/fta/CC_Props/re_is_Cauchy.con". +inline procedural "cic:/CoRN/fta/CC_Props/re_is_Cauchy.con" as lemma. -inline procedural "cic:/CoRN/fta/CC_Props/im_is_Cauchy.con". +inline procedural "cic:/CoRN/fta/CC_Props/im_is_Cauchy.con" as lemma. -inline procedural "cic:/CoRN/fta/CC_Props/CC_Cauchy2re.con". +inline procedural "cic:/CoRN/fta/CC_Props/CC_Cauchy2re.con" as definition. -inline procedural "cic:/CoRN/fta/CC_Props/CC_Cauchy2im.con". +inline procedural "cic:/CoRN/fta/CC_Props/CC_Cauchy2im.con" as definition. -inline procedural "cic:/CoRN/fta/CC_Props/LimCC.con". +inline procedural "cic:/CoRN/fta/CC_Props/LimCC.con" as definition. -inline procedural "cic:/CoRN/fta/CC_Props/CC_SeqLimit.con". +inline procedural "cic:/CoRN/fta/CC_Props/CC_SeqLimit.con" as definition. -inline procedural "cic:/CoRN/fta/CC_Props/AbsSmall_sqr.con". +inline procedural "cic:/CoRN/fta/CC_Props/AbsSmall_sqr.con" as lemma. -inline procedural "cic:/CoRN/fta/CC_Props/AbsSmall_AbsCC.con". +inline procedural "cic:/CoRN/fta/CC_Props/AbsSmall_AbsCC.con" as lemma. -inline procedural "cic:/CoRN/fta/CC_Props/LimCC_is_lim.con". +inline procedural "cic:/CoRN/fta/CC_Props/LimCC_is_lim.con" as lemma. -inline procedural "cic:/CoRN/fta/CC_Props/CC_SeqLimit_uniq.con". +inline procedural "cic:/CoRN/fta/CC_Props/CC_SeqLimit_uniq.con" as lemma. -inline procedural "cic:/CoRN/fta/CC_Props/CC_SeqLimit_unq.con". +inline procedural "cic:/CoRN/fta/CC_Props/CC_SeqLimit_unq.con" as lemma. (*#* ** Continuity for [CC] *) @@ -81,21 +81,21 @@ alias id "f" = "cic:/CoRN/fta/CC_Props/Continuity_for_CC/f.var". (* (CSetoid_un_op CC). *) -inline procedural "cic:/CoRN/fta/CC_Props/CCfunLim.con". +inline procedural "cic:/CoRN/fta/CC_Props/CCfunLim.con" as definition. -inline procedural "cic:/CoRN/fta/CC_Props/CCcontinAt.con". +inline procedural "cic:/CoRN/fta/CC_Props/CCcontinAt.con" as definition. -inline procedural "cic:/CoRN/fta/CC_Props/CCcontin.con". +inline procedural "cic:/CoRN/fta/CC_Props/CCcontin.con" as definition. -inline procedural "cic:/CoRN/fta/CC_Props/CCfunLim_SeqLimit.con". +inline procedural "cic:/CoRN/fta/CC_Props/CCfunLim_SeqLimit.con" as lemma. -inline procedural "cic:/CoRN/fta/CC_Props/f_seq.con". +inline procedural "cic:/CoRN/fta/CC_Props/f_seq.con" as definition. -inline procedural "cic:/CoRN/fta/CC_Props/poly_pres_lim.con". +inline procedural "cic:/CoRN/fta/CC_Props/poly_pres_lim.con" as lemma. (* UNEXPORTED End Continuity_for_CC *) -inline procedural "cic:/CoRN/fta/CC_Props/seq_yields_zero.con". +inline procedural "cic:/CoRN/fta/CC_Props/seq_yields_zero.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/fta/CPoly_Contin1.mma b/helm/software/matita/contribs/CoRN-Procedural/fta/CPoly_Contin1.mma index ace7f60a2..e389d23de 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/fta/CPoly_Contin1.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/fta/CPoly_Contin1.mma @@ -27,11 +27,11 @@ include "fta/CC_Props.ma". Section Mult_CC_Continuous *) -inline procedural "cic:/CoRN/fta/CPoly_Contin1/mult_absCC.con". +inline procedural "cic:/CoRN/fta/CPoly_Contin1/mult_absCC.con" as lemma. -inline procedural "cic:/CoRN/fta/CPoly_Contin1/estimate_absCC.con". +inline procedural "cic:/CoRN/fta/CPoly_Contin1/estimate_absCC.con" as lemma. -inline procedural "cic:/CoRN/fta/CPoly_Contin1/mult_CC_contin.con". +inline procedural "cic:/CoRN/fta/CPoly_Contin1/mult_CC_contin.con" as lemma. (* UNEXPORTED End Mult_CC_Continuous @@ -48,9 +48,9 @@ Section CPoly_CC_Continuous alias id "g" = "cic:/CoRN/fta/CPoly_Contin1/CPoly_CC_Continuous/g.var". -inline procedural "cic:/CoRN/fta/CPoly_Contin1/cpoly_CC_contin.con". +inline procedural "cic:/CoRN/fta/CPoly_Contin1/cpoly_CC_contin.con" as lemma. -inline procedural "cic:/CoRN/fta/CPoly_Contin1/contin_polyCC.con". +inline procedural "cic:/CoRN/fta/CPoly_Contin1/contin_polyCC.con" as lemma. (* UNEXPORTED End CPoly_CC_Continuous diff --git a/helm/software/matita/contribs/CoRN-Procedural/fta/CPoly_Rev.mma b/helm/software/matita/contribs/CoRN-Procedural/fta/CPoly_Rev.mma index 695052340..5e31ee33e 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/fta/CPoly_Rev.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/fta/CPoly_Rev.mma @@ -37,43 +37,43 @@ alias id "R" = "cic:/CoRN/fta/CPoly_Rev/Monomials/R.var". (* begin hide *) -inline procedural "cic:/CoRN/fta/CPoly_Rev/Monomials/RX.con" "Monomials__". +inline procedural "cic:/CoRN/fta/CPoly_Rev/Monomials/RX.con" "Monomials__" as definition. (* end hide *) -inline procedural "cic:/CoRN/fta/CPoly_Rev/monom.con". +inline procedural "cic:/CoRN/fta/CPoly_Rev/monom.con" as definition. -inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_coeff.con". +inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_coeff.con" as lemma. -inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_coeff'.con". +inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_coeff'.con" as lemma. (* UNEXPORTED Hint Resolve monom_coeff monom_coeff': algebra. *) -inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_degree.con". +inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_degree.con" as lemma. -inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_S.con". +inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_S.con" as lemma. (* UNEXPORTED Hint Resolve monom_S: algebra. *) -inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_wd_lft.con". +inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_wd_lft.con" as lemma. (* UNEXPORTED Hint Resolve monom_wd_lft: algebra_c. *) -inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_mult'.con". +inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_mult'.con" as lemma. (* UNEXPORTED Hint Resolve monom_mult': algebra. *) -inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_mult.con". +inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_mult.con" as lemma. -inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_sum.con". +inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_sum.con" as lemma. (* UNEXPORTED End Monomials @@ -95,69 +95,69 @@ alias id "R" = "cic:/CoRN/fta/CPoly_Rev/Poly_Reverse/R.var". (* begin hide *) -inline procedural "cic:/CoRN/fta/CPoly_Rev/Poly_Reverse/RX.con" "Poly_Reverse__". +inline procedural "cic:/CoRN/fta/CPoly_Rev/Poly_Reverse/RX.con" "Poly_Reverse__" as definition. (* end hide *) -inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev.con". +inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev.con" as definition. -inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_coeff.con". +inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_coeff.con" as lemma. -inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_coeff'.con". +inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_coeff'.con" as lemma. (* UNEXPORTED Hint Resolve Rev_coeff Rev_coeff': algebra. *) -inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_wd.con". +inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_wd.con" as lemma. (* UNEXPORTED Hint Resolve Rev_wd: algebra_c. *) -inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_rev.con". +inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_rev.con" as lemma. (* UNEXPORTED Hint Resolve Rev_rev: algebra. *) -inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_degree_le.con". +inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_degree_le.con" as lemma. -inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_degree.con". +inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_degree.con" as lemma. -inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_monom.con". +inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_monom.con" as lemma. (* UNEXPORTED Hint Resolve Rev_monom: algebra. *) -inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_zero.con". +inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_zero.con" as lemma. (* UNEXPORTED Hint Resolve Rev_zero: algebra. *) -inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_plus.con". +inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_plus.con" as lemma. (* UNEXPORTED Hint Resolve Rev_plus: algebra. *) -inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_minus.con". +inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_minus.con" as lemma. (* UNEXPORTED Hint Resolve Rev_minus: algebra. *) -inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_sum0.con". +inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_sum0.con" as lemma. (* UNEXPORTED Hint Resolve Rev_sum0: algebra. *) -inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_sum.con". +inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_sum.con" as lemma. -inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_mult.con". +inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_mult.con" as lemma. (* UNEXPORTED End Poly_Reverse diff --git a/helm/software/matita/contribs/CoRN-Procedural/fta/CPoly_Shift.mma b/helm/software/matita/contribs/CoRN-Procedural/fta/CPoly_Shift.mma index 00ce892b4..652319b4c 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/fta/CPoly_Shift.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/fta/CPoly_Shift.mma @@ -30,23 +30,23 @@ and we only need it for [CC]. Section Poly_Shifted *) -inline procedural "cic:/CoRN/fta/CPoly_Shift/Shift.con". +inline procedural "cic:/CoRN/fta/CPoly_Shift/Shift.con" as definition. -inline procedural "cic:/CoRN/fta/CPoly_Shift/Shift_apply.con". +inline procedural "cic:/CoRN/fta/CPoly_Shift/Shift_apply.con" as lemma. (* UNEXPORTED Hint Resolve Shift_apply: algebra. *) -inline procedural "cic:/CoRN/fta/CPoly_Shift/Shift_wdr.con". +inline procedural "cic:/CoRN/fta/CPoly_Shift/Shift_wdr.con" as lemma. -inline procedural "cic:/CoRN/fta/CPoly_Shift/Shift_shift.con". +inline procedural "cic:/CoRN/fta/CPoly_Shift/Shift_shift.con" as lemma. -inline procedural "cic:/CoRN/fta/CPoly_Shift/Shift_mult.con". +inline procedural "cic:/CoRN/fta/CPoly_Shift/Shift_mult.con" as lemma. -inline procedural "cic:/CoRN/fta/CPoly_Shift/Shift_degree_le.con". +inline procedural "cic:/CoRN/fta/CPoly_Shift/Shift_degree_le.con" as lemma. -inline procedural "cic:/CoRN/fta/CPoly_Shift/Shift_monic.con". +inline procedural "cic:/CoRN/fta/CPoly_Shift/Shift_monic.con" as lemma. (* UNEXPORTED End Poly_Shifted diff --git a/helm/software/matita/contribs/CoRN-Procedural/fta/FTA.mma b/helm/software/matita/contribs/CoRN-Procedural/fta/FTA.mma index acdca7ba0..d8c24667c 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/fta/FTA.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/fta/FTA.mma @@ -38,7 +38,7 @@ alias id "n" = "cic:/CoRN/fta/FTA/FTA_reg'/n.var". alias id "f_degree" = "cic:/CoRN/fta/FTA/FTA_reg'/f_degree.var". -inline procedural "cic:/CoRN/fta/FTA/FTA_reg'.con". +inline procedural "cic:/CoRN/fta/FTA/FTA_reg'.con" as lemma. (* UNEXPORTED End FTA_reg' @@ -65,15 +65,15 @@ alias id "c" = "cic:/CoRN/fta/FTA/FTA_1/c.var". alias id "f_c" = "cic:/CoRN/fta/FTA/FTA_1/f_c.var". -inline procedural "cic:/CoRN/fta/FTA/FTA_1a.con". +inline procedural "cic:/CoRN/fta/FTA/FTA_1a.con" as lemma. -inline procedural "cic:/CoRN/fta/FTA/FTA_1/g.con" "FTA_1__". +inline procedural "cic:/CoRN/fta/FTA/FTA_1/g.con" "FTA_1__" as definition. -inline procedural "cic:/CoRN/fta/FTA/FTA_1b.con". +inline procedural "cic:/CoRN/fta/FTA/FTA_1b.con" as lemma. -inline procedural "cic:/CoRN/fta/FTA/FTA_1.con". +inline procedural "cic:/CoRN/fta/FTA/FTA_1.con" as lemma. -inline procedural "cic:/CoRN/fta/FTA/FTA_1'.con". +inline procedural "cic:/CoRN/fta/FTA/FTA_1'.con" as lemma. (* UNEXPORTED End FTA_1 @@ -83,11 +83,11 @@ End FTA_1 Section Fund_Thm_Alg *) -inline procedural "cic:/CoRN/fta/FTA/FTA'.con". +inline procedural "cic:/CoRN/fta/FTA/FTA'.con" as lemma. -inline procedural "cic:/CoRN/fta/FTA/FTA.con". +inline procedural "cic:/CoRN/fta/FTA/FTA.con" as lemma. -inline procedural "cic:/CoRN/fta/FTA/FTA_a_la_Henk.con". +inline procedural "cic:/CoRN/fta/FTA/FTA_a_la_Henk.con" as lemma. (* UNEXPORTED End Fund_Thm_Alg diff --git a/helm/software/matita/contribs/CoRN-Procedural/fta/FTAreg.mma b/helm/software/matita/contribs/CoRN-Procedural/fta/FTAreg.mma index 58c776f63..d96c06c8c 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/fta/FTAreg.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/fta/FTAreg.mma @@ -81,21 +81,21 @@ inline procedural "cic:/CoRN/fta/FTAreg/Knes_tupp.ind". cic:/matita/CoRN-Procedural/fta/FTAreg/Kntup.con *) -inline procedural "cic:/CoRN/fta/FTAreg/Knes_fun.con". +inline procedural "cic:/CoRN/fta/FTAreg/Knes_fun.con" as definition. -inline procedural "cic:/CoRN/fta/FTAreg/Knes_fun_it.con". +inline procedural "cic:/CoRN/fta/FTAreg/Knes_fun_it.con" as definition. -inline procedural "cic:/CoRN/fta/FTAreg/sK.con". +inline procedural "cic:/CoRN/fta/FTAreg/sK.con" as definition. -inline procedural "cic:/CoRN/fta/FTAreg/sK_c.con". +inline procedural "cic:/CoRN/fta/FTAreg/sK_c.con" as lemma. -inline procedural "cic:/CoRN/fta/FTAreg/sK_c0.con". +inline procedural "cic:/CoRN/fta/FTAreg/sK_c0.con" as lemma. -inline procedural "cic:/CoRN/fta/FTAreg/sK_prop1.con". +inline procedural "cic:/CoRN/fta/FTAreg/sK_prop1.con" as lemma. -inline procedural "cic:/CoRN/fta/FTAreg/sK_it.con". +inline procedural "cic:/CoRN/fta/FTAreg/sK_it.con" as lemma. -inline procedural "cic:/CoRN/fta/FTAreg/sK_prop2.con". +inline procedural "cic:/CoRN/fta/FTAreg/sK_prop2.con" as lemma. (* UNEXPORTED End Kneser_Sequence @@ -108,7 +108,7 @@ Section Seq_Exists_Main (*#* **Main results *) -inline procedural "cic:/CoRN/fta/FTAreg/seq_exists.con". +inline procedural "cic:/CoRN/fta/FTAreg/seq_exists.con" as lemma. (* UNEXPORTED End Seq_Exists_Main @@ -138,7 +138,7 @@ alias id "zltc" = "cic:/CoRN/fta/FTAreg/N_Exists/zltc.var". (* begin hide *) -inline procedural "cic:/CoRN/fta/FTAreg/N_Exists/q_.con" "N_Exists__". +inline procedural "cic:/CoRN/fta/FTAreg/N_Exists/q_.con" "N_Exists__" as definition. (* end hide *) @@ -146,7 +146,7 @@ alias id "e" = "cic:/CoRN/fta/FTAreg/N_Exists/e.var". alias id "zlte" = "cic:/CoRN/fta/FTAreg/N_Exists/zlte.var". -inline procedural "cic:/CoRN/fta/FTAreg/N_exists.con". +inline procedural "cic:/CoRN/fta/FTAreg/N_exists.con" as lemma. (* UNEXPORTED End N_Exists @@ -183,39 +183,39 @@ alias id "zltc" = "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/zltc.var". (* begin hide *) -inline procedural "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/q_.con" "Seq_is_CC_CAuchy__". +inline procedural "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/q_.con" "Seq_is_CC_CAuchy__" as definition. -inline procedural "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/nrtq.con" "Seq_is_CC_CAuchy__". +inline procedural "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/nrtq.con" "Seq_is_CC_CAuchy__" as definition. -inline procedural "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/nrtc.con" "Seq_is_CC_CAuchy__". +inline procedural "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/nrtc.con" "Seq_is_CC_CAuchy__" as definition. -inline procedural "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/nrtqlt1.con" "Seq_is_CC_CAuchy__". +inline procedural "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/nrtqlt1.con" "Seq_is_CC_CAuchy__" as definition. -inline procedural "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/nrtq_.con" "Seq_is_CC_CAuchy__". +inline procedural "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/nrtq_.con" "Seq_is_CC_CAuchy__" as definition. (* end hide *) -inline procedural "cic:/CoRN/fta/FTAreg/zlt_nrtq.con". +inline procedural "cic:/CoRN/fta/FTAreg/zlt_nrtq.con" as lemma. -inline procedural "cic:/CoRN/fta/FTAreg/zlt_nrtc.con". +inline procedural "cic:/CoRN/fta/FTAreg/zlt_nrtc.con" as lemma. -inline procedural "cic:/CoRN/fta/FTAreg/nrt_pow.con". +inline procedural "cic:/CoRN/fta/FTAreg/nrt_pow.con" as lemma. -inline procedural "cic:/CoRN/fta/FTAreg/abs_pow_ltRe.con". +inline procedural "cic:/CoRN/fta/FTAreg/abs_pow_ltRe.con" as lemma. -inline procedural "cic:/CoRN/fta/FTAreg/abs_pow_ltIm.con". +inline procedural "cic:/CoRN/fta/FTAreg/abs_pow_ltIm.con" as lemma. -inline procedural "cic:/CoRN/fta/FTAreg/SublemmaRe.con". +inline procedural "cic:/CoRN/fta/FTAreg/SublemmaRe.con" as lemma. -inline procedural "cic:/CoRN/fta/FTAreg/SublemmaIm.con". +inline procedural "cic:/CoRN/fta/FTAreg/SublemmaIm.con" as lemma. -inline procedural "cic:/CoRN/fta/FTAreg/seq_is_CC_Cauchy.con". +inline procedural "cic:/CoRN/fta/FTAreg/seq_is_CC_Cauchy.con" as lemma. (* UNEXPORTED End Seq_is_CC_CAuchy *) -inline procedural "cic:/CoRN/fta/FTAreg/FTA_monic.con". +inline procedural "cic:/CoRN/fta/FTAreg/FTA_monic.con" as lemma. -inline procedural "cic:/CoRN/fta/FTAreg/FTA_reg.con". +inline procedural "cic:/CoRN/fta/FTAreg/FTA_reg.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/fta/KeyLemma.mma b/helm/software/matita/contribs/CoRN-Procedural/fta/KeyLemma.mma index a49f0f47e..78240853d 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/fta/KeyLemma.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/fta/KeyLemma.mma @@ -57,101 +57,101 @@ alias id "a_0" = "cic:/CoRN/fta/KeyLemma/Key_Lemma/a_0.var". alias id "eps_le_a_0" = "cic:/CoRN/fta/KeyLemma/Key_Lemma/eps_le_a_0.var". -inline procedural "cic:/CoRN/fta/KeyLemma/a_0_eps_nonneg.con". +inline procedural "cic:/CoRN/fta/KeyLemma/a_0_eps_nonneg.con" as lemma. -inline procedural "cic:/CoRN/fta/KeyLemma/a_0_eps_fuzz.con". +inline procedural "cic:/CoRN/fta/KeyLemma/a_0_eps_fuzz.con" as lemma. -inline procedural "cic:/CoRN/fta/KeyLemma/lem_1a.con". +inline procedural "cic:/CoRN/fta/KeyLemma/lem_1a.con" as lemma. -inline procedural "cic:/CoRN/fta/KeyLemma/lem_1b.con". +inline procedural "cic:/CoRN/fta/KeyLemma/lem_1b.con" as lemma. -inline procedural "cic:/CoRN/fta/KeyLemma/lem_1c.con". +inline procedural "cic:/CoRN/fta/KeyLemma/lem_1c.con" as lemma. -inline procedural "cic:/CoRN/fta/KeyLemma/lem_1.con". +inline procedural "cic:/CoRN/fta/KeyLemma/lem_1.con" as lemma. -inline procedural "cic:/CoRN/fta/KeyLemma/p3m.con". +inline procedural "cic:/CoRN/fta/KeyLemma/p3m.con" as definition. -inline procedural "cic:/CoRN/fta/KeyLemma/p3m_pos.con". +inline procedural "cic:/CoRN/fta/KeyLemma/p3m_pos.con" as lemma. -inline procedural "cic:/CoRN/fta/KeyLemma/p3m_S.con". +inline procedural "cic:/CoRN/fta/KeyLemma/p3m_S.con" as lemma. (* UNEXPORTED Hint Resolve p3m_S: algebra. *) -inline procedural "cic:/CoRN/fta/KeyLemma/p3m_P.con". +inline procedural "cic:/CoRN/fta/KeyLemma/p3m_P.con" as lemma. -inline procedural "cic:/CoRN/fta/KeyLemma/p3m_aux.con". +inline procedural "cic:/CoRN/fta/KeyLemma/p3m_aux.con" as lemma. -inline procedural "cic:/CoRN/fta/KeyLemma/p3m_pow.con". +inline procedural "cic:/CoRN/fta/KeyLemma/p3m_pow.con" as lemma. (* UNEXPORTED Hint Resolve p3m_aux: algebra. *) -inline procedural "cic:/CoRN/fta/KeyLemma/p3m_0.con". +inline procedural "cic:/CoRN/fta/KeyLemma/p3m_0.con" as lemma. (* UNEXPORTED Hint Resolve p3m_0: algebra. *) -inline procedural "cic:/CoRN/fta/KeyLemma/third_pos.con". +inline procedural "cic:/CoRN/fta/KeyLemma/third_pos.con" as lemma. (* UNEXPORTED Hint Resolve third_pos: algebra. *) -inline procedural "cic:/CoRN/fta/KeyLemma/third_less_one.con". +inline procedural "cic:/CoRN/fta/KeyLemma/third_less_one.con" as lemma. (* UNEXPORTED Hint Resolve third_less_one: algebra. *) -inline procedural "cic:/CoRN/fta/KeyLemma/p3m_mon.con". +inline procedural "cic:/CoRN/fta/KeyLemma/p3m_mon.con" as lemma. -inline procedural "cic:/CoRN/fta/KeyLemma/p3m_mon'.con". +inline procedural "cic:/CoRN/fta/KeyLemma/p3m_mon'.con" as lemma. -inline procedural "cic:/CoRN/fta/KeyLemma/p3m_small.con". +inline procedural "cic:/CoRN/fta/KeyLemma/p3m_small.con" as lemma. -inline procedural "cic:/CoRN/fta/KeyLemma/p3m_smaller.con". +inline procedural "cic:/CoRN/fta/KeyLemma/p3m_smaller.con" as lemma. -inline procedural "cic:/CoRN/fta/KeyLemma/chfun.con". +inline procedural "cic:/CoRN/fta/KeyLemma/chfun.con" as definition. -inline procedural "cic:/CoRN/fta/KeyLemma/chfun_1.con". +inline procedural "cic:/CoRN/fta/KeyLemma/chfun_1.con" as lemma. -inline procedural "cic:/CoRN/fta/KeyLemma/chfun_2.con". +inline procedural "cic:/CoRN/fta/KeyLemma/chfun_2.con" as lemma. -inline procedural "cic:/CoRN/fta/KeyLemma/chfun_3.con". +inline procedural "cic:/CoRN/fta/KeyLemma/chfun_3.con" as lemma. -inline procedural "cic:/CoRN/fta/KeyLemma/chfun_4.con". +inline procedural "cic:/CoRN/fta/KeyLemma/chfun_4.con" as lemma. -inline procedural "cic:/CoRN/fta/KeyLemma/Halfeps.con". +inline procedural "cic:/CoRN/fta/KeyLemma/Halfeps.con" as definition. -inline procedural "cic:/CoRN/fta/KeyLemma/Halfeps_pos.con". +inline procedural "cic:/CoRN/fta/KeyLemma/Halfeps_pos.con" as lemma. -inline procedural "cic:/CoRN/fta/KeyLemma/Halfeps_Halfeps.con". +inline procedural "cic:/CoRN/fta/KeyLemma/Halfeps_Halfeps.con" as lemma. (* UNEXPORTED Hint Resolve Halfeps_Halfeps: algebra. *) -inline procedural "cic:/CoRN/fta/KeyLemma/Halfeps_eps.con". +inline procedural "cic:/CoRN/fta/KeyLemma/Halfeps_eps.con" as lemma. -inline procedural "cic:/CoRN/fta/KeyLemma/Halfeps_trans.con". +inline procedural "cic:/CoRN/fta/KeyLemma/Halfeps_trans.con" as lemma. -inline procedural "cic:/CoRN/fta/KeyLemma/Key_1a.con". +inline procedural "cic:/CoRN/fta/KeyLemma/Key_1a.con" as lemma. (* UNEXPORTED Hint Resolve Key_1a: algebra. *) -inline procedural "cic:/CoRN/fta/KeyLemma/Key_1b.con". +inline procedural "cic:/CoRN/fta/KeyLemma/Key_1b.con" as lemma. -inline procedural "cic:/CoRN/fta/KeyLemma/Key_1.con". +inline procedural "cic:/CoRN/fta/KeyLemma/Key_1.con" as lemma. -inline procedural "cic:/CoRN/fta/KeyLemma/Key_2.con". +inline procedural "cic:/CoRN/fta/KeyLemma/Key_2.con" as lemma. -inline procedural "cic:/CoRN/fta/KeyLemma/Key.con". +inline procedural "cic:/CoRN/fta/KeyLemma/Key.con" as lemma. (* end hide *) diff --git a/helm/software/matita/contribs/CoRN-Procedural/fta/KneserLemma.mma b/helm/software/matita/contribs/CoRN-Procedural/fta/KneserLemma.mma index 1df1bc9cc..1d5430cd5 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/fta/KneserLemma.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/fta/KneserLemma.mma @@ -49,9 +49,9 @@ alias id "gt_n_0" = "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/gt_n_0.var". (* begin hide *) -inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b_0.con" "Kneser_Lemma__". +inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b_0.con" "Kneser_Lemma__" as definition. -inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b_n.con" "Kneser_Lemma__". +inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b_n.con" "Kneser_Lemma__" as definition. (* end hide *) @@ -75,69 +75,69 @@ alias id "b_0_lt_c" = "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b_0_lt_c.var". (* begin hide *) -inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/two_n.con" "Kneser_Lemma__". +inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/two_n.con" "Kneser_Lemma__" as definition. -inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/Small.con" "Kneser_Lemma__". +inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/Small.con" "Kneser_Lemma__" as definition. -inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/Smaller.con" "Kneser_Lemma__". +inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/Smaller.con" "Kneser_Lemma__" as definition. -inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/Smallest.con" "Kneser_Lemma__". +inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/Smallest.con" "Kneser_Lemma__" as definition. -inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/q.con" "Kneser_Lemma__". +inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/q.con" "Kneser_Lemma__" as definition. (* end hide *) -inline procedural "cic:/CoRN/fta/KneserLemma/b_0'_exists.con". +inline procedural "cic:/CoRN/fta/KneserLemma/b_0'_exists.con" as lemma. -inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/eta_0.con" "Kneser_Lemma__". +inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/eta_0.con" "Kneser_Lemma__" as definition. -inline procedural "cic:/CoRN/fta/KneserLemma/eta_0_pos.con". +inline procedural "cic:/CoRN/fta/KneserLemma/eta_0_pos.con" as lemma. -inline procedural "cic:/CoRN/fta/KneserLemma/eta_exists.con". +inline procedural "cic:/CoRN/fta/KneserLemma/eta_exists.con" as lemma. -inline procedural "cic:/CoRN/fta/KneserLemma/eps_exists_1.con". +inline procedural "cic:/CoRN/fta/KneserLemma/eps_exists_1.con" as lemma. (* less_cotransitive_unfolded on {Zero [<] y[/]x[//]H3[-]Half[*]eps} + {y[/]x[//]H3[-]Half[*]eps [<] Half[*]eps}. *) -inline procedural "cic:/CoRN/fta/KneserLemma/eps_exists.con". +inline procedural "cic:/CoRN/fta/KneserLemma/eps_exists.con" as lemma. (* begin hide *) -inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/a.con" "Kneser_Lemma__". +inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/a.con" "Kneser_Lemma__" as definition. (* end hide *) -inline procedural "cic:/CoRN/fta/KneserLemma/z_exists.con". +inline procedural "cic:/CoRN/fta/KneserLemma/z_exists.con" as lemma. (* end hide *) -inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_1'.con". +inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_1'.con" as lemma. -inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_1''.con". +inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_1''.con" as lemma. -inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_1.con". +inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_1.con" as lemma. -inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_2a.con". +inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_2a.con" as lemma. -inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_2b.con". +inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_2b.con" as lemma. (* end hide *) -inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_2c.con". +inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_2c.con" as lemma. (* end hide *) -inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_2.con". +inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_2.con" as lemma. (* end hide *) -inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_3.con". +inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_3.con" as lemma. (* UNEXPORTED End Kneser_Lemma *) -inline procedural "cic:/CoRN/fta/KneserLemma/Kneser.con". +inline procedural "cic:/CoRN/fta/KneserLemma/Kneser.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/fta/MainLemma.mma b/helm/software/matita/contribs/CoRN-Procedural/fta/MainLemma.mma index c3c9669c5..48a403135 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/fta/MainLemma.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/fta/MainLemma.mma @@ -61,7 +61,7 @@ alias id "a_0" = "cic:/CoRN/fta/MainLemma/Main_Lemma/a_0.var". alias id "eps_le_a_0" = "cic:/CoRN/fta/MainLemma/Main_Lemma/eps_le_a_0.var". -inline procedural "cic:/CoRN/fta/MainLemma/a_0_pos.con". +inline procedural "cic:/CoRN/fta/MainLemma/a_0_pos.con" as lemma. (*#* %\begin{convention}% We define the following local abbreviations: @@ -74,49 +74,49 @@ inline procedural "cic:/CoRN/fta/MainLemma/a_0_pos.con". (* begin hide *) -inline procedural "cic:/CoRN/fta/MainLemma/Main_Lemma/two_n.con" "Main_Lemma__". +inline procedural "cic:/CoRN/fta/MainLemma/Main_Lemma/two_n.con" "Main_Lemma__" as definition. -inline procedural "cic:/CoRN/fta/MainLemma/Main_Lemma/Small.con" "Main_Lemma__". +inline procedural "cic:/CoRN/fta/MainLemma/Main_Lemma/Small.con" "Main_Lemma__" as definition. -inline procedural "cic:/CoRN/fta/MainLemma/Main_Lemma/Smaller.con" "Main_Lemma__". +inline procedural "cic:/CoRN/fta/MainLemma/Main_Lemma/Smaller.con" "Main_Lemma__" as definition. (* end hide *) -inline procedural "cic:/CoRN/fta/MainLemma/Main_1a'.con". +inline procedural "cic:/CoRN/fta/MainLemma/Main_1a'.con" as lemma. (* end hide *) -inline procedural "cic:/CoRN/fta/MainLemma/Main_1b'.con". +inline procedural "cic:/CoRN/fta/MainLemma/Main_1b'.con" as lemma. (* end hide *) -inline procedural "cic:/CoRN/fta/MainLemma/Main_1a.con". +inline procedural "cic:/CoRN/fta/MainLemma/Main_1a.con" as lemma. (* end hide *) -inline procedural "cic:/CoRN/fta/MainLemma/Main_1b.con". +inline procedural "cic:/CoRN/fta/MainLemma/Main_1b.con" as lemma. (* end hide *) -inline procedural "cic:/CoRN/fta/MainLemma/Main_1.con". +inline procedural "cic:/CoRN/fta/MainLemma/Main_1.con" as lemma. (* end hide *) -inline procedural "cic:/CoRN/fta/MainLemma/Main_2'.con". +inline procedural "cic:/CoRN/fta/MainLemma/Main_2'.con" as lemma. -inline procedural "cic:/CoRN/fta/MainLemma/Main_2.con". +inline procedural "cic:/CoRN/fta/MainLemma/Main_2.con" as lemma. (* end hide *) -inline procedural "cic:/CoRN/fta/MainLemma/Main_3a.con". +inline procedural "cic:/CoRN/fta/MainLemma/Main_3a.con" as lemma. (* end hide *) -inline procedural "cic:/CoRN/fta/MainLemma/Main_3.con". +inline procedural "cic:/CoRN/fta/MainLemma/Main_3.con" as lemma. (* end hide *) -inline procedural "cic:/CoRN/fta/MainLemma/Main.con". +inline procedural "cic:/CoRN/fta/MainLemma/Main.con" as lemma. (* end hide *) diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/COrdLemmas.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/COrdLemmas.mma index 185700c77..51b18daa0 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/COrdLemmas.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/COrdLemmas.mma @@ -39,27 +39,27 @@ refinement). alias id "F" = "cic:/CoRN/ftc/COrdLemmas/Lemmas/F.var". -inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_lt.con". +inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_lt.con" as lemma. -inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun.con". +inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun.con" as definition. -inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_1.con". +inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_1.con" as lemma. -inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_2a.con". +inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_2a.con" as lemma. -inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_2.con". +inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_2.con" as lemma. -inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_3a.con". +inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_3a.con" as lemma. -inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_3b.con". +inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_3b.con" as lemma. -inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_4a.con". +inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_4a.con" as lemma. -inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_4b.con". +inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_4b.con" as lemma. -inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_4c.con". +inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_4c.con" as lemma. -inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_4d.con". +inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_4d.con" as lemma. (* begin hide *) @@ -83,7 +83,7 @@ structure of the arguments is analyzed in more detail. inline procedural "cic:/CoRN/ftc/COrdLemmas/Sumx_Sum_Sum (* end show *) - (* begin hide *).con". + (* begin hide *).con" as lemma. (* end hide *) @@ -91,7 +91,7 @@ inline procedural "cic:/CoRN/ftc/COrdLemmas/Sumx_Sum_Sum inline procedural "cic:/CoRN/ftc/COrdLemmas/str_Sumx_Sum_Sum (* end show *) - (* begin hide *).con". + (* begin hide *).con" as lemma. (* UNEXPORTED End Lemmas @@ -101,7 +101,7 @@ End Lemmas Section More_Lemmas *) -inline procedural "cic:/CoRN/ftc/COrdLemmas/More_Lemmas/f'.con" "More_Lemmas__". +inline procedural "cic:/CoRN/ftc/COrdLemmas/More_Lemmas/f'.con" "More_Lemmas__" as definition. (* end hide *) @@ -111,7 +111,7 @@ alias id "F" = "cic:/CoRN/ftc/COrdLemmas/More_Lemmas/F.var". inline procedural "cic:/CoRN/ftc/COrdLemmas/str_Sumx_Sum_Sum' (* end show *) - (* begin hide *).con". + (* begin hide *).con" as lemma. (* end hide *) diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/CalculusTheorems.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/CalculusTheorems.mma index 5626821f4..cc413f469 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/CalculusTheorems.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/CalculusTheorems.mma @@ -41,52 +41,52 @@ continuous function commutes with the limit of a numerical sequence (sometimes called Heine continuity). *) -inline procedural "cic:/CoRN/ftc/CalculusTheorems/Continuous_imp_comm_Lim.con". +inline procedural "cic:/CoRN/ftc/CalculusTheorems/Continuous_imp_comm_Lim.con" as lemma. (*#* This is a tricky result: if [F] is continuous and positive in both [[a,b]] and [(b,c]], then it is positive in [[a,c]]. *) -inline procedural "cic:/CoRN/ftc/CalculusTheorems/Continuous_imp_pos.con". +inline procedural "cic:/CoRN/ftc/CalculusTheorems/Continuous_imp_pos.con" as lemma. (*#* Similar results for increasing functions: *) -inline procedural "cic:/CoRN/ftc/CalculusTheorems/strict_inc_glues.con". +inline procedural "cic:/CoRN/ftc/CalculusTheorems/strict_inc_glues.con" as lemma. -inline procedural "cic:/CoRN/ftc/CalculusTheorems/strict_inc_glues'.con". +inline procedural "cic:/CoRN/ftc/CalculusTheorems/strict_inc_glues'.con" as lemma. -inline procedural "cic:/CoRN/ftc/CalculusTheorems/strict_dec_glues.con". +inline procedural "cic:/CoRN/ftc/CalculusTheorems/strict_dec_glues.con" as lemma. -inline procedural "cic:/CoRN/ftc/CalculusTheorems/strict_dec_glues'.con". +inline procedural "cic:/CoRN/ftc/CalculusTheorems/strict_dec_glues'.con" as lemma. (*#* More on glueing intervals. *) -inline procedural "cic:/CoRN/ftc/CalculusTheorems/olor_pos_clor_nonneg.con". +inline procedural "cic:/CoRN/ftc/CalculusTheorems/olor_pos_clor_nonneg.con" as lemma. -inline procedural "cic:/CoRN/ftc/CalculusTheorems/olor_pos_olcr_nonneg.con". +inline procedural "cic:/CoRN/ftc/CalculusTheorems/olor_pos_olcr_nonneg.con" as lemma. -inline procedural "cic:/CoRN/ftc/CalculusTheorems/olor_pos_clcr_nonneg.con". +inline procedural "cic:/CoRN/ftc/CalculusTheorems/olor_pos_clcr_nonneg.con" as lemma. (*#* Any function that has the null function as its derivative must be constant. *) -inline procedural "cic:/CoRN/ftc/CalculusTheorems/FConst_prop.con". +inline procedural "cic:/CoRN/ftc/CalculusTheorems/FConst_prop.con" as lemma. (*#* As a corollary, two functions with the same derivative must differ by a constant. *) -inline procedural "cic:/CoRN/ftc/CalculusTheorems/Feq_crit_with_const.con". +inline procedural "cic:/CoRN/ftc/CalculusTheorems/Feq_crit_with_const.con" as lemma. (*#* This yields the following known result: any differential equation of the form [f'=g] with initial condition [f(a) [=] b] has a unique solution. *) -inline procedural "cic:/CoRN/ftc/CalculusTheorems/Feq_criterium.con". +inline procedural "cic:/CoRN/ftc/CalculusTheorems/Feq_criterium.con" as lemma. (*#* Finally, a well known result: any function with a (strictly) positive @@ -95,11 +95,11 @@ quite similar the proofs are completely different, both from the formalization and from the mathematical point of view. *) -inline procedural "cic:/CoRN/ftc/CalculusTheorems/Derivative_imp_resp_less.con". +inline procedural "cic:/CoRN/ftc/CalculusTheorems/Derivative_imp_resp_less.con" as lemma. -inline procedural "cic:/CoRN/ftc/CalculusTheorems/Derivative_imp_resp_leEq.con". +inline procedural "cic:/CoRN/ftc/CalculusTheorems/Derivative_imp_resp_leEq.con" as lemma. -inline procedural "cic:/CoRN/ftc/CalculusTheorems/Derivative_imp_resp_less'.con". +inline procedural "cic:/CoRN/ftc/CalculusTheorems/Derivative_imp_resp_less'.con" as lemma. (*#* From these results we can finally prove that exponentiation to a real power preserves the less or equal than relation! @@ -113,7 +113,7 @@ Opaque nring. Transparent nring. *) -inline procedural "cic:/CoRN/ftc/CalculusTheorems/nexp_resp_leEq_odd.con". +inline procedural "cic:/CoRN/ftc/CalculusTheorems/nexp_resp_leEq_odd.con" as lemma. (* UNEXPORTED End Various_Theorems diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/Composition.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/Composition.mma index 2d2ebfbab..7fa209cee 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/Composition.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/Composition.mma @@ -69,7 +69,7 @@ alias id "Hcd" = "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/Hcd.va (* begin hide *) -inline procedural "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/I.con" "Maps_into_Compacts__Part_Funct__". +inline procedural "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/I.con" "Maps_into_Compacts__Part_Funct__" as definition. (* end hide *) @@ -79,7 +79,7 @@ alias id "Hf" = "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/Hf.var" (* end show *) -inline procedural "cic:/CoRN/ftc/Composition/maps_into_compacts.con". +inline procedural "cic:/CoRN/ftc/Composition/maps_into_compacts.con" as definition. (* begin show *) @@ -87,13 +87,13 @@ alias id "maps" = "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/maps. (* end show *) -inline procedural "cic:/CoRN/ftc/Composition/maps_lemma'.con". +inline procedural "cic:/CoRN/ftc/Composition/maps_lemma'.con" as lemma. -inline procedural "cic:/CoRN/ftc/Composition/maps_lemma.con". +inline procedural "cic:/CoRN/ftc/Composition/maps_lemma.con" as lemma. -inline procedural "cic:/CoRN/ftc/Composition/maps_lemma_less.con". +inline procedural "cic:/CoRN/ftc/Composition/maps_lemma_less.con" as lemma. -inline procedural "cic:/CoRN/ftc/Composition/maps_lemma_inc.con". +inline procedural "cic:/CoRN/ftc/Composition/maps_lemma_inc.con" as lemma. (* UNEXPORTED End Part_Funct @@ -138,7 +138,7 @@ alias id "maps" = "cic:/CoRN/ftc/Composition/Mapping/maps.var". (* end show *) -inline procedural "cic:/CoRN/ftc/Composition/included_comp.con". +inline procedural "cic:/CoRN/ftc/Composition/included_comp.con" as lemma. (* UNEXPORTED End Mapping @@ -161,7 +161,7 @@ alias id "Hab" = "cic:/CoRN/ftc/Composition/Interval_Continuity/Hab.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/Composition/Interval_Continuity/I.con" "Interval_Continuity__". +inline procedural "cic:/CoRN/ftc/Composition/Interval_Continuity/I.con" "Interval_Continuity__" as definition. (* end hide *) @@ -185,7 +185,7 @@ alias id "Hmap" = "cic:/CoRN/ftc/Composition/Interval_Continuity/Hmap.var". (* end show *) -inline procedural "cic:/CoRN/ftc/Composition/Continuous_I_comp.con". +inline procedural "cic:/CoRN/ftc/Composition/Continuous_I_comp.con" as lemma. (* UNEXPORTED End Interval_Continuity @@ -222,11 +222,11 @@ alias id "Hcd'" = "cic:/CoRN/ftc/Composition/Derivative/Hcd'.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/Composition/Derivative/Hab.con" "Derivative__". +inline procedural "cic:/CoRN/ftc/Composition/Derivative/Hab.con" "Derivative__" as definition. -inline procedural "cic:/CoRN/ftc/Composition/Derivative/Hcd.con" "Derivative__". +inline procedural "cic:/CoRN/ftc/Composition/Derivative/Hcd.con" "Derivative__" as definition. -inline procedural "cic:/CoRN/ftc/Composition/Derivative/I.con" "Derivative__". +inline procedural "cic:/CoRN/ftc/Composition/Derivative/I.con" "Derivative__" as definition. (* end hide *) @@ -240,17 +240,17 @@ alias id "Hmap" = "cic:/CoRN/ftc/Composition/Derivative/Hmap.var". (* end show *) -inline procedural "cic:/CoRN/ftc/Composition/included_comp'.con". +inline procedural "cic:/CoRN/ftc/Composition/included_comp'.con" as lemma. -inline procedural "cic:/CoRN/ftc/Composition/maps'.con". +inline procedural "cic:/CoRN/ftc/Composition/maps'.con" as lemma. -inline procedural "cic:/CoRN/ftc/Composition/Derivative_I_comp.con". +inline procedural "cic:/CoRN/ftc/Composition/Derivative_I_comp.con" as lemma. (*#* The next lemma will be useful when we move on to differentiability. *) -inline procedural "cic:/CoRN/ftc/Composition/Diffble_I_comp_aux.con". +inline procedural "cic:/CoRN/ftc/Composition/Diffble_I_comp_aux.con" as lemma. (* UNEXPORTED End Derivative @@ -283,11 +283,11 @@ alias id "Hcd'" = "cic:/CoRN/ftc/Composition/Differentiability/Hcd'.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/Composition/Differentiability/Hab.con" "Differentiability__". +inline procedural "cic:/CoRN/ftc/Composition/Differentiability/Hab.con" "Differentiability__" as definition. -inline procedural "cic:/CoRN/ftc/Composition/Differentiability/Hcd.con" "Differentiability__". +inline procedural "cic:/CoRN/ftc/Composition/Differentiability/Hcd.con" "Differentiability__" as definition. -inline procedural "cic:/CoRN/ftc/Composition/Differentiability/I.con" "Differentiability__". +inline procedural "cic:/CoRN/ftc/Composition/Differentiability/I.con" "Differentiability__" as definition. (* end hide *) @@ -301,7 +301,7 @@ alias id "Hmap" = "cic:/CoRN/ftc/Composition/Differentiability/Hmap.var". (* end show *) -inline procedural "cic:/CoRN/ftc/Composition/Diffble_I_comp.con". +inline procedural "cic:/CoRN/ftc/Composition/Diffble_I_comp.con" as lemma. (* UNEXPORTED End Differentiability @@ -327,13 +327,13 @@ alias id "pI" = "cic:/CoRN/ftc/Composition/Generalized_Intervals/pI.var". alias id "pJ" = "cic:/CoRN/ftc/Composition/Generalized_Intervals/pJ.var". -inline procedural "cic:/CoRN/ftc/Composition/maps_compacts_into.con". +inline procedural "cic:/CoRN/ftc/Composition/maps_compacts_into.con" as definition. (*#* Now everything comes naturally: *) -inline procedural "cic:/CoRN/ftc/Composition/comp_inc_lemma.con". +inline procedural "cic:/CoRN/ftc/Composition/comp_inc_lemma.con" as lemma. alias id "F" = "cic:/CoRN/ftc/Composition/Generalized_Intervals/F.var". @@ -349,7 +349,7 @@ alias id "Hmap" = "cic:/CoRN/ftc/Composition/Generalized_Intervals/Hmap.var". (* end show *) -inline procedural "cic:/CoRN/ftc/Composition/Continuous_comp.con". +inline procedural "cic:/CoRN/ftc/Composition/Continuous_comp.con" as lemma. (* begin show *) @@ -357,7 +357,7 @@ alias id "Hmap'" = "cic:/CoRN/ftc/Composition/Generalized_Intervals/Hmap'.var". (* end show *) -inline procedural "cic:/CoRN/ftc/Composition/Derivative_comp.con". +inline procedural "cic:/CoRN/ftc/Composition/Derivative_comp.con" as lemma. (* UNEXPORTED End Generalized_Intervals @@ -371,21 +371,21 @@ Section Corollaries Finally, some criteria to prove that a function with a specific domain maps compacts into compacts: *) -inline procedural "cic:/CoRN/ftc/Composition/positive_fun.con". +inline procedural "cic:/CoRN/ftc/Composition/positive_fun.con" as definition. -inline procedural "cic:/CoRN/ftc/Composition/negative_fun.con". +inline procedural "cic:/CoRN/ftc/Composition/negative_fun.con" as definition. -inline procedural "cic:/CoRN/ftc/Composition/positive_imp_maps_compacts_into.con". +inline procedural "cic:/CoRN/ftc/Composition/positive_imp_maps_compacts_into.con" as lemma. -inline procedural "cic:/CoRN/ftc/Composition/negative_imp_maps_compacts_into.con". +inline procedural "cic:/CoRN/ftc/Composition/negative_imp_maps_compacts_into.con" as lemma. -inline procedural "cic:/CoRN/ftc/Composition/Continuous_imp_maps_compacts_into.con". +inline procedural "cic:/CoRN/ftc/Composition/Continuous_imp_maps_compacts_into.con" as lemma. (*#* As a corollary, we get the generalization of differentiability property. *) -inline procedural "cic:/CoRN/ftc/Composition/Diffble_comp.con". +inline procedural "cic:/CoRN/ftc/Composition/Diffble_comp.con" as lemma. (* UNEXPORTED End Corollaries diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/Continuity.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/Continuity.mma index 28b8c5efa..ff66216f5 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/Continuity.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/Continuity.mma @@ -60,7 +60,7 @@ alias id "Hab" = "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/Hab.var (* begin hide *) -inline procedural "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/I.con" "Definitions_and_Basic_Results__". +inline procedural "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/I.con" "Definitions_and_Basic_Results__" as definition. (* end hide *) @@ -68,19 +68,19 @@ alias id "F" = "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/F.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/P.con" "Definitions_and_Basic_Results__". +inline procedural "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/P.con" "Definitions_and_Basic_Results__" as definition. (* end hide *) -inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I.con". +inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I.con" as definition. (*#* For convenience, we distinguish the two properties of continuous functions. *) -inline procedural "cic:/CoRN/ftc/Continuity/contin_imp_inc.con". +inline procedural "cic:/CoRN/ftc/Continuity/contin_imp_inc.con" as lemma. -inline procedural "cic:/CoRN/ftc/Continuity/contin_prop.con". +inline procedural "cic:/CoRN/ftc/Continuity/contin_prop.con" as lemma. (*#* Assume [F] to be continuous in [I]. Then it has a least upper bound and a greater lower bound on [I]. @@ -90,65 +90,65 @@ alias id "contF" = "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/contF (* begin hide *) -inline procedural "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/Hinc'.con" "Definitions_and_Basic_Results__". +inline procedural "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/Hinc'.con" "Definitions_and_Basic_Results__" as definition. (* end hide *) -inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_imp_tb_image.con". +inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_imp_tb_image.con" as lemma. -inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_imp_lub.con". +inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_imp_lub.con" as lemma. -inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_imp_glb.con". +inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_imp_glb.con" as lemma. (*#* We now make this glb and lub into operators. *) -inline procedural "cic:/CoRN/ftc/Continuity/lub_funct.con". +inline procedural "cic:/CoRN/ftc/Continuity/lub_funct.con" as definition. -inline procedural "cic:/CoRN/ftc/Continuity/glb_funct.con". +inline procedural "cic:/CoRN/ftc/Continuity/glb_funct.con" as definition. (*#* These operators have the expected properties. *) -inline procedural "cic:/CoRN/ftc/Continuity/lub_is_lub.con". +inline procedural "cic:/CoRN/ftc/Continuity/lub_is_lub.con" as lemma. -inline procedural "cic:/CoRN/ftc/Continuity/glb_is_glb.con". +inline procedural "cic:/CoRN/ftc/Continuity/glb_is_glb.con" as lemma. -inline procedural "cic:/CoRN/ftc/Continuity/glb_prop.con". +inline procedural "cic:/CoRN/ftc/Continuity/glb_prop.con" as lemma. -inline procedural "cic:/CoRN/ftc/Continuity/lub_prop.con". +inline procedural "cic:/CoRN/ftc/Continuity/lub_prop.con" as lemma. (*#* The norm of a function is defined as being the supremum of its absolute value; that is equivalent to the following definition (which is often more convenient to use). *) -inline procedural "cic:/CoRN/ftc/Continuity/Norm_Funct.con". +inline procedural "cic:/CoRN/ftc/Continuity/Norm_Funct.con" as definition. (*#* The norm effectively bounds the absolute value of a function. *) -inline procedural "cic:/CoRN/ftc/Continuity/norm_bnd_AbsIR.con". +inline procedural "cic:/CoRN/ftc/Continuity/norm_bnd_AbsIR.con" as lemma. (*#* The following is another way of characterizing the norm: *) -inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_imp_abs_lub.con". +inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_imp_abs_lub.con" as lemma. (*#* We now prove some basic properties of the norm---namely that it is positive, and that it provides a least upper bound for the absolute value of its argument. *) -inline procedural "cic:/CoRN/ftc/Continuity/positive_norm.con". +inline procedural "cic:/CoRN/ftc/Continuity/positive_norm.con" as lemma. -inline procedural "cic:/CoRN/ftc/Continuity/norm_fun_lub.con". +inline procedural "cic:/CoRN/ftc/Continuity/norm_fun_lub.con" as lemma. -inline procedural "cic:/CoRN/ftc/Continuity/leEq_Norm_Funct.con". +inline procedural "cic:/CoRN/ftc/Continuity/leEq_Norm_Funct.con" as lemma. -inline procedural "cic:/CoRN/ftc/Continuity/less_Norm_Funct.con". +inline procedural "cic:/CoRN/ftc/Continuity/less_Norm_Funct.con" as lemma. (* UNEXPORTED End Definitions_and_Basic_Results @@ -179,7 +179,7 @@ alias id "Hab" = "cic:/CoRN/ftc/Continuity/Local_Results/Hab.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/Continuity/Local_Results/I.con" "Local_Results__". +inline procedural "cic:/CoRN/ftc/Continuity/Local_Results/I.con" "Local_Results__" as definition. (* end hide *) @@ -189,9 +189,9 @@ alias id "G" = "cic:/CoRN/ftc/Continuity/Local_Results/G.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/Continuity/Local_Results/P.con" "Local_Results__". +inline procedural "cic:/CoRN/ftc/Continuity/Local_Results/P.con" "Local_Results__" as definition. -inline procedural "cic:/CoRN/ftc/Continuity/Local_Results/Q.con" "Local_Results__". +inline procedural "cic:/CoRN/ftc/Continuity/Local_Results/Q.con" "Local_Results__" as definition. (* end hide *) @@ -203,31 +203,31 @@ alias id "incG" = "cic:/CoRN/ftc/Continuity/Local_Results/incG.var". The first result does not require the function to be continuous; however, its preconditions are easily verified by continuous functions, which justifies its inclusion in this section. *) -inline procedural "cic:/CoRN/ftc/Continuity/cont_no_sign_change.con". +inline procedural "cic:/CoRN/ftc/Continuity/cont_no_sign_change.con" as lemma. -inline procedural "cic:/CoRN/ftc/Continuity/cont_no_sign_change_pos.con". +inline procedural "cic:/CoRN/ftc/Continuity/cont_no_sign_change_pos.con" as lemma. -inline procedural "cic:/CoRN/ftc/Continuity/cont_no_sign_change_neg.con". +inline procedural "cic:/CoRN/ftc/Continuity/cont_no_sign_change_neg.con" as lemma. (*#* Being continuous is an extensional property. *) -inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_wd.con". +inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_wd.con" as lemma. (*#* A continuous function remains continuous if you restrict its domain. *) -inline procedural "cic:/CoRN/ftc/Continuity/included_imp_contin.con". +inline procedural "cic:/CoRN/ftc/Continuity/included_imp_contin.con" as lemma. (*#* Constant functions and identity are continuous. *) -inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_const.con". +inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_const.con" as lemma. -inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_id.con". +inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_id.con" as lemma. (*#* Assume [F] and [G] are continuous in [I]. Then functions derived from these through algebraic operations are also continuous, provided (in the case of reciprocal and division) some extra conditions are met. @@ -237,11 +237,11 @@ alias id "contF" = "cic:/CoRN/ftc/Continuity/Local_Results/contF.var". alias id "contG" = "cic:/CoRN/ftc/Continuity/Local_Results/contG.var". -inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_plus.con". +inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_plus.con" as lemma. -inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_inv.con". +inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_inv.con" as lemma. -inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_mult.con". +inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_mult.con" as lemma. (* UNEXPORTED Opaque AbsIR Max. @@ -251,7 +251,7 @@ Opaque AbsIR Max. Transparent AbsIR Max. *) -inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_max.con". +inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_max.con" as lemma. (* begin show *) @@ -261,7 +261,7 @@ alias id "Hg''" = "cic:/CoRN/ftc/Continuity/Local_Results/Hg''.var". (* end show *) -inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_recip.con". +inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_recip.con" as lemma. (* UNEXPORTED End Local_Results @@ -283,7 +283,7 @@ alias id "Hab" = "cic:/CoRN/ftc/Continuity/Corolaries/Hab.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/Continuity/Corolaries/I.con" "Corolaries__". +inline procedural "cic:/CoRN/ftc/Continuity/Corolaries/I.con" "Corolaries__" as definition. (* end hide *) @@ -293,9 +293,9 @@ alias id "G" = "cic:/CoRN/ftc/Continuity/Corolaries/G.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/Continuity/Corolaries/P.con" "Corolaries__". +inline procedural "cic:/CoRN/ftc/Continuity/Corolaries/P.con" "Corolaries__" as definition. -inline procedural "cic:/CoRN/ftc/Continuity/Corolaries/Q.con" "Corolaries__". +inline procedural "cic:/CoRN/ftc/Continuity/Corolaries/Q.con" "Corolaries__" as definition. (* end hide *) @@ -310,21 +310,21 @@ exponentiation is proved by induction, appealing to the results on product and constant functions. *) -inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_minus.con". +inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_minus.con" as lemma. -inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_scal.con". +inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_scal.con" as lemma. -inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_nth.con". +inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_nth.con" as lemma. -inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_min.con". +inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_min.con" as lemma. -inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_abs.con". +inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_abs.con" as lemma. alias id "Hg'" = "cic:/CoRN/ftc/Continuity/Corolaries/Hg'.var". alias id "Hg''" = "cic:/CoRN/ftc/Continuity/Corolaries/Hg''.var". -inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_div.con". +inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_div.con" as lemma. (* UNEXPORTED End Corolaries @@ -352,15 +352,15 @@ alias id "Hab'" = "cic:/CoRN/ftc/Continuity/Other/Sums/Hab'.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/Continuity/Other/Sums/I.con" "Other__Sums__". +inline procedural "cic:/CoRN/ftc/Continuity/Other/Sums/I.con" "Other__Sums__" as definition. (* end hide *) -inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_Sum0.con". +inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_Sum0.con" as lemma. -inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_Sumx.con". +inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_Sumx.con" as lemma. -inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_Sum.con". +inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_Sum.con" as lemma. (* UNEXPORTED End Sums @@ -370,27 +370,27 @@ End Sums For practical purposes, these characterization results are useful: *) -inline procedural "cic:/CoRN/ftc/Continuity/lub_charact.con". +inline procedural "cic:/CoRN/ftc/Continuity/lub_charact.con" as lemma. -inline procedural "cic:/CoRN/ftc/Continuity/glb_charact.con". +inline procedural "cic:/CoRN/ftc/Continuity/glb_charact.con" as lemma. (*#* The following result is also extremely useful, as it allows us to set a lower bound on the glb of a function. *) -inline procedural "cic:/CoRN/ftc/Continuity/leEq_glb.con". +inline procedural "cic:/CoRN/ftc/Continuity/leEq_glb.con" as lemma. (*#* The norm is also an extensional property. *) -inline procedural "cic:/CoRN/ftc/Continuity/Norm_Funct_wd.con". +inline procedural "cic:/CoRN/ftc/Continuity/Norm_Funct_wd.con" as lemma. (*#* The value of the norm is covariant with the length of the interval. *) -inline procedural "cic:/CoRN/ftc/Continuity/included_imp_norm_leEq.con". +inline procedural "cic:/CoRN/ftc/Continuity/included_imp_norm_leEq.con" as lemma. (* UNEXPORTED End Other diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/Derivative.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/Derivative.mma index 5b43f6380..b593df9de 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/Derivative.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/Derivative.mma @@ -59,9 +59,9 @@ alias id "Hab'" = "cic:/CoRN/ftc/Derivative/Definitions/Hab'.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/Derivative/Definitions/Hab.con" "Definitions__". +inline procedural "cic:/CoRN/ftc/Derivative/Definitions/Hab.con" "Definitions__" as definition. -inline procedural "cic:/CoRN/ftc/Derivative/Definitions/I.con" "Definitions__". +inline procedural "cic:/CoRN/ftc/Derivative/Definitions/I.con" "Definitions__" as definition. (* end hide *) @@ -69,11 +69,11 @@ alias id "F" = "cic:/CoRN/ftc/Derivative/Definitions/F.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/Derivative/Definitions/P.con" "Definitions__". +inline procedural "cic:/CoRN/ftc/Derivative/Definitions/P.con" "Definitions__" as definition. (* end hide *) -inline procedural "cic:/CoRN/ftc/Derivative/Derivative_I.con". +inline procedural "cic:/CoRN/ftc/Derivative/Derivative_I.con" as definition. (* UNEXPORTED End Definitions @@ -98,9 +98,9 @@ alias id "Hab'" = "cic:/CoRN/ftc/Derivative/Basic_Properties/Hab'.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/Derivative/Basic_Properties/Hab.con" "Basic_Properties__". +inline procedural "cic:/CoRN/ftc/Derivative/Basic_Properties/Hab.con" "Basic_Properties__" as definition. -inline procedural "cic:/CoRN/ftc/Derivative/Basic_Properties/I.con" "Basic_Properties__". +inline procedural "cic:/CoRN/ftc/Derivative/Basic_Properties/I.con" "Basic_Properties__" as definition. (* end hide *) @@ -108,7 +108,7 @@ inline procedural "cic:/CoRN/ftc/Derivative/Basic_Properties/I.con" "Basic_Prope Like we did for equality, we begin by stating a lemma that makes proofs of derivation easier in practice. *) -inline procedural "cic:/CoRN/ftc/Derivative/Derivative_I_char.con". +inline procedural "cic:/CoRN/ftc/Derivative/Derivative_I_char.con" as lemma. (* end hide *) @@ -124,21 +124,21 @@ alias id "H" = "cic:/CoRN/ftc/Derivative/Basic_Properties/H.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/Derivative/Basic_Properties/P.con" "Basic_Properties__". +inline procedural "cic:/CoRN/ftc/Derivative/Basic_Properties/P.con" "Basic_Properties__" as definition. -inline procedural "cic:/CoRN/ftc/Derivative/Basic_Properties/Q.con" "Basic_Properties__". +inline procedural "cic:/CoRN/ftc/Derivative/Basic_Properties/Q.con" "Basic_Properties__" as definition. -inline procedural "cic:/CoRN/ftc/Derivative/Basic_Properties/R.con" "Basic_Properties__". +inline procedural "cic:/CoRN/ftc/Derivative/Basic_Properties/R.con" "Basic_Properties__" as definition. (* end hide *) -inline procedural "cic:/CoRN/ftc/Derivative/Derivative_I_wdl.con". +inline procedural "cic:/CoRN/ftc/Derivative/Derivative_I_wdl.con" as lemma. -inline procedural "cic:/CoRN/ftc/Derivative/Derivative_I_wdr.con". +inline procedural "cic:/CoRN/ftc/Derivative/Derivative_I_wdr.con" as lemma. (* begin hide *) -inline procedural "cic:/CoRN/ftc/Derivative/Basic_Properties/Derivative_I_unique_lemma.con" "Basic_Properties__". +inline procedural "cic:/CoRN/ftc/Derivative/Basic_Properties/Derivative_I_unique_lemma.con" "Basic_Properties__" as definition. (* end hide *) @@ -146,15 +146,15 @@ inline procedural "cic:/CoRN/ftc/Derivative/Basic_Properties/Derivative_I_unique Derivative is unique. *) -inline procedural "cic:/CoRN/ftc/Derivative/Derivative_I_unique.con". +inline procedural "cic:/CoRN/ftc/Derivative/Derivative_I_unique.con" as lemma. (*#* Finally, the set where we are considering the relation is included in the domain of both functions. *) -inline procedural "cic:/CoRN/ftc/Derivative/derivative_imp_inc.con". +inline procedural "cic:/CoRN/ftc/Derivative/derivative_imp_inc.con" as lemma. -inline procedural "cic:/CoRN/ftc/Derivative/derivative_imp_inc'.con". +inline procedural "cic:/CoRN/ftc/Derivative/derivative_imp_inc'.con" as lemma. (*#* Any function that is or has a derivative is continuous. @@ -162,9 +162,9 @@ Any function that is or has a derivative is continuous. alias id "Hab''" = "cic:/CoRN/ftc/Derivative/Basic_Properties/Hab''.var". -inline procedural "cic:/CoRN/ftc/Derivative/deriv_imp_contin'_I.con". +inline procedural "cic:/CoRN/ftc/Derivative/deriv_imp_contin'_I.con" as lemma. -inline procedural "cic:/CoRN/ftc/Derivative/deriv_imp_contin_I.con". +inline procedural "cic:/CoRN/ftc/Derivative/deriv_imp_contin_I.con" as lemma. (* UNEXPORTED End Basic_Properties @@ -174,5 +174,5 @@ End Basic_Properties If [G] is the derivative of [F] in a given interval, then [G] is also the derivative of [F] in any smaller interval. *) -inline procedural "cic:/CoRN/ftc/Derivative/included_imp_deriv.con". +inline procedural "cic:/CoRN/ftc/Derivative/included_imp_deriv.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/DerivativeOps.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/DerivativeOps.mma index 2f2ac499e..2e3636d80 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/DerivativeOps.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/DerivativeOps.mma @@ -44,7 +44,7 @@ alias id "Hab" = "cic:/CoRN/ftc/DerivativeOps/Lemmas/Hab.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/DerivativeOps/Lemmas/I.con" "Lemmas__". +inline procedural "cic:/CoRN/ftc/DerivativeOps/Lemmas/I.con" "Lemmas__" as definition. (* end hide *) @@ -52,7 +52,7 @@ alias id "F" = "cic:/CoRN/ftc/DerivativeOps/Lemmas/F.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/DerivativeOps/Lemmas/P.con" "Lemmas__". +inline procedural "cic:/CoRN/ftc/DerivativeOps/Lemmas/P.con" "Lemmas__" as definition. (* end hide *) @@ -62,7 +62,7 @@ alias id "Fbnd" = "cic:/CoRN/ftc/DerivativeOps/Lemmas/Fbnd.var". (* end show *) -inline procedural "cic:/CoRN/ftc/DerivativeOps/bnd_away_zero_square.con". +inline procedural "cic:/CoRN/ftc/DerivativeOps/bnd_away_zero_square.con" as lemma. (* UNEXPORTED End Lemmas @@ -89,15 +89,15 @@ alias id "Hab'" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/Hab'.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/DerivativeOps/Local_Results/Hab.con" "Local_Results__". +inline procedural "cic:/CoRN/ftc/DerivativeOps/Local_Results/Hab.con" "Local_Results__" as definition. -inline procedural "cic:/CoRN/ftc/DerivativeOps/Local_Results/I.con" "Local_Results__". +inline procedural "cic:/CoRN/ftc/DerivativeOps/Local_Results/I.con" "Local_Results__" as definition. (* end hide *) -inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_const.con". +inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_const.con" as lemma. -inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_id.con". +inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_id.con" as lemma. alias id "F" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/F.var". @@ -111,11 +111,11 @@ alias id "derF" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/derF.var". alias id "derG" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/derG.var". -inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_plus.con". +inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_plus.con" as lemma. -inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_inv.con". +inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_inv.con" as lemma. -inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_mult.con". +inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_mult.con" as lemma. (*#* As was the case for continuity, the rule for the reciprocal function has a side condition. @@ -127,7 +127,7 @@ alias id "Fbnd" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/Fbnd.var". (* end show *) -inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_recip.con". +inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_recip.con" as lemma. (* UNEXPORTED End Local_Results @@ -154,9 +154,9 @@ alias id "Hab'" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/Hab'.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/DerivativeOps/Corolaries/Hab.con" "Corolaries__". +inline procedural "cic:/CoRN/ftc/DerivativeOps/Corolaries/Hab.con" "Corolaries__" as definition. -inline procedural "cic:/CoRN/ftc/DerivativeOps/Corolaries/I.con" "Corolaries__". +inline procedural "cic:/CoRN/ftc/DerivativeOps/Corolaries/I.con" "Corolaries__" as definition. (* end hide *) @@ -176,15 +176,15 @@ alias id "derG" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/derG.var". From this lemmas the rules for the other algebraic operations follow directly. *) -inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_minus.con". +inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_minus.con" as lemma. -inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_scal.con". +inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_scal.con" as lemma. -inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_nth.con". +inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_nth.con" as lemma. alias id "Gbnd" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/Gbnd.var". -inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_div.con". +inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_div.con" as lemma. (* UNEXPORTED End Corolaries @@ -213,15 +213,15 @@ alias id "Hab'" = "cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/Hab'.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/I.con" "Derivative_Sums__". +inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/I.con" "Derivative_Sums__" as definition. (* end hide *) -inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_Sum0.con". +inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_Sum0.con" as lemma. -inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_Sumx.con". +inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_Sumx.con" as lemma. -inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_Sum.con". +inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_Sum.con" as lemma. (* UNEXPORTED End Derivative_Sums diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/Differentiability.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/Differentiability.mma index e0f259017..ad8d9b631 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/Differentiability.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/Differentiability.mma @@ -56,7 +56,7 @@ interval and eliminate the existencial quantifier without any problems. *) -inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I.con". +inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I.con" as definition. (* UNEXPORTED End Definitions @@ -76,7 +76,7 @@ From this point on, we just prove results analogous to the ones for derivability A function differentiable in [[a,b]] is differentiable in every proper compact subinterval of [[a,b]]. *) -inline procedural "cic:/CoRN/ftc/Differentiability/included_imp_diffble.con". +inline procedural "cic:/CoRN/ftc/Differentiability/included_imp_diffble.con" as lemma. (*#* A function differentiable in an interval is everywhere defined in that interval. @@ -90,19 +90,19 @@ alias id "Hab'" = "cic:/CoRN/ftc/Differentiability/Local_Properties/Hab'.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/Differentiability/Local_Properties/Hab.con" "Local_Properties__". +inline procedural "cic:/CoRN/ftc/Differentiability/Local_Properties/Hab.con" "Local_Properties__" as definition. -inline procedural "cic:/CoRN/ftc/Differentiability/Local_Properties/I.con" "Local_Properties__". +inline procedural "cic:/CoRN/ftc/Differentiability/Local_Properties/I.con" "Local_Properties__" as definition. (* end hide *) -inline procedural "cic:/CoRN/ftc/Differentiability/diffble_imp_inc.con". +inline procedural "cic:/CoRN/ftc/Differentiability/diffble_imp_inc.con" as lemma. (*#* If a function has a derivative in an interval then it is differentiable in that interval. *) -inline procedural "cic:/CoRN/ftc/Differentiability/deriv_imp_Diffble_I.con". +inline procedural "cic:/CoRN/ftc/Differentiability/deriv_imp_Diffble_I.con" as lemma. (* UNEXPORTED End Local_Properties @@ -128,9 +128,9 @@ alias id "Hab'" = "cic:/CoRN/ftc/Differentiability/Operations/Hab'.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/Differentiability/Operations/Hab.con" "Operations__". +inline procedural "cic:/CoRN/ftc/Differentiability/Operations/Hab.con" "Operations__" as definition. -inline procedural "cic:/CoRN/ftc/Differentiability/Operations/I.con" "Operations__". +inline procedural "cic:/CoRN/ftc/Differentiability/Operations/I.con" "Operations__" as definition. (* end hide *) @@ -138,9 +138,9 @@ inline procedural "cic:/CoRN/ftc/Differentiability/Operations/I.con" "Operations Section Constants *) -inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_const.con". +inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_const.con" as lemma. -inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_id.con". +inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_id.con" as lemma. (* UNEXPORTED End Constants @@ -156,7 +156,7 @@ alias id "H" = "cic:/CoRN/ftc/Differentiability/Operations/Well_Definedness/H.va alias id "diffF" = "cic:/CoRN/ftc/Differentiability/Operations/Well_Definedness/diffF.var". -inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_wd.con". +inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_wd.con" as lemma. (* UNEXPORTED End Well_Definedness @@ -170,11 +170,11 @@ alias id "diffF" = "cic:/CoRN/ftc/Differentiability/Operations/diffF.var". alias id "diffG" = "cic:/CoRN/ftc/Differentiability/Operations/diffG.var". -inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_plus.con". +inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_plus.con" as lemma. -inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_inv.con". +inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_inv.con" as lemma. -inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_mult.con". +inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_mult.con" as lemma. (* begin show *) @@ -182,7 +182,7 @@ alias id "Gbnd" = "cic:/CoRN/ftc/Differentiability/Operations/Gbnd.var". (* end show *) -inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_recip.con". +inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_recip.con" as lemma. (* UNEXPORTED End Operations @@ -200,9 +200,9 @@ alias id "Hab'" = "cic:/CoRN/ftc/Differentiability/Corollaries/Hab'.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/Differentiability/Corollaries/Hab.con" "Corollaries__". +inline procedural "cic:/CoRN/ftc/Differentiability/Corollaries/Hab.con" "Corollaries__" as definition. -inline procedural "cic:/CoRN/ftc/Differentiability/Corollaries/I.con" "Corollaries__". +inline procedural "cic:/CoRN/ftc/Differentiability/Corollaries/I.con" "Corollaries__" as definition. (* end hide *) @@ -214,15 +214,15 @@ alias id "diffF" = "cic:/CoRN/ftc/Differentiability/Corollaries/diffF.var". alias id "diffG" = "cic:/CoRN/ftc/Differentiability/Corollaries/diffG.var". -inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_minus.con". +inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_minus.con" as lemma. -inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_scal.con". +inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_scal.con" as lemma. -inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_nth.con". +inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_nth.con" as lemma. alias id "Gbnd" = "cic:/CoRN/ftc/Differentiability/Corollaries/Gbnd.var". -inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_div.con". +inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_div.con" as lemma. (* UNEXPORTED End Corollaries @@ -243,11 +243,11 @@ alias id "b" = "cic:/CoRN/ftc/Differentiability/Other_Properties/b.var". alias id "Hab'" = "cic:/CoRN/ftc/Differentiability/Other_Properties/Hab'.var". -inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_Sum0.con". +inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_Sum0.con" as lemma. -inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_Sumx.con". +inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_Sumx.con" as lemma. -inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_Sum.con". +inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_Sum.con" as lemma. (* UNEXPORTED End Other_Properties @@ -260,7 +260,7 @@ Finally, a differentiable function is continuous. %\end{convention}% *) -inline procedural "cic:/CoRN/ftc/Differentiability/diffble_imp_contin_I.con". +inline procedural "cic:/CoRN/ftc/Differentiability/diffble_imp_contin_I.con" as lemma. (* UNEXPORTED Hint Immediate included_imp_contin deriv_imp_contin_I deriv_imp_contin'_I diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/FTC.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/FTC.mma index 9412847b9..9eee7432c 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/FTC.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/FTC.mma @@ -59,11 +59,11 @@ alias id "a" = "cic:/CoRN/ftc/FTC/Indefinite_Integral/a.var". alias id "Ha" = "cic:/CoRN/ftc/FTC/Indefinite_Integral/Ha.var". -inline procedural "cic:/CoRN/ftc/FTC/prim_lemma.con". +inline procedural "cic:/CoRN/ftc/FTC/prim_lemma.con" as lemma. -inline procedural "cic:/CoRN/ftc/FTC/Fprim_strext.con". +inline procedural "cic:/CoRN/ftc/FTC/Fprim_strext.con" as lemma. -inline procedural "cic:/CoRN/ftc/FTC/Fprim.con". +inline procedural "cic:/CoRN/ftc/FTC/Fprim.con" as definition. (* UNEXPORTED End Indefinite_Integral @@ -104,11 +104,11 @@ alias id "Hx0" = "cic:/CoRN/ftc/FTC/FTC/Hx0.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/FTC/FTC/G.con" "FTC__". +inline procedural "cic:/CoRN/ftc/FTC/FTC/G.con" "FTC__" as definition. (* end hide *) -inline procedural "cic:/CoRN/ftc/FTC/Continuous_prim.con". +inline procedural "cic:/CoRN/ftc/FTC/Continuous_prim.con" as lemma. (*#* The derivative of [G] is simply [F]. @@ -116,7 +116,7 @@ The derivative of [G] is simply [F]. alias id "pJ" = "cic:/CoRN/ftc/FTC/FTC/pJ.var". -inline procedural "cic:/CoRN/ftc/FTC/FTC1.con". +inline procedural "cic:/CoRN/ftc/FTC/FTC1.con" as theorem. (*#* Any other function [G0] with derivative [F] must differ from [G] by a constant. @@ -126,7 +126,7 @@ alias id "G0" = "cic:/CoRN/ftc/FTC/FTC/G0.var". alias id "derG0" = "cic:/CoRN/ftc/FTC/FTC/derG0.var". -inline procedural "cic:/CoRN/ftc/FTC/FTC2.con". +inline procedural "cic:/CoRN/ftc/FTC/FTC2.con" as theorem. (*#* The following is another statement of the Fundamental Theorem of Calculus, also known as Barrow's rule. @@ -134,7 +134,7 @@ The following is another statement of the Fundamental Theorem of Calculus, also (* begin hide *) -inline procedural "cic:/CoRN/ftc/FTC/FTC/G0_inc.con" "FTC__". +inline procedural "cic:/CoRN/ftc/FTC/FTC/G0_inc.con" "FTC__" as definition. (* end hide *) @@ -142,7 +142,7 @@ inline procedural "cic:/CoRN/ftc/FTC/FTC/G0_inc.con" "FTC__". Opaque G. *) -inline procedural "cic:/CoRN/ftc/FTC/Barrow.con". +inline procedural "cic:/CoRN/ftc/FTC/Barrow.con" as theorem. (* end hide *) @@ -226,9 +226,9 @@ alias id "Hx0'" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/Hx0'.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/g.con" "Limit_of_Integral_Seq__Compact__". +inline procedural "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/g.con" "Limit_of_Integral_Seq__Compact__" as definition. -inline procedural "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/G.con" "Limit_of_Integral_Seq__Compact__". +inline procedural "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/G.con" "Limit_of_Integral_Seq__Compact__" as definition. (* end hide *) @@ -240,7 +240,7 @@ alias id "contG" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/contG.var". (* end show *) -inline procedural "cic:/CoRN/ftc/FTC/fun_lim_seq_integral.con". +inline procedural "cic:/CoRN/ftc/FTC/fun_lim_seq_integral.con" as lemma. (* UNEXPORTED End Compact @@ -250,9 +250,9 @@ End Compact And now we can generalize it step by step. *) -inline procedural "cic:/CoRN/ftc/FTC/limit_of_integral.con". +inline procedural "cic:/CoRN/ftc/FTC/limit_of_integral.con" as lemma. -inline procedural "cic:/CoRN/ftc/FTC/limit_of_Integral.con". +inline procedural "cic:/CoRN/ftc/FTC/limit_of_Integral.con" as lemma. (* UNEXPORTED Section General @@ -274,9 +274,9 @@ alias id "Hx0" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/Hx0.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/g.con" "Limit_of_Integral_Seq__General__". +inline procedural "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/g.con" "Limit_of_Integral_Seq__General__" as definition. -inline procedural "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/G.con" "Limit_of_Integral_Seq__General__". +inline procedural "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/G.con" "Limit_of_Integral_Seq__General__" as definition. (* end hide *) @@ -284,7 +284,7 @@ alias id "contg" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/contg.var". alias id "contG" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/contG.var". -inline procedural "cic:/CoRN/ftc/FTC/fun_lim_seq_integral_IR.con". +inline procedural "cic:/CoRN/ftc/FTC/fun_lim_seq_integral_IR.con" as lemma. (* UNEXPORTED End General @@ -331,7 +331,7 @@ alias id "convG" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/convG.var". alias id "derf" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/derf.var". -inline procedural "cic:/CoRN/ftc/FTC/fun_lim_seq_derivative.con". +inline procedural "cic:/CoRN/ftc/FTC/fun_lim_seq_derivative.con" as lemma. (* UNEXPORTED End Limit_of_Derivative_Seq @@ -363,7 +363,7 @@ alias id "convG" = "cic:/CoRN/ftc/FTC/Derivative_Series/convG.var". alias id "derF" = "cic:/CoRN/ftc/FTC/Derivative_Series/derF.var". -inline procedural "cic:/CoRN/ftc/FTC/Derivative_FSeries.con". +inline procedural "cic:/CoRN/ftc/FTC/Derivative_FSeries.con" as lemma. (* UNEXPORTED End Derivative_Series diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/FunctSequence.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/FunctSequence.mma index 3fac327f1..0a3c1ce29 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/FunctSequence.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/FunctSequence.mma @@ -58,7 +58,7 @@ alias id "Hab" = "cic:/CoRN/ftc/FunctSequence/Definitions/Hab.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/FunctSequence/Definitions/I.con" "Definitions__". +inline procedural "cic:/CoRN/ftc/FunctSequence/Definitions/I.con" "Definitions__" as definition. (* end hide *) @@ -72,55 +72,55 @@ alias id "contF" = "cic:/CoRN/ftc/FunctSequence/Definitions/contF.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/FunctSequence/Definitions/incf.con" "Definitions__". +inline procedural "cic:/CoRN/ftc/FunctSequence/Definitions/incf.con" "Definitions__" as definition. -inline procedural "cic:/CoRN/ftc/FunctSequence/Definitions/incF.con" "Definitions__". +inline procedural "cic:/CoRN/ftc/FunctSequence/Definitions/incF.con" "Definitions__" as definition. (* end hide *) -inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq.con" as definition. -inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_seq'.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_seq'.con" as definition. -inline procedural "cic:/CoRN/ftc/FunctSequence/conv_norm_fun_seq.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/conv_norm_fun_seq.con" as definition. -inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq1.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq1.con" as definition. -inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq'.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq'.con" as definition. -inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq2.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq2.con" as definition. (*#* These definitions are all shown to be equivalent. *) -inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq_seq'.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq_seq'.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq'_seq.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq'_seq.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSequence/conv_Cauchy_fun_seq'.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/conv_Cauchy_fun_seq'.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq_seq2.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq_seq2.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq2_seq.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq2_seq.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_seq'_norm.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_seq'_norm.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_norm_seq.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_norm_seq.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq1_seq'.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq1_seq'.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq'_seq1.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq'_seq1.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq_seq1.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq_seq1.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq1_seq.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq1_seq.con" as lemma. (*#* A Cauchy sequence of functions is pointwise a Cauchy sequence. *) -inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_real.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_real.con" as lemma. (* UNEXPORTED End Definitions @@ -138,7 +138,7 @@ alias id "Hab" = "cic:/CoRN/ftc/FunctSequence/More_Definitions/Hab.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/FunctSequence/More_Definitions/I.con" "More_Definitions__". +inline procedural "cic:/CoRN/ftc/FunctSequence/More_Definitions/I.con" "More_Definitions__" as definition. (* end hide *) @@ -152,7 +152,7 @@ continuous function. Notice that we do not quantify directly over partial functions, for reasons which were already explained. *) -inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_seq.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_seq.con" as definition. (*#* It is useful to extract the limit as a partial function: @@ -164,7 +164,7 @@ alias id "H" = "cic:/CoRN/ftc/FunctSequence/More_Definitions/H.var". (* end show *) -inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq_Lim.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq_Lim.con" as definition. (* UNEXPORTED End More_Definitions @@ -187,7 +187,7 @@ alias id "Hab" = "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/Hab.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/I.con" "Irrelevance_of_Proofs__". +inline procedural "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/I.con" "Irrelevance_of_Proofs__" as definition. (* end hide *) @@ -211,15 +211,15 @@ alias id "contF0" = "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/contF0.va (* end show *) -inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_seq'_wd.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_seq'_wd.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq'_wd.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq'_wd.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq2_wd.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq2_wd.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSequence/conv_norm_fun_seq_wd.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/conv_norm_fun_seq_wd.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq1_wd.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq1_wd.con" as lemma. (* UNEXPORTED End Irrelevance_of_Proofs @@ -229,7 +229,7 @@ End Irrelevance_of_Proofs Section More_Proof_Irrelevance *) -inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_seq_wd.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_seq_wd.con" as lemma. (* UNEXPORTED End More_Proof_Irrelevance @@ -254,7 +254,7 @@ alias id "Hab" = "cic:/CoRN/ftc/FunctSequence/More_Properties/Hab.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/FunctSequence/More_Properties/I.con" "More_Properties__". +inline procedural "cic:/CoRN/ftc/FunctSequence/More_Properties/I.con" "More_Properties__" as definition. (* end hide *) @@ -274,7 +274,7 @@ alias id "contg0" = "cic:/CoRN/ftc/FunctSequence/More_Properties/contg0.var". (* end show *) -inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_conv_fun_seq'.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_conv_fun_seq'.con" as lemma. alias id "F" = "cic:/CoRN/ftc/FunctSequence/More_Properties/F.var". @@ -292,33 +292,33 @@ alias id "contG0" = "cic:/CoRN/ftc/FunctSequence/More_Properties/contG0.var". (* end show *) -inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_seq'_wdl.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_seq'_wdl.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_seq'_wdr.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_seq'_wdr.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_seq'_wdl'.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_seq'_wdl'.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_seq'_wdr'.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_seq'_wdr'.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq_wd.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq_wd.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_cont_Lim.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_cont_Lim.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_conv_fun_seq.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_conv_fun_seq.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSequence/conv_Cauchy_fun_seq.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/conv_Cauchy_fun_seq.con" as lemma. (*#* More interesting is the fact that a convergent sequence of functions converges pointwise as a sequence of real numbers. *) -inline procedural "cic:/CoRN/ftc/FunctSequence/fun_conv_imp_seq_conv.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/fun_conv_imp_seq_conv.con" as lemma. (*#* And a sequence of real numbers converges iff the corresponding sequence of constant functions converges to the corresponding constant function. *) -inline procedural "cic:/CoRN/ftc/FunctSequence/seq_conv_imp_fun_conv.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/seq_conv_imp_fun_conv.con" as lemma. (* UNEXPORTED End More_Properties @@ -345,7 +345,7 @@ alias id "Hab" = "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/Hab.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/I.con" "Algebraic_Properties__". +inline procedural "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/I.con" "Algebraic_Properties__" as definition. (* end hide *) @@ -361,14 +361,14 @@ alias id "contg" = "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/contg.var". First, the limit function is unique. *) -inline procedural "cic:/CoRN/ftc/FunctSequence/FLim_unique.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/FLim_unique.con" as lemma. (*#* Constant sequences (not sequences of constant functions!) always converge. *) -inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_const.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_const.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Cauchy_prop_const.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Cauchy_prop_const.con" as lemma. (*#* We now prove that if two sequences converge than their sum (difference, product) also converge to the sum (difference, product) of their limits. @@ -392,21 +392,21 @@ alias id "convG" = "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/convG.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/incf.con" "Algebraic_Properties__". +inline procedural "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/incf.con" "Algebraic_Properties__" as definition. -inline procedural "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/incg.con" "Algebraic_Properties__". +inline procedural "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/incg.con" "Algebraic_Properties__" as definition. -inline procedural "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/incF.con" "Algebraic_Properties__". +inline procedural "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/incF.con" "Algebraic_Properties__" as definition. -inline procedural "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/incG.con" "Algebraic_Properties__". +inline procedural "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/incG.con" "Algebraic_Properties__" as definition. (* end hide *) -inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_plus'.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_plus'.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_minus'.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_minus'.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_mult'.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_mult'.con" as lemma. (* UNEXPORTED End Algebraic_Properties @@ -424,7 +424,7 @@ alias id "Hab" = "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/Hab.var" (* begin hide *) -inline procedural "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/I.con" "More_Algebraic_Properties__". +inline procedural "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/I.con" "More_Algebraic_Properties__" as definition. (* end hide *) @@ -448,17 +448,17 @@ alias id "Hg" = "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/Hg.var". (* end hide *) -inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_plus.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_plus.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Cauchy_prop_plus.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Cauchy_prop_plus.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_minus.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_minus.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Cauchy_prop_minus.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Cauchy_prop_minus.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_mult.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_mult.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Cauchy_prop_mult.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Cauchy_prop_mult.con" as lemma. (* UNEXPORTED End More_Algebraic_Properties @@ -476,7 +476,7 @@ alias id "Hab" = "cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/Ha (* begin hide *) -inline procedural "cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/I.con" "Still_More_Algebraic_Properties__". +inline procedural "cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/I.con" "Still_More_Algebraic_Properties__" as definition. (* end hide *) @@ -490,9 +490,9 @@ alias id "Hf" = "cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/Hf. As a corollary, we get the analogous property for the sequence of algebraic inverse functions. *) -inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_inv.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_inv.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Cauchy_prop_inv.con". +inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Cauchy_prop_inv.con" as lemma. (* UNEXPORTED End Still_More_Algebraic_Properties diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/FunctSeries.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/FunctSeries.mma index 1ea656200..49acbf1cf 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/FunctSeries.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/FunctSeries.mma @@ -59,17 +59,17 @@ alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/Definitions/Hab.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/FunctSeries/Definitions/I.con" "Definitions__". +inline procedural "cic:/CoRN/ftc/FunctSeries/Definitions/I.con" "Definitions__" as definition. (* end hide *) alias id "f" = "cic:/CoRN/ftc/FunctSeries/Definitions/f.var". -inline procedural "cic:/CoRN/ftc/FunctSeries/fun_seq_part_sum.con". +inline procedural "cic:/CoRN/ftc/FunctSeries/fun_seq_part_sum.con" as definition. -inline procedural "cic:/CoRN/ftc/FunctSeries/fun_seq_part_sum_cont.con". +inline procedural "cic:/CoRN/ftc/FunctSeries/fun_seq_part_sum_cont.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSeries/fun_series_convergent.con". +inline procedural "cic:/CoRN/ftc/FunctSeries/fun_series_convergent.con" as definition. (*#* For what comes up next we need to know that the convergence of a @@ -77,7 +77,7 @@ series of functions implies pointwise convergence of the corresponding real number series. *) -inline procedural "cic:/CoRN/ftc/FunctSeries/fun_series_conv_imp_conv.con". +inline procedural "cic:/CoRN/ftc/FunctSeries/fun_series_conv_imp_conv.con" as lemma. (*#* We then define the sum of the series as being the pointwise sum of the corresponding series. @@ -91,15 +91,15 @@ alias id "H" = "cic:/CoRN/ftc/FunctSeries/Definitions/H.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/FunctSeries/Definitions/contf.con" "Definitions__". +inline procedural "cic:/CoRN/ftc/FunctSeries/Definitions/contf.con" "Definitions__" as definition. -inline procedural "cic:/CoRN/ftc/FunctSeries/Definitions/incf.con" "Definitions__". +inline procedural "cic:/CoRN/ftc/FunctSeries/Definitions/incf.con" "Definitions__" as definition. (* end hide *) -inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_strext.con". +inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_strext.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum.con". +inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum.con" as definition. (* UNEXPORTED End Definitions @@ -127,7 +127,7 @@ alias id "f" = "cic:/CoRN/ftc/FunctSeries/More_Definitions/f.var". (*#* A series can also be absolutely convergent. *) -inline procedural "cic:/CoRN/ftc/FunctSeries/fun_series_abs_convergent.con". +inline procedural "cic:/CoRN/ftc/FunctSeries/fun_series_abs_convergent.con" as definition. (* UNEXPORTED End More_Definitions @@ -150,19 +150,19 @@ alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/Operations/Hab.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/FunctSeries/Operations/I.con" "Operations__". +inline procedural "cic:/CoRN/ftc/FunctSeries/Operations/I.con" "Operations__" as definition. (* end hide *) -inline procedural "cic:/CoRN/ftc/FunctSeries/fun_seq_part_sum_n.con". +inline procedural "cic:/CoRN/ftc/FunctSeries/fun_seq_part_sum_n.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSeries/conv_fun_const_series.con". +inline procedural "cic:/CoRN/ftc/FunctSeries/conv_fun_const_series.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSeries/fun_const_series_sum.con". +inline procedural "cic:/CoRN/ftc/FunctSeries/fun_const_series_sum.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSeries/conv_zero_fun_series.con". +inline procedural "cic:/CoRN/ftc/FunctSeries/conv_zero_fun_series.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_zero.con". +inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_zero.con" as lemma. (* begin show *) @@ -172,7 +172,7 @@ alias id "g" = "cic:/CoRN/ftc/FunctSeries/Operations/g.var". (* end show *) -inline procedural "cic:/CoRN/ftc/FunctSeries/fun_series_convergent_wd.con". +inline procedural "cic:/CoRN/ftc/FunctSeries/fun_series_convergent_wd.con" as lemma. (* begin show *) @@ -182,15 +182,15 @@ alias id "convG" = "cic:/CoRN/ftc/FunctSeries/Operations/convG.var". (* end show *) -inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_wd'.con". +inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_wd'.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSeries/conv_fun_series_plus.con". +inline procedural "cic:/CoRN/ftc/FunctSeries/conv_fun_series_plus.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_plus.con". +inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_plus.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSeries/conv_fun_series_minus.con". +inline procedural "cic:/CoRN/ftc/FunctSeries/conv_fun_series_minus.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_min.con". +inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_min.con" as lemma. (*#* %\begin{convention}% Let [c:IR]. @@ -203,9 +203,9 @@ alias id "H" = "cic:/CoRN/ftc/FunctSeries/Operations/H.var". alias id "contH" = "cic:/CoRN/ftc/FunctSeries/Operations/contH.var". -inline procedural "cic:/CoRN/ftc/FunctSeries/conv_fun_series_scal.con". +inline procedural "cic:/CoRN/ftc/FunctSeries/conv_fun_series_scal.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_scal.con". +inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_scal.con" as lemma. (* UNEXPORTED End Operations @@ -223,7 +223,7 @@ alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/More_Operations/Hab.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/FunctSeries/More_Operations/I.con" "More_Operations__". +inline procedural "cic:/CoRN/ftc/FunctSeries/More_Operations/I.con" "More_Operations__" as definition. (* end hide *) @@ -231,9 +231,9 @@ alias id "f" = "cic:/CoRN/ftc/FunctSeries/More_Operations/f.var". alias id "convF" = "cic:/CoRN/ftc/FunctSeries/More_Operations/convF.var". -inline procedural "cic:/CoRN/ftc/FunctSeries/conv_fun_series_inv.con". +inline procedural "cic:/CoRN/ftc/FunctSeries/conv_fun_series_inv.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_inv.con". +inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_inv.con" as lemma. (* UNEXPORTED End More_Operations @@ -259,15 +259,15 @@ partial sums; as a corollary we get the continuity of the sum of the series. *) -inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_char'.con". +inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_char'.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSeries/fun_series_conv.con". +inline procedural "cic:/CoRN/ftc/FunctSeries/fun_series_conv.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_cont.con". +inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_cont.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_char.con". +inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_char.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_as_Lim.con". +inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_as_Lim.con" as lemma. (* UNEXPORTED End Other_Results @@ -294,7 +294,7 @@ alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/Hab.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/I.con" "Convergence_Criteria__". +inline procedural "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/I.con" "Convergence_Criteria__" as definition. (* end hide *) @@ -342,21 +342,21 @@ Transparent fun_seq_part_sum. Opaque fun_seq_part_sum. *) -inline procedural "cic:/CoRN/ftc/FunctSeries/fun_str_comparison.con". +inline procedural "cic:/CoRN/ftc/FunctSeries/fun_str_comparison.con" as lemma. (* UNEXPORTED Transparent FAbs. *) -inline procedural "cic:/CoRN/ftc/FunctSeries/fun_comparison.con". +inline procedural "cic:/CoRN/ftc/FunctSeries/fun_comparison.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSeries/abs_imp_conv.con". +inline procedural "cic:/CoRN/ftc/FunctSeries/abs_imp_conv.con" as lemma. (* UNEXPORTED Opaque FAbs. *) -inline procedural "cic:/CoRN/ftc/FunctSeries/fun_ratio_test_conv.con". +inline procedural "cic:/CoRN/ftc/FunctSeries/fun_ratio_test_conv.con" as lemma. (* UNEXPORTED End Convergence_Criteria diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/FunctSums.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/FunctSums.mma index e94e9d0f9..3475e34fb 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/FunctSums.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/FunctSums.mma @@ -44,9 +44,9 @@ $\sum_{i=m}^nf_i$#the sum of fm through fn# ( [FSum]). *) -inline procedural "cic:/CoRN/ftc/FunctSums/FSum0.con". +inline procedural "cic:/CoRN/ftc/FunctSums/FSum0.con" as definition. -inline procedural "cic:/CoRN/ftc/FunctSums/FSum.con". +inline procedural "cic:/CoRN/ftc/FunctSums/FSum.con" as definition. (*#* Although [FSum] is here defined directly, it has the same relationship @@ -58,37 +58,37 @@ mentioned, their forming too big a type makes it impossible to use those results. *) -inline procedural "cic:/CoRN/ftc/FunctSums/FSum_FSum0.con". +inline procedural "cic:/CoRN/ftc/FunctSums/FSum_FSum0.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSums/FSum0_wd.con". +inline procedural "cic:/CoRN/ftc/FunctSums/FSum0_wd.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSums/FSum_one.con". +inline procedural "cic:/CoRN/ftc/FunctSums/FSum_one.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSums/FSum_FSum.con". +inline procedural "cic:/CoRN/ftc/FunctSums/FSum_FSum.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSums/FSum_first.con". +inline procedural "cic:/CoRN/ftc/FunctSums/FSum_first.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSums/FSum_last.con". +inline procedural "cic:/CoRN/ftc/FunctSums/FSum_last.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSums/FSum_last'.con". +inline procedural "cic:/CoRN/ftc/FunctSums/FSum_last'.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSums/FSum_wd.con". +inline procedural "cic:/CoRN/ftc/FunctSums/FSum_wd.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSums/FSum_plus_FSum.con". +inline procedural "cic:/CoRN/ftc/FunctSums/FSum_plus_FSum.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSums/inv_FSum.con". +inline procedural "cic:/CoRN/ftc/FunctSums/inv_FSum.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSums/FSum_minus_FSum.con". +inline procedural "cic:/CoRN/ftc/FunctSums/FSum_minus_FSum.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSums/FSum_wd'.con". +inline procedural "cic:/CoRN/ftc/FunctSums/FSum_wd'.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSums/FSum_resp_less.con". +inline procedural "cic:/CoRN/ftc/FunctSums/FSum_resp_less.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSums/FSum_resp_leEq.con". +inline procedural "cic:/CoRN/ftc/FunctSums/FSum_resp_leEq.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSums/FSum_comm_scal.con". +inline procedural "cic:/CoRN/ftc/FunctSums/FSum_comm_scal.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSums/FSum_comm_scal'.con". +inline procedural "cic:/CoRN/ftc/FunctSums/FSum_comm_scal'.con" as lemma. (*#* Also important is the case when we have a finite family @@ -96,15 +96,15 @@ $\{f_i\}_{i=0}^{n-1}$ of #exactly n# functions; in this case we need to use the [FSumx] operator. *) -inline procedural "cic:/CoRN/ftc/FunctSums/FSumx.con". +inline procedural "cic:/CoRN/ftc/FunctSums/FSumx.con" as definition. (*#* This operator is well defined, as expected. *) -inline procedural "cic:/CoRN/ftc/FunctSums/FSumx_wd.con". +inline procedural "cic:/CoRN/ftc/FunctSums/FSumx_wd.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSums/FSumx_wd'.con". +inline procedural "cic:/CoRN/ftc/FunctSums/FSumx_wd'.con" as lemma. (*#* As was already the case for [Sumx], in many cases we will need to @@ -113,9 +113,9 @@ explicitly assume that $f_i$#f1# is independent of the proof that function $f_i$#fi#. *) -inline procedural "cic:/CoRN/ftc/FunctSums/ext_fun_seq.con". +inline procedural "cic:/CoRN/ftc/FunctSums/ext_fun_seq.con" as definition. -inline procedural "cic:/CoRN/ftc/FunctSums/ext_fun_seq'.con". +inline procedural "cic:/CoRN/ftc/FunctSums/ext_fun_seq'.con" as definition. (* UNEXPORTED Implicit Arguments ext_fun_seq [n]. @@ -129,35 +129,35 @@ Implicit Arguments ext_fun_seq' [n]. Under these assumptions, we can characterize the domain and the value of the sum function from the domains and values of the summands: *) -inline procedural "cic:/CoRN/ftc/FunctSums/FSumx_pred.con". +inline procedural "cic:/CoRN/ftc/FunctSums/FSumx_pred.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSums/FSumx_pred'.con". +inline procedural "cic:/CoRN/ftc/FunctSums/FSumx_pred'.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSums/FSumx_char.con". +inline procedural "cic:/CoRN/ftc/FunctSums/FSumx_char.con" as lemma. (*#* As we did for arbitrary groups, it is often useful to rewrite this sums as ordinary sums. *) -inline procedural "cic:/CoRN/ftc/FunctSums/FSumx_to_FSum.con". +inline procedural "cic:/CoRN/ftc/FunctSums/FSumx_to_FSum.con" as definition. -inline procedural "cic:/CoRN/ftc/FunctSums/FSumx_lt.con". +inline procedural "cic:/CoRN/ftc/FunctSums/FSumx_lt.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSums/FSumx_le.con". +inline procedural "cic:/CoRN/ftc/FunctSums/FSumx_le.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSums/FSum_FSumx_to_FSum.con". +inline procedural "cic:/CoRN/ftc/FunctSums/FSum_FSumx_to_FSum.con" as lemma. (*#* Some useful lemmas follow. *) -inline procedural "cic:/CoRN/ftc/FunctSums/FSum0_0.con". +inline procedural "cic:/CoRN/ftc/FunctSums/FSum0_0.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSums/FSum0_S.con". +inline procedural "cic:/CoRN/ftc/FunctSums/FSum0_S.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSums/FSum_0.con". +inline procedural "cic:/CoRN/ftc/FunctSums/FSum_0.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSums/FSum_S.con". +inline procedural "cic:/CoRN/ftc/FunctSums/FSum_S.con" as lemma. -inline procedural "cic:/CoRN/ftc/FunctSums/FSum_FSum0'.con". +inline procedural "cic:/CoRN/ftc/FunctSums/FSum_FSum0'.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/Integral.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/Integral.mma index 1fa68f385..adfac8d02 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/Integral.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/Integral.mma @@ -30,9 +30,9 @@ include "ftc/RefLemma.ma". Section Lemmas *) -inline procedural "cic:/CoRN/ftc/Integral/Lemmas/Sumx_wd_weird.con" "Lemmas__". +inline procedural "cic:/CoRN/ftc/Integral/Lemmas/Sumx_wd_weird.con" "Lemmas__" as definition. -inline procedural "cic:/CoRN/ftc/Integral/Sumx_weird_lemma.con". +inline procedural "cic:/CoRN/ftc/Integral/Sumx_weird_lemma.con" as lemma. (* UNEXPORTED End Lemmas @@ -65,13 +65,13 @@ alias id "Hab" = "cic:/CoRN/ftc/Integral/Integral/Hab.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/Integral/Integral/I.con" "Integral__". +inline procedural "cic:/CoRN/ftc/Integral/Integral/I.con" "Integral__" as definition. alias id "F" = "cic:/CoRN/ftc/Integral/Integral/F.var". alias id "contF" = "cic:/CoRN/ftc/Integral/Integral/contF.var". -inline procedural "cic:/CoRN/ftc/Integral/Integral/contF'.con" "Integral__". +inline procedural "cic:/CoRN/ftc/Integral/Integral/contF'.con" "Integral__" as definition. (* end hide *) @@ -79,11 +79,11 @@ inline procedural "cic:/CoRN/ftc/Integral/Integral/contF'.con" "Integral__". Section Darboux_Sum *) -inline procedural "cic:/CoRN/ftc/Integral/integral_seq.con". +inline procedural "cic:/CoRN/ftc/Integral/integral_seq.con" as definition. -inline procedural "cic:/CoRN/ftc/Integral/Cauchy_Darboux_Seq.con". +inline procedural "cic:/CoRN/ftc/Integral/Cauchy_Darboux_Seq.con" as lemma. -inline procedural "cic:/CoRN/ftc/Integral/integral.con". +inline procedural "cic:/CoRN/ftc/Integral/integral.con" as definition. (* UNEXPORTED End Darboux_Sum @@ -114,7 +114,7 @@ alias id "He" = "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/He.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/d.con" "Integral__Integral_Thm__". +inline procedural "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/d.con" "Integral__Integral_Thm__" as definition. (* end hide *) @@ -128,7 +128,7 @@ alias id "HfP'" = "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/HfP'.var". alias id "incF" = "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/incF.var". -inline procedural "cic:/CoRN/ftc/Integral/partition_Sum_conv_integral.con". +inline procedural "cic:/CoRN/ftc/Integral/partition_Sum_conv_integral.con" as lemma. (* UNEXPORTED End Integral_Thm @@ -154,7 +154,7 @@ alias id "Hab" = "cic:/CoRN/ftc/Integral/Basic_Properties/Hab.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/Integral/Basic_Properties/I.con" "Basic_Properties__". +inline procedural "cic:/CoRN/ftc/Integral/Basic_Properties/I.con" "Basic_Properties__" as definition. (* end hide *) @@ -174,13 +174,13 @@ alias id "contF" = "cic:/CoRN/ftc/Integral/Basic_Properties/Well_Definedness/con alias id "contG" = "cic:/CoRN/ftc/Integral/Basic_Properties/Well_Definedness/contG.var". -inline procedural "cic:/CoRN/ftc/Integral/integral_strext.con". +inline procedural "cic:/CoRN/ftc/Integral/integral_strext.con" as lemma. -inline procedural "cic:/CoRN/ftc/Integral/integral_strext'.con". +inline procedural "cic:/CoRN/ftc/Integral/integral_strext'.con" as lemma. -inline procedural "cic:/CoRN/ftc/Integral/integral_wd.con". +inline procedural "cic:/CoRN/ftc/Integral/integral_wd.con" as lemma. -inline procedural "cic:/CoRN/ftc/Integral/integral_wd'.con". +inline procedural "cic:/CoRN/ftc/Integral/integral_wd'.con" as lemma. (* UNEXPORTED End Well_Definedness @@ -198,7 +198,7 @@ Opaque Even_Partition. The integral is a linear and monotonous function; in order to prove these facts we also need the important equalities $\int_a^bdx=b-a$#∫abdx=b-a# and $\int_a^af(x)dx=0$#∫aa=0#. *) -inline procedural "cic:/CoRN/ftc/Integral/integral_one.con". +inline procedural "cic:/CoRN/ftc/Integral/integral_one.con" as lemma. alias id "F" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity/F.var". @@ -208,15 +208,15 @@ alias id "contF" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monoto alias id "contG" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity/contG.var". -inline procedural "cic:/CoRN/ftc/Integral/integral_comm_scal.con". +inline procedural "cic:/CoRN/ftc/Integral/integral_comm_scal.con" as lemma. -inline procedural "cic:/CoRN/ftc/Integral/integral_plus.con". +inline procedural "cic:/CoRN/ftc/Integral/integral_plus.con" as lemma. (* UNEXPORTED Transparent Even_Partition. *) -inline procedural "cic:/CoRN/ftc/Integral/integral_empty.con". +inline procedural "cic:/CoRN/ftc/Integral/integral_empty.con" as lemma. (* UNEXPORTED End Linearity_and_Monotonicity @@ -246,19 +246,19 @@ alias id "beta" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monoton (* begin hide *) -inline procedural "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/h.con" "Basic_Properties__Linearity_and_Monotonicity'__". +inline procedural "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/h.con" "Basic_Properties__Linearity_and_Monotonicity'__" as definition. (* end hide *) alias id "contH" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/contH.var". -inline procedural "cic:/CoRN/ftc/Integral/linear_integral.con". +inline procedural "cic:/CoRN/ftc/Integral/linear_integral.con" as lemma. (* UNEXPORTED Opaque nring. *) -inline procedural "cic:/CoRN/ftc/Integral/monotonous_integral.con". +inline procedural "cic:/CoRN/ftc/Integral/monotonous_integral.con" as lemma. (* UNEXPORTED Transparent nring. @@ -284,21 +284,21 @@ alias id "contG" = "cic:/CoRN/ftc/Integral/Basic_Properties/Corollaries/contG.va As corollaries we can calculate integrals of group operations applied to functions. *) -inline procedural "cic:/CoRN/ftc/Integral/integral_const.con". +inline procedural "cic:/CoRN/ftc/Integral/integral_const.con" as lemma. -inline procedural "cic:/CoRN/ftc/Integral/integral_minus.con". +inline procedural "cic:/CoRN/ftc/Integral/integral_minus.con" as lemma. -inline procedural "cic:/CoRN/ftc/Integral/integral_inv.con". +inline procedural "cic:/CoRN/ftc/Integral/integral_inv.con" as lemma. (*#* We can also bound integrals by bounding the integrated functions. *) -inline procedural "cic:/CoRN/ftc/Integral/lb_integral.con". +inline procedural "cic:/CoRN/ftc/Integral/lb_integral.con" as lemma. -inline procedural "cic:/CoRN/ftc/Integral/ub_integral.con". +inline procedural "cic:/CoRN/ftc/Integral/ub_integral.con" as lemma. -inline procedural "cic:/CoRN/ftc/Integral/integral_leEq_norm.con". +inline procedural "cic:/CoRN/ftc/Integral/integral_leEq_norm.con" as lemma. (* UNEXPORTED End Corollaries @@ -357,31 +357,31 @@ alias id "Q" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_J (* begin hide *) -inline procedural "cic:/CoRN/ftc/Integral/partition_join_aux.con". +inline procedural "cic:/CoRN/ftc/Integral/partition_join_aux.con" as lemma. (* end hide *) -inline procedural "cic:/CoRN/ftc/Integral/partition_join_fun.con". +inline procedural "cic:/CoRN/ftc/Integral/partition_join_fun.con" as definition. (* begin hide *) -inline procedural "cic:/CoRN/ftc/Integral/pjf_1.con". +inline procedural "cic:/CoRN/ftc/Integral/pjf_1.con" as lemma. -inline procedural "cic:/CoRN/ftc/Integral/pjf_2.con". +inline procedural "cic:/CoRN/ftc/Integral/pjf_2.con" as lemma. -inline procedural "cic:/CoRN/ftc/Integral/pjf_2'.con". +inline procedural "cic:/CoRN/ftc/Integral/pjf_2'.con" as lemma. -inline procedural "cic:/CoRN/ftc/Integral/pjf_3.con". +inline procedural "cic:/CoRN/ftc/Integral/pjf_3.con" as lemma. -inline procedural "cic:/CoRN/ftc/Integral/partition_join_prf1.con". +inline procedural "cic:/CoRN/ftc/Integral/partition_join_prf1.con" as lemma. -inline procedural "cic:/CoRN/ftc/Integral/partition_join_prf2.con". +inline procedural "cic:/CoRN/ftc/Integral/partition_join_prf2.con" as lemma. -inline procedural "cic:/CoRN/ftc/Integral/partition_join_start.con". +inline procedural "cic:/CoRN/ftc/Integral/partition_join_start.con" as lemma. -inline procedural "cic:/CoRN/ftc/Integral/partition_join_finish.con". +inline procedural "cic:/CoRN/ftc/Integral/partition_join_finish.con" as lemma. -inline procedural "cic:/CoRN/ftc/Integral/partition_join.con". +inline procedural "cic:/CoRN/ftc/Integral/partition_join.con" as definition. (* end hide *) @@ -404,25 +404,25 @@ alias id "HfQ'" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partitio (* begin hide *) -inline procedural "cic:/CoRN/ftc/Integral/partition_join_aux'.con". +inline procedural "cic:/CoRN/ftc/Integral/partition_join_aux'.con" as lemma. (* end hide *) -inline procedural "cic:/CoRN/ftc/Integral/partition_join_pts.con". +inline procedural "cic:/CoRN/ftc/Integral/partition_join_pts.con" as definition. (* begin hide *) -inline procedural "cic:/CoRN/ftc/Integral/pjp_1.con". +inline procedural "cic:/CoRN/ftc/Integral/pjp_1.con" as lemma. -inline procedural "cic:/CoRN/ftc/Integral/pjp_2.con". +inline procedural "cic:/CoRN/ftc/Integral/pjp_2.con" as lemma. -inline procedural "cic:/CoRN/ftc/Integral/pjp_3.con". +inline procedural "cic:/CoRN/ftc/Integral/pjp_3.con" as lemma. (* end hide *) -inline procedural "cic:/CoRN/ftc/Integral/partition_join_Pts_in_partition.con". +inline procedural "cic:/CoRN/ftc/Integral/partition_join_Pts_in_partition.con" as lemma. -inline procedural "cic:/CoRN/ftc/Integral/partition_join_Pts_wd.con". +inline procedural "cic:/CoRN/ftc/Integral/partition_join_Pts_wd.con" as lemma. (* UNEXPORTED Opaque partition_join. @@ -448,9 +448,9 @@ Opaque minus. Transparent minus. *) -inline procedural "cic:/CoRN/ftc/Integral/partition_join_Sum_lemma.con". +inline procedural "cic:/CoRN/ftc/Integral/partition_join_Sum_lemma.con" as lemma. -inline procedural "cic:/CoRN/ftc/Integral/partition_join_mesh.con". +inline procedural "cic:/CoRN/ftc/Integral/partition_join_mesh.con" as lemma. (* UNEXPORTED End Partition_Join @@ -464,7 +464,7 @@ With these results in mind, the following is a trivial consequence: Opaque Even_Partition. *) -inline procedural "cic:/CoRN/ftc/Integral/integral_plus_integral.con". +inline procedural "cic:/CoRN/ftc/Integral/integral_plus_integral.con" as lemma. (* UNEXPORTED End Integral_Sum @@ -482,11 +482,11 @@ End Basic_Properties The following are simple consequences of this result and of previous ones. *) -inline procedural "cic:/CoRN/ftc/Integral/integral_less_norm.con". +inline procedural "cic:/CoRN/ftc/Integral/integral_less_norm.con" as lemma. (* end hide *) -inline procedural "cic:/CoRN/ftc/Integral/integral_gt_zero.con". +inline procedural "cic:/CoRN/ftc/Integral/integral_gt_zero.con" as lemma. (* end hide *) diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/IntervalFunct.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/IntervalFunct.mma index 03e744da8..80303c0dd 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/IntervalFunct.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/IntervalFunct.mma @@ -53,7 +53,7 @@ alias id "Hab" = "cic:/CoRN/ftc/IntervalFunct/Operations/Hab.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/IntervalFunct/Operations/I.con" "Operations__". +inline procedural "cic:/CoRN/ftc/IntervalFunct/Operations/I.con" "Operations__" as definition. (* end hide *) @@ -74,37 +74,37 @@ Constant and identity functions are defined. alias id "c" = "cic:/CoRN/ftc/IntervalFunct/Operations/Const/c.var". -inline procedural "cic:/CoRN/ftc/IntervalFunct/IConst_strext.con". +inline procedural "cic:/CoRN/ftc/IntervalFunct/IConst_strext.con" as lemma. -inline procedural "cic:/CoRN/ftc/IntervalFunct/IConst.con". +inline procedural "cic:/CoRN/ftc/IntervalFunct/IConst.con" as definition. (* UNEXPORTED End Const *) -inline procedural "cic:/CoRN/ftc/IntervalFunct/IId_strext.con". +inline procedural "cic:/CoRN/ftc/IntervalFunct/IId_strext.con" as lemma. -inline procedural "cic:/CoRN/ftc/IntervalFunct/IId.con". +inline procedural "cic:/CoRN/ftc/IntervalFunct/IId.con" as definition. (*#* Next, we define addition, algebraic inverse, subtraction and product of functions. *) -inline procedural "cic:/CoRN/ftc/IntervalFunct/IPlus_strext.con". +inline procedural "cic:/CoRN/ftc/IntervalFunct/IPlus_strext.con" as lemma. -inline procedural "cic:/CoRN/ftc/IntervalFunct/IPlus.con". +inline procedural "cic:/CoRN/ftc/IntervalFunct/IPlus.con" as definition. -inline procedural "cic:/CoRN/ftc/IntervalFunct/IInv_strext.con". +inline procedural "cic:/CoRN/ftc/IntervalFunct/IInv_strext.con" as lemma. -inline procedural "cic:/CoRN/ftc/IntervalFunct/IInv.con". +inline procedural "cic:/CoRN/ftc/IntervalFunct/IInv.con" as definition. -inline procedural "cic:/CoRN/ftc/IntervalFunct/IMinus_strext.con". +inline procedural "cic:/CoRN/ftc/IntervalFunct/IMinus_strext.con" as lemma. -inline procedural "cic:/CoRN/ftc/IntervalFunct/IMinus.con". +inline procedural "cic:/CoRN/ftc/IntervalFunct/IMinus.con" as definition. -inline procedural "cic:/CoRN/ftc/IntervalFunct/IMult_strext.con". +inline procedural "cic:/CoRN/ftc/IntervalFunct/IMult_strext.con" as lemma. -inline procedural "cic:/CoRN/ftc/IntervalFunct/IMult.con". +inline procedural "cic:/CoRN/ftc/IntervalFunct/IMult.con" as definition. (* UNEXPORTED Section Nth_Power @@ -116,9 +116,9 @@ Exponentiation to a natural power [n] is also useful. alias id "n" = "cic:/CoRN/ftc/IntervalFunct/Operations/Nth_Power/n.var". -inline procedural "cic:/CoRN/ftc/IntervalFunct/INth_strext.con". +inline procedural "cic:/CoRN/ftc/IntervalFunct/INth_strext.con" as lemma. -inline procedural "cic:/CoRN/ftc/IntervalFunct/INth.con". +inline procedural "cic:/CoRN/ftc/IntervalFunct/INth.con" as definition. (* UNEXPORTED End Nth_Power @@ -138,13 +138,13 @@ alias id "Hg" = "cic:/CoRN/ftc/IntervalFunct/Operations/Recip_Div/Hg.var". (* end show *) -inline procedural "cic:/CoRN/ftc/IntervalFunct/IRecip_strext.con". +inline procedural "cic:/CoRN/ftc/IntervalFunct/IRecip_strext.con" as lemma. -inline procedural "cic:/CoRN/ftc/IntervalFunct/IRecip.con". +inline procedural "cic:/CoRN/ftc/IntervalFunct/IRecip.con" as definition. -inline procedural "cic:/CoRN/ftc/IntervalFunct/IDiv_strext.con". +inline procedural "cic:/CoRN/ftc/IntervalFunct/IDiv_strext.con" as lemma. -inline procedural "cic:/CoRN/ftc/IntervalFunct/IDiv.con". +inline procedural "cic:/CoRN/ftc/IntervalFunct/IDiv.con" as definition. (* UNEXPORTED End Recip_Div @@ -154,9 +154,9 @@ End Recip_Div Absolute value will also be needed at some point. *) -inline procedural "cic:/CoRN/ftc/IntervalFunct/IAbs_strext.con". +inline procedural "cic:/CoRN/ftc/IntervalFunct/IAbs_strext.con" as lemma. -inline procedural "cic:/CoRN/ftc/IntervalFunct/IAbs.con". +inline procedural "cic:/CoRN/ftc/IntervalFunct/IAbs.con" as definition. (* UNEXPORTED End Operations @@ -192,7 +192,7 @@ alias id "Hab" = "cic:/CoRN/ftc/IntervalFunct/Composition/Hab.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/IntervalFunct/Composition/I.con" "Composition__". +inline procedural "cic:/CoRN/ftc/IntervalFunct/Composition/I.con" "Composition__" as definition. (* end hide *) @@ -204,7 +204,7 @@ alias id "Hab'" = "cic:/CoRN/ftc/IntervalFunct/Composition/Hab'.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/IntervalFunct/Composition/I'.con" "Composition__". +inline procedural "cic:/CoRN/ftc/IntervalFunct/Composition/I'.con" "Composition__" as definition. (* end hide *) @@ -214,9 +214,9 @@ alias id "g" = "cic:/CoRN/ftc/IntervalFunct/Composition/g.var". alias id "Hfg" = "cic:/CoRN/ftc/IntervalFunct/Composition/Hfg.var". -inline procedural "cic:/CoRN/ftc/IntervalFunct/IComp_strext.con". +inline procedural "cic:/CoRN/ftc/IntervalFunct/IComp_strext.con" as lemma. -inline procedural "cic:/CoRN/ftc/IntervalFunct/IComp.con". +inline procedural "cic:/CoRN/ftc/IntervalFunct/IComp.con" as definition. (* UNEXPORTED End Composition diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/MoreFunSeries.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/MoreFunSeries.mma index e201d4ecc..44391b4de 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/MoreFunSeries.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/MoreFunSeries.mma @@ -60,25 +60,25 @@ alias id "contf" = "cic:/CoRN/ftc/MoreFunSeries/Definitions/contf.var". alias id "contF" = "cic:/CoRN/ftc/MoreFunSeries/Definitions/contF.var". -inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_IR.con" as definition. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq_IR.con" as definition. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_IR.con" as definition. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq2_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq2_IR.con" as definition. (*#* The equivalences between these definitions still hold. *) -inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_Cauchy_fun_seq'_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_Cauchy_fun_seq'_IR.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_seq2_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_seq2_IR.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq2_seq_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq2_seq_IR.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_real_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_real_IR.con" as lemma. (* UNEXPORTED End Definitions @@ -104,9 +104,9 @@ alias id "conv" = "cic:/CoRN/ftc/MoreFunSeries/More_Definitions/conv.var". (* end show *) -inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_Lim_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_Lim_IR.con" as definition. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_Lim_char.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_Lim_char.con" as lemma. (* UNEXPORTED End More_Definitions @@ -143,11 +143,11 @@ alias id "contF0" = "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/contF0.va (* end show *) -inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wd_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wd_IR.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq2_wd_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq2_wd_IR.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq_wd_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq_wd_IR.con" as lemma. (* UNEXPORTED End Irrelevance_of_Proofs @@ -179,7 +179,7 @@ alias id "contg0" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contg0.var". (* end show *) -inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_conv_fun_seq'_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_conv_fun_seq'_IR.con" as lemma. alias id "F" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/F.var". @@ -197,19 +197,19 @@ alias id "contG0" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contG0.var". (* end show *) -inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wdl_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wdl_IR.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wdr_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wdr_IR.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wdl'_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wdl'_IR.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wdr'_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wdr'_IR.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_cont_Lim_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_cont_Lim_IR.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_conv_fun_seq_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_conv_fun_seq_IR.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_Cauchy_fun_seq_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_Cauchy_fun_seq_IR.con" as lemma. (* UNEXPORTED End More_Properties @@ -238,13 +238,13 @@ alias id "contf" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/contf.var". alias id "contg" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/contg.var". -inline procedural "cic:/CoRN/ftc/MoreFunSeries/FLim_unique_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/FLim_unique_IR.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_wd_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_wd_IR.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_const_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_const_IR.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_const_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_const_IR.con" as lemma. alias id "F" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/F.var". @@ -262,11 +262,11 @@ alias id "convG" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/convG.var". (* end show *) -inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_plus'_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_plus'_IR.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_minus'_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_minus'_IR.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_mult'_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_mult'_IR.con" as lemma. (* UNEXPORTED End Algebraic_Properties @@ -298,21 +298,21 @@ alias id "Hg" = "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/Hg.var". (* end show *) -inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_plus_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_plus_IR.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_plus.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_plus.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_inv_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_inv_IR.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_inv.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_inv.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_minus_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_minus_IR.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_minus.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_minus.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_mult_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_mult_IR.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_mult.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_mult.con" as lemma. (* UNEXPORTED End More_Algebraic_Properties @@ -327,15 +327,15 @@ Section Other Finally, we define a mapping between sequences of real numbers and sequences of (constant) functions and prove that convergence is preserved. *) -inline procedural "cic:/CoRN/ftc/MoreFunSeries/seq_to_funseq.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/seq_to_funseq.con" as definition. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/funseq_conv.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/funseq_conv.con" as lemma. (*#* Another interesting fact: if a sequence of constant functions converges then it must converge to a constant function. *) -inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_const_Lim.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_const_Lim.con" as lemma. (* UNEXPORTED End Other @@ -356,9 +356,9 @@ alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/Series_Definitions/J.var". alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/Series_Definitions/f.var". -inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_series_convergent_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_series_convergent_IR.con" as definition. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_series_conv_imp_conv_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_series_conv_imp_conv_IR.con" as lemma. (* begin show *) @@ -366,21 +366,21 @@ alias id "H" = "cic:/CoRN/ftc/MoreFunSeries/Series_Definitions/H.var". (* end show *) -inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_series_inc_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_series_inc_IR.con" as lemma. (*#* Assume [h(x)] is the pointwise series of [f(x)] *) (* begin hide *) -inline procedural "cic:/CoRN/ftc/MoreFunSeries/Series_Definitions/h.con" "Series_Definitions__". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/Series_Definitions/h.con" "Series_Definitions__" as definition. (* end hide *) -inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_strext_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_strext_IR.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum.con" as definition. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_char.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_char.con" as lemma. (* UNEXPORTED End Series_Definitions @@ -402,7 +402,7 @@ alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/More_Series_Definitions/f.var". Absolute convergence still exists. *) -inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_series_abs_convergent_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_series_abs_convergent_IR.con" as definition. (* UNEXPORTED End More_Series_Definitions @@ -420,13 +420,13 @@ alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/Convergence_Results/J.var". alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/Convergence_Results/f.var". -inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_conv.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_conv.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/convergent_imp_inc.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/convergent_imp_inc.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/convergent_imp_Continuous.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/convergent_imp_Continuous.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/Continuous_FSeries_Sum.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/Continuous_FSeries_Sum.con" as lemma. (* UNEXPORTED End Convergence_Results @@ -451,19 +451,19 @@ Convergence is well defined and preserved by operations. alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/Operations/J.var". -inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_const_series_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_const_series_IR.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_const_series_Sum_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_const_series_Sum_IR.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_zero_fun_series_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_zero_fun_series_IR.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_zero_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_zero_IR.con" as lemma. alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/Operations/f.var". alias id "g" = "cic:/CoRN/ftc/MoreFunSeries/Operations/g.var". -inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_series_convergent_wd_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_series_convergent_wd_IR.con" as lemma. (* begin show *) @@ -473,19 +473,19 @@ alias id "convG" = "cic:/CoRN/ftc/MoreFunSeries/Operations/convG.var". (* end show *) -inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_wd'.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_wd'.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_plus_conv.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_plus_conv.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_plus.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_plus.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_inv_conv.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_inv_conv.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_inv.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_inv.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_minus_conv.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_minus_conv.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_minus.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_minus.con" as lemma. (*#* %\begin{convention}% Let [c:IR] and [H:PartIR] be continuous in [J]. @@ -498,9 +498,9 @@ alias id "H" = "cic:/CoRN/ftc/MoreFunSeries/Operations/H.var". alias id "contH" = "cic:/CoRN/ftc/MoreFunSeries/Operations/contH.var". -inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_scal_conv.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_scal_conv.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_scal.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_scal.con" as lemma. (* UNEXPORTED End Operations @@ -522,13 +522,13 @@ alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/Convergence_Criteria/f.var". alias id "contF" = "cic:/CoRN/ftc/MoreFunSeries/Convergence_Criteria/contF.var". -inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_str_comparison_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_str_comparison_IR.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_comparison_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_comparison_IR.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/abs_imp_conv_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/abs_imp_conv_IR.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_ratio_test_conv_IR.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_ratio_test_conv_IR.con" as lemma. (* UNEXPORTED End Convergence_Criteria @@ -553,15 +553,15 @@ alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/Insert_Series/f.var". alias id "convF" = "cic:/CoRN/ftc/MoreFunSeries/Insert_Series/convF.var". -inline procedural "cic:/CoRN/ftc/MoreFunSeries/insert_series.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/insert_series.con" as definition. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/insert_series_cont.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/insert_series_cont.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/insert_series_sum_char.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/insert_series_sum_char.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/insert_series_conv.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/insert_series_conv.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunSeries/insert_series_sum.con". +inline procedural "cic:/CoRN/ftc/MoreFunSeries/insert_series_sum.con" as lemma. (* UNEXPORTED End Insert_Series diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/MoreFunctions.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/MoreFunctions.mma index 23b99d713..b90197e3b 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/MoreFunctions.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/MoreFunctions.mma @@ -48,7 +48,7 @@ alias id "I" = "cic:/CoRN/ftc/MoreFunctions/Basic_Results/I.var". Trivial stuff. *) -inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_imp_inc.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_imp_inc.con" as lemma. (*#* %\begin{convention}% Assume that [I] is compact and [F] is continuous in [I]. @@ -61,7 +61,7 @@ alias id "F" = "cic:/CoRN/ftc/MoreFunctions/Basic_Results/F.var". alias id "contF" = "cic:/CoRN/ftc/MoreFunctions/Basic_Results/contF.var". -inline procedural "cic:/CoRN/ftc/MoreFunctions/continuous_compact.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/continuous_compact.con" as lemma. (* begin show *) @@ -69,11 +69,11 @@ alias id "Hinc" = "cic:/CoRN/ftc/MoreFunctions/Basic_Results/Hinc.var". (* end show *) -inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_I_imp_tb_image.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_I_imp_tb_image.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/FNorm.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/FNorm.con" as definition. -inline procedural "cic:/CoRN/ftc/MoreFunctions/FNorm_bnd_AbsIR.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/FNorm_bnd_AbsIR.con" as lemma. (* UNEXPORTED End Basic_Results @@ -97,7 +97,7 @@ alias id "F" = "cic:/CoRN/ftc/MoreFunctions/Other_Results/F.var". alias id "G" = "cic:/CoRN/ftc/MoreFunctions/Other_Results/G.var". -inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_wd.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_wd.con" as lemma. (* begin show *) @@ -107,29 +107,29 @@ alias id "contG" = "cic:/CoRN/ftc/MoreFunctions/Other_Results/contG.var". (* end show *) -inline procedural "cic:/CoRN/ftc/MoreFunctions/included_imp_Continuous.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/included_imp_Continuous.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Included_imp_Continuous.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Included_imp_Continuous.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_const.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_const.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_id.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_id.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_plus.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_plus.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_inv.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_inv.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_minus.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_minus.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_mult.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_mult.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_nth.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_nth.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_scal.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_scal.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_abs.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_abs.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_recip.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_recip.con" as lemma. (* UNEXPORTED End Other_Results @@ -161,9 +161,9 @@ alias id "contF" = "cic:/CoRN/ftc/MoreFunctions/Corollaries/contF.var". alias id "contG" = "cic:/CoRN/ftc/MoreFunctions/Corollaries/contG.var". -inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_div.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_div.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/FNorm_wd.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/FNorm_wd.con" as lemma. (* UNEXPORTED End Corollaries @@ -179,7 +179,7 @@ Section Sums alias id "I" = "cic:/CoRN/ftc/MoreFunctions/Sums/I.var". -inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_Sumx.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_Sumx.con" as lemma. (*#* %\begin{convention}% Assume [f] is a sequence of continuous functions. @@ -190,9 +190,9 @@ alias id "f" = "cic:/CoRN/ftc/MoreFunctions/Sums/f.var". alias id "contF" = "cic:/CoRN/ftc/MoreFunctions/Sums/contF.var". -inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_Sum0.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_Sum0.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_Sum.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_Sum.con" as lemma. (* UNEXPORTED End Sums @@ -224,19 +224,19 @@ alias id "G" = "cic:/CoRN/ftc/MoreFunctions/Basic_Properties/G.var". alias id "H" = "cic:/CoRN/ftc/MoreFunctions/Basic_Properties/H.var". -inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_wdl.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_wdl.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_wdr.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_wdr.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_unique.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_unique.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_inc.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_inc.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_inc'.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_inc'.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_Continuous.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_Continuous.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_Continuous'.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_Continuous'.con" as lemma. (* UNEXPORTED End Basic_Properties @@ -276,27 +276,27 @@ alias id "derF" = "cic:/CoRN/ftc/MoreFunctions/More_Results/derF.var". alias id "derG" = "cic:/CoRN/ftc/MoreFunctions/More_Results/derG.var". -inline procedural "cic:/CoRN/ftc/MoreFunctions/included_imp_Derivative.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/included_imp_Derivative.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Included_imp_Derivative.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Included_imp_Derivative.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_const.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_const.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_id.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_id.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_plus.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_plus.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_inv.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_inv.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_minus.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_minus.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_mult.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_mult.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_scal.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_scal.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_nth.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_nth.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_recip.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_recip.con" as lemma. (* UNEXPORTED End More_Results @@ -328,7 +328,7 @@ alias id "Gbnd" = "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/Gbnd.var". (* end show *) -inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_div.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_div.con" as lemma. (* UNEXPORTED End More_Corollaries @@ -342,7 +342,7 @@ alias id "I" = "cic:/CoRN/ftc/MoreFunctions/More_Sums/I.var". alias id "pI" = "cic:/CoRN/ftc/MoreFunctions/More_Sums/pI.var". -inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_Sumx.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_Sumx.con" as lemma. (* begin show *) @@ -354,9 +354,9 @@ alias id "derF" = "cic:/CoRN/ftc/MoreFunctions/More_Sums/derF.var". (* end show *) -inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_Sum0.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_Sum0.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_Sum.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_Sum.con" as lemma. (* UNEXPORTED End More_Sums @@ -375,11 +375,11 @@ alias id "I" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/I.var". alias id "pI" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/pI.var". -inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_imp_inc.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_imp_inc.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_Diffble.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_Diffble.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_wd.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_wd.con" as lemma. alias id "F" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/F.var". @@ -394,27 +394,27 @@ alias id "diffG" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/diffG.v %\end{convention}% *) -inline procedural "cic:/CoRN/ftc/MoreFunctions/included_imp_Diffble.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/included_imp_Diffble.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Included_imp_Diffble.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Included_imp_Diffble.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_const.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_const.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_id.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_id.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_plus.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_plus.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_inv.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_inv.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_minus.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_minus.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_mult.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_mult.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_nth.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_nth.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_scal.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_scal.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_recip.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_recip.con" as lemma. (* UNEXPORTED End Diffble_Basic_Properties @@ -440,13 +440,13 @@ alias id "diffF" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/diffF.var". alias id "diffG" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/diffG.var". -inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_div.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_div.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_Sum0.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_Sum0.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_Sumx.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_Sumx.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_Sum.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_Sum.con" as lemma. (* UNEXPORTED End Diffble_Corollaries @@ -480,18 +480,18 @@ alias id "F" = "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Definitions/F.var". alias id "diffF" = "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Definitions/diffF.var". -inline procedural "cic:/CoRN/ftc/MoreFunctions/N_Deriv_fun.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/N_Deriv_fun.con" as definition. inline procedural "cic:/CoRN/ftc/MoreFunctions/N_Deriv_char - (* begin hide *).con". + (* begin hide *).con" as lemma. (* end hide *) -inline procedural "cic:/CoRN/ftc/MoreFunctions/N_Deriv_strext.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/N_Deriv_strext.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/N_Deriv_wd.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/N_Deriv_wd.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/N_Deriv.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/N_Deriv.con" as definition. (* UNEXPORTED End Definitions @@ -505,39 +505,39 @@ Section Basic_Results All the usual results hold. *) -inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_n_wd.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_n_wd.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_wdr.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_wdr.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_wdl.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_wdl.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_unique.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_unique.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_n_imp_Diffble.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_n_imp_Diffble.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Diffble.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Diffble.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/le_imp_Diffble_n.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/le_imp_Diffble_n.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_n_imp_le.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_n_imp_le.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_n_imp_inc.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_n_imp_inc.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Diffble_n.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Diffble_n.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_inc.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_inc.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_inc'.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_inc'.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/included_imp_Derivative_n.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/included_imp_Derivative_n.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/included_imp_Diffble_n.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/included_imp_Diffble_n.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Included_imp_Derivative_n.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Included_imp_Derivative_n.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Included_imp_Diffble_n.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Included_imp_Diffble_n.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_plus.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_plus.con" as lemma. (* UNEXPORTED End Basic_Results @@ -551,21 +551,21 @@ Section More_Results Some new results hold, too: *) -inline procedural "cic:/CoRN/ftc/MoreFunctions/N_Deriv_Feq.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/N_Deriv_Feq.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/N_Deriv_lemma.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/N_Deriv_lemma.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/N_Deriv_S.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/N_Deriv_S.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/N_Deriv_plus.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/N_Deriv_plus.con" as lemma. (*#* Some useful characterization results. *) -inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_O.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_O.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_Sn.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_Sn.con" as lemma. (* UNEXPORTED End More_Results @@ -587,9 +587,9 @@ alias id "diffF" = "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Derivating_Diffbl (* end show *) -inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_imp_Diffble_n.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_imp_Diffble_n.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Deriv.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Deriv.con" as definition. (* UNEXPORTED End Derivating_Diffble @@ -603,19 +603,19 @@ Section Corollaries %\ldots%#...# for which the expected property also holds. *) -inline procedural "cic:/CoRN/ftc/MoreFunctions/Deriv_lemma.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Deriv_lemma.con" as lemma. (*#* Some more interesting properties. *) -inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_1.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_1.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_chain.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_chain.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Continuous.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Continuous.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Continuous'.con". +inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Continuous'.con" as lemma. (* UNEXPORTED End Corollaries diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/MoreIntegrals.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/MoreIntegrals.mma index 7cae25fb1..26de7113f 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/MoreIntegrals.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/MoreIntegrals.mma @@ -52,9 +52,9 @@ alias id "b" = "cic:/CoRN/ftc/MoreIntegrals/Lemmas/b.var". alias id "Hab" = "cic:/CoRN/ftc/MoreIntegrals/Lemmas/Hab.var". -inline procedural "cic:/CoRN/ftc/MoreIntegrals/compact_inc_Min_lft.con". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/compact_inc_Min_lft.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntegrals/compact_inc_Min_rht.con". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/compact_inc_Min_rht.con" as lemma. (* UNEXPORTED End Lemmas @@ -82,13 +82,13 @@ alias id "F" = "cic:/CoRN/ftc/MoreIntegrals/Definitions/F.var". alias id "HF" = "cic:/CoRN/ftc/MoreIntegrals/Definitions/HF.var". -inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_inc1.con". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_inc1.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_inc2.con". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_inc2.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral.con". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral.con" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_integral.con". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_integral.con" as lemma. (* UNEXPORTED End Definitions @@ -122,41 +122,41 @@ alias id "contF" = "cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/contF.var alias id "contG" = "cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/contG.var". -inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_strext.con". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_strext.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_strext'.con". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_strext'.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_wd.con". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_wd.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_wd'.con". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_wd'.con" as lemma. (*#* The integral is a linear operator. *) -inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_const.con". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_const.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_comm_scal.con". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_comm_scal.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_plus.con". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_plus.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_inv.con". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_inv.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_minus.con". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_minus.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntegrals/linear_Integral.con". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/linear_Integral.con" as lemma. (*#* If the endpoints are equal then the integral vanishes. *) -inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_empty.con". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_empty.con" as lemma. (*#* And the norm provides an upper bound for the absolute value of the integral. *) -inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_leEq_norm.con". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_leEq_norm.con" as lemma. (* UNEXPORTED End Properties_of_Integral @@ -170,9 +170,9 @@ Section More_Properties Two other ways of stating the addition law for domains. *) -inline procedural "cic:/CoRN/ftc/MoreIntegrals/integral_plus_Integral.con". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/integral_plus_Integral.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntegrals/integral_plus_integral'.con". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/integral_plus_integral'.con" as lemma. (*#* And now we can prove the addition law for domains with our general operator. @@ -215,47 +215,47 @@ alias id "Habc" = "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_abc_ab.con" "More_Properties__". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_abc_ab.con" "More_Properties__" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_abc_ac.con" "More_Properties__". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_abc_ac.con" "More_Properties__" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_abc_cb.con" "More_Properties__". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_abc_cb.con" "More_Properties__" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_abc_a.con" "More_Properties__". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_abc_a.con" "More_Properties__" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_abc_b.con" "More_Properties__". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_abc_b.con" "More_Properties__" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_abc_c.con" "More_Properties__". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_abc_c.con" "More_Properties__" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_ab_a.con" "More_Properties__". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_ab_a.con" "More_Properties__" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_cb_c.con" "More_Properties__". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_cb_c.con" "More_Properties__" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_ac_a.con" "More_Properties__". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_ac_a.con" "More_Properties__" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_ab_b.con" "More_Properties__". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_ab_b.con" "More_Properties__" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_cb_b.con" "More_Properties__". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_cb_b.con" "More_Properties__" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_ac_c.con" "More_Properties__". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_ac_c.con" "More_Properties__" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_abc.con" "More_Properties__". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_abc.con" "More_Properties__" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_ab.con" "More_Properties__". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_ab.con" "More_Properties__" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_ac.con" "More_Properties__". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_ac.con" "More_Properties__" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_cb.con" "More_Properties__". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_cb.con" "More_Properties__" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_a.con" "More_Properties__". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_a.con" "More_Properties__" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_b.con" "More_Properties__". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_b.con" "More_Properties__" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_c.con" "More_Properties__". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_c.con" "More_Properties__" as definition. (* end hide *) -inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_plus_Integral.con". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_plus_Integral.con" as lemma. (*#* Notice that, unlike in the classical case, an extra hypothesis (the @@ -282,19 +282,19 @@ alias id "contF" = "cic:/CoRN/ftc/MoreIntegrals/Corollaries/contF.var". (*#* As a corollary, we get the following rule: *) -inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_op.con". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_op.con" as lemma. (*#* Finally, some miscellaneous results: *) -inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_less_norm.con". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_less_norm.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntegrals/ub_Integral.con". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/ub_Integral.con" as lemma. (* UNEXPORTED End Corollaries *) -inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_ap_zero.con". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_eq_zero.con". +inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_eq_zero.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/MoreIntervals.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/MoreIntervals.mma index 83214c0b5..68c9aeadf 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/MoreIntervals.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/MoreIntervals.mma @@ -105,7 +105,7 @@ inline procedural "cic:/CoRN/ftc/MoreIntervals/interval.ind". To each interval a predicate (set) is assigned by the following map: *) -inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop.con" as definition. (* begin hide *) @@ -123,67 +123,67 @@ We now define what it means for an interval to be nonvoid, proper, finite and compact in the obvious way. *) -inline procedural "cic:/CoRN/ftc/MoreIntervals/nonvoid.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/nonvoid.con" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntervals/proper.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/proper.con" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntervals/finite.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/finite.con" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_.con" as definition. (*#* Finite intervals have a left end and a right end. *) -inline procedural "cic:/CoRN/ftc/MoreIntervals/left_end.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/left_end.con" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntervals/right_end.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/right_end.con" as definition. (*#* Some trivia: compact intervals are finite; proper intervals are nonvoid; an interval is nonvoid iff it contains some point. *) -inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_finite.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_finite.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntervals/proper_nonvoid.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/proper_nonvoid.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntervals/nonvoid_point.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/nonvoid_point.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntervals/nonvoid_char.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/nonvoid_char.con" as lemma. (*#* For practical reasons it helps to define left end and right end of compact intervals. *) -inline procedural "cic:/CoRN/ftc/MoreIntervals/Lend.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/Lend.con" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntervals/Rend.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/Rend.con" as definition. (*#* In a compact interval, the left end is always less than or equal to the right end. *) -inline procedural "cic:/CoRN/ftc/MoreIntervals/Lend_leEq_Rend.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/Lend_leEq_Rend.con" as lemma. (*#* Some nice characterizations of inclusion: *) -inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_included.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_included.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntervals/included_interval'.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/included_interval'.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntervals/included_interval.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/included_interval.con" as lemma. (*#* A weirder inclusion result. *) -inline procedural "cic:/CoRN/ftc/MoreIntervals/included3_interval.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/included3_interval.con" as lemma. (*#* Finally, all intervals are characterized by well defined predicates. *) -inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_wd.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_wd.con" as lemma. (* UNEXPORTED End Intervals @@ -224,17 +224,17 @@ alias id "x" = "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Single_Compact alias id "Hx" = "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Single_Compact_Interval/Hx.var". -inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_single.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_single.con" as definition. (*#* This interval contains [x] and only (elements equal to) [x]; furthermore, for every (well-defined) [P], if $x\in P$#x∈P# then $[x,x]\subseteq P$#[x,x]⊆P#. *) -inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_single_prop.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_single_prop.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_single_pt.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_single_pt.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_single_inc.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_single_inc.con" as lemma. (* UNEXPORTED End Single_Compact_Interval @@ -244,7 +244,7 @@ End Single_Compact_Interval The special case of intervals is worth singling out, as one of the hypothesis becomes a theorem. *) -inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_single_iprop.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_single_iprop.con" as definition. (*#* Now for more interesting and important results. @@ -260,49 +260,49 @@ Section Proper_Compact_with_One_or_Two_Points (* begin hide *) -inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip1'.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__". +inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip1'.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip1''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__". +inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip1''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip1'''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__". +inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip1'''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip1''''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__". +inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip1''''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip2.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__". +inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip2.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip2'.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__". +inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip2'.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip2''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__". +inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip2''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip2'''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__". +inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip2'''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip3.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__". +inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip3.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip3'.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__". +inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip3'.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip3''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__". +inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip3''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip3'''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__". +inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip3'''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__" as definition. (* end hide *) -inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_in_interval.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_in_interval.con" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_compact_in_interval.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_compact_in_interval.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntervals/proper_compact_in_interval.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/proper_compact_in_interval.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntervals/proper_compact_in_interval'.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/proper_compact_in_interval'.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntervals/included_compact_in_interval.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/included_compact_in_interval.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval'.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval'.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval_inc1.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval_inc1.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval_inc2.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval_inc2.con" as lemma. (*#* If [x [=] y] then the construction yields the same interval whether we @@ -311,43 +311,43 @@ stage, which is why we formalized this result as a functional definition rather than as an existential formula. *) -inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_in_interval_wd1.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_in_interval_wd1.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_in_interval_wd2.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_in_interval_wd2.con" as lemma. (*#* We can make an analogous construction for two points. *) -inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_in_interval2.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_in_interval2.con" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_compact_in_interval2.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_compact_in_interval2.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntervals/proper_compact_in_interval2.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/proper_compact_in_interval2.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntervals/proper_compact_in_interval2'.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/proper_compact_in_interval2'.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntervals/included_compact_in_interval2.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/included_compact_in_interval2.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval2x.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval2x.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval2y.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval2y.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval2x'.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval2x'.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval2y'.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval2y'.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval2_inc1.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval2_inc1.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval2_inc2.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval2_inc2.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_in_interval_x_lft.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_in_interval_x_lft.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_in_interval_y_lft.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_in_interval_y_lft.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_in_interval_x_rht.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_in_interval_x_rht.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_in_interval_y_rht.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_in_interval_y_rht.con" as lemma. (* UNEXPORTED End Proper_Compact_with_One_or_Two_Points @@ -357,9 +357,9 @@ End Proper_Compact_with_One_or_Two_Points Compact intervals are exactly compact intervals(!). *) -inline procedural "cic:/CoRN/ftc/MoreIntervals/interval_compact_inc.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/interval_compact_inc.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_interval_inc.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_interval_inc.con" as lemma. (*#* A generalization of the previous results: if $[a,b]\subseteq J$#[a,b]⊆J# @@ -367,7 +367,7 @@ and [J] is proper, then we can find a proper interval [[a',b']] such that $[a,b]\subseteq[a',b']\subseteq J$#[a,b]⊆[a',b']⊆J#. *) -inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_proper_in_interval.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_proper_in_interval.con" as lemma. (* UNEXPORTED End Compact_Constructions @@ -393,15 +393,15 @@ alias id "n" = "cic:/CoRN/ftc/MoreIntervals/Functions/n.var". alias id "I" = "cic:/CoRN/ftc/MoreIntervals/Functions/I.var". -inline procedural "cic:/CoRN/ftc/MoreIntervals/Continuous.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/Continuous.con" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntervals/Derivative.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/Derivative.con" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntervals/Diffble.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/Diffble.con" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntervals/Derivative_n.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/Derivative_n.con" as definition. -inline procedural "cic:/CoRN/ftc/MoreIntervals/Diffble_n.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/Diffble_n.con" as definition. (* UNEXPORTED End Functions @@ -415,17 +415,17 @@ Section Reflexivity_Properties In the case of compact intervals, this definitions collapse to the old ones. *) -inline procedural "cic:/CoRN/ftc/MoreIntervals/Continuous_Int.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/Continuous_Int.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntervals/Int_Continuous.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/Int_Continuous.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntervals/Derivative_Int.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/Derivative_Int.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntervals/Int_Derivative.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/Int_Derivative.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntervals/Diffble_Int.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/Diffble_Int.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntervals/Int_Diffble.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/Int_Diffble.con" as lemma. (* UNEXPORTED End Reflexivity_Properties @@ -439,11 +439,11 @@ Section Lemmas Interestingly, inclusion and equality in an interval are also characterizable in a similar way: *) -inline procedural "cic:/CoRN/ftc/MoreIntervals/included_imp_inc.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/included_imp_inc.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntervals/included_Feq''.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/included_Feq''.con" as lemma. -inline procedural "cic:/CoRN/ftc/MoreIntervals/included_Feq'.con". +inline procedural "cic:/CoRN/ftc/MoreIntervals/included_Feq'.con" as lemma. (* UNEXPORTED End Lemmas diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/NthDerivative.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/NthDerivative.mma index a814c6faf..2834afd35 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/NthDerivative.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/NthDerivative.mma @@ -48,13 +48,13 @@ alias id "Hab'" = "cic:/CoRN/ftc/NthDerivative/Nth_Derivative/Hab'.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/NthDerivative/Nth_Derivative/Hab.con" "Nth_Derivative__". +inline procedural "cic:/CoRN/ftc/NthDerivative/Nth_Derivative/Hab.con" "Nth_Derivative__" as definition. -inline procedural "cic:/CoRN/ftc/NthDerivative/Nth_Derivative/I.con" "Nth_Derivative__". +inline procedural "cic:/CoRN/ftc/NthDerivative/Nth_Derivative/I.con" "Nth_Derivative__" as definition. (* end hide *) -inline procedural "cic:/CoRN/ftc/NthDerivative/Derivative_I_n.con". +inline procedural "cic:/CoRN/ftc/NthDerivative/Derivative_I_n.con" as definition. (*#* Unlike first order differentiability, for our definition to be @@ -63,7 +63,7 @@ to be [n] times differentiable instead of quantifying over the [Derivative_I_n] relation. *) -inline procedural "cic:/CoRN/ftc/NthDerivative/Diffble_I_n.con". +inline procedural "cic:/CoRN/ftc/NthDerivative/Diffble_I_n.con" as definition. (* UNEXPORTED End Nth_Derivative @@ -94,19 +94,19 @@ alias id "Hab'" = "cic:/CoRN/ftc/NthDerivative/Trivia/Hab'.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/NthDerivative/Trivia/Hab.con" "Trivia__". +inline procedural "cic:/CoRN/ftc/NthDerivative/Trivia/Hab.con" "Trivia__" as definition. -inline procedural "cic:/CoRN/ftc/NthDerivative/Trivia/I.con" "Trivia__". +inline procedural "cic:/CoRN/ftc/NthDerivative/Trivia/I.con" "Trivia__" as definition. (* end hide *) -inline procedural "cic:/CoRN/ftc/NthDerivative/Diffble_I_n_wd.con". +inline procedural "cic:/CoRN/ftc/NthDerivative/Diffble_I_n_wd.con" as lemma. -inline procedural "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_wdr.con". +inline procedural "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_wdr.con" as lemma. -inline procedural "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_wdl.con". +inline procedural "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_wdl.con" as lemma. -inline procedural "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_unique.con". +inline procedural "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_unique.con" as lemma. (* UNEXPORTED End Trivia @@ -132,9 +132,9 @@ alias id "Hab'" = "cic:/CoRN/ftc/NthDerivative/Basic_Results/Hab'.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/NthDerivative/Basic_Results/Hab.con" "Basic_Results__". +inline procedural "cic:/CoRN/ftc/NthDerivative/Basic_Results/Hab.con" "Basic_Results__" as definition. -inline procedural "cic:/CoRN/ftc/NthDerivative/Basic_Results/I.con" "Basic_Results__". +inline procedural "cic:/CoRN/ftc/NthDerivative/Basic_Results/I.con" "Basic_Results__" as definition. (* end hide *) @@ -142,15 +142,15 @@ inline procedural "cic:/CoRN/ftc/NthDerivative/Basic_Results/I.con" "Basic_Resul We begin by showing that having a higher order derivative implies being differentiable. *) -inline procedural "cic:/CoRN/ftc/NthDerivative/Diffble_I_n_imp_diffble.con". +inline procedural "cic:/CoRN/ftc/NthDerivative/Diffble_I_n_imp_diffble.con" as lemma. -inline procedural "cic:/CoRN/ftc/NthDerivative/deriv_n_imp_diffble.con". +inline procedural "cic:/CoRN/ftc/NthDerivative/deriv_n_imp_diffble.con" as lemma. (*#* If a function is [n] times differentiable then it is also [m] times differentiable for every [m] less or equal than [n]. *) -inline procedural "cic:/CoRN/ftc/NthDerivative/le_imp_Diffble_I.con". +inline procedural "cic:/CoRN/ftc/NthDerivative/le_imp_Diffble_I.con" as lemma. (*#* The next result consolidates our intuition that a function is [n] @@ -158,31 +158,31 @@ times differentiable if we can build from it a chain of [n] derivatives. *) -inline procedural "cic:/CoRN/ftc/NthDerivative/Diffble_I_imp_le.con". +inline procedural "cic:/CoRN/ftc/NthDerivative/Diffble_I_imp_le.con" as lemma. (*#* As expected, an [n] times differentiable in [[a,b]] function must be defined in that interval. *) -inline procedural "cic:/CoRN/ftc/NthDerivative/Diffble_I_n_imp_inc.con". +inline procedural "cic:/CoRN/ftc/NthDerivative/Diffble_I_n_imp_inc.con" as lemma. (*#* Also, the notions of derivative and differentiability are related as expected. *) -inline procedural "cic:/CoRN/ftc/NthDerivative/Diffble_I_n_imp_deriv_n.con". +inline procedural "cic:/CoRN/ftc/NthDerivative/Diffble_I_n_imp_deriv_n.con" as lemma. -inline procedural "cic:/CoRN/ftc/NthDerivative/deriv_n_imp_Diffble_I_n.con". +inline procedural "cic:/CoRN/ftc/NthDerivative/deriv_n_imp_Diffble_I_n.con" as lemma. (*#* From this we can prove that if [F] has an nth order derivative in [[a,b]] then both [F] and its derivative are defined in that interval. *) -inline procedural "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_imp_inc.con". +inline procedural "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_imp_inc.con" as lemma. -inline procedural "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_imp_inc'.con". +inline procedural "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_imp_inc'.con" as lemma. (* UNEXPORTED Section aux @@ -202,9 +202,9 @@ alias id "diffFn" = "cic:/CoRN/ftc/NthDerivative/Basic_Results/aux/diffFn.var". (* end show *) -inline procedural "cic:/CoRN/ftc/NthDerivative/deriv_1_deriv.con". +inline procedural "cic:/CoRN/ftc/NthDerivative/deriv_1_deriv.con" as lemma. -inline procedural "cic:/CoRN/ftc/NthDerivative/deriv_1_deriv'.con". +inline procedural "cic:/CoRN/ftc/NthDerivative/deriv_1_deriv'.con" as lemma. (* UNEXPORTED End aux @@ -214,15 +214,15 @@ End aux As usual, nth order derivability is preserved by shrinking the interval. *) -inline procedural "cic:/CoRN/ftc/NthDerivative/included_imp_deriv_n.con". +inline procedural "cic:/CoRN/ftc/NthDerivative/included_imp_deriv_n.con" as lemma. -inline procedural "cic:/CoRN/ftc/NthDerivative/included_imp_diffble_n.con". +inline procedural "cic:/CoRN/ftc/NthDerivative/included_imp_diffble_n.con" as lemma. (*#* And finally we have an addition rule for the order of the derivative. *) -inline procedural "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_plus.con". +inline procedural "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_plus.con" as lemma. (* UNEXPORTED End Basic_Results @@ -240,9 +240,9 @@ alias id "Hab'" = "cic:/CoRN/ftc/NthDerivative/More_Results/Hab'.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/NthDerivative/More_Results/Hab.con" "More_Results__". +inline procedural "cic:/CoRN/ftc/NthDerivative/More_Results/Hab.con" "More_Results__" as definition. -inline procedural "cic:/CoRN/ftc/NthDerivative/More_Results/I.con" "More_Results__". +inline procedural "cic:/CoRN/ftc/NthDerivative/More_Results/I.con" "More_Results__" as definition. (* end hide *) @@ -254,27 +254,27 @@ elimination which we would get if we had defined nth differentiability as an existential quantification of the nth derivative relation. *) -inline procedural "cic:/CoRN/ftc/NthDerivative/n_deriv_I.con". +inline procedural "cic:/CoRN/ftc/NthDerivative/n_deriv_I.con" as definition. (*#* This operator is well defined and works as expected. *) -inline procedural "cic:/CoRN/ftc/NthDerivative/n_deriv_I_wd.con". +inline procedural "cic:/CoRN/ftc/NthDerivative/n_deriv_I_wd.con" as lemma. -inline procedural "cic:/CoRN/ftc/NthDerivative/n_deriv_lemma.con". +inline procedural "cic:/CoRN/ftc/NthDerivative/n_deriv_lemma.con" as lemma. -inline procedural "cic:/CoRN/ftc/NthDerivative/n_deriv_inc.con". +inline procedural "cic:/CoRN/ftc/NthDerivative/n_deriv_inc.con" as lemma. -inline procedural "cic:/CoRN/ftc/NthDerivative/n_deriv_inc'.con". +inline procedural "cic:/CoRN/ftc/NthDerivative/n_deriv_inc'.con" as lemma. (*#* Some basic properties of this operation. *) -inline procedural "cic:/CoRN/ftc/NthDerivative/n_Sn_deriv.con". +inline procedural "cic:/CoRN/ftc/NthDerivative/n_Sn_deriv.con" as lemma. -inline procedural "cic:/CoRN/ftc/NthDerivative/n_deriv_plus.con". +inline procedural "cic:/CoRN/ftc/NthDerivative/n_deriv_plus.con" as lemma. (* UNEXPORTED End More_Results @@ -288,11 +288,11 @@ Section More_on_n_deriv Some not so basic properties of this operation (needed in rather specific situations). *) -inline procedural "cic:/CoRN/ftc/NthDerivative/n_deriv_I_wd'.con". +inline procedural "cic:/CoRN/ftc/NthDerivative/n_deriv_I_wd'.con" as lemma. -inline procedural "cic:/CoRN/ftc/NthDerivative/n_deriv_I_wd''.con". +inline procedural "cic:/CoRN/ftc/NthDerivative/n_deriv_I_wd''.con" as lemma. -inline procedural "cic:/CoRN/ftc/NthDerivative/n_deriv_I_strext'.con". +inline procedural "cic:/CoRN/ftc/NthDerivative/n_deriv_I_strext'.con" as lemma. (* UNEXPORTED End More_on_n_deriv diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/PartFunEquality.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/PartFunEquality.mma index 3b22af3fd..eabeadd4b 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/PartFunEquality.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/PartFunEquality.mma @@ -38,7 +38,7 @@ given predicate rather than to the predicate itself. The following definition makes this possible. *) -inline procedural "cic:/CoRN/ftc/PartFunEquality/subset.con". +inline procedural "cic:/CoRN/ftc/PartFunEquality/subset.con" as definition. (*#* The core of our work will revolve around the following fundamental @@ -50,7 +50,7 @@ it is easier to consider a generic case%.}%. This file is concerned with proving the main properties of this equality relation. *) -inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq.con". +inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq.con" as definition. (*#* Notice that, because the quantification over the proofs is universal, @@ -93,9 +93,9 @@ alias id "G" = "cic:/CoRN/ftc/PartFunEquality/Equality_Results/G.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/PartFunEquality/Equality_Results/P.con" "Equality_Results__". +inline procedural "cic:/CoRN/ftc/PartFunEquality/Equality_Results/P.con" "Equality_Results__" as definition. -inline procedural "cic:/CoRN/ftc/PartFunEquality/Equality_Results/Q.con" "Equality_Results__". +inline procedural "cic:/CoRN/ftc/PartFunEquality/Equality_Results/Q.con" "Equality_Results__" as definition. (* end hide *) @@ -106,11 +106,11 @@ We start with two lemmas which make it much easier to prove and use this definition: *) -inline procedural "cic:/CoRN/ftc/PartFunEquality/eq_imp_Feq.con". +inline procedural "cic:/CoRN/ftc/PartFunEquality/eq_imp_Feq.con" as lemma. -inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_imp_eq.con". +inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_imp_eq.con" as lemma. -inline procedural "cic:/CoRN/ftc/PartFunEquality/included_IR.con". +inline procedural "cic:/CoRN/ftc/PartFunEquality/included_IR.con" as lemma. (* UNEXPORTED End Equality_Results @@ -128,7 +128,7 @@ Section Some_More If two function coincide on a given subset then they coincide in any smaller subset. *) -inline procedural "cic:/CoRN/ftc/PartFunEquality/included_Feq.con". +inline procedural "cic:/CoRN/ftc/PartFunEquality/included_Feq.con" as lemma. (* UNEXPORTED End Some_More @@ -160,11 +160,11 @@ alias id "F" = "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Definitions/F.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Definitions/P.con" "Away_from_Zero__Definitions__". +inline procedural "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Definitions/P.con" "Away_from_Zero__Definitions__" as definition. (* end hide *) -inline procedural "cic:/CoRN/ftc/PartFunEquality/bnd_away_zero.con". +inline procedural "cic:/CoRN/ftc/PartFunEquality/bnd_away_zero.con" as definition. (*#* If [F] is bounded away from zero in [I] then [F] is necessarily apart from zero in [I]; also this means that [I] is included in the domain of [{1/}F]. @@ -176,11 +176,11 @@ alias id "Hf" = "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Definitions/Hf.var (* end show *) -inline procedural "cic:/CoRN/ftc/PartFunEquality/bnd_imp_ap_zero.con". +inline procedural "cic:/CoRN/ftc/PartFunEquality/bnd_imp_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/ftc/PartFunEquality/bnd_imp_inc_recip.con". +inline procedural "cic:/CoRN/ftc/PartFunEquality/bnd_imp_inc_recip.con" as lemma. -inline procedural "cic:/CoRN/ftc/PartFunEquality/bnd_imp_inc_div.con". +inline procedural "cic:/CoRN/ftc/PartFunEquality/bnd_imp_inc_div.con" as lemma. (* UNEXPORTED End Definitions @@ -199,25 +199,25 @@ alias id "P" = "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/P.var". alias id "Q" = "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Q.var". -inline procedural "cic:/CoRN/ftc/PartFunEquality/included_imp_bnd.con". +inline procedural "cic:/CoRN/ftc/PartFunEquality/included_imp_bnd.con" as lemma. -inline procedural "cic:/CoRN/ftc/PartFunEquality/FRestr_bnd.con". +inline procedural "cic:/CoRN/ftc/PartFunEquality/FRestr_bnd.con" as lemma. (*#* A function is said to be bounded away from zero everywhere if it is bounded away from zero in every compact subinterval of its domain; a similar definition is made for arbitrary sets, which will be necessary for future work. *) -inline procedural "cic:/CoRN/ftc/PartFunEquality/bnd_away_zero_everywhere.con". +inline procedural "cic:/CoRN/ftc/PartFunEquality/bnd_away_zero_everywhere.con" as definition. -inline procedural "cic:/CoRN/ftc/PartFunEquality/bnd_away_zero_in_P.con". +inline procedural "cic:/CoRN/ftc/PartFunEquality/bnd_away_zero_in_P.con" as definition. (*#* An immediate consequence: *) -inline procedural "cic:/CoRN/ftc/PartFunEquality/bnd_in_P_imp_ap_zero.con". +inline procedural "cic:/CoRN/ftc/PartFunEquality/bnd_in_P_imp_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/ftc/PartFunEquality/FRestr_bnd'.con". +inline procedural "cic:/CoRN/ftc/PartFunEquality/FRestr_bnd'.con" as lemma. (* UNEXPORTED End Away_from_Zero @@ -271,11 +271,11 @@ alias id "G" = "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Feq_Equivalence/G alias id "H" = "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Feq_Equivalence/H.var". -inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_reflexive.con". +inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_reflexive.con" as lemma. -inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_symmetric.con". +inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_symmetric.con" as lemma. -inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_transitive.con". +inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_transitive.con" as lemma. (* UNEXPORTED End Feq_Equivalence @@ -297,23 +297,23 @@ alias id "G" = "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Operations/G.var" alias id "G'" = "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Operations/G'.var". -inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_plus.con". +inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_plus.con" as lemma. -inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_inv.con". +inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_inv.con" as lemma. -inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_minus.con". +inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_minus.con" as lemma. -inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_mult.con". +inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_mult.con" as lemma. -inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_nth.con". +inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_nth.con" as lemma. -inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_recip.con". +inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_recip.con" as lemma. -inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_recip'.con". +inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_recip'.con" as lemma. -inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_div.con". +inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_div.con" as lemma. -inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_div'.con". +inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_div'.con" as lemma. (*#* Notice that in the case of division we only need to require boundedness away from zero for one of the functions (as they are equal); thus the two last lemmas are stated in two different ways, as according to the context one or the other condition may be easier to prove. @@ -321,13 +321,13 @@ Notice that in the case of division we only need to require boundedness away fro The restriction of a function is well defined. *) -inline procedural "cic:/CoRN/ftc/PartFunEquality/FRestr_wd.con". +inline procedural "cic:/CoRN/ftc/PartFunEquality/FRestr_wd.con" as lemma. (*#* The image of a set is extensional. *) -inline procedural "cic:/CoRN/ftc/PartFunEquality/fun_image_wd.con". +inline procedural "cic:/CoRN/ftc/PartFunEquality/fun_image_wd.con" as lemma. (* UNEXPORTED End Operations @@ -357,7 +357,7 @@ alias id "F" = "cic:/CoRN/ftc/PartFunEquality/Nth_Power/F.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/PartFunEquality/Nth_Power/P.con" "Nth_Power__". +inline procedural "cic:/CoRN/ftc/PartFunEquality/Nth_Power/P.con" "Nth_Power__" as definition. (* end hide *) @@ -367,13 +367,13 @@ alias id "H" = "cic:/CoRN/ftc/PartFunEquality/Nth_Power/H.var". alias id "Hf" = "cic:/CoRN/ftc/PartFunEquality/Nth_Power/Hf.var". -inline procedural "cic:/CoRN/ftc/PartFunEquality/FNth_zero.con". +inline procedural "cic:/CoRN/ftc/PartFunEquality/FNth_zero.con" as lemma. alias id "n" = "cic:/CoRN/ftc/PartFunEquality/Nth_Power/n.var". alias id "H'" = "cic:/CoRN/ftc/PartFunEquality/Nth_Power/H'.var". -inline procedural "cic:/CoRN/ftc/PartFunEquality/FNth_mult.con". +inline procedural "cic:/CoRN/ftc/PartFunEquality/FNth_mult.con" as lemma. (* UNEXPORTED End Nth_Power @@ -397,7 +397,7 @@ alias id "Hab" = "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/Hab.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/I.con" "Strong_Nth_Power__". +inline procedural "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/I.con" "Strong_Nth_Power__" as definition. (* end hide *) @@ -405,9 +405,9 @@ alias id "F" = "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/F.var". alias id "incF" = "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/incF.var". -inline procedural "cic:/CoRN/ftc/PartFunEquality/FNth_zero'.con". +inline procedural "cic:/CoRN/ftc/PartFunEquality/FNth_zero'.con" as lemma. -inline procedural "cic:/CoRN/ftc/PartFunEquality/FNth_mult'.con". +inline procedural "cic:/CoRN/ftc/PartFunEquality/FNth_mult'.con" as lemma. (* UNEXPORTED End Strong_Nth_Power diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/PartInterval.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/PartInterval.mma index e01c35e39..93c906356 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/PartInterval.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/PartInterval.mma @@ -53,15 +53,15 @@ alias id "Hab" = "cic:/CoRN/ftc/PartInterval/Conversion/Hab.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/PartInterval/Conversion/I.con" "Conversion__". +inline procedural "cic:/CoRN/ftc/PartInterval/Conversion/I.con" "Conversion__" as definition. (* end hide *) alias id "Hf" = "cic:/CoRN/ftc/PartInterval/Conversion/Hf.var". -inline procedural "cic:/CoRN/ftc/PartInterval/IntPartIR_strext.con". +inline procedural "cic:/CoRN/ftc/PartInterval/IntPartIR_strext.con" as lemma. -inline procedural "cic:/CoRN/ftc/PartInterval/IntPartIR.con". +inline procedural "cic:/CoRN/ftc/PartInterval/IntPartIR.con" as definition. (* UNEXPORTED End Conversion @@ -88,15 +88,15 @@ alias id "Hab" = "cic:/CoRN/ftc/PartInterval/AntiConversion/Hab.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/PartInterval/AntiConversion/I.con" "AntiConversion__". +inline procedural "cic:/CoRN/ftc/PartInterval/AntiConversion/I.con" "AntiConversion__" as definition. (* end hide *) alias id "f" = "cic:/CoRN/ftc/PartInterval/AntiConversion/f.var". -inline procedural "cic:/CoRN/ftc/PartInterval/PartInt_strext.con". +inline procedural "cic:/CoRN/ftc/PartInterval/PartInt_strext.con" as lemma. -inline procedural "cic:/CoRN/ftc/PartInterval/PartInt.con". +inline procedural "cic:/CoRN/ftc/PartInterval/PartInt.con" as definition. (* UNEXPORTED End AntiConversion @@ -114,7 +114,7 @@ Section Inverses In one direction these operators are inverses. *) -inline procedural "cic:/CoRN/ftc/PartInterval/int_part_int.con". +inline procedural "cic:/CoRN/ftc/PartInterval/int_part_int.con" as lemma. (* UNEXPORTED End Inverses @@ -149,7 +149,7 @@ alias id "Hab" = "cic:/CoRN/ftc/PartInterval/Equivalences/Hab.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/PartInterval/Equivalences/I.con" "Equivalences__". +inline procedural "cic:/CoRN/ftc/PartInterval/Equivalences/I.con" "Equivalences__" as definition. (* end hide *) @@ -161,19 +161,19 @@ alias id "Ff" = "cic:/CoRN/ftc/PartInterval/Equivalences/Ff.var". alias id "Gg" = "cic:/CoRN/ftc/PartInterval/Equivalences/Gg.var". -inline procedural "cic:/CoRN/ftc/PartInterval/part_int_const.con". +inline procedural "cic:/CoRN/ftc/PartInterval/part_int_const.con" as lemma. -inline procedural "cic:/CoRN/ftc/PartInterval/part_int_id.con". +inline procedural "cic:/CoRN/ftc/PartInterval/part_int_id.con" as lemma. -inline procedural "cic:/CoRN/ftc/PartInterval/part_int_plus.con". +inline procedural "cic:/CoRN/ftc/PartInterval/part_int_plus.con" as lemma. -inline procedural "cic:/CoRN/ftc/PartInterval/part_int_inv.con". +inline procedural "cic:/CoRN/ftc/PartInterval/part_int_inv.con" as lemma. -inline procedural "cic:/CoRN/ftc/PartInterval/part_int_minus.con". +inline procedural "cic:/CoRN/ftc/PartInterval/part_int_minus.con" as lemma. -inline procedural "cic:/CoRN/ftc/PartInterval/part_int_mult.con". +inline procedural "cic:/CoRN/ftc/PartInterval/part_int_mult.con" as lemma. -inline procedural "cic:/CoRN/ftc/PartInterval/part_int_nth.con". +inline procedural "cic:/CoRN/ftc/PartInterval/part_int_nth.con" as lemma. (* begin show *) @@ -183,9 +183,9 @@ alias id "Hg" = "cic:/CoRN/ftc/PartInterval/Equivalences/Hg.var". (* end show *) -inline procedural "cic:/CoRN/ftc/PartInterval/part_int_recip.con". +inline procedural "cic:/CoRN/ftc/PartInterval/part_int_recip.con" as lemma. -inline procedural "cic:/CoRN/ftc/PartInterval/part_int_div.con". +inline procedural "cic:/CoRN/ftc/PartInterval/part_int_div.con" as lemma. (* UNEXPORTED End Equivalences diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/Partitions.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/Partitions.mma index 0e224f38e..5488ba0e7 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/Partitions.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/Partitions.mma @@ -58,9 +58,9 @@ cic:/matita/CoRN-Procedural/ftc/Partitions/Pts.con [i < j] and that [ai] is in [[a,b]] for all [i]. *) -inline procedural "cic:/CoRN/ftc/Partitions/Partition_mon.con". +inline procedural "cic:/CoRN/ftc/Partitions/Partition_mon.con" as lemma. -inline procedural "cic:/CoRN/ftc/Partitions/Partition_in_compact.con". +inline procedural "cic:/CoRN/ftc/Partitions/Partition_in_compact.con" as lemma. (*#* Each partition of [[a,b]] implies a partition of the interval @@ -69,9 +69,9 @@ important role in much of our future work, so we take some care to define it. *) -inline procedural "cic:/CoRN/ftc/Partitions/part_pred_lemma.con". +inline procedural "cic:/CoRN/ftc/Partitions/part_pred_lemma.con" as lemma. -inline procedural "cic:/CoRN/ftc/Partitions/Partition_Dom.con". +inline procedural "cic:/CoRN/ftc/Partitions/Partition_Dom.con" as definition. (*#* The mesh of a partition is the greatest distance between two @@ -85,11 +85,11 @@ of defining the minimum and maximum of the empty list to be [0] actually helps us in this case. *) -inline procedural "cic:/CoRN/ftc/Partitions/Part_Mesh_List.con". +inline procedural "cic:/CoRN/ftc/Partitions/Part_Mesh_List.con" as definition. -inline procedural "cic:/CoRN/ftc/Partitions/Mesh.con". +inline procedural "cic:/CoRN/ftc/Partitions/Mesh.con" as definition. -inline procedural "cic:/CoRN/ftc/Partitions/AntiMesh.con". +inline procedural "cic:/CoRN/ftc/Partitions/AntiMesh.con" as definition. (*#* Even partitions (partitions where all the points are evenly spaced) @@ -97,11 +97,11 @@ will also play a central role in our work; the first two lemmas are presented simply to make the definition of even partition lighter. *) -inline procedural "cic:/CoRN/ftc/Partitions/even_part_1.con". +inline procedural "cic:/CoRN/ftc/Partitions/even_part_1.con" as lemma. -inline procedural "cic:/CoRN/ftc/Partitions/even_part_2.con". +inline procedural "cic:/CoRN/ftc/Partitions/even_part_2.con" as lemma. -inline procedural "cic:/CoRN/ftc/Partitions/Even_Partition.con". +inline procedural "cic:/CoRN/ftc/Partitions/Even_Partition.con" as definition. (* UNEXPORTED Section Refinements @@ -126,9 +126,9 @@ We now define what it means for a partition [Q] to be a refinement of [P] and prove the main property of refinements. *) -inline procedural "cic:/CoRN/ftc/Partitions/Refinement.con". +inline procedural "cic:/CoRN/ftc/Partitions/Refinement.con" as definition. -inline procedural "cic:/CoRN/ftc/Partitions/Refinement_prop.con". +inline procedural "cic:/CoRN/ftc/Partitions/Refinement_prop.con" as lemma. (*#* We will also need to consider arbitrary sums %of the form @@ -139,11 +139,11 @@ For this, we again need a choice function [x] which has to satisfy some condition. We define the condition and the sum for a fixed [P]: *) -inline procedural "cic:/CoRN/ftc/Partitions/Points_in_Partition.con". +inline procedural "cic:/CoRN/ftc/Partitions/Points_in_Partition.con" as definition. -inline procedural "cic:/CoRN/ftc/Partitions/Pts_part_lemma.con". +inline procedural "cic:/CoRN/ftc/Partitions/Pts_part_lemma.con" as lemma. -inline procedural "cic:/CoRN/ftc/Partitions/Partition_Sum.con". +inline procedural "cic:/CoRN/ftc/Partitions/Partition_Sum.con" as definition. (* UNEXPORTED End Refinements @@ -173,7 +173,7 @@ alias id "Hab" = "cic:/CoRN/ftc/Partitions/Definitions/Hab.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/Partitions/Definitions/I.con" "Definitions__". +inline procedural "cic:/CoRN/ftc/Partitions/Definitions/I.con" "Definitions__" as definition. (* end hide *) @@ -194,11 +194,11 @@ alias id "m" = "cic:/CoRN/ftc/Partitions/Definitions/Getting_Points/m.var". alias id "Q" = "cic:/CoRN/ftc/Partitions/Definitions/Getting_Points/Q.var". -inline procedural "cic:/CoRN/ftc/Partitions/Partition_imp_points.con". +inline procedural "cic:/CoRN/ftc/Partitions/Partition_imp_points.con" as definition. -inline procedural "cic:/CoRN/ftc/Partitions/Partition_imp_points_1.con". +inline procedural "cic:/CoRN/ftc/Partitions/Partition_imp_points_1.con" as lemma. -inline procedural "cic:/CoRN/ftc/Partitions/Partition_imp_points_2.con". +inline procedural "cic:/CoRN/ftc/Partitions/Partition_imp_points_2.con" as lemma. (* UNEXPORTED End Getting_Points @@ -212,7 +212,7 @@ alias id "F" = "cic:/CoRN/ftc/Partitions/Definitions/F.var". alias id "contF" = "cic:/CoRN/ftc/Partitions/Definitions/contF.var". -inline procedural "cic:/CoRN/ftc/Partitions/Even_Partition_Sum.con". +inline procedural "cic:/CoRN/ftc/Partitions/Even_Partition_Sum.con" as definition. (* UNEXPORTED End Definitions @@ -275,21 +275,21 @@ Section Lemmas If a partition has more than one point then its mesh list is nonempty. *) -inline procedural "cic:/CoRN/ftc/Partitions/length_Part_Mesh_List.con". +inline procedural "cic:/CoRN/ftc/Partitions/length_Part_Mesh_List.con" as lemma. (*#* Any element of the auxiliary list defined to calculate the mesh of a partition has a very specific form. *) -inline procedural "cic:/CoRN/ftc/Partitions/Part_Mesh_List_lemma.con". +inline procedural "cic:/CoRN/ftc/Partitions/Part_Mesh_List_lemma.con" as lemma. (*#* Mesh and antimesh are always nonnegative. *) -inline procedural "cic:/CoRN/ftc/Partitions/Mesh_nonneg.con". +inline procedural "cic:/CoRN/ftc/Partitions/Mesh_nonneg.con" as lemma. -inline procedural "cic:/CoRN/ftc/Partitions/AntiMesh_nonneg.con". +inline procedural "cic:/CoRN/ftc/Partitions/AntiMesh_nonneg.con" as lemma. (*#* Most important, [AntiMesh] and [Mesh] provide lower and upper bounds @@ -306,7 +306,7 @@ alias id "b" = "cic:/CoRN/ftc/Partitions/Lemmas/b.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/Partitions/Lemmas/I.con" "Lemmas__". +inline procedural "cic:/CoRN/ftc/Partitions/Lemmas/I.con" "Lemmas__" as definition. (* end hide *) @@ -316,11 +316,11 @@ alias id "n" = "cic:/CoRN/ftc/Partitions/Lemmas/n.var". alias id "P" = "cic:/CoRN/ftc/Partitions/Lemmas/P.var". -inline procedural "cic:/CoRN/ftc/Partitions/Mesh_lemma.con". +inline procedural "cic:/CoRN/ftc/Partitions/Mesh_lemma.con" as lemma. -inline procedural "cic:/CoRN/ftc/Partitions/AntiMesh_lemma.con". +inline procedural "cic:/CoRN/ftc/Partitions/AntiMesh_lemma.con" as lemma. -inline procedural "cic:/CoRN/ftc/Partitions/Mesh_leEq.con". +inline procedural "cic:/CoRN/ftc/Partitions/Mesh_leEq.con" as lemma. (* UNEXPORTED End Lemmas @@ -333,15 +333,15 @@ Section Even_Partitions (*#* More technical stuff. Two equal partitions have the same mesh. *) -inline procedural "cic:/CoRN/ftc/Partitions/Mesh_wd.con". +inline procedural "cic:/CoRN/ftc/Partitions/Mesh_wd.con" as lemma. -inline procedural "cic:/CoRN/ftc/Partitions/Mesh_wd'.con". +inline procedural "cic:/CoRN/ftc/Partitions/Mesh_wd'.con" as lemma. (*#* The mesh of an even partition is easily calculated. *) -inline procedural "cic:/CoRN/ftc/Partitions/even_partition_Mesh.con". +inline procedural "cic:/CoRN/ftc/Partitions/even_partition_Mesh.con" as lemma. (*#* ** Miscellaneous %\begin{convention}% Throughout this section, let [a,b:IR] and [I] be [[a,b]]. @@ -354,7 +354,7 @@ alias id "b" = "cic:/CoRN/ftc/Partitions/Even_Partitions/b.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/Partitions/Even_Partitions/I.con" "Even_Partitions__". +inline procedural "cic:/CoRN/ftc/Partitions/Even_Partitions/I.con" "Even_Partitions__" as definition. (* end hide *) @@ -364,9 +364,9 @@ alias id "Hab" = "cic:/CoRN/ftc/Partitions/Even_Partitions/Hab.var". An interesting property: in a partition, if [ai [<] aj] then [i < j]. *) -inline procedural "cic:/CoRN/ftc/Partitions/Partition_Points_mon.con". +inline procedural "cic:/CoRN/ftc/Partitions/Partition_Points_mon.con" as lemma. -inline procedural "cic:/CoRN/ftc/Partitions/refinement_resp_mult.con". +inline procedural "cic:/CoRN/ftc/Partitions/refinement_resp_mult.con" as lemma. (*#* %\begin{convention}% Assume [m,n] are positive natural numbers and @@ -387,13 +387,13 @@ alias id "Hn" = "cic:/CoRN/ftc/Partitions/Even_Partitions/Hn.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/Partitions/Even_Partitions/P.con" "Even_Partitions__". +inline procedural "cic:/CoRN/ftc/Partitions/Even_Partitions/P.con" "Even_Partitions__" as definition. -inline procedural "cic:/CoRN/ftc/Partitions/Even_Partitions/Q.con" "Even_Partitions__". +inline procedural "cic:/CoRN/ftc/Partitions/Even_Partitions/Q.con" "Even_Partitions__" as definition. (* end hide *) -inline procedural "cic:/CoRN/ftc/Partitions/even_partition_refinement.con". +inline procedural "cic:/CoRN/ftc/Partitions/even_partition_refinement.con" as lemma. (* UNEXPORTED End Even_Partitions @@ -414,7 +414,7 @@ alias id "b" = "cic:/CoRN/ftc/Partitions/More_Definitions/b.var". alias id "Hab" = "cic:/CoRN/ftc/Partitions/More_Definitions/Hab.var". -inline procedural "cic:/CoRN/ftc/Partitions/_Separated.con". +inline procedural "cic:/CoRN/ftc/Partitions/_Separated.con" as definition. (*#* Two partitions are said to be (mutually) separated if they are both @@ -434,7 +434,7 @@ alias id "P" = "cic:/CoRN/ftc/Partitions/More_Definitions/P.var". alias id "Q" = "cic:/CoRN/ftc/Partitions/More_Definitions/Q.var". -inline procedural "cic:/CoRN/ftc/Partitions/Separated.con". +inline procedural "cic:/CoRN/ftc/Partitions/Separated.con" as definition. (* UNEXPORTED End More_Definitions @@ -458,7 +458,7 @@ alias id "b" = "cic:/CoRN/ftc/Partitions/Sep_Partitions/b.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/Partitions/Sep_Partitions/I.con" "Sep_Partitions__". +inline procedural "cic:/CoRN/ftc/Partitions/Sep_Partitions/I.con" "Sep_Partitions__" as definition. (* end hide *) @@ -468,7 +468,7 @@ alias id "Hab" = "cic:/CoRN/ftc/Partitions/Sep_Partitions/Hab.var". The antimesh of a separated partition is always positive. *) -inline procedural "cic:/CoRN/ftc/Partitions/pos_AntiMesh.con". +inline procedural "cic:/CoRN/ftc/Partitions/pos_AntiMesh.con" as lemma. (*#* A partition can have only one point iff the endpoints of the interval @@ -476,11 +476,11 @@ are the same; moreover, if the partition is separated and the endpoints of the interval are the same then it must have one point. *) -inline procedural "cic:/CoRN/ftc/Partitions/partition_length_zero.con". +inline procedural "cic:/CoRN/ftc/Partitions/partition_length_zero.con" as lemma. -inline procedural "cic:/CoRN/ftc/Partitions/_Separated_imp_length_zero.con". +inline procedural "cic:/CoRN/ftc/Partitions/_Separated_imp_length_zero.con" as lemma. -inline procedural "cic:/CoRN/ftc/Partitions/partition_less_imp_gt_zero.con". +inline procedural "cic:/CoRN/ftc/Partitions/partition_less_imp_gt_zero.con" as lemma. (* UNEXPORTED End Sep_Partitions diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/RefLemma.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/RefLemma.mma index 12ea49f4d..6fa5d117c 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/RefLemma.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/RefLemma.mma @@ -87,7 +87,7 @@ alias id "Hab" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Hab.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/I.con" "Refinement_Lemma__". +inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/I.con" "Refinement_Lemma__" as definition. (* end hide *) @@ -99,7 +99,7 @@ alias id "incF" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/incF.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/contF'.con" "Refinement_Lemma__". +inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/contF'.con" "Refinement_Lemma__" as definition. (* end hide *) @@ -128,7 +128,7 @@ alias id "He" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/ (* begin hide *) -inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/d.con" "Refinement_Lemma__First_Refinement_Lemma__". +inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/d.con" "Refinement_Lemma__First_Refinement_Lemma__" as definition. (* end hide *) @@ -158,31 +158,31 @@ alias id "HfQ'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemm (* begin hide *) -inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/sub.con" "Refinement_Lemma__First_Refinement_Lemma__". +inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/sub.con" "Refinement_Lemma__First_Refinement_Lemma__" as definition. -inline procedural "cic:/CoRN/ftc/RefLemma/RL_sub_0.con". +inline procedural "cic:/CoRN/ftc/RefLemma/RL_sub_0.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefLemma/RL_sub_n.con". +inline procedural "cic:/CoRN/ftc/RefLemma/RL_sub_n.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefLemma/RL_sub_mon.con". +inline procedural "cic:/CoRN/ftc/RefLemma/RL_sub_mon.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefLemma/RL_sub_mon'.con". +inline procedural "cic:/CoRN/ftc/RefLemma/RL_sub_mon'.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefLemma/RL_sub_hyp.con". +inline procedural "cic:/CoRN/ftc/RefLemma/RL_sub_hyp.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefLemma/RL_sub_S.con". +inline procedural "cic:/CoRN/ftc/RefLemma/RL_sub_S.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/H.con" "Refinement_Lemma__First_Refinement_Lemma__". +inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/H.con" "Refinement_Lemma__First_Refinement_Lemma__" as definition. -inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/H'.con" "Refinement_Lemma__First_Refinement_Lemma__". +inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/H'.con" "Refinement_Lemma__First_Refinement_Lemma__" as definition. -inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/H0.con" "Refinement_Lemma__First_Refinement_Lemma__". +inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/H0.con" "Refinement_Lemma__First_Refinement_Lemma__" as definition. -inline procedural "cic:/CoRN/ftc/RefLemma/RL_sub_SS.con". +inline procedural "cic:/CoRN/ftc/RefLemma/RL_sub_SS.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefLemma/RL_h.con". +inline procedural "cic:/CoRN/ftc/RefLemma/RL_h.con" as definition. -inline procedural "cic:/CoRN/ftc/RefLemma/RL_g.con". +inline procedural "cic:/CoRN/ftc/RefLemma/RL_g.con" as definition. (* NOTATION Notation g := RL_g. @@ -192,7 +192,7 @@ Notation g := RL_g. Notation h := RL_h. *) -inline procedural "cic:/CoRN/ftc/RefLemma/ref_calc1.con". +inline procedural "cic:/CoRN/ftc/RefLemma/ref_calc1.con" as lemma. (* NOTATION Notation just1 := (incF _ (Pts_part_lemma _ _ _ _ _ _ HfP _ _)). @@ -202,23 +202,23 @@ Notation just1 := (incF _ (Pts_part_lemma _ _ _ _ _ _ HfP _ _)). Notation just2 := (incF _ (Pts_part_lemma _ _ _ _ _ _ HfQ _ _)). *) -inline procedural "cic:/CoRN/ftc/RefLemma/ref_calc2.con". +inline procedural "cic:/CoRN/ftc/RefLemma/ref_calc2.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefLemma/ref_calc3.con". +inline procedural "cic:/CoRN/ftc/RefLemma/ref_calc3.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefLemma/ref_calc4.con". +inline procedural "cic:/CoRN/ftc/RefLemma/ref_calc4.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefLemma/ref_calc5.con". +inline procedural "cic:/CoRN/ftc/RefLemma/ref_calc5.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefLemma/ref_calc6.con". +inline procedural "cic:/CoRN/ftc/RefLemma/ref_calc6.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefLemma/ref_calc7.con". +inline procedural "cic:/CoRN/ftc/RefLemma/ref_calc7.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefLemma/ref_calc8.con". +inline procedural "cic:/CoRN/ftc/RefLemma/ref_calc8.con" as lemma. (* end hide *) -inline procedural "cic:/CoRN/ftc/RefLemma/first_refinement_lemma.con". +inline procedural "cic:/CoRN/ftc/RefLemma/first_refinement_lemma.con" as lemma. (* UNEXPORTED End First_Refinement_Lemma @@ -270,9 +270,9 @@ alias id "He'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemm (* begin hide *) -inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/d.con" "Refinement_Lemma__Second_Refinement_Lemma__". +inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/d.con" "Refinement_Lemma__Second_Refinement_Lemma__" as definition. -inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/d'.con" "Refinement_Lemma__Second_Refinement_Lemma__". +inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/d'.con" "Refinement_Lemma__Second_Refinement_Lemma__" as definition. (* end hide *) @@ -292,7 +292,7 @@ alias id "HfR" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemm alias id "HfR'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HfR'.var". -inline procedural "cic:/CoRN/ftc/RefLemma/second_refinement_lemma.con". +inline procedural "cic:/CoRN/ftc/RefLemma/second_refinement_lemma.con" as lemma. (* UNEXPORTED End Second_Refinement_Lemma @@ -336,9 +336,9 @@ alias id "He'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma (* begin hide *) -inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/d.con" "Refinement_Lemma__Third_Refinement_Lemma__". +inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/d.con" "Refinement_Lemma__Third_Refinement_Lemma__" as definition. -inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/d'.con" "Refinement_Lemma__Third_Refinement_Lemma__". +inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/d'.con" "Refinement_Lemma__Third_Refinement_Lemma__" as definition. (* end hide *) @@ -366,69 +366,69 @@ alias id "Hbeta" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lem (* begin hide *) -inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/alpha.con" "Refinement_Lemma__Third_Refinement_Lemma__". +inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/alpha.con" "Refinement_Lemma__Third_Refinement_Lemma__" as definition. -inline procedural "cic:/CoRN/ftc/RefLemma/RL_alpha.con". +inline procedural "cic:/CoRN/ftc/RefLemma/RL_alpha.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/csi1.con" "Refinement_Lemma__Third_Refinement_Lemma__". +inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/csi1.con" "Refinement_Lemma__Third_Refinement_Lemma__" as definition. -inline procedural "cic:/CoRN/ftc/RefLemma/RL_csi1.con". +inline procedural "cic:/CoRN/ftc/RefLemma/RL_csi1.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/delta1.con" "Refinement_Lemma__Third_Refinement_Lemma__". +inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/delta1.con" "Refinement_Lemma__Third_Refinement_Lemma__" as definition. -inline procedural "cic:/CoRN/ftc/RefLemma/RL_delta1.con". +inline procedural "cic:/CoRN/ftc/RefLemma/RL_delta1.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/P'.con" "Refinement_Lemma__Third_Refinement_Lemma__". +inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/P'.con" "Refinement_Lemma__Third_Refinement_Lemma__" as definition. -inline procedural "cic:/CoRN/ftc/RefLemma/RL_P'_sep.con". +inline procedural "cic:/CoRN/ftc/RefLemma/RL_P'_sep.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefLemma/RL_P'_Mesh.con". +inline procedural "cic:/CoRN/ftc/RefLemma/RL_P'_Mesh.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/fP'.con" "Refinement_Lemma__Third_Refinement_Lemma__". +inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/fP'.con" "Refinement_Lemma__Third_Refinement_Lemma__" as definition. -inline procedural "cic:/CoRN/ftc/RefLemma/RL_fP'_in_P'.con". +inline procedural "cic:/CoRN/ftc/RefLemma/RL_fP'_in_P'.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefLemma/RL_P'_P_sum.con". +inline procedural "cic:/CoRN/ftc/RefLemma/RL_P'_P_sum.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/csi2.con" "Refinement_Lemma__Third_Refinement_Lemma__". +inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/csi2.con" "Refinement_Lemma__Third_Refinement_Lemma__" as definition. -inline procedural "cic:/CoRN/ftc/RefLemma/RL_csi2.con". +inline procedural "cic:/CoRN/ftc/RefLemma/RL_csi2.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/delta2.con" "Refinement_Lemma__Third_Refinement_Lemma__". +inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/delta2.con" "Refinement_Lemma__Third_Refinement_Lemma__" as definition. -inline procedural "cic:/CoRN/ftc/RefLemma/RL_delta2.con". +inline procedural "cic:/CoRN/ftc/RefLemma/RL_delta2.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/R'.con" "Refinement_Lemma__Third_Refinement_Lemma__". +inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/R'.con" "Refinement_Lemma__Third_Refinement_Lemma__" as definition. -inline procedural "cic:/CoRN/ftc/RefLemma/RL_R'_sep.con". +inline procedural "cic:/CoRN/ftc/RefLemma/RL_R'_sep.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefLemma/RL_R'_Mesh.con". +inline procedural "cic:/CoRN/ftc/RefLemma/RL_R'_Mesh.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/fR'.con" "Refinement_Lemma__Third_Refinement_Lemma__". +inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/fR'.con" "Refinement_Lemma__Third_Refinement_Lemma__" as definition. -inline procedural "cic:/CoRN/ftc/RefLemma/RL_fR'_in_R'.con". +inline procedural "cic:/CoRN/ftc/RefLemma/RL_fR'_in_R'.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefLemma/RL_R'_R_sum.con". +inline procedural "cic:/CoRN/ftc/RefLemma/RL_R'_R_sum.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/csi3.con" "Refinement_Lemma__Third_Refinement_Lemma__". +inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/csi3.con" "Refinement_Lemma__Third_Refinement_Lemma__" as definition. -inline procedural "cic:/CoRN/ftc/RefLemma/RL_csi3.con". +inline procedural "cic:/CoRN/ftc/RefLemma/RL_csi3.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/Q.con" "Refinement_Lemma__Third_Refinement_Lemma__". +inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/Q.con" "Refinement_Lemma__Third_Refinement_Lemma__" as definition. -inline procedural "cic:/CoRN/ftc/RefLemma/RL_Q_Mesh.con". +inline procedural "cic:/CoRN/ftc/RefLemma/RL_Q_Mesh.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefLemma/RL_Q_sep.con". +inline procedural "cic:/CoRN/ftc/RefLemma/RL_Q_sep.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/fQ.con" "Refinement_Lemma__Third_Refinement_Lemma__". +inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/fQ.con" "Refinement_Lemma__Third_Refinement_Lemma__" as definition. -inline procedural "cic:/CoRN/ftc/RefLemma/RL_fQ_in_Q.con". +inline procedural "cic:/CoRN/ftc/RefLemma/RL_fQ_in_Q.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefLemma/RL_Q_P'_sum.con". +inline procedural "cic:/CoRN/ftc/RefLemma/RL_Q_P'_sum.con" as lemma. (* end hide *) -inline procedural "cic:/CoRN/ftc/RefLemma/third_refinement_lemma.con". +inline procedural "cic:/CoRN/ftc/RefLemma/third_refinement_lemma.con" as lemma. (* UNEXPORTED End Third_Refinement_Lemma @@ -440,13 +440,13 @@ Section Fourth_Refinement_Lemma (* begin hide *) -inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/Fa.con" "Refinement_Lemma__Fourth_Refinement_Lemma__". +inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/Fa.con" "Refinement_Lemma__Fourth_Refinement_Lemma__" as definition. (* NOTATION Notation just := (fun z => incF _ (Pts_part_lemma _ _ _ _ _ _ z _ _)). *) -inline procedural "cic:/CoRN/ftc/RefLemma/RL_sum_lemma_aux.con". +inline procedural "cic:/CoRN/ftc/RefLemma/RL_sum_lemma_aux.con" as lemma. (* end hide *) @@ -473,9 +473,9 @@ alias id "He'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemm (* begin hide *) -inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/d.con" "Refinement_Lemma__Fourth_Refinement_Lemma__". +inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/d.con" "Refinement_Lemma__Fourth_Refinement_Lemma__" as definition. -inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/d'.con" "Refinement_Lemma__Fourth_Refinement_Lemma__". +inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/d'.con" "Refinement_Lemma__Fourth_Refinement_Lemma__" as definition. (* end hide *) @@ -501,7 +501,7 @@ alias id "Hab'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lem (* end show *) -inline procedural "cic:/CoRN/ftc/RefLemma/fourth_refinement_lemma.con". +inline procedural "cic:/CoRN/ftc/RefLemma/fourth_refinement_lemma.con" as lemma. (* UNEXPORTED End Fourth_Refinement_Lemma @@ -531,9 +531,9 @@ alias id "He'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/ (* begin hide *) -inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/d.con" "Refinement_Lemma__Main_Refinement_Lemma__". +inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/d.con" "Refinement_Lemma__Main_Refinement_Lemma__" as definition. -inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/d'.con" "Refinement_Lemma__Main_Refinement_Lemma__". +inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/d'.con" "Refinement_Lemma__Main_Refinement_Lemma__" as definition. (* end hide *) @@ -553,7 +553,7 @@ alias id "HfR" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/ alias id "HfR'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HfR'.var". -inline procedural "cic:/CoRN/ftc/RefLemma/refinement_lemma.con". +inline procedural "cic:/CoRN/ftc/RefLemma/refinement_lemma.con" as lemma. (* UNEXPORTED End Main_Refinement_Lemma diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/RefSepRef.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/RefSepRef.mma index d344f47ad..a8205ce4c 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/RefSepRef.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/RefSepRef.mma @@ -34,7 +34,7 @@ alias id "b" = "cic:/CoRN/ftc/RefSepRef/Refining_Separated/b.var". alias id "Hab" = "cic:/CoRN/ftc/RefSepRef/Refining_Separated/Hab.var". -inline procedural "cic:/CoRN/ftc/RefSepRef/Refining_Separated/I.con" "Refining_Separated__". +inline procedural "cic:/CoRN/ftc/RefSepRef/Refining_Separated/I.con" "Refining_Separated__" as definition. alias id "F" = "cic:/CoRN/ftc/RefSepRef/Refining_Separated/F.var". @@ -52,91 +52,91 @@ alias id "R" = "cic:/CoRN/ftc/RefSepRef/Refining_Separated/R.var". alias id "HPR" = "cic:/CoRN/ftc/RefSepRef/Refining_Separated/HPR.var". -inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_HP.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_HP.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_HP'.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_HP'.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_HR.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_HR.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_HR'.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_HR'.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_mn0.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_mn0.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_nm0.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_nm0.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_H'.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_H'.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSepRef/Refining_Separated/f'.con" "Refining_Separated__". +inline procedural "cic:/CoRN/ftc/RefSepRef/Refining_Separated/f'.con" "Refining_Separated__" as definition. -inline procedural "cic:/CoRN/ftc/RefSepRef/Refining_Separated/g'.con" "Refining_Separated__". +inline procedural "cic:/CoRN/ftc/RefSepRef/Refining_Separated/g'.con" "Refining_Separated__" as definition. -inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_f'_nlnf.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_f'_nlnf.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_g'_nlnf.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_g'_nlnf.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_f'_mon.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_f'_mon.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_g'_mon.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_g'_mon.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_f'_ap_g'.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_f'_ap_g'.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSepRef/Refining_Separated/h.con" "Refining_Separated__". +inline procedural "cic:/CoRN/ftc/RefSepRef/Refining_Separated/h.con" "Refining_Separated__" as definition. -inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_h_nlnf.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_h_nlnf.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_h_mon.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_h_mon.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_h_mon'.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_h_mon'.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_h_f'.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_h_f'.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_h_g'.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_h_g'.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_h_PropAll.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_h_PropAll.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_h_PropEx.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_h_PropEx.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_fun.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_fun.con" as definition. -inline procedural "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_lemma1.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_lemma1.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_lemma3.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_lemma3.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_lemma4.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_lemma4.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_lemma2.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_lemma2.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSepRef/Separated_Refinement.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/Separated_Refinement.con" as definition. -inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxP.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxP.con" as definition. -inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxR.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxR.con" as definition. -inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxP_lemma0.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxP_lemma0.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_h_inj.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_h_inj.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxP_lemmai.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxP_lemmai.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxP_lemman.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxP_lemman.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxP_lemma1.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxP_lemma1.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxP_lemma2.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxP_lemma2.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_lft.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_lft.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxR_lemma0.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxR_lemma0.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxR_lemmai.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxR_lemmai.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxR_lemmam.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxR_lemmam.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxR_lemma1.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxR_lemma1.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxR_lemma2.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxR_lemma2.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_rht.con". +inline procedural "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_rht.con" as lemma. (* UNEXPORTED End Refining_Separated diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/RefSeparated.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/RefSeparated.mma index 4a26edaef..7d0106093 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/RefSeparated.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/RefSeparated.mma @@ -34,7 +34,7 @@ alias id "b" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/b.var". alias id "Hab" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Hab.var". -inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/I.con" "Separating__Separated__". +inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/I.con" "Separating__Separated__" as definition. alias id "F" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/F.var". @@ -56,47 +56,47 @@ alias id "HP" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/HP.var". alias id "HR" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/HR.var". -inline procedural "cic:/CoRN/ftc/RefSeparated/RS_pos_n.con". +inline procedural "cic:/CoRN/ftc/RefSeparated/RS_pos_n.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparated/RS_pos_m.con". +inline procedural "cic:/CoRN/ftc/RefSeparated/RS_pos_m.con" as lemma. alias id "alpha" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/alpha.var". alias id "Halpha" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Halpha.var". -inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/e.con" "Separating__Separated__". +inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/e.con" "Separating__Separated__" as definition. -inline procedural "cic:/CoRN/ftc/RefSeparated/RS_He.con". +inline procedural "cic:/CoRN/ftc/RefSeparated/RS_He.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/contF'.con" "Separating__Separated__". +inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/contF'.con" "Separating__Separated__" as definition. -inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/d.con" "Separating__Separated__". +inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/d.con" "Separating__Separated__" as definition. -inline procedural "cic:/CoRN/ftc/RefSeparated/RS_Hd.con". +inline procedural "cic:/CoRN/ftc/RefSeparated/RS_Hd.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparated/RS_Hd'.con". +inline procedural "cic:/CoRN/ftc/RefSeparated/RS_Hd'.con" as lemma. alias id "csi" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/csi.var". alias id "Hcsi" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Hcsi.var". -inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/M.con" "Separating__Separated__". +inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/M.con" "Separating__Separated__" as definition. -inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/deltaP.con" "Separating__Separated__". +inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/deltaP.con" "Separating__Separated__" as definition. -inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/deltaR.con" "Separating__Separated__". +inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/deltaR.con" "Separating__Separated__" as definition. -inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/delta.con" "Separating__Separated__". +inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/delta.con" "Separating__Separated__" as definition. -inline procedural "cic:/CoRN/ftc/RefSeparated/RS_delta_deltaP.con". +inline procedural "cic:/CoRN/ftc/RefSeparated/RS_delta_deltaP.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparated/RS_delta_deltaR.con". +inline procedural "cic:/CoRN/ftc/RefSeparated/RS_delta_deltaR.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparated/RS_delta_csi.con". +inline procedural "cic:/CoRN/ftc/RefSeparated/RS_delta_csi.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparated/RS_delta_d.con". +inline procedural "cic:/CoRN/ftc/RefSeparated/RS_delta_d.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparated/RS_delta_pos.con". +inline procedural "cic:/CoRN/ftc/RefSeparated/RS_delta_pos.con" as lemma. (* UNEXPORTED Section Defining_ai' @@ -106,57 +106,57 @@ alias id "i" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/i. alias id "Hi" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/Hi.var". -inline procedural "cic:/CoRN/ftc/RefSeparated/separation_conseq.con". +inline procedural "cic:/CoRN/ftc/RefSeparated/separation_conseq.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/pred1.con" "Separating__Separated__Defining_ai'__". +inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/pred1.con" "Separating__Separated__Defining_ai'__" as definition. -inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/pred2.con" "Separating__Separated__Defining_ai'__". +inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/pred2.con" "Separating__Separated__Defining_ai'__" as definition. -inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_aux_lemma.con". +inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_aux_lemma.con" as lemma. alias id "Hi0" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/Hi0.var". alias id "Hin" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/Hin.var". -inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_fun_i.con". +inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_fun_i.con" as definition. -inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_leEq.con". +inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_leEq.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_less.con". +inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_less.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_ap.con". +inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_ap.con" as lemma. (* UNEXPORTED End Defining_ai' *) -inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_fun.con". +inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_fun.con" as definition. -inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_fun_i_delta.con". +inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_fun_i_delta.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_fun_delta.con". +inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_fun_delta.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_mon_i.con". +inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_mon_i.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_mon.con". +inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_mon.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_fun_i_wd.con". +inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_fun_i_wd.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_fun_wd.con". +inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_fun_wd.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_part.con". +inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_part.con" as definition. -inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_lemma.con". +inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_lemma.con" as lemma. alias id "g" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/g.var". alias id "gP" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/gP.var". -inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_points.con". +inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_points.con" as definition. -inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_points_lemma.con". +inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_points_lemma.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_aux.con". +inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_aux.con" as lemma. (* NOTATION Notation just1 := (incF _ (Pts_part_lemma _ _ _ _ _ _ gP _ _)). @@ -167,9 +167,9 @@ Notation just2 := (incF _ (Pts_part_lemma _ _ _ _ _ _ sep__sep_points_lemma _ _)). *) -inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_Sum.con". +inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_Sum.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_Mesh.con". +inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_Mesh.con" as lemma. (* UNEXPORTED End Separating__Separated diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/RefSeparating.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/RefSeparating.mma index 1cb7b194f..a3d193ec8 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/RefSeparating.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/RefSeparating.mma @@ -34,7 +34,7 @@ alias id "b" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/b.var". alias id "Hab" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/Hab.var". -inline procedural "cic:/CoRN/ftc/RefSeparating/Separating_Partition/I.con" "Separating_Partition__". +inline procedural "cic:/CoRN/ftc/RefSeparating/Separating_Partition/I.con" "Separating_Partition__" as definition. alias id "F" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/F.var". @@ -56,81 +56,81 @@ alias id "csi" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/csi.var". alias id "Hcsi" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/Hcsi.var". -inline procedural "cic:/CoRN/ftc/RefSeparating/Separating_Partition/M.con" "Separating_Partition__". +inline procedural "cic:/CoRN/ftc/RefSeparating/Separating_Partition/M.con" "Separating_Partition__" as definition. -inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_pos_n.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_pos_n.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparating/SPap_n.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/SPap_n.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparating/Separating_Partition/delta.con" "Separating_Partition__". +inline procedural "cic:/CoRN/ftc/RefSeparating/Separating_Partition/delta.con" "Separating_Partition__" as definition. -inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_delta_pos.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_delta_pos.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_delta_csi.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_delta_csi.con" as lemma. alias id "Hab''" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/Hab''.var". -inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_lemma.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_lemma.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_h.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_h.con" as definition. -inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_h_bnd.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_h_bnd.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_h_mon_1.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_h_mon_1.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_h_mon_2.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_h_mon_2.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_h_mon_3.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_h_mon_3.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_app_n.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_app_n.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_h_lemma.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_h_lemma.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_h_lemma2.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_h_lemma2.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_h_lemma3.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_h_lemma3.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_delta2_delta4.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_delta2_delta4.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_m1.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_m1.con" as definition. -inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_m.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_m.con" as definition. (* NOTATION Notation m := RS'_m. *) -inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_length.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_length.con" as definition. -inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_m_m1.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_m_m1.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_pos_m.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_pos_m.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun.con" as definition. -inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun_bnd.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun_bnd.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun_0.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun_0.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun_i.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun_i.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun_m.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun_m.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun_i'.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun_i'.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun_bnd'.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun_bnd'.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun_wd.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun_wd.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun_mon.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun_mon.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part.con" as definition. -inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun_mon_pts.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun_mon_pts.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_mon.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_mon.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_mon_Mesh.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_mon_Mesh.con" as lemma. alias id "g" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/g.var". @@ -138,17 +138,17 @@ alias id "gP" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/gP.var". alias id "gP'" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/gP'.var". -inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_pts.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_pts.con" as definition. -inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_pts_lemma.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_pts_lemma.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_pts_in_Partition.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_pts_in_Partition.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_Hsep_S.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_Hsep_S.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_Hsep.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_Hsep.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_h.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_h.con" as definition. (* NOTATION Notation h := RS'_h. @@ -163,17 +163,17 @@ Notation just2 := (incF _ (Pts_part_lemma _ _ _ _ _ _ sep__part_pts_in_Partition _ _)). *) -inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_suRS'_m1.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_suRS'_m1.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_Sum2.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_Sum2.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_Sum3.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_Sum3.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_Sum4.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_Sum4.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_aux.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_aux.con" as lemma. -inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_Sum.con". +inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_Sum.con" as lemma. (* UNEXPORTED End Separating_Partition diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/Rolle.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/Rolle.mma index c55574312..aad4660f4 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/Rolle.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/Rolle.mma @@ -46,9 +46,9 @@ alias id "b" = "cic:/CoRN/ftc/Rolle/Rolle/b.var". alias id "Hab'" = "cic:/CoRN/ftc/Rolle/Rolle/Hab'.var". -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hab.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hab.con" "Rolle__" as definition. -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/I.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/I.con" "Rolle__" as definition. alias id "F" = "cic:/CoRN/ftc/Rolle/Rolle/F.var". @@ -74,83 +74,83 @@ alias id "e" = "cic:/CoRN/ftc/Rolle/Rolle/e.var". alias id "He" = "cic:/CoRN/ftc/Rolle/Rolle/He.var". -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/contF'.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/contF'.con" "Rolle__" as definition. -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/derivF.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/derivF.con" "Rolle__" as definition. -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma2.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma2.con" "Rolle__" as definition. -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/df.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/df.con" "Rolle__" as definition. -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hdf.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hdf.con" "Rolle__" as definition. -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hf.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hf.con" "Rolle__" as definition. -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma3.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma3.con" "Rolle__" as definition. -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/df'.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/df'.con" "Rolle__" as definition. -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hdf'.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hdf'.con" "Rolle__" as definition. -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hf'.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hf'.con" "Rolle__" as definition. -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/d.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/d.con" "Rolle__" as definition. -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hd.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hd.con" "Rolle__" as definition. -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/incF.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/incF.con" "Rolle__" as definition. -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/n.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/n.con" "Rolle__" as definition. -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/fcp.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/fcp.con" "Rolle__" as definition. -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma1.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma1.con" "Rolle__" as definition. -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/incF'.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/incF'.con" "Rolle__" as definition. -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/fcp'.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/fcp'.con" "Rolle__" as definition. (* NOTATION Notation cp := (compact_part a b Hab' d Hd). *) -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma4.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma4.con" "Rolle__" as definition. -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma5.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma5.con" "Rolle__" as definition. -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma6.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma6.con" "Rolle__" as definition. -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma7.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma7.con" "Rolle__" as definition. -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/j.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/j.con" "Rolle__" as definition. -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hj.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hj.con" "Rolle__" as definition. -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hj'.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hj'.con" "Rolle__" as definition. -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/k.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/k.con" "Rolle__" as definition. -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hk.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hk.con" "Rolle__" as definition. -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hk'.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hk'.con" "Rolle__" as definition. -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma8.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma8.con" "Rolle__" as definition. -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma9.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma9.con" "Rolle__" as definition. -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma10.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma10.con" "Rolle__" as definition. -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma11.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma11.con" "Rolle__" as definition. -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma12.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma12.con" "Rolle__" as definition. -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma13.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma13.con" "Rolle__" as definition. -inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma15.con" "Rolle__". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma15.con" "Rolle__" as definition. (* end hide *) -inline procedural "cic:/CoRN/ftc/Rolle/Rolle.con". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle.con" as theorem. (* UNEXPORTED End Rolle @@ -172,9 +172,9 @@ alias id "Hab'" = "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/Hab'.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/Hab.con" "Law_of_the_Mean__". +inline procedural "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/Hab.con" "Law_of_the_Mean__" as definition. -inline procedural "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/I.con" "Law_of_the_Mean__". +inline procedural "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/I.con" "Law_of_the_Mean__" as definition. (* end hide *) @@ -192,7 +192,7 @@ alias id "HB" = "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/HB.var". (* end show *) -inline procedural "cic:/CoRN/ftc/Rolle/Law_of_the_Mean_I.con". +inline procedural "cic:/CoRN/ftc/Rolle/Law_of_the_Mean_I.con" as lemma. (* UNEXPORTED End Law_of_the_Mean @@ -214,7 +214,7 @@ alias id "Hab'" = "cic:/CoRN/ftc/Rolle/Corollaries/Hab'.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/Rolle/Corollaries/Hab.con" "Corollaries__". +inline procedural "cic:/CoRN/ftc/Rolle/Corollaries/Hab.con" "Corollaries__" as definition. (* end hide *) @@ -226,9 +226,9 @@ alias id "HF" = "cic:/CoRN/ftc/Rolle/Corollaries/HF.var". (* end show *) -inline procedural "cic:/CoRN/ftc/Rolle/Rolle'.con". +inline procedural "cic:/CoRN/ftc/Rolle/Rolle'.con" as theorem. -inline procedural "cic:/CoRN/ftc/Rolle/Law_of_the_Mean'_I.con". +inline procedural "cic:/CoRN/ftc/Rolle/Law_of_the_Mean'_I.con" as lemma. (* UNEXPORTED End Corollaries @@ -264,19 +264,19 @@ alias id "derF" = "cic:/CoRN/ftc/Rolle/Generalizations/derF.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/Rolle/Generalizations/incF.con" "Generalizations__". +inline procedural "cic:/CoRN/ftc/Rolle/Generalizations/incF.con" "Generalizations__" as definition. -inline procedural "cic:/CoRN/ftc/Rolle/Generalizations/incF'.con" "Generalizations__". +inline procedural "cic:/CoRN/ftc/Rolle/Generalizations/incF'.con" "Generalizations__" as definition. (* end hide *) -inline procedural "cic:/CoRN/ftc/Rolle/Law_of_the_Mean.con". +inline procedural "cic:/CoRN/ftc/Rolle/Law_of_the_Mean.con" as theorem. (*#* We further generalize the mean law by writing as an explicit bound. *) -inline procedural "cic:/CoRN/ftc/Rolle/Law_of_the_Mean_ineq.con". +inline procedural "cic:/CoRN/ftc/Rolle/Law_of_the_Mean_ineq.con" as theorem. (* UNEXPORTED End Generalizations diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/StrongIVT.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/StrongIVT.mma index 6c0ad134b..536695ff5 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/StrongIVT.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/StrongIVT.mma @@ -44,9 +44,9 @@ alias id "Hab" = "cic:/CoRN/ftc/StrongIVT/IVT'/Hab.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/I.con" "IVT'__". +inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/I.con" "IVT'__" as definition. -inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/I'.con" "IVT'__". +inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/I'.con" "IVT'__" as definition. (* end hide *) @@ -56,7 +56,7 @@ alias id "contF" = "cic:/CoRN/ftc/StrongIVT/IVT'/contF.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/incF.con" "IVT'__". +inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/incF.con" "IVT'__" as definition. (* end hide *) @@ -68,11 +68,11 @@ alias id "incrF" = "cic:/CoRN/ftc/StrongIVT/IVT'/incrF.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/Ha.con" "IVT'__". +inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/Ha.con" "IVT'__" as definition. -inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/Hb.con" "IVT'__". +inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/Hb.con" "IVT'__" as definition. -inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/HFab'.con" "IVT'__". +inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/HFab'.con" "IVT'__" as definition. (* end hide *) @@ -86,51 +86,51 @@ alias id "Hzb" = "cic:/CoRN/ftc/StrongIVT/IVT'/Hzb.var". (* end show *) -inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_seq_lemma.con". +inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_seq_lemma.con" as lemma. (* end hide *) inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_aux_seq_type.ind". -inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_iter.con". +inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_iter.con" as definition. -inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_seq.con". +inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_seq.con" as definition. -inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq.con". +inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq.con" as definition. -inline procedural "cic:/CoRN/ftc/StrongIVT/b'_seq.con". +inline procedural "cic:/CoRN/ftc/StrongIVT/b'_seq.con" as definition. -inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_I.con". +inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_I.con" as definition. -inline procedural "cic:/CoRN/ftc/StrongIVT/b'_seq_I.con". +inline procedural "cic:/CoRN/ftc/StrongIVT/b'_seq_I.con" as definition. -inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_less_b'_seq.con". +inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_less_b'_seq.con" as lemma. -inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_less_z.con". +inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_less_z.con" as lemma. -inline procedural "cic:/CoRN/ftc/StrongIVT/z_less_b'_seq.con". +inline procedural "cic:/CoRN/ftc/StrongIVT/z_less_b'_seq.con" as lemma. -inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_mon.con". +inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_mon.con" as lemma. -inline procedural "cic:/CoRN/ftc/StrongIVT/b'_seq_mon.con". +inline procedural "cic:/CoRN/ftc/StrongIVT/b'_seq_mon.con" as lemma. -inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_b'_seq_dist_n.con". +inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_b'_seq_dist_n.con" as lemma. -inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_b'_seq_dist.con". +inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_b'_seq_dist.con" as lemma. -inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_Cauchy.con". +inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_Cauchy.con" as lemma. -inline procedural "cic:/CoRN/ftc/StrongIVT/b'_seq_Cauchy.con". +inline procedural "cic:/CoRN/ftc/StrongIVT/b'_seq_Cauchy.con" as lemma. -inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/xa.con" "IVT'__". +inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/xa.con" "IVT'__" as definition. -inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/xb.con" "IVT'__". +inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/xb.con" "IVT'__" as definition. -inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_b'_seq_lim.con". +inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_b'_seq_lim.con" as lemma. -inline procedural "cic:/CoRN/ftc/StrongIVT/xa'_in_interval.con". +inline procedural "cic:/CoRN/ftc/StrongIVT/xa'_in_interval.con" as lemma. -inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_I.con". +inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_I.con" as lemma. (* UNEXPORTED End IVT' @@ -142,21 +142,21 @@ We now generalize the various statements of the intermediate value theorem to more widely applicable forms. *) -inline procedural "cic:/CoRN/ftc/StrongIVT/Weak_IVT.con". +inline procedural "cic:/CoRN/ftc/StrongIVT/Weak_IVT.con" as lemma. -inline procedural "cic:/CoRN/ftc/StrongIVT/IVT_inc.con". +inline procedural "cic:/CoRN/ftc/StrongIVT/IVT_inc.con" as lemma. (* UNEXPORTED Transparent Min. *) -inline procedural "cic:/CoRN/ftc/StrongIVT/IVT_dec.con". +inline procedural "cic:/CoRN/ftc/StrongIVT/IVT_dec.con" as lemma. -inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_inc.con". +inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_inc.con" as lemma. (* UNEXPORTED Transparent Min. *) -inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_dec.con". +inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_dec.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/Taylor.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/Taylor.mma index 75f07a002..56b2057f1 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/Taylor.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/Taylor.mma @@ -45,7 +45,7 @@ alias id "F" = "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/F.var". (* begin show *) -inline procedural "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/deriv_Sn.con" "More_Taylor_Defs__". +inline procedural "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/deriv_Sn.con" "More_Taylor_Defs__" as definition. (* end show *) @@ -59,31 +59,31 @@ alias id "Hb" = "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/Hb.var". (* begin show *) -inline procedural "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/fi.con" "More_Taylor_Defs__". +inline procedural "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/fi.con" "More_Taylor_Defs__" as definition. -inline procedural "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/funct_i.con" "More_Taylor_Defs__". +inline procedural "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/funct_i.con" "More_Taylor_Defs__" as definition. (* end show *) -inline procedural "cic:/CoRN/ftc/Taylor/Taylor_Seq'.con". +inline procedural "cic:/CoRN/ftc/Taylor/Taylor_Seq'.con" as definition. (* begin hide *) -inline procedural "cic:/CoRN/ftc/Taylor/TaylorB.con". +inline procedural "cic:/CoRN/ftc/Taylor/TaylorB.con" as lemma. (* end hide *) -inline procedural "cic:/CoRN/ftc/Taylor/Taylor_Rem.con". +inline procedural "cic:/CoRN/ftc/Taylor/Taylor_Rem.con" as definition. (* begin hide *) -inline procedural "cic:/CoRN/ftc/Taylor/Taylor_Sumx_lemma.con". +inline procedural "cic:/CoRN/ftc/Taylor/Taylor_Sumx_lemma.con" as lemma. -inline procedural "cic:/CoRN/ftc/Taylor/Taylor_lemma_ap.con". +inline procedural "cic:/CoRN/ftc/Taylor/Taylor_lemma_ap.con" as lemma. (* end hide *) -inline procedural "cic:/CoRN/ftc/Taylor/Taylor'.con". +inline procedural "cic:/CoRN/ftc/Taylor/Taylor'.con" as theorem. (* UNEXPORTED End More_Taylor_Defs @@ -132,21 +132,21 @@ alias id "Hb" = "cic:/CoRN/ftc/Taylor/Taylor_Theorem/Hb.var". (* begin show *) -inline procedural "cic:/CoRN/ftc/Taylor/Taylor_Theorem/funct_i.con" "Taylor_Theorem__". +inline procedural "cic:/CoRN/ftc/Taylor/Taylor_Theorem/funct_i.con" "Taylor_Theorem__" as definition. -inline procedural "cic:/CoRN/ftc/Taylor/Taylor_Seq.con". +inline procedural "cic:/CoRN/ftc/Taylor/Taylor_Seq.con" as definition. -inline procedural "cic:/CoRN/ftc/Taylor/Taylor_Theorem/deriv_Sn.con" "Taylor_Theorem__". +inline procedural "cic:/CoRN/ftc/Taylor/Taylor_Theorem/deriv_Sn.con" "Taylor_Theorem__" as definition. (* end show *) -inline procedural "cic:/CoRN/ftc/Taylor/Taylor_aux.con". +inline procedural "cic:/CoRN/ftc/Taylor/Taylor_aux.con" as lemma. (* UNEXPORTED Transparent N_Deriv. *) -inline procedural "cic:/CoRN/ftc/Taylor/Taylor.con". +inline procedural "cic:/CoRN/ftc/Taylor/Taylor.con" as theorem. (* UNEXPORTED End Taylor_Theorem diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/TaylorLemma.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/TaylorLemma.mma index 8b016e4f2..427b0adfb 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/TaylorLemma.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/TaylorLemma.mma @@ -50,11 +50,11 @@ alias id "Hap" = "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Hap.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Hab'.con" "Taylor_Defs__". +inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Hab'.con" "Taylor_Defs__" as definition. -inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Hab.con" "Taylor_Defs__". +inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Hab.con" "Taylor_Defs__" as definition. -inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/I.con" "Taylor_Defs__". +inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/I.con" "Taylor_Defs__" as definition. (* end hide *) @@ -66,7 +66,7 @@ alias id "Hb" = "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Hb.var". (* begin show *) -inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/fi.con" "Taylor_Defs__". +inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/fi.con" "Taylor_Defs__" as definition. (* end show *) @@ -77,7 +77,7 @@ $f_i=f^{(i)}$#fi=f(i)#. (* begin hide *) -inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma1.con". +inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma1.con" as lemma. (* end hide *) @@ -92,9 +92,9 @@ corresponding to [a] and [b]. (* begin hide *) -inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/TL_compact_a.con" "Taylor_Defs__". +inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/TL_compact_a.con" "Taylor_Defs__" as definition. -inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/TL_compact_b.con" "Taylor_Defs__". +inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/TL_compact_b.con" "Taylor_Defs__" as definition. (* NOTATION Notation A := (Build_subcsetoid_crr IR _ _ TL_compact_a). @@ -108,33 +108,33 @@ Notation B := (Build_subcsetoid_crr IR _ _ TL_compact_b). (* begin show *) -inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/funct_i.con" "Taylor_Defs__". +inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/funct_i.con" "Taylor_Defs__" as definition. (* end show *) (* begin hide *) -inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/funct_i'.con" "Taylor_Defs__". +inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/funct_i'.con" "Taylor_Defs__" as definition. -inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_a_i.con". +inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_a_i.con" as lemma. -inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_b_i.con". +inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_b_i.con" as lemma. -inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_x_i.con". +inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_x_i.con" as lemma. -inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_a_i'.con". +inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_a_i'.con" as lemma. -inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_b_i'.con". +inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_b_i'.con" as lemma. -inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_x_i'.con". +inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_x_i'.con" as lemma. -inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma2.con". +inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma2.con" as lemma. -inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma2'.con". +inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma2'.con" as lemma. -inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma3.con". +inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma3.con" as lemma. -inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma3'.con". +inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma3'.con" as lemma. (* end hide *) @@ -143,13 +143,13 @@ Adding the previous expressions up to a given bound [n] gives us the Taylor sum of order [n]. *) -inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_seq'.con". +inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_seq'.con" as definition. (* begin hide *) -inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Taylor_seq'_aux.con" "Taylor_Defs__". +inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Taylor_seq'_aux.con" "Taylor_Defs__" as definition. -inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_lemma_a.con". +inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_lemma_a.con" as lemma. (* end hide *) @@ -157,21 +157,21 @@ inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_lemma_a.con". It is easy to show that [b] is in the domain of this series, which allows us to write down the Taylor remainder around [b]. *) -inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_lemma_b.con". +inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_lemma_b.con" as lemma. (* begin hide *) -inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_lemma_a'.con". +inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_lemma_a'.con" as lemma. -inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_lemma_b'.con". +inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_lemma_b'.con" as lemma. (* end hide *) -inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_rem.con". +inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_rem.con" as definition. (* begin hide *) -inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/g.con" "Taylor_Defs__". +inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/g.con" "Taylor_Defs__" as definition. (* UNEXPORTED Opaque Taylor_seq'_aux Taylor_rem. @@ -197,7 +197,7 @@ Opaque funct_i'. Opaque funct_i. *) -inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma4.con". +inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma4.con" as lemma. (* UNEXPORTED Transparent funct_i funct_i'. @@ -219,15 +219,15 @@ Opaque FSumx. Opaque funct_i'. *) -inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma5.con". +inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma5.con" as lemma. (* UNEXPORTED Transparent funct_i' FSumx. *) -inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/funct_aux.con" "Taylor_Defs__". +inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/funct_aux.con" "Taylor_Defs__" as definition. -inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma6.con". +inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma6.con" as lemma. (* UNEXPORTED Ltac Lazy_Included := @@ -251,9 +251,9 @@ Ltac Lazy_Eq := | apply csf_wd_unfolded ]; Algebra. *) -inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma7.con". +inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma7.con" as lemma. -inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma8.con". +inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma8.con" as lemma. (* UNEXPORTED Opaque funct_aux. @@ -263,15 +263,15 @@ Opaque funct_aux. Transparent funct_aux. *) -inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma9.con". +inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma9.con" as lemma. -inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/g'.con" "Taylor_Defs__". +inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/g'.con" "Taylor_Defs__" as definition. (* UNEXPORTED Opaque Taylor_rem funct_aux. *) -inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma10.con". +inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma10.con" as lemma. (* UNEXPORTED Transparent Taylor_rem funct_aux. @@ -292,19 +292,19 @@ alias id "He" = "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/He.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma11.con". +inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma11.con" as lemma. (* end hide *) (* begin show *) -inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/deriv_Sn'.con" "Taylor_Defs__". +inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/deriv_Sn'.con" "Taylor_Defs__" as definition. (* end show *) (* begin hide *) -inline procedural "cic:/CoRN/ftc/TaylorLemma/TLH.con". +inline procedural "cic:/CoRN/ftc/TaylorLemma/TLH.con" as lemma. (* end hide *) @@ -320,7 +320,7 @@ Opaque Taylor_rem. Transparent Taylor_rem funct_aux. *) -inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma.con". +inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma.con" as lemma. (* UNEXPORTED End Taylor_Defs diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/WeakIVT.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/WeakIVT.mma index 750fce585..b4302f58b 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/WeakIVT.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/WeakIVT.mma @@ -53,7 +53,7 @@ alias id "Hab" = "cic:/CoRN/ftc/WeakIVT/Lemma1/Hab.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/WeakIVT/Lemma1/I.con" "Lemma1__". +inline procedural "cic:/CoRN/ftc/WeakIVT/Lemma1/I.con" "Lemma1__" as definition. (* end hide *) @@ -72,7 +72,7 @@ We begin by proving that, if [f(a) [<] f(b)], then for every [y] in enough to [z]. *) -inline procedural "cic:/CoRN/ftc/WeakIVT/Weak_IVT_ap_lft.con". +inline procedural "cic:/CoRN/ftc/WeakIVT/Weak_IVT_ap_lft.con" as lemma. (* UNEXPORTED End Lemma1 @@ -90,7 +90,7 @@ alias id "Hab" = "cic:/CoRN/ftc/WeakIVT/Lemma2/Hab.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/WeakIVT/Lemma2/I.con" "Lemma2__". +inline procedural "cic:/CoRN/ftc/WeakIVT/Lemma2/I.con" "Lemma2__" as definition. (* end hide *) @@ -102,7 +102,7 @@ alias id "contF" = "cic:/CoRN/ftc/WeakIVT/Lemma2/contF.var". If [f(b) [<] f(a)], a similar result holds: *) -inline procedural "cic:/CoRN/ftc/WeakIVT/Weak_IVT_ap_rht.con". +inline procedural "cic:/CoRN/ftc/WeakIVT/Weak_IVT_ap_rht.con" as lemma. (* UNEXPORTED End Lemma2 @@ -130,7 +130,7 @@ alias id "Hab" = "cic:/CoRN/ftc/WeakIVT/IVT/Hab.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/WeakIVT/IVT/I.con" "IVT__". +inline procedural "cic:/CoRN/ftc/WeakIVT/IVT/I.con" "IVT__" as definition. (* end hide *) @@ -140,7 +140,7 @@ alias id "contF" = "cic:/CoRN/ftc/WeakIVT/IVT/contF.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/WeakIVT/IVT/incF.con" "IVT__". +inline procedural "cic:/CoRN/ftc/WeakIVT/IVT/incF.con" "IVT__" as definition. (* end hide *) @@ -152,11 +152,11 @@ alias id "incrF" = "cic:/CoRN/ftc/WeakIVT/IVT/incrF.var". (* begin hide *) -inline procedural "cic:/CoRN/ftc/WeakIVT/IVT/Ha.con" "IVT__". +inline procedural "cic:/CoRN/ftc/WeakIVT/IVT/Ha.con" "IVT__" as definition. -inline procedural "cic:/CoRN/ftc/WeakIVT/IVT/Hb.con" "IVT__". +inline procedural "cic:/CoRN/ftc/WeakIVT/IVT/Hb.con" "IVT__" as definition. -inline procedural "cic:/CoRN/ftc/WeakIVT/IVT/HFab'.con" "IVT__". +inline procedural "cic:/CoRN/ftc/WeakIVT/IVT/HFab'.con" "IVT__" as definition. (* end hide *) @@ -175,7 +175,7 @@ we can find [x' [<] y'] such that $|x'-y'|=\frac23|x-y|$#|x'-y'|=2/3|x-y|# and [x' [<=] z [<=] y']. *) -inline procedural "cic:/CoRN/ftc/WeakIVT/IVT_seq_lemma.con". +inline procedural "cic:/CoRN/ftc/WeakIVT/IVT_seq_lemma.con" as lemma. (* end hide *) @@ -185,49 +185,49 @@ We now iterate this construction. inline procedural "cic:/CoRN/ftc/WeakIVT/IVT_aux_seq_type.ind". -inline procedural "cic:/CoRN/ftc/WeakIVT/IVT_iter.con". +inline procedural "cic:/CoRN/ftc/WeakIVT/IVT_iter.con" as definition. -inline procedural "cic:/CoRN/ftc/WeakIVT/IVT_seq.con". +inline procedural "cic:/CoRN/ftc/WeakIVT/IVT_seq.con" as definition. (*#* We now define the sequences built from this iteration, starting with [a] and [b]. *) -inline procedural "cic:/CoRN/ftc/WeakIVT/a_seq.con". +inline procedural "cic:/CoRN/ftc/WeakIVT/a_seq.con" as definition. -inline procedural "cic:/CoRN/ftc/WeakIVT/b_seq.con". +inline procedural "cic:/CoRN/ftc/WeakIVT/b_seq.con" as definition. -inline procedural "cic:/CoRN/ftc/WeakIVT/a_seq_I.con". +inline procedural "cic:/CoRN/ftc/WeakIVT/a_seq_I.con" as definition. -inline procedural "cic:/CoRN/ftc/WeakIVT/b_seq_I.con". +inline procedural "cic:/CoRN/ftc/WeakIVT/b_seq_I.con" as definition. -inline procedural "cic:/CoRN/ftc/WeakIVT/a_seq_less_b_seq.con". +inline procedural "cic:/CoRN/ftc/WeakIVT/a_seq_less_b_seq.con" as lemma. -inline procedural "cic:/CoRN/ftc/WeakIVT/a_seq_leEq_z.con". +inline procedural "cic:/CoRN/ftc/WeakIVT/a_seq_leEq_z.con" as lemma. -inline procedural "cic:/CoRN/ftc/WeakIVT/z_leEq_b_seq.con". +inline procedural "cic:/CoRN/ftc/WeakIVT/z_leEq_b_seq.con" as lemma. -inline procedural "cic:/CoRN/ftc/WeakIVT/a_seq_mon.con". +inline procedural "cic:/CoRN/ftc/WeakIVT/a_seq_mon.con" as lemma. -inline procedural "cic:/CoRN/ftc/WeakIVT/b_seq_mon.con". +inline procedural "cic:/CoRN/ftc/WeakIVT/b_seq_mon.con" as lemma. -inline procedural "cic:/CoRN/ftc/WeakIVT/a_seq_b_seq_dist_n.con". +inline procedural "cic:/CoRN/ftc/WeakIVT/a_seq_b_seq_dist_n.con" as lemma. -inline procedural "cic:/CoRN/ftc/WeakIVT/a_seq_b_seq_dist.con". +inline procedural "cic:/CoRN/ftc/WeakIVT/a_seq_b_seq_dist.con" as lemma. -inline procedural "cic:/CoRN/ftc/WeakIVT/a_seq_Cauchy.con". +inline procedural "cic:/CoRN/ftc/WeakIVT/a_seq_Cauchy.con" as lemma. -inline procedural "cic:/CoRN/ftc/WeakIVT/b_seq_Cauchy.con". +inline procedural "cic:/CoRN/ftc/WeakIVT/b_seq_Cauchy.con" as lemma. -inline procedural "cic:/CoRN/ftc/WeakIVT/IVT/xa.con" "IVT__". +inline procedural "cic:/CoRN/ftc/WeakIVT/IVT/xa.con" "IVT__" as definition. -inline procedural "cic:/CoRN/ftc/WeakIVT/IVT/xb.con" "IVT__". +inline procedural "cic:/CoRN/ftc/WeakIVT/IVT/xb.con" "IVT__" as definition. -inline procedural "cic:/CoRN/ftc/WeakIVT/a_seq_b_seq_lim.con". +inline procedural "cic:/CoRN/ftc/WeakIVT/a_seq_b_seq_lim.con" as lemma. -inline procedural "cic:/CoRN/ftc/WeakIVT/xa_in_interval.con". +inline procedural "cic:/CoRN/ftc/WeakIVT/xa_in_interval.con" as lemma. -inline procedural "cic:/CoRN/ftc/WeakIVT/IVT_I.con". +inline procedural "cic:/CoRN/ftc/WeakIVT/IVT_I.con" as lemma. (* UNEXPORTED End IVT diff --git a/helm/software/matita/contribs/CoRN-Procedural/metrics/CMetricSpaces.mma b/helm/software/matita/contribs/CoRN-Procedural/metrics/CMetricSpaces.mma index 670bf8655..b0d848ec0 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/metrics/CMetricSpaces.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/metrics/CMetricSpaces.mma @@ -46,11 +46,11 @@ Section MS_basics (*#* **Metric Space basics *) -inline procedural "cic:/CoRN/metrics/CMetricSpaces/d_CMetricSpace_apdiag_imp_grzero.con". +inline procedural "cic:/CoRN/metrics/CMetricSpaces/d_CMetricSpace_apdiag_imp_grzero.con" as lemma. -inline procedural "cic:/CoRN/metrics/CMetricSpaces/d_zero_imp_eq.con". +inline procedural "cic:/CoRN/metrics/CMetricSpaces/d_zero_imp_eq.con" as lemma. -inline procedural "cic:/CoRN/metrics/CMetricSpaces/is_CMetricSpace_diag_zero.con". +inline procedural "cic:/CoRN/metrics/CMetricSpaces/is_CMetricSpace_diag_zero.con" as lemma. (* UNEXPORTED End MS_basics @@ -67,9 +67,9 @@ Section prodandsub The product of two metric spaces is again a metric space. *) -inline procedural "cic:/CoRN/metrics/CMetricSpaces/Prod0CMetricSpaces_apdiag_grzero.con". +inline procedural "cic:/CoRN/metrics/CMetricSpaces/Prod0CMetricSpaces_apdiag_grzero.con" as lemma. -inline procedural "cic:/CoRN/metrics/CMetricSpaces/Prod0CMetricSpace.con". +inline procedural "cic:/CoRN/metrics/CMetricSpaces/Prod0CMetricSpace.con" as definition. (*#* A subspace of a metric space is again a metric space. @@ -79,9 +79,9 @@ A subspace of a metric space is again a metric space. Implicit Arguments SubPsMetricSpace [X]. *) -inline procedural "cic:/CoRN/metrics/CMetricSpaces/SubMetricSpace_apdiag_grzero.con". +inline procedural "cic:/CoRN/metrics/CMetricSpaces/SubMetricSpace_apdiag_grzero.con" as lemma. -inline procedural "cic:/CoRN/metrics/CMetricSpaces/SubMetricSpace.con". +inline procedural "cic:/CoRN/metrics/CMetricSpaces/SubMetricSpace.con" as definition. (* UNEXPORTED Implicit Arguments SubMetricSpace [X]. @@ -102,69 +102,69 @@ Section Zeroff Not all pseudo metric spaces are a metric space: *) -inline procedural "cic:/CoRN/metrics/CMetricSpaces/zf_nis_CMetricSpace.con". +inline procedural "cic:/CoRN/metrics/CMetricSpaces/zf_nis_CMetricSpace.con" as lemma. (*#* But a pseudo metric space induces a metric space: *) -inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_ap.con". +inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_ap.con" as definition. -inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_eq.con". +inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_eq.con" as definition. -inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_ap_irreflexive.con". +inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_ap_irreflexive.con" as lemma. -inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_ap_symmetric.con". +inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_ap_symmetric.con" as lemma. -inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_ap_cotransitive.con". +inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_ap_cotransitive.con" as lemma. -inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_ap_tight.con". +inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_ap_tight.con" as lemma. -inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_CSet_is_CSetoid.con". +inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_CSet_is_CSetoid.con" as definition. -inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_CSetoid.con". +inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_CSetoid.con" as definition. -inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_d.con". +inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_d.con" as definition. -inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_d_strext.con". +inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_d_strext.con" as lemma. -inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_d.con". +inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_d.con" as definition. -inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_d_com.con". +inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_d_com.con" as lemma. -inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_d_nneg.con". +inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_d_nneg.con" as lemma. -inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_d_pos_imp_ap.con". +inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_d_pos_imp_ap.con" as lemma. -inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_d_tri_ineq.con". +inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_d_tri_ineq.con" as lemma. -inline procedural "cic:/CoRN/metrics/CMetricSpaces/QuotientCSetoid_is_CPsMetricSpace.con". +inline procedural "cic:/CoRN/metrics/CMetricSpaces/QuotientCSetoid_is_CPsMetricSpace.con" as definition. -inline procedural "cic:/CoRN/metrics/CMetricSpaces/QuotientCPsMetricSpace.con". +inline procedural "cic:/CoRN/metrics/CMetricSpaces/QuotientCPsMetricSpace.con" as definition. -inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_d_apdiag_grzero.con". +inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_d_apdiag_grzero.con" as lemma. -inline procedural "cic:/CoRN/metrics/CMetricSpaces/QuotientCMetricSpace.con". +inline procedural "cic:/CoRN/metrics/CMetricSpaces/QuotientCMetricSpace.con" as definition. (*#* Some pseudo metric spaces already are a metric space: *) -inline procedural "cic:/CoRN/metrics/CMetricSpaces/dIR_apdiag_grzero.con". +inline procedural "cic:/CoRN/metrics/CMetricSpaces/dIR_apdiag_grzero.con" as lemma. -inline procedural "cic:/CoRN/metrics/CMetricSpaces/IR_as_CMetricSpace.con". +inline procedural "cic:/CoRN/metrics/CMetricSpaces/IR_as_CMetricSpace.con" as definition. (*#* In that case the induced metric space is equivalent to the original one: *) -inline procedural "cic:/CoRN/metrics/CMetricSpaces/emb.con". +inline procedural "cic:/CoRN/metrics/CMetricSpaces/emb.con" as definition. -inline procedural "cic:/CoRN/metrics/CMetricSpaces/emb_strext.con". +inline procedural "cic:/CoRN/metrics/CMetricSpaces/emb_strext.con" as lemma. -inline procedural "cic:/CoRN/metrics/CMetricSpaces/Emb.con". +inline procedural "cic:/CoRN/metrics/CMetricSpaces/Emb.con" as definition. -inline procedural "cic:/CoRN/metrics/CMetricSpaces/Quotient_pres_CMetricSpace.con". +inline procedural "cic:/CoRN/metrics/CMetricSpaces/Quotient_pres_CMetricSpace.con" as lemma. (* UNEXPORTED End Zeroff @@ -187,17 +187,17 @@ Implicit Arguments MSseqLimit [X]. (* begin hide *) -inline procedural "cic:/CoRN/metrics/CMetricSpaces/nz.con". +inline procedural "cic:/CoRN/metrics/CMetricSpaces/nz.con" as lemma. (* end hide *) (* begin hide *) -inline procedural "cic:/CoRN/metrics/CMetricSpaces/d_wd.con". +inline procedural "cic:/CoRN/metrics/CMetricSpaces/d_wd.con" as lemma. (* end hide *) -inline procedural "cic:/CoRN/metrics/CMetricSpaces/unique_MSseqLim.con". +inline procedural "cic:/CoRN/metrics/CMetricSpaces/unique_MSseqLim.con" as lemma. (* UNEXPORTED End Limitt diff --git a/helm/software/matita/contribs/CoRN-Procedural/metrics/CPMSTheory.mma b/helm/software/matita/contribs/CoRN-Procedural/metrics/CPMSTheory.mma index 24b6b8bb0..04afb43c8 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/metrics/CPMSTheory.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/metrics/CPMSTheory.mma @@ -35,19 +35,19 @@ finite sets of representants, instead of finite subsetoids. This seems to make the proofs a bit easier. *) -inline procedural "cic:/CoRN/metrics/CPMSTheory/MSmember.con". +inline procedural "cic:/CoRN/metrics/CPMSTheory/MSmember.con" as definition. (* UNEXPORTED Implicit Arguments MSmember [X]. *) -inline procedural "cic:/CoRN/metrics/CPMSTheory/to_IR.con". +inline procedural "cic:/CoRN/metrics/CPMSTheory/to_IR.con" as definition. -inline procedural "cic:/CoRN/metrics/CPMSTheory/from_IR.con". +inline procedural "cic:/CoRN/metrics/CPMSTheory/from_IR.con" as definition. -inline procedural "cic:/CoRN/metrics/CPMSTheory/list_IR.con". +inline procedural "cic:/CoRN/metrics/CPMSTheory/list_IR.con" as definition. -inline procedural "cic:/CoRN/metrics/CPMSTheory/is_P.con". +inline procedural "cic:/CoRN/metrics/CPMSTheory/is_P.con" as lemma. (*#* If a real number is element of a list in the above defined sense, @@ -55,14 +55,14 @@ it is an element of the list in the sense of [member], that uses the setoid equality. *) -inline procedural "cic:/CoRN/metrics/CPMSTheory/member1.con". +inline procedural "cic:/CoRN/metrics/CPMSTheory/member1.con" as lemma. (*#* The image under a certain mapping of an element of a list $l$ #l# is member of the list of images of elements of $l$ #l#. *) -inline procedural "cic:/CoRN/metrics/CPMSTheory/map_member.con". +inline procedural "cic:/CoRN/metrics/CPMSTheory/map_member.con" as lemma. (* UNEXPORTED End lists @@ -75,13 +75,13 @@ Section loc_and_bound (*#* **Pseudo Metric Space theory *) -inline procedural "cic:/CoRN/metrics/CPMSTheory/Re_co_do.con". +inline procedural "cic:/CoRN/metrics/CPMSTheory/Re_co_do.con" as definition. -inline procedural "cic:/CoRN/metrics/CPMSTheory/Re_co_do_strext.con". +inline procedural "cic:/CoRN/metrics/CPMSTheory/Re_co_do_strext.con" as lemma. -inline procedural "cic:/CoRN/metrics/CPMSTheory/re_co_do.con". +inline procedural "cic:/CoRN/metrics/CPMSTheory/re_co_do.con" as definition. -inline procedural "cic:/CoRN/metrics/CPMSTheory/re_co_do_well_def.con". +inline procedural "cic:/CoRN/metrics/CPMSTheory/re_co_do_well_def.con" as lemma. (* UNEXPORTED Implicit Arguments MSmember [X]. @@ -92,11 +92,11 @@ Again we see that the image under a certain mapping of an element of a list $l$ #l# is member of the list of images of elements of $l$ #l#. *) -inline procedural "cic:/CoRN/metrics/CPMSTheory/map_member'.con". +inline procedural "cic:/CoRN/metrics/CPMSTheory/map_member'.con" as lemma. -inline procedural "cic:/CoRN/metrics/CPMSTheory/bounded.con". +inline procedural "cic:/CoRN/metrics/CPMSTheory/bounded.con" as definition. -inline procedural "cic:/CoRN/metrics/CPMSTheory/MStotally_bounded.con". +inline procedural "cic:/CoRN/metrics/CPMSTheory/MStotally_bounded.con" as definition. (*#* Total boundedness is preserved under uniformly continuous mappings. @@ -106,18 +106,18 @@ Total boundedness is preserved under uniformly continuous mappings. Implicit Arguments SubPsMetricSpace [X]. *) -inline procedural "cic:/CoRN/metrics/CPMSTheory/unicon_resp_totallybounded.con". +inline procedural "cic:/CoRN/metrics/CPMSTheory/unicon_resp_totallybounded.con" as lemma. -inline procedural "cic:/CoRN/metrics/CPMSTheory/MStotallybounded_totallybounded.con". +inline procedural "cic:/CoRN/metrics/CPMSTheory/MStotallybounded_totallybounded.con" as lemma. (*#* Every image under an uniformly continuous function of an totally bounded pseudo metric space has an infimum and a supremum. *) -inline procedural "cic:/CoRN/metrics/CPMSTheory/infimum_exists.con". +inline procedural "cic:/CoRN/metrics/CPMSTheory/infimum_exists.con" as lemma. -inline procedural "cic:/CoRN/metrics/CPMSTheory/supremum_exists.con". +inline procedural "cic:/CoRN/metrics/CPMSTheory/supremum_exists.con" as lemma. (*#* A subspace $P$#P# of a pseudo metric space $X$#X# is said to be located if for all @@ -129,25 +129,25 @@ between $x$#x# and the elements of $P$#P#. Implicit Arguments dsub'_as_cs_fun [X]. *) -inline procedural "cic:/CoRN/metrics/CPMSTheory/located.con". +inline procedural "cic:/CoRN/metrics/CPMSTheory/located.con" as definition. (* UNEXPORTED Implicit Arguments located [X]. *) -inline procedural "cic:/CoRN/metrics/CPMSTheory/located'.con". +inline procedural "cic:/CoRN/metrics/CPMSTheory/located'.con" as definition. (* UNEXPORTED Implicit Arguments located' [X]. *) -inline procedural "cic:/CoRN/metrics/CPMSTheory/located_imp_located'.con". +inline procedural "cic:/CoRN/metrics/CPMSTheory/located_imp_located'.con" as lemma. (*#* Every totally bounded pseudo metric space is located. *) -inline procedural "cic:/CoRN/metrics/CPMSTheory/MStotally_bounded_imp_located.con". +inline procedural "cic:/CoRN/metrics/CPMSTheory/MStotally_bounded_imp_located.con" as lemma. (*#* For all $x$#x# in a pseudo metric space $X$#X#, for all located subspaces $P$#P# of $X$#X#, @@ -158,9 +158,9 @@ $d(x,y)\leq \mbox{inf}\{d(x,p)|p \in P\}+(n+1)^{-1}$ one to use the latter as an argument of [map]. *) -inline procedural "cic:/CoRN/metrics/CPMSTheory/Floc.con". +inline procedural "cic:/CoRN/metrics/CPMSTheory/Floc.con" as definition. -inline procedural "cic:/CoRN/metrics/CPMSTheory/Flocfun.con". +inline procedural "cic:/CoRN/metrics/CPMSTheory/Flocfun.con" as definition. (*#* A located subset $P$#P# of a totally bounded pseudo metric space $X$ @@ -168,33 +168,33 @@ A located subset $P$#P# of a totally bounded pseudo metric space $X$ bounded. *) -inline procedural "cic:/CoRN/metrics/CPMSTheory/locatedsub_totallybounded_imp_totallyboundedsub.con". +inline procedural "cic:/CoRN/metrics/CPMSTheory/locatedsub_totallybounded_imp_totallyboundedsub.con" as lemma. (*#* Here are some definitions that could come in handy: *) -inline procedural "cic:/CoRN/metrics/CPMSTheory/MSCauchy_seq.con". +inline procedural "cic:/CoRN/metrics/CPMSTheory/MSCauchy_seq.con" as definition. (* UNEXPORTED Implicit Arguments MSseqLimit' [X]. *) -inline procedural "cic:/CoRN/metrics/CPMSTheory/MSComplete.con". +inline procedural "cic:/CoRN/metrics/CPMSTheory/MSComplete.con" as definition. (*#* A compact pseudo metric space is a pseudo metric space which is complete and totally bounded. *) -inline procedural "cic:/CoRN/metrics/CPMSTheory/MSCompact.con". +inline procedural "cic:/CoRN/metrics/CPMSTheory/MSCompact.con" as definition. (*#* A subset $P$#P# is %\emph{open}%#open# if for all $x$#x# in $P$#P# there exists an open sphere with centre $x$#x# that is contained in $P$#P#. *) -inline procedural "cic:/CoRN/metrics/CPMSTheory/open.con". +inline procedural "cic:/CoRN/metrics/CPMSTheory/open.con" as definition. (* UNEXPORTED Implicit Arguments open [X]. @@ -206,7 +206,7 @@ element $x$#x# of a located pseudo metric space $X$#X# and the ele subspace $P$#P# of $X$#X#. *) -inline procedural "cic:/CoRN/metrics/CPMSTheory/infima.con". +inline procedural "cic:/CoRN/metrics/CPMSTheory/infima.con" as definition. (* UNEXPORTED Implicit Arguments infima [X]. @@ -218,7 +218,7 @@ A non-empty totally bounded sub-pseudo-metric-space $P$#P# is said to be all points that are in some sense close to $P$#P#. *) -inline procedural "cic:/CoRN/metrics/CPMSTheory/well_contained.con". +inline procedural "cic:/CoRN/metrics/CPMSTheory/well_contained.con" as definition. (* UNEXPORTED End loc_and_bound diff --git a/helm/software/matita/contribs/CoRN-Procedural/metrics/CPseudoMSpaces.mma b/helm/software/matita/contribs/CoRN-Procedural/metrics/CPseudoMSpaces.mma index 916a3a11e..9774f2a62 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/metrics/CPseudoMSpaces.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/metrics/CPseudoMSpaces.mma @@ -45,13 +45,13 @@ Set Implicit Arguments. Unset Strict Implicit. *) -inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/com.con". +inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/com.con" as definition. -inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/nneg.con". +inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/nneg.con" as definition. -inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/pos_imp_ap.con". +inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/pos_imp_ap.con" as definition. -inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/tri_ineq.con". +inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/tri_ineq.con" as definition. (* UNEXPORTED Set Strict Implicit. @@ -61,9 +61,9 @@ Set Strict Implicit. Unset Implicit Arguments. *) -inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/diag_zero.con". +inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/diag_zero.con" as definition. -inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/apdiag_imp_grzero.con". +inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/apdiag_imp_grzero.con" as definition. (* UNEXPORTED End Relations @@ -113,15 +113,15 @@ Let [A] be a pseudo metric space. alias id "A" = "cic:/CoRN/metrics/CPseudoMSpaces/PsMS_axioms/A.var". -inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/CPsMetricSpace_is_CPsMetricSpace.con". +inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/CPsMetricSpace_is_CPsMetricSpace.con" as lemma. -inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/d_com.con". +inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/d_com.con" as lemma. -inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/d_nneg.con". +inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/d_nneg.con" as lemma. -inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/d_pos_imp_ap.con". +inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/d_pos_imp_ap.con" as lemma. -inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/d_tri_ineq.con". +inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/d_tri_ineq.con" as lemma. (* UNEXPORTED End PsMS_axioms @@ -139,18 +139,18 @@ Let [Y] be a pseudo metric space. alias id "Y" = "cic:/CoRN/metrics/CPseudoMSpaces/PsMS_basics/Y.var". -inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/rev_tri_ineq.con". +inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/rev_tri_ineq.con" as lemma. (*#* Instead of taking [pos_imp_ap] as axiom, we could as well have taken [diag_zero]. *) -inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/diag_zero_imp_pos_imp_ap.con". +inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/diag_zero_imp_pos_imp_ap.con" as lemma. -inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/pos_imp_ap_imp_diag_zero.con". +inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/pos_imp_ap_imp_diag_zero.con" as lemma. -inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/is_CPsMetricSpace_diag_zero.con". +inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/is_CPsMetricSpace_diag_zero.con" as lemma. (* UNEXPORTED End PsMS_basics @@ -168,23 +168,23 @@ Every setoid forms with the binary function that always returns zero, a pseudo metric space. *) -inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/zero_fun.con". +inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/zero_fun.con" as definition. -inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_strext.con". +inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_strext.con" as lemma. -inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/Zero_fun.con". +inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/Zero_fun.con" as definition. -inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_com.con". +inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_com.con" as lemma. -inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_nneg.con". +inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_nneg.con" as lemma. -inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_pos_imp_ap.con". +inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_pos_imp_ap.con" as lemma. -inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_tri_ineq.con". +inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_tri_ineq.con" as lemma. -inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/zf_is_CPsMetricSpace.con". +inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/zf_is_CPsMetricSpace.con" as definition. -inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/zf_as_CPsMetricSpace.con". +inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/zf_as_CPsMetricSpace.con" as definition. (* UNEXPORTED End Zerof diff --git a/helm/software/matita/contribs/CoRN-Procedural/metrics/ContFunctions.mma b/helm/software/matita/contribs/CoRN-Procedural/metrics/ContFunctions.mma index b9da5007a..1d6d82e96 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/metrics/ContFunctions.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/metrics/ContFunctions.mma @@ -38,19 +38,19 @@ alias id "B" = "cic:/CoRN/metrics/ContFunctions/Continuous_functions/B.var". We will look at some notions of continuous functions. *) -inline procedural "cic:/CoRN/metrics/ContFunctions/continuous.con". +inline procedural "cic:/CoRN/metrics/ContFunctions/continuous.con" as definition. -inline procedural "cic:/CoRN/metrics/ContFunctions/continuous'.con". +inline procedural "cic:/CoRN/metrics/ContFunctions/continuous'.con" as definition. -inline procedural "cic:/CoRN/metrics/ContFunctions/uni_continuous.con". +inline procedural "cic:/CoRN/metrics/ContFunctions/uni_continuous.con" as definition. -inline procedural "cic:/CoRN/metrics/ContFunctions/uni_continuous'.con". +inline procedural "cic:/CoRN/metrics/ContFunctions/uni_continuous'.con" as definition. -inline procedural "cic:/CoRN/metrics/ContFunctions/uni_continuous''.con". +inline procedural "cic:/CoRN/metrics/ContFunctions/uni_continuous''.con" as definition. -inline procedural "cic:/CoRN/metrics/ContFunctions/lipschitz.con". +inline procedural "cic:/CoRN/metrics/ContFunctions/lipschitz.con" as definition. -inline procedural "cic:/CoRN/metrics/ContFunctions/lipschitz'.con". +inline procedural "cic:/CoRN/metrics/ContFunctions/lipschitz'.con" as definition. (* UNEXPORTED End Continuous_functions @@ -90,32 +90,32 @@ Section Lemmas (* begin hide *) -inline procedural "cic:/CoRN/metrics/ContFunctions/nexp_power.con". +inline procedural "cic:/CoRN/metrics/ContFunctions/nexp_power.con" as lemma. (* end hide *) -inline procedural "cic:/CoRN/metrics/ContFunctions/continuous_imp_continuous'.con". +inline procedural "cic:/CoRN/metrics/ContFunctions/continuous_imp_continuous'.con" as lemma. -inline procedural "cic:/CoRN/metrics/ContFunctions/continuous'_imp_continuous.con". +inline procedural "cic:/CoRN/metrics/ContFunctions/continuous'_imp_continuous.con" as lemma. -inline procedural "cic:/CoRN/metrics/ContFunctions/uni_continuous_imp_uni_continuous'.con". +inline procedural "cic:/CoRN/metrics/ContFunctions/uni_continuous_imp_uni_continuous'.con" as lemma. -inline procedural "cic:/CoRN/metrics/ContFunctions/uni_continuous'_imp_uni_continuous.con". +inline procedural "cic:/CoRN/metrics/ContFunctions/uni_continuous'_imp_uni_continuous.con" as lemma. -inline procedural "cic:/CoRN/metrics/ContFunctions/uni_continuous'_imp_uni_continuous''.con". +inline procedural "cic:/CoRN/metrics/ContFunctions/uni_continuous'_imp_uni_continuous''.con" as lemma. -inline procedural "cic:/CoRN/metrics/ContFunctions/lipschitz_imp_lipschitz'.con". +inline procedural "cic:/CoRN/metrics/ContFunctions/lipschitz_imp_lipschitz'.con" as lemma. -inline procedural "cic:/CoRN/metrics/ContFunctions/lipschitz'_imp_lipschitz.con". +inline procedural "cic:/CoRN/metrics/ContFunctions/lipschitz'_imp_lipschitz.con" as lemma. (*#* Every uniformly continuous function is continuous and every Lipschitz function is uniformly continuous. *) -inline procedural "cic:/CoRN/metrics/ContFunctions/uni_continuous_imp_continuous.con". +inline procedural "cic:/CoRN/metrics/ContFunctions/uni_continuous_imp_continuous.con" as lemma. -inline procedural "cic:/CoRN/metrics/ContFunctions/lipschitz_imp_uni_continuous.con". +inline procedural "cic:/CoRN/metrics/ContFunctions/lipschitz_imp_uni_continuous.con" as lemma. (* UNEXPORTED End Lemmas @@ -133,11 +133,11 @@ The identity function is Lipschitz. Hence it is uniformly continuous and continuous. *) -inline procedural "cic:/CoRN/metrics/ContFunctions/id_is_lipschitz.con". +inline procedural "cic:/CoRN/metrics/ContFunctions/id_is_lipschitz.con" as lemma. -inline procedural "cic:/CoRN/metrics/ContFunctions/id_is_uni_continuous.con". +inline procedural "cic:/CoRN/metrics/ContFunctions/id_is_uni_continuous.con" as lemma. -inline procedural "cic:/CoRN/metrics/ContFunctions/id_is_continuous.con". +inline procedural "cic:/CoRN/metrics/ContFunctions/id_is_continuous.con" as lemma. (* UNEXPORTED End Identity @@ -162,11 +162,11 @@ alias id "B" = "cic:/CoRN/metrics/ContFunctions/Constant/B.var". alias id "X" = "cic:/CoRN/metrics/ContFunctions/Constant/X.var". -inline procedural "cic:/CoRN/metrics/ContFunctions/const_fun_is_lipschitz.con". +inline procedural "cic:/CoRN/metrics/ContFunctions/const_fun_is_lipschitz.con" as lemma. -inline procedural "cic:/CoRN/metrics/ContFunctions/const_fun_is_uni_continuous.con". +inline procedural "cic:/CoRN/metrics/ContFunctions/const_fun_is_uni_continuous.con" as lemma. -inline procedural "cic:/CoRN/metrics/ContFunctions/const_fun_is_continuous.con". +inline procedural "cic:/CoRN/metrics/ContFunctions/const_fun_is_continuous.con" as lemma. (* UNEXPORTED End Constant @@ -199,11 +199,11 @@ alias id "C" = "cic:/CoRN/metrics/ContFunctions/Composition/C.var". alias id "g" = "cic:/CoRN/metrics/ContFunctions/Composition/g.var". -inline procedural "cic:/CoRN/metrics/ContFunctions/comp_resp_lipschitz.con". +inline procedural "cic:/CoRN/metrics/ContFunctions/comp_resp_lipschitz.con" as lemma. -inline procedural "cic:/CoRN/metrics/ContFunctions/comp_resp_uni_continuous.con". +inline procedural "cic:/CoRN/metrics/ContFunctions/comp_resp_uni_continuous.con" as lemma. -inline procedural "cic:/CoRN/metrics/ContFunctions/comp_resp_continuous.con". +inline procedural "cic:/CoRN/metrics/ContFunctions/comp_resp_continuous.con" as lemma. (* UNEXPORTED End Composition @@ -216,29 +216,29 @@ Section Limit (*#* **Limit *) -inline procedural "cic:/CoRN/metrics/ContFunctions/MSseqLimit.con". +inline procedural "cic:/CoRN/metrics/ContFunctions/MSseqLimit.con" as definition. (* UNEXPORTED Implicit Arguments MSseqLimit [X]. *) -inline procedural "cic:/CoRN/metrics/ContFunctions/MSseqLimit'.con". +inline procedural "cic:/CoRN/metrics/ContFunctions/MSseqLimit'.con" as definition. (* UNEXPORTED Implicit Arguments MSseqLimit' [X]. *) -inline procedural "cic:/CoRN/metrics/ContFunctions/MSseqLimit_imp_MSseqLimit'.con". +inline procedural "cic:/CoRN/metrics/ContFunctions/MSseqLimit_imp_MSseqLimit'.con" as lemma. -inline procedural "cic:/CoRN/metrics/ContFunctions/MSseqLimit'_imp_MSseqLimit.con". +inline procedural "cic:/CoRN/metrics/ContFunctions/MSseqLimit'_imp_MSseqLimit.con" as lemma. -inline procedural "cic:/CoRN/metrics/ContFunctions/seqcontinuous'.con". +inline procedural "cic:/CoRN/metrics/ContFunctions/seqcontinuous'.con" as definition. (* UNEXPORTED Implicit Arguments seqcontinuous' [A B]. *) -inline procedural "cic:/CoRN/metrics/ContFunctions/continuous'_imp_seqcontinuous'.con". +inline procedural "cic:/CoRN/metrics/ContFunctions/continuous'_imp_seqcontinuous'.con" as lemma. (* UNEXPORTED End Limit diff --git a/helm/software/matita/contribs/CoRN-Procedural/metrics/Equiv.mma b/helm/software/matita/contribs/CoRN-Procedural/metrics/Equiv.mma index 5e5908494..8886328aa 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/metrics/Equiv.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/metrics/Equiv.mma @@ -32,31 +32,31 @@ We say that two pseudo metric spaces are equivalent, when there exists a bijective, structure-preserving function between them. *) -inline procedural "cic:/CoRN/metrics/Equiv/equivalent_psmetric.con". +inline procedural "cic:/CoRN/metrics/Equiv/equivalent_psmetric.con" as definition. -inline procedural "cic:/CoRN/metrics/Equiv/isopsmetry.con". +inline procedural "cic:/CoRN/metrics/Equiv/isopsmetry.con" as definition. (* UNEXPORTED Implicit Arguments isopsmetry [X Y]. *) -inline procedural "cic:/CoRN/metrics/Equiv/isopsmetry_imp_bij.con". +inline procedural "cic:/CoRN/metrics/Equiv/isopsmetry_imp_bij.con" as lemma. -inline procedural "cic:/CoRN/metrics/Equiv/isopsmetry_imp_lipschitz.con". +inline procedural "cic:/CoRN/metrics/Equiv/isopsmetry_imp_lipschitz.con" as lemma. -inline procedural "cic:/CoRN/metrics/Equiv/id_is_isopsmetry.con". +inline procedural "cic:/CoRN/metrics/Equiv/id_is_isopsmetry.con" as lemma. -inline procedural "cic:/CoRN/metrics/Equiv/comp_resp_isopsmetry.con". +inline procedural "cic:/CoRN/metrics/Equiv/comp_resp_isopsmetry.con" as lemma. -inline procedural "cic:/CoRN/metrics/Equiv/inv_isopsmetry.con". +inline procedural "cic:/CoRN/metrics/Equiv/inv_isopsmetry.con" as lemma. -inline procedural "cic:/CoRN/metrics/Equiv/MSequivalent.con". +inline procedural "cic:/CoRN/metrics/Equiv/MSequivalent.con" as definition. (*#* Not all pseudo metric spaces are equivalent: *) -inline procedural "cic:/CoRN/metrics/Equiv/MSequivalent_discr.con". +inline procedural "cic:/CoRN/metrics/Equiv/MSequivalent_discr.con" as lemma. (* UNEXPORTED End equivalent diff --git a/helm/software/matita/contribs/CoRN-Procedural/metrics/IR_CPMSpace.mma b/helm/software/matita/contribs/CoRN-Procedural/metrics/IR_CPMSpace.mma index efddeec10..24e2717f4 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/metrics/IR_CPMSpace.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/metrics/IR_CPMSpace.mma @@ -37,43 +37,43 @@ Let [X] be a pseudo metric space. The real numbers with the usual distance form a pseudo metric space. *) -inline procedural "cic:/CoRN/metrics/IR_CPMSpace/dIR.con". +inline procedural "cic:/CoRN/metrics/IR_CPMSpace/dIR.con" as definition. -inline procedural "cic:/CoRN/metrics/IR_CPMSpace/bin_fun_strext_dIR.con". +inline procedural "cic:/CoRN/metrics/IR_CPMSpace/bin_fun_strext_dIR.con" as lemma. -inline procedural "cic:/CoRN/metrics/IR_CPMSpace/dIR_as_CSetoid_fun.con". +inline procedural "cic:/CoRN/metrics/IR_CPMSpace/dIR_as_CSetoid_fun.con" as definition. -inline procedural "cic:/CoRN/metrics/IR_CPMSpace/dIR_nneg.con". +inline procedural "cic:/CoRN/metrics/IR_CPMSpace/dIR_nneg.con" as lemma. -inline procedural "cic:/CoRN/metrics/IR_CPMSpace/dIR_com.con". +inline procedural "cic:/CoRN/metrics/IR_CPMSpace/dIR_com.con" as lemma. -inline procedural "cic:/CoRN/metrics/IR_CPMSpace/dIR_pos_imp_ap.con". +inline procedural "cic:/CoRN/metrics/IR_CPMSpace/dIR_pos_imp_ap.con" as lemma. (* begin hide *) -inline procedural "cic:/CoRN/metrics/IR_CPMSpace/IR_tri_ineq.con". +inline procedural "cic:/CoRN/metrics/IR_CPMSpace/IR_tri_ineq.con" as lemma. (* end hide *) -inline procedural "cic:/CoRN/metrics/IR_CPMSpace/dIR_tri_ineq.con". +inline procedural "cic:/CoRN/metrics/IR_CPMSpace/dIR_tri_ineq.con" as lemma. -inline procedural "cic:/CoRN/metrics/IR_CPMSpace/IR_dIR_is_CPsMetricSpace.con". +inline procedural "cic:/CoRN/metrics/IR_CPMSpace/IR_dIR_is_CPsMetricSpace.con" as definition. -inline procedural "cic:/CoRN/metrics/IR_CPMSpace/IR_as_CPsMetricSpace.con". +inline procedural "cic:/CoRN/metrics/IR_CPMSpace/IR_as_CPsMetricSpace.con" as definition. alias id "X" = "cic:/CoRN/metrics/IR_CPMSpace/Reals/X.var". -inline procedural "cic:/CoRN/metrics/IR_CPMSpace/rev_tri_ineq'.con". +inline procedural "cic:/CoRN/metrics/IR_CPMSpace/rev_tri_ineq'.con" as lemma. (*#* A pseudo metric is Lipschitz. Hence it is uniformly continuous and continuous. *) -inline procedural "cic:/CoRN/metrics/IR_CPMSpace/d_is_lipschitz.con". +inline procedural "cic:/CoRN/metrics/IR_CPMSpace/d_is_lipschitz.con" as lemma. -inline procedural "cic:/CoRN/metrics/IR_CPMSpace/d_is_uni_continuous.con". +inline procedural "cic:/CoRN/metrics/IR_CPMSpace/d_is_uni_continuous.con" as lemma. -inline procedural "cic:/CoRN/metrics/IR_CPMSpace/d_is_continuous.con". +inline procedural "cic:/CoRN/metrics/IR_CPMSpace/d_is_continuous.con" as lemma. (* UNEXPORTED End Reals @@ -91,11 +91,11 @@ The sum of two Lipschitz/uniformly continous/continuous functions is again Lipschitz/uniformly continuous/continuous. *) -inline procedural "cic:/CoRN/metrics/IR_CPMSpace/plus_resp_lipschitz.con". +inline procedural "cic:/CoRN/metrics/IR_CPMSpace/plus_resp_lipschitz.con" as lemma. -inline procedural "cic:/CoRN/metrics/IR_CPMSpace/plus_resp_uni_continuous.con". +inline procedural "cic:/CoRN/metrics/IR_CPMSpace/plus_resp_uni_continuous.con" as lemma. -inline procedural "cic:/CoRN/metrics/IR_CPMSpace/plus_resp_continuous.con". +inline procedural "cic:/CoRN/metrics/IR_CPMSpace/plus_resp_continuous.con" as lemma. (* UNEXPORTED End Addition diff --git a/helm/software/matita/contribs/CoRN-Procedural/metrics/Prod_Sub.mma b/helm/software/matita/contribs/CoRN-Procedural/metrics/Prod_Sub.mma index f63bc9e69..2ab75daa0 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/metrics/Prod_Sub.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/metrics/Prod_Sub.mma @@ -35,15 +35,15 @@ This is %\emph{not}% #not# the one used to make the metric of $\RR^{2}$ #IR2# out of the metric of $\RR$ #IR#. *) -inline procedural "cic:/CoRN/metrics/Prod_Sub/dprod0.con". +inline procedural "cic:/CoRN/metrics/Prod_Sub/dprod0.con" as definition. -inline procedural "cic:/CoRN/metrics/Prod_Sub/dprod0_strext.con". +inline procedural "cic:/CoRN/metrics/Prod_Sub/dprod0_strext.con" as lemma. -inline procedural "cic:/CoRN/metrics/Prod_Sub/d_prod0.con". +inline procedural "cic:/CoRN/metrics/Prod_Sub/d_prod0.con" as definition. -inline procedural "cic:/CoRN/metrics/Prod_Sub/prod0cpsmetricspace_is_CPsMetricSpace.con". +inline procedural "cic:/CoRN/metrics/Prod_Sub/prod0cpsmetricspace_is_CPsMetricSpace.con" as lemma. -inline procedural "cic:/CoRN/metrics/Prod_Sub/Prod0CPsMetricSpace.con". +inline procedural "cic:/CoRN/metrics/Prod_Sub/Prod0CPsMetricSpace.con" as definition. (* UNEXPORTED End prodpsmetrics @@ -61,45 +61,45 @@ The pseudo metric on a subspace $Y$ #Y# of a pseudo metric space $X$ #X# is the pseudo metric on $X$ #X# restricted to $Y$ #Y#. *) -inline procedural "cic:/CoRN/metrics/Prod_Sub/restr_bin_fun.con". +inline procedural "cic:/CoRN/metrics/Prod_Sub/restr_bin_fun.con" as definition. (* UNEXPORTED Implicit Arguments restr_bin_fun [X]. *) -inline procedural "cic:/CoRN/metrics/Prod_Sub/restr_bin_fun'.con". +inline procedural "cic:/CoRN/metrics/Prod_Sub/restr_bin_fun'.con" as definition. (* UNEXPORTED Implicit Arguments restr_bin_fun' [X]. *) -inline procedural "cic:/CoRN/metrics/Prod_Sub/restr_bin_fun_strext.con". +inline procedural "cic:/CoRN/metrics/Prod_Sub/restr_bin_fun_strext.con" as lemma. -inline procedural "cic:/CoRN/metrics/Prod_Sub/Build_SubCSetoid_bin_fun.con". +inline procedural "cic:/CoRN/metrics/Prod_Sub/Build_SubCSetoid_bin_fun.con" as definition. -inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub.con". +inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub.con" as definition. (* UNEXPORTED Implicit Arguments dsub [X]. *) -inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub_com.con". +inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub_com.con" as lemma. -inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub_nneg.con". +inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub_nneg.con" as lemma. -inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub_pos_imp_ap.con". +inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub_pos_imp_ap.con" as lemma. -inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub_tri_ineq.con". +inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub_tri_ineq.con" as lemma. -inline procedural "cic:/CoRN/metrics/Prod_Sub/is_SubPsMetricSpace.con". +inline procedural "cic:/CoRN/metrics/Prod_Sub/is_SubPsMetricSpace.con" as definition. -inline procedural "cic:/CoRN/metrics/Prod_Sub/SubPsMetricSpace.con". +inline procedural "cic:/CoRN/metrics/Prod_Sub/SubPsMetricSpace.con" as definition. (* UNEXPORTED Implicit Arguments SubPsMetricSpace [X]. *) -inline procedural "cic:/CoRN/metrics/Prod_Sub/from_SubPsMetricSpace.con". +inline procedural "cic:/CoRN/metrics/Prod_Sub/from_SubPsMetricSpace.con" as definition. (*#* The function [dsub'] is used in the definition of %''located''% #"located"#. @@ -107,21 +107,21 @@ It enables one to speak about a distance between an element of a pseudo metric space and a certain subspace. *) -inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub'.con". +inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub'.con" as definition. (* UNEXPORTED Implicit Arguments dsub' [X]. *) -inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub'_strext.con". +inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub'_strext.con" as lemma. -inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub'_as_cs_fun.con". +inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub'_as_cs_fun.con" as definition. (* UNEXPORTED Implicit Arguments dsub'_as_cs_fun [X]. *) -inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub'_uni_continuous''.con". +inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub'_uni_continuous''.con" as lemma. (* UNEXPORTED End subpsmetrics diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/abgroups/QSposabgroup.mma b/helm/software/matita/contribs/CoRN-Procedural/model/abgroups/QSposabgroup.mma index ab852c45b..e01f261c9 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/abgroups/QSposabgroup.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/abgroups/QSposabgroup.mma @@ -26,7 +26,7 @@ include "algebra/CAbGroups.ma". The positive rational numbers form with the operation $(x,y) \mapsto xy/2$ #(x,y) ↦ xy/2# an abelian group. *) -inline procedural "cic:/CoRN/model/abgroups/QSposabgroup/Qpos_multdiv2_is_CAbGroup.con". +inline procedural "cic:/CoRN/model/abgroups/QSposabgroup/Qpos_multdiv2_is_CAbGroup.con" as lemma. -inline procedural "cic:/CoRN/model/abgroups/QSposabgroup/Qpos_multdiv2_as_CAbGroup.con". +inline procedural "cic:/CoRN/model/abgroups/QSposabgroup/Qpos_multdiv2_as_CAbGroup.con" as definition. diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/abgroups/Qabgroup.mma b/helm/software/matita/contribs/CoRN-Procedural/model/abgroups/Qabgroup.mma index 7dd20bc46..568d785f4 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/abgroups/Qabgroup.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/abgroups/Qabgroup.mma @@ -29,7 +29,7 @@ include "algebra/CAbGroups.ma". CAbGroup. *) -inline procedural "cic:/CoRN/model/abgroups/Qabgroup/Q_is_CAbGroup.con". +inline procedural "cic:/CoRN/model/abgroups/Qabgroup/Q_is_CAbGroup.con" as lemma. -inline procedural "cic:/CoRN/model/abgroups/Qabgroup/Q_as_CAbGroup.con". +inline procedural "cic:/CoRN/model/abgroups/Qabgroup/Q_as_CAbGroup.con" as definition. diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/abgroups/Qposabgroup.mma b/helm/software/matita/contribs/CoRN-Procedural/model/abgroups/Qposabgroup.mma index 161364874..de1f95602 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/abgroups/Qposabgroup.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/abgroups/Qposabgroup.mma @@ -26,7 +26,7 @@ include "algebra/CAbGroups.ma". The positive rationals form with the multiplication a CAbgroup. *) -inline procedural "cic:/CoRN/model/abgroups/Qposabgroup/Qpos_mult_is_CAbGroup.con". +inline procedural "cic:/CoRN/model/abgroups/Qposabgroup/Qpos_mult_is_CAbGroup.con" as definition. -inline procedural "cic:/CoRN/model/abgroups/Qposabgroup/Qpos_mult_as_CAbGroup.con". +inline procedural "cic:/CoRN/model/abgroups/Qposabgroup/Qpos_mult_as_CAbGroup.con" as definition. diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/abgroups/Zabgroup.mma b/helm/software/matita/contribs/CoRN-Procedural/model/abgroups/Zabgroup.mma index 694fce22d..69d1e1bd6 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/abgroups/Zabgroup.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/abgroups/Zabgroup.mma @@ -25,9 +25,9 @@ include "algebra/CAbGroups.ma". (*#* **Example of an abelian group: $\langle$#⟨#[Z],[[+]]$\rangle$#⟩# *) -inline procedural "cic:/CoRN/model/abgroups/Zabgroup/Z_is_CAbGroup.con". +inline procedural "cic:/CoRN/model/abgroups/Zabgroup/Z_is_CAbGroup.con" as lemma. -inline procedural "cic:/CoRN/model/abgroups/Zabgroup/Z_as_CAbGroup.con". +inline procedural "cic:/CoRN/model/abgroups/Zabgroup/Z_as_CAbGroup.con" as definition. (*#* The term [Z_as_CAbGroup] is of type [CAbGroup]. Hence we have proven that [Z] is a constructive Abelian group. *) diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/fields/Qfield.mma b/helm/software/matita/contribs/CoRN-Procedural/model/fields/Qfield.mma index 7a8bfb38a..cd1b552cf 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/fields/Qfield.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/fields/Qfield.mma @@ -27,7 +27,7 @@ As we have seen, there is a inverse for the multiplication for non-zeroes. So, [Q] not only forms a ring, but even a field. *) -inline procedural "cic:/CoRN/model/fields/Qfield/Q_is_CField.con". +inline procedural "cic:/CoRN/model/fields/Qfield/Q_is_CField.con" as lemma. -inline procedural "cic:/CoRN/model/fields/Qfield/Q_as_CField.con". +inline procedural "cic:/CoRN/model/fields/Qfield/Q_as_CField.con" as definition. diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/groups/QSposgroup.mma b/helm/software/matita/contribs/CoRN-Procedural/model/groups/QSposgroup.mma index 64d774c50..edddc7076 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/groups/QSposgroup.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/groups/QSposgroup.mma @@ -27,7 +27,7 @@ The positive rationals form with the operation $(x,y) \mapsto xy/2$ #(x,y) ↦ xy/2# a CGroup. *) -inline procedural "cic:/CoRN/model/groups/QSposgroup/Qpos_multdiv2_is_CGroup.con". +inline procedural "cic:/CoRN/model/groups/QSposgroup/Qpos_multdiv2_is_CGroup.con" as lemma. -inline procedural "cic:/CoRN/model/groups/QSposgroup/Qpos_multdiv2_as_CGroup.con". +inline procedural "cic:/CoRN/model/groups/QSposgroup/Qpos_multdiv2_as_CGroup.con" as definition. diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/groups/Qgroup.mma b/helm/software/matita/contribs/CoRN-Procedural/model/groups/Qgroup.mma index 9398c0626..080e86fad 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/groups/Qgroup.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/groups/Qgroup.mma @@ -26,7 +26,7 @@ include "algebra/CGroups.ma". The rational numbers with addition form a group. The inverse function is taking the opposite. *) -inline procedural "cic:/CoRN/model/groups/Qgroup/Q_is_CGroup.con". +inline procedural "cic:/CoRN/model/groups/Qgroup/Q_is_CGroup.con" as lemma. -inline procedural "cic:/CoRN/model/groups/Qgroup/Q_as_CGroup.con". +inline procedural "cic:/CoRN/model/groups/Qgroup/Q_as_CGroup.con" as definition. diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/groups/Qposgroup.mma b/helm/software/matita/contribs/CoRN-Procedural/model/groups/Qposgroup.mma index 90d5b8419..00cc590ad 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/groups/Qposgroup.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/groups/Qposgroup.mma @@ -26,7 +26,7 @@ include "algebra/CGroups.ma". The positive rational numbers form a multiplicative group. *) -inline procedural "cic:/CoRN/model/groups/Qposgroup/Qpos_is_CGroup.con". +inline procedural "cic:/CoRN/model/groups/Qposgroup/Qpos_is_CGroup.con" as lemma. -inline procedural "cic:/CoRN/model/groups/Qposgroup/Qpos_as_CGroup.con". +inline procedural "cic:/CoRN/model/groups/Qposgroup/Qpos_as_CGroup.con" as definition. diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/groups/Zgroup.mma b/helm/software/matita/contribs/CoRN-Procedural/model/groups/Zgroup.mma index 3d98cc340..ba3b1642b 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/groups/Zgroup.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/groups/Zgroup.mma @@ -25,9 +25,9 @@ include "algebra/CGroups.ma". (*#* **Example of a group: $\langle$#⟨#[Z],[[+]]$\rangle$#⟩# *) -inline procedural "cic:/CoRN/model/groups/Zgroup/Z_is_CGroup.con". +inline procedural "cic:/CoRN/model/groups/Zgroup/Z_is_CGroup.con" as lemma. -inline procedural "cic:/CoRN/model/groups/Zgroup/Z_as_CGroup.con". +inline procedural "cic:/CoRN/model/groups/Zgroup/Z_as_CGroup.con" as definition. (*#* The term [Z_as_CGroup] is of type [CGroup]. Hence we have proven that [Z] is a constructive group. *) diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/monoids/Nmonoid.mma b/helm/software/matita/contribs/CoRN-Procedural/model/monoids/Nmonoid.mma index 0468f456d..cd3d80f21 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/monoids/Nmonoid.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/monoids/Nmonoid.mma @@ -26,15 +26,15 @@ include "algebra/CMonoids.ma". Zero is an unit for the addition. *) -inline procedural "cic:/CoRN/model/monoids/Nmonoid/O_as_rht_unit.con". +inline procedural "cic:/CoRN/model/monoids/Nmonoid/O_as_rht_unit.con" as lemma. -inline procedural "cic:/CoRN/model/monoids/Nmonoid/O_as_lft_unit.con". +inline procedural "cic:/CoRN/model/monoids/Nmonoid/O_as_lft_unit.con" as lemma. -inline procedural "cic:/CoRN/model/monoids/Nmonoid/nat_is_CMonoid.con". +inline procedural "cic:/CoRN/model/monoids/Nmonoid/nat_is_CMonoid.con" as definition. (*#* Whence we can define ##%\emph{%the monoid of natural numbers%}%##: *) -inline procedural "cic:/CoRN/model/monoids/Nmonoid/nat_as_CMonoid.con". +inline procedural "cic:/CoRN/model/monoids/Nmonoid/nat_as_CMonoid.con" as definition. diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/monoids/Nposmonoid.mma b/helm/software/matita/contribs/CoRN-Procedural/model/monoids/Nposmonoid.mma index d66014b2d..bd0f386b6 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/monoids/Nposmonoid.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/monoids/Nposmonoid.mma @@ -27,14 +27,14 @@ One is the right unit as well as the left unit of the multiplication on the positive natural numbers. *) -inline procedural "cic:/CoRN/model/monoids/Nposmonoid/rhtunitNpos.con". +inline procedural "cic:/CoRN/model/monoids/Nposmonoid/rhtunitNpos.con" as lemma. -inline procedural "cic:/CoRN/model/monoids/Nposmonoid/lftunitNpos.con". +inline procedural "cic:/CoRN/model/monoids/Nposmonoid/lftunitNpos.con" as lemma. (*#* So, the positive natural numbers with multiplication form a CMonoid. *) -inline procedural "cic:/CoRN/model/monoids/Nposmonoid/Nposmult_is_CMonoid.con". +inline procedural "cic:/CoRN/model/monoids/Nposmonoid/Nposmult_is_CMonoid.con" as definition. -inline procedural "cic:/CoRN/model/monoids/Nposmonoid/Nposmult_as_CMonoid.con". +inline procedural "cic:/CoRN/model/monoids/Nposmonoid/Nposmult_as_CMonoid.con" as definition. diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/monoids/QSposmonoid.mma b/helm/software/matita/contribs/CoRN-Procedural/model/monoids/QSposmonoid.mma index 6dfd8114b..50866dfdf 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/monoids/QSposmonoid.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/monoids/QSposmonoid.mma @@ -27,11 +27,11 @@ Two is the unit of the operation $(x,y) \mapsto xy/2$ #(x,y) ↦ xy/2# on the positive rationals. So we have another monoid structure on the positive rational numbers. *) -inline procedural "cic:/CoRN/model/monoids/QSposmonoid/QTWOpos_is_rht_unit.con". +inline procedural "cic:/CoRN/model/monoids/QSposmonoid/QTWOpos_is_rht_unit.con" as lemma. -inline procedural "cic:/CoRN/model/monoids/QSposmonoid/QTWOpos_is_lft_unit.con". +inline procedural "cic:/CoRN/model/monoids/QSposmonoid/QTWOpos_is_lft_unit.con" as lemma. -inline procedural "cic:/CoRN/model/monoids/QSposmonoid/Qpos_multdiv2_is_CMonoid.con". +inline procedural "cic:/CoRN/model/monoids/QSposmonoid/Qpos_multdiv2_is_CMonoid.con" as definition. -inline procedural "cic:/CoRN/model/monoids/QSposmonoid/Qpos_multdiv2_as_CMonoid.con". +inline procedural "cic:/CoRN/model/monoids/QSposmonoid/Qpos_multdiv2_as_CMonoid.con" as definition. diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/monoids/Qmonoid.mma b/helm/software/matita/contribs/CoRN-Procedural/model/monoids/Qmonoid.mma index bf45b45e2..3acc779a6 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/monoids/Qmonoid.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/monoids/Qmonoid.mma @@ -27,23 +27,23 @@ include "algebra/CMonoids.ma". The rational numbers form with addition a CMonoid. [QZERO] is the unit. *) -inline procedural "cic:/CoRN/model/monoids/Qmonoid/ZEROQ_as_rht_unit3.con". +inline procedural "cic:/CoRN/model/monoids/Qmonoid/ZEROQ_as_rht_unit3.con" as lemma. -inline procedural "cic:/CoRN/model/monoids/Qmonoid/ZEROQ_as_lft_unit3.con". +inline procedural "cic:/CoRN/model/monoids/Qmonoid/ZEROQ_as_lft_unit3.con" as lemma. -inline procedural "cic:/CoRN/model/monoids/Qmonoid/Q_is_CMonoid.con". +inline procedural "cic:/CoRN/model/monoids/Qmonoid/Q_is_CMonoid.con" as definition. -inline procedural "cic:/CoRN/model/monoids/Qmonoid/Q_as_CMonoid.con". +inline procedural "cic:/CoRN/model/monoids/Qmonoid/Q_as_CMonoid.con" as definition. (*#* ***$\langle$#⟨#[Q],[[*]]$\rangle$#⟩# Also with multiplication Q forms a CMonoid. Here, the unit is [QONE]. *) -inline procedural "cic:/CoRN/model/monoids/Qmonoid/ONEQ_as_rht_unit.con". +inline procedural "cic:/CoRN/model/monoids/Qmonoid/ONEQ_as_rht_unit.con" as lemma. -inline procedural "cic:/CoRN/model/monoids/Qmonoid/ONEQ_as_lft_unit.con". +inline procedural "cic:/CoRN/model/monoids/Qmonoid/ONEQ_as_lft_unit.con" as lemma. -inline procedural "cic:/CoRN/model/monoids/Qmonoid/Q_mul_is_CMonoid.con". +inline procedural "cic:/CoRN/model/monoids/Qmonoid/Q_mul_is_CMonoid.con" as definition. -inline procedural "cic:/CoRN/model/monoids/Qmonoid/Q_mul_as_CMonoid.con". +inline procedural "cic:/CoRN/model/monoids/Qmonoid/Q_mul_as_CMonoid.con" as definition. diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/monoids/Qposmonoid.mma b/helm/software/matita/contribs/CoRN-Procedural/model/monoids/Qposmonoid.mma index 36f936c97..3c2fe2a68 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/monoids/Qposmonoid.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/monoids/Qposmonoid.mma @@ -26,11 +26,11 @@ include "algebra/CMonoids.ma". One is the unit for multiplication on positive integers. Therefore the positive rational numbers together with the multiplication are a CMonoid. *) -inline procedural "cic:/CoRN/model/monoids/Qposmonoid/QONEpos_is_rht_unit.con". +inline procedural "cic:/CoRN/model/monoids/Qposmonoid/QONEpos_is_rht_unit.con" as lemma. -inline procedural "cic:/CoRN/model/monoids/Qposmonoid/QONEpos_is_lft_unit.con". +inline procedural "cic:/CoRN/model/monoids/Qposmonoid/QONEpos_is_lft_unit.con" as lemma. -inline procedural "cic:/CoRN/model/monoids/Qposmonoid/Qpos_mult_is_CMonoid.con". +inline procedural "cic:/CoRN/model/monoids/Qposmonoid/Qpos_mult_is_CMonoid.con" as definition. -inline procedural "cic:/CoRN/model/monoids/Qposmonoid/Qpos_mult_as_CMonoid.con". +inline procedural "cic:/CoRN/model/monoids/Qposmonoid/Qpos_mult_as_CMonoid.con" as definition. diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/monoids/Zmonoid.mma b/helm/software/matita/contribs/CoRN-Procedural/model/monoids/Zmonoid.mma index 56274de97..57a8e014f 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/monoids/Zmonoid.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/monoids/Zmonoid.mma @@ -28,13 +28,13 @@ We use the addition [ZERO] (defined in the standard library) as the unit of monoid: *) -inline procedural "cic:/CoRN/model/monoids/Zmonoid/ZERO_as_rht_unit.con". +inline procedural "cic:/CoRN/model/monoids/Zmonoid/ZERO_as_rht_unit.con" as lemma. -inline procedural "cic:/CoRN/model/monoids/Zmonoid/ZERO_as_lft_unit.con". +inline procedural "cic:/CoRN/model/monoids/Zmonoid/ZERO_as_lft_unit.con" as lemma. -inline procedural "cic:/CoRN/model/monoids/Zmonoid/Z_is_CMonoid.con". +inline procedural "cic:/CoRN/model/monoids/Zmonoid/Z_is_CMonoid.con" as definition. -inline procedural "cic:/CoRN/model/monoids/Zmonoid/Z_as_CMonoid.con". +inline procedural "cic:/CoRN/model/monoids/Zmonoid/Z_as_CMonoid.con" as definition. (*#* The term [Z_as_CMonoid] is of type [CMonoid]. Hence we have proven that [Z] is a constructive monoid. @@ -43,13 +43,13 @@ As the multiplicative unit we should use [`1`], which is [(POS xH)] in the representation we have for integers. *) -inline procedural "cic:/CoRN/model/monoids/Zmonoid/ONE_as_rht_unit.con". +inline procedural "cic:/CoRN/model/monoids/Zmonoid/ONE_as_rht_unit.con" as lemma. -inline procedural "cic:/CoRN/model/monoids/Zmonoid/ONE_as_lft_unit.con". +inline procedural "cic:/CoRN/model/monoids/Zmonoid/ONE_as_lft_unit.con" as lemma. -inline procedural "cic:/CoRN/model/monoids/Zmonoid/Z_mul_is_CMonoid.con". +inline procedural "cic:/CoRN/model/monoids/Zmonoid/Z_mul_is_CMonoid.con" as definition. -inline procedural "cic:/CoRN/model/monoids/Zmonoid/Z_mul_as_CMonoid.con". +inline procedural "cic:/CoRN/model/monoids/Zmonoid/Z_mul_as_CMonoid.con" as definition. (*#* The term [Z_mul_as_CMonoid] is another term of type [CMonoid]. *) diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/non_examples/N_no_group.mma b/helm/software/matita/contribs/CoRN-Procedural/model/non_examples/N_no_group.mma index f629e104a..5ae9aa35d 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/non_examples/N_no_group.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/non_examples/N_no_group.mma @@ -26,10 +26,10 @@ include "algebra/CGroups.ma". There is no inverse function for the natural numbers with addition. *) -inline procedural "cic:/CoRN/model/non_examples/N_no_group/no_inverse_nat_plus.con". +inline procedural "cic:/CoRN/model/non_examples/N_no_group/no_inverse_nat_plus.con" as lemma. (*#* Hence they do not form a CGroup. *) -inline procedural "cic:/CoRN/model/non_examples/N_no_group/no_group_nat_plus.con". +inline procedural "cic:/CoRN/model/non_examples/N_no_group/no_group_nat_plus.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/non_examples/Npos_no_group.mma b/helm/software/matita/contribs/CoRN-Procedural/model/non_examples/Npos_no_group.mma index 52a0062ca..ab83d888c 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/non_examples/Npos_no_group.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/non_examples/Npos_no_group.mma @@ -26,10 +26,10 @@ include "model/monoids/Nposmonoid.ma". There is no inverse for multiplication on the positive natural numbers. *) -inline procedural "cic:/CoRN/model/non_examples/Npos_no_group/no_inverse_Nposmult.con". +inline procedural "cic:/CoRN/model/non_examples/Npos_no_group/no_inverse_Nposmult.con" as lemma. (*#* Hence the natural numbers with multiplication do not form a group. *) -inline procedural "cic:/CoRN/model/non_examples/Npos_no_group/no_group_Nposmult.con". +inline procedural "cic:/CoRN/model/non_examples/Npos_no_group/no_group_Nposmult.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/non_examples/Npos_no_monoid.mma b/helm/software/matita/contribs/CoRN-Procedural/model/non_examples/Npos_no_monoid.mma index e181473da..c61d3ce5b 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/non_examples/Npos_no_monoid.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/non_examples/Npos_no_monoid.mma @@ -26,11 +26,11 @@ include "algebra/CMonoids.ma". There is no right unit for the addition on the positive natural numbers. *) -inline procedural "cic:/CoRN/model/non_examples/Npos_no_monoid/no_rht_unit_Npos.con". +inline procedural "cic:/CoRN/model/non_examples/Npos_no_monoid/no_rht_unit_Npos.con" as lemma. (*#* Therefore the set of positive natural numbers doesn't form a group with addition. *) -inline procedural "cic:/CoRN/model/non_examples/Npos_no_monoid/no_monoid_Npos.con". +inline procedural "cic:/CoRN/model/non_examples/Npos_no_monoid/no_monoid_Npos.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/ordfields/Qordfield.mma b/helm/software/matita/contribs/CoRN-Procedural/model/ordfields/Qordfield.mma index c6f25816f..4e0416090 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/ordfields/Qordfield.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/ordfields/Qordfield.mma @@ -26,11 +26,11 @@ include "algebra/COrdFields.ma". [Q] is an archemaedian ordered field. *) -inline procedural "cic:/CoRN/model/ordfields/Qordfield/Qlt_is_strict_order.con". +inline procedural "cic:/CoRN/model/ordfields/Qordfield/Qlt_is_strict_order.con" as definition. -inline procedural "cic:/CoRN/model/ordfields/Qordfield/Q_is_COrdField.con". +inline procedural "cic:/CoRN/model/ordfields/Qordfield/Q_is_COrdField.con" as definition. -inline procedural "cic:/CoRN/model/ordfields/Qordfield/Q_as_COrdField.con". +inline procedural "cic:/CoRN/model/ordfields/Qordfield/Q_as_COrdField.con" as definition. -inline procedural "cic:/CoRN/model/ordfields/Qordfield/Q_is_archemaedian.con". +inline procedural "cic:/CoRN/model/ordfields/Qordfield/Q_is_archemaedian.con" as theorem. diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/reals/Cauchy_IR.mma b/helm/software/matita/contribs/CoRN-Procedural/model/reals/Cauchy_IR.mma index e2adce7d6..afa798ade 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/reals/Cauchy_IR.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/reals/Cauchy_IR.mma @@ -28,7 +28,7 @@ arbitrary archimedian ordered field. Plugging in [Q] we get the model of the real numbers as Cauchy sequences of rationals. *) -inline procedural "cic:/CoRN/model/reals/Cauchy_IR/Cauchy_IR.con". +inline procedural "cic:/CoRN/model/reals/Cauchy_IR/Cauchy_IR.con" as definition. (*#* The term [Cauchy_IR] is of type [CReals]. *) diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/rings/Qring.mma b/helm/software/matita/contribs/CoRN-Procedural/model/rings/Qring.mma index 91bf33b9c..a35056ca3 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/rings/Qring.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/rings/Qring.mma @@ -29,18 +29,18 @@ Because [Q] forms an abelian group with addition, a monoid with multiplication and it satisfies the distributive law, it is a ring. *) -inline procedural "cic:/CoRN/model/rings/Qring/Q_mult_plus_is_dist.con". +inline procedural "cic:/CoRN/model/rings/Qring/Q_mult_plus_is_dist.con" as lemma. -inline procedural "cic:/CoRN/model/rings/Qring/Q_is_CRing.con". +inline procedural "cic:/CoRN/model/rings/Qring/Q_is_CRing.con" as definition. -inline procedural "cic:/CoRN/model/rings/Qring/Q_as_CRing.con". +inline procedural "cic:/CoRN/model/rings/Qring/Q_as_CRing.con" as definition. (*#* The following lemmas are used in the proof that [Q] is Archimeadian. *) -inline procedural "cic:/CoRN/model/rings/Qring/injz_Nring.con". +inline procedural "cic:/CoRN/model/rings/Qring/injz_Nring.con" as lemma. -inline procedural "cic:/CoRN/model/rings/Qring/injZ_eq.con". +inline procedural "cic:/CoRN/model/rings/Qring/injZ_eq.con" as lemma. -inline procedural "cic:/CoRN/model/rings/Qring/nring_Q.con". +inline procedural "cic:/CoRN/model/rings/Qring/nring_Q.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/rings/Zring.mma b/helm/software/matita/contribs/CoRN-Procedural/model/rings/Zring.mma index d9f0aa8e3..5d4356867 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/rings/Zring.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/rings/Zring.mma @@ -27,11 +27,11 @@ include "algebra/CRings.ma". The multiplication and the addition are distributive. *) -inline procedural "cic:/CoRN/model/rings/Zring/Z_mult_plus_is_dist.con". +inline procedural "cic:/CoRN/model/rings/Zring/Z_mult_plus_is_dist.con" as lemma. -inline procedural "cic:/CoRN/model/rings/Zring/Z_is_CRing.con". +inline procedural "cic:/CoRN/model/rings/Zring/Z_is_CRing.con" as definition. -inline procedural "cic:/CoRN/model/rings/Zring/Z_as_CRing.con". +inline procedural "cic:/CoRN/model/rings/Zring/Z_as_CRing.con" as definition. (*#* The term [Z_as_CRing] is of type [CRing]. Hence we have proven that [Z] is a constructive ring. *) diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/semigroups/Npossemigroup.mma b/helm/software/matita/contribs/CoRN-Procedural/model/semigroups/Npossemigroup.mma index 01d06e0ab..d4e0faa47 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/semigroups/Npossemigroup.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/semigroups/Npossemigroup.mma @@ -30,13 +30,13 @@ The positive natural numbers form together with addition a subsemigroup of the semigroup of the natural numbers with addition. *) -inline procedural "cic:/CoRN/model/semigroups/Npossemigroup/Npos_as_CSemiGroup.con". +inline procedural "cic:/CoRN/model/semigroups/Npossemigroup/Npos_as_CSemiGroup.con" as definition. (*#* ***$\langle$#⟨#[Npos],[[*]]$\rangle$#⟩# Also together with multiplication, the positive numbers form a semigroup. *) -inline procedural "cic:/CoRN/model/semigroups/Npossemigroup/Nposmult_is_CSemiGroup.con". +inline procedural "cic:/CoRN/model/semigroups/Npossemigroup/Nposmult_is_CSemiGroup.con" as lemma. -inline procedural "cic:/CoRN/model/semigroups/Npossemigroup/Nposmult_as_CSemiGroup.con". +inline procedural "cic:/CoRN/model/semigroups/Npossemigroup/Nposmult_as_CSemiGroup.con" as definition. diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/semigroups/Nsemigroup.mma b/helm/software/matita/contribs/CoRN-Procedural/model/semigroups/Nsemigroup.mma index 781ea6306..cd2568ee5 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/semigroups/Nsemigroup.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/semigroups/Nsemigroup.mma @@ -28,5 +28,5 @@ include "algebra/CSemiGroups.ma". (*#* Because addition is associative, the natural numbers form a CSemiGroup. *) -inline procedural "cic:/CoRN/model/semigroups/Nsemigroup/nat_as_CSemiGroup.con". +inline procedural "cic:/CoRN/model/semigroups/Nsemigroup/nat_as_CSemiGroup.con" as definition. diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/semigroups/QSpossemigroup.mma b/helm/software/matita/contribs/CoRN-Procedural/model/semigroups/QSpossemigroup.mma index 6793e8fdd..3c445a4cf 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/semigroups/QSpossemigroup.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/semigroups/QSpossemigroup.mma @@ -27,5 +27,5 @@ The positive rationals form with the operation $(x,y) \mapsto xy/2$#(x,y) ↦ xy/2# a CSemiGroup. *) -inline procedural "cic:/CoRN/model/semigroups/QSpossemigroup/Qpos_multdiv2_as_CSemiGroup.con". +inline procedural "cic:/CoRN/model/semigroups/QSpossemigroup/Qpos_multdiv2_as_CSemiGroup.con" as definition. diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/semigroups/Qpossemigroup.mma b/helm/software/matita/contribs/CoRN-Procedural/model/semigroups/Qpossemigroup.mma index 313c498c2..c6910430a 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/semigroups/Qpossemigroup.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/semigroups/Qpossemigroup.mma @@ -26,5 +26,5 @@ include "algebra/CSemiGroups.ma". The positive rationals form with the multiplication a CSemiGroup. *) -inline procedural "cic:/CoRN/model/semigroups/Qpossemigroup/Qpos_mult_as_CSemiGroup.con". +inline procedural "cic:/CoRN/model/semigroups/Qpossemigroup/Qpos_mult_as_CSemiGroup.con" as definition. diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/semigroups/Qsemigroup.mma b/helm/software/matita/contribs/CoRN-Procedural/model/semigroups/Qsemigroup.mma index b449027ea..c52808095 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/semigroups/Qsemigroup.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/semigroups/Qsemigroup.mma @@ -26,10 +26,10 @@ include "algebra/CSemiGroups.ma". ***$\langle$#⟨#[Q],[[+]]$\rangle$#⟩# *) -inline procedural "cic:/CoRN/model/semigroups/Qsemigroup/Q_as_CSemiGroup.con". +inline procedural "cic:/CoRN/model/semigroups/Qsemigroup/Q_as_CSemiGroup.con" as definition. (*#* ***$\langle$#⟨#[Q],[[*]]$\rangle$#⟩# *) -inline procedural "cic:/CoRN/model/semigroups/Qsemigroup/Q_mul_as_CSemiGroup.con". +inline procedural "cic:/CoRN/model/semigroups/Qsemigroup/Q_mul_as_CSemiGroup.con" as definition. diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/semigroups/Zsemigroup.mma b/helm/software/matita/contribs/CoRN-Procedural/model/semigroups/Zsemigroup.mma index 191277b5f..2f29fc077 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/semigroups/Zsemigroup.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/semigroups/Zsemigroup.mma @@ -26,12 +26,12 @@ include "algebra/CSemiGroups.ma". ***$\langle$#⟨#[Z],[[+]]$\rangle$#⟩# *) -inline procedural "cic:/CoRN/model/semigroups/Zsemigroup/Z_as_CSemiGroup.con". +inline procedural "cic:/CoRN/model/semigroups/Zsemigroup/Z_as_CSemiGroup.con" as definition. (*#* The term [Z_as_CSemiGroup] is of type [CSemiGroup]. Hence we have proven that [Z] is a constructive semi-group. *) (*#* ***$\langle$#⟨#[Z],[[*]]$\rangle$#⟩# *) -inline procedural "cic:/CoRN/model/semigroups/Zsemigroup/Z_mul_as_CSemiGroup.con". +inline procedural "cic:/CoRN/model/semigroups/Zsemigroup/Z_mul_as_CSemiGroup.con" as definition. diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/setoids/Npossetoid.mma b/helm/software/matita/contribs/CoRN-Procedural/model/setoids/Npossetoid.mma index 4fa49cc5a..dda551fcf 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/setoids/Npossetoid.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/setoids/Npossetoid.mma @@ -31,38 +31,38 @@ The positive natural numbers [Npos] will be defined as a subsetoid of the natural numbers. *) -inline procedural "cic:/CoRN/model/setoids/Npossetoid/Npos.con". +inline procedural "cic:/CoRN/model/setoids/Npossetoid/Npos.con" as definition. -inline procedural "cic:/CoRN/model/setoids/Npossetoid/NposP.con". +inline procedural "cic:/CoRN/model/setoids/Npossetoid/NposP.con" as definition. (*#* One and two are elements of it. *) -inline procedural "cic:/CoRN/model/setoids/Npossetoid/ONEpos.con". +inline procedural "cic:/CoRN/model/setoids/Npossetoid/ONEpos.con" as definition. -inline procedural "cic:/CoRN/model/setoids/Npossetoid/TWOpos.con". +inline procedural "cic:/CoRN/model/setoids/Npossetoid/TWOpos.con" as definition. (*#* ***Addition and multiplication Because addition and multiplication preserve positivity, we can define them on this subsetoid. *) -inline procedural "cic:/CoRN/model/setoids/Npossetoid/plus_resp_Npos.con". +inline procedural "cic:/CoRN/model/setoids/Npossetoid/plus_resp_Npos.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Npossetoid/Npos_plus.con". +inline procedural "cic:/CoRN/model/setoids/Npossetoid/Npos_plus.con" as definition. -inline procedural "cic:/CoRN/model/setoids/Npossetoid/mult_resp_Npos.con". +inline procedural "cic:/CoRN/model/setoids/Npossetoid/mult_resp_Npos.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Npossetoid/Npos_mult.con". +inline procedural "cic:/CoRN/model/setoids/Npossetoid/Npos_mult.con" as definition. (*#* The addition has no right unit on this set. *) -inline procedural "cic:/CoRN/model/setoids/Npossetoid/no_rht_unit_Npos1.con". +inline procedural "cic:/CoRN/model/setoids/Npossetoid/no_rht_unit_Npos1.con" as lemma. (*#* And the multiplication doesn't have an inverse, because there can't be an inverse for 2. *) -inline procedural "cic:/CoRN/model/setoids/Npossetoid/no_inverse_Nposmult1.con". +inline procedural "cic:/CoRN/model/setoids/Npossetoid/no_inverse_Nposmult1.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/setoids/Nsetoid.mma b/helm/software/matita/contribs/CoRN-Procedural/model/setoids/Nsetoid.mma index 036fc51f1..810847175 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/setoids/Nsetoid.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/setoids/Nsetoid.mma @@ -27,38 +27,38 @@ include "algebra/CSetoidFun.ma". We will show that the natural numbers form a CSetoid. *) -inline procedural "cic:/CoRN/model/setoids/Nsetoid/ap_nat_irreflexive.con". +inline procedural "cic:/CoRN/model/setoids/Nsetoid/ap_nat_irreflexive.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Nsetoid/ap_nat_symmetric.con". +inline procedural "cic:/CoRN/model/setoids/Nsetoid/ap_nat_symmetric.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Nsetoid/ap_nat_cotransitive.con". +inline procedural "cic:/CoRN/model/setoids/Nsetoid/ap_nat_cotransitive.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Nsetoid/ap_nat_tight.con". +inline procedural "cic:/CoRN/model/setoids/Nsetoid/ap_nat_tight.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Nsetoid/ap_nat_is_apartness.con". +inline procedural "cic:/CoRN/model/setoids/Nsetoid/ap_nat_is_apartness.con" as definition. -inline procedural "cic:/CoRN/model/setoids/Nsetoid/nat_as_CSetoid.con". +inline procedural "cic:/CoRN/model/setoids/Nsetoid/nat_as_CSetoid.con" as definition. (*#* ***Addition *) -inline procedural "cic:/CoRN/model/setoids/Nsetoid/plus_wd.con". +inline procedural "cic:/CoRN/model/setoids/Nsetoid/plus_wd.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Nsetoid/plus_strext.con". +inline procedural "cic:/CoRN/model/setoids/Nsetoid/plus_strext.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Nsetoid/plus_is_bin_fun.con". +inline procedural "cic:/CoRN/model/setoids/Nsetoid/plus_is_bin_fun.con" as definition. (*#* It is associative and commutative. *) -inline procedural "cic:/CoRN/model/setoids/Nsetoid/plus_is_assoc.con". +inline procedural "cic:/CoRN/model/setoids/Nsetoid/plus_is_assoc.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Nsetoid/plus_is_commut.con". +inline procedural "cic:/CoRN/model/setoids/Nsetoid/plus_is_commut.con" as lemma. (*#* ***Multiplication *) -inline procedural "cic:/CoRN/model/setoids/Nsetoid/mult_strext.con". +inline procedural "cic:/CoRN/model/setoids/Nsetoid/mult_strext.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Nsetoid/mult_as_bin_fun.con". +inline procedural "cic:/CoRN/model/setoids/Nsetoid/mult_as_bin_fun.con" as definition. diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/setoids/Qpossetoid.mma b/helm/software/matita/contribs/CoRN-Procedural/model/setoids/Qpossetoid.mma index 8e935b1d8..fb7426c78 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/setoids/Qpossetoid.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/setoids/Qpossetoid.mma @@ -30,18 +30,18 @@ We will examine the subsetoid of positive rationals of the setoid of rational numbers. *) -inline procedural "cic:/CoRN/model/setoids/Qpossetoid/Qpos.con". +inline procedural "cic:/CoRN/model/setoids/Qpossetoid/Qpos.con" as definition. -inline procedural "cic:/CoRN/model/setoids/Qpossetoid/QposP.con". +inline procedural "cic:/CoRN/model/setoids/Qpossetoid/QposP.con" as definition. (*#* One, two and four are elements of it. *) -inline procedural "cic:/CoRN/model/setoids/Qpossetoid/QONEpos.con". +inline procedural "cic:/CoRN/model/setoids/Qpossetoid/QONEpos.con" as definition. -inline procedural "cic:/CoRN/model/setoids/Qpossetoid/QTWOpos.con". +inline procedural "cic:/CoRN/model/setoids/Qpossetoid/QTWOpos.con" as definition. -inline procedural "cic:/CoRN/model/setoids/Qpossetoid/QFOURpos.con". +inline procedural "cic:/CoRN/model/setoids/Qpossetoid/QFOURpos.con" as definition. (*#* ***Multiplication As we have seen, multiplication preserves positivity, so we can restrict it @@ -49,49 +49,49 @@ As we have seen, multiplication preserves positivity, so we can restrict it nice properties. *) -inline procedural "cic:/CoRN/model/setoids/Qpossetoid/Qmult_pres_pos1.con". +inline procedural "cic:/CoRN/model/setoids/Qpossetoid/Qmult_pres_pos1.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Qpossetoid/Qpos_mult.con". +inline procedural "cic:/CoRN/model/setoids/Qpossetoid/Qpos_mult.con" as definition. -inline procedural "cic:/CoRN/model/setoids/Qpossetoid/associative_Qpos_mult.con". +inline procedural "cic:/CoRN/model/setoids/Qpossetoid/associative_Qpos_mult.con" as lemma. (*#* ***Inverse We restrict the domain of the inverse to the set of positive rationals. *) -inline procedural "cic:/CoRN/model/setoids/Qpossetoid/Qpos_inv.con". +inline procedural "cic:/CoRN/model/setoids/Qpossetoid/Qpos_inv.con" as definition. (*#* The restricted inverse preserves positivity. *) -inline procedural "cic:/CoRN/model/setoids/Qpossetoid/inv_pres_pos1.con". +inline procedural "cic:/CoRN/model/setoids/Qpossetoid/inv_pres_pos1.con" as lemma. (*#* Now, we can also restrict the co-domain. *) -inline procedural "cic:/CoRN/model/setoids/Qpossetoid/Qpos_Qpos_inv.con". +inline procedural "cic:/CoRN/model/setoids/Qpossetoid/Qpos_Qpos_inv.con" as definition. (*#* This restricted inverse map appears a setoid function. *) -inline procedural "cic:/CoRN/model/setoids/Qpossetoid/Qpos_Qpos_inv_strong_ext.con". +inline procedural "cic:/CoRN/model/setoids/Qpossetoid/Qpos_Qpos_inv_strong_ext.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Qpossetoid/Qpos_Qpos_inv_op.con". +inline procedural "cic:/CoRN/model/setoids/Qpossetoid/Qpos_Qpos_inv_op.con" as definition. (*#* ***Special multiplication and inverse We define [multdiv2]: $(x,y) \mapsto xy/2$ #(x,y) ↦ xy/2#. *) -inline procedural "cic:/CoRN/model/setoids/Qpossetoid/Qpos_div2.con". +inline procedural "cic:/CoRN/model/setoids/Qpossetoid/Qpos_div2.con" as definition. -inline procedural "cic:/CoRN/model/setoids/Qpossetoid/multdiv2.con". +inline procedural "cic:/CoRN/model/setoids/Qpossetoid/multdiv2.con" as definition. -inline procedural "cic:/CoRN/model/setoids/Qpossetoid/associative_multdiv2.con". +inline procedural "cic:/CoRN/model/setoids/Qpossetoid/associative_multdiv2.con" as lemma. (*#* And its inverse [multdiv4]: $x \mapsto 4/x$ #x ↦ 4/x#. *) -inline procedural "cic:/CoRN/model/setoids/Qpossetoid/mult4.con". +inline procedural "cic:/CoRN/model/setoids/Qpossetoid/mult4.con" as definition. -inline procedural "cic:/CoRN/model/setoids/Qpossetoid/divmult4.con". +inline procedural "cic:/CoRN/model/setoids/Qpossetoid/divmult4.con" as definition. diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/setoids/Qsetoid.mma b/helm/software/matita/contribs/CoRN-Procedural/model/setoids/Qsetoid.mma index 2fff7848c..4fa3c33fa 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/setoids/Qsetoid.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/setoids/Qsetoid.mma @@ -26,63 +26,63 @@ include "algebra/CSetoidFun.ma". ***Setoid *) -inline procedural "cic:/CoRN/model/setoids/Qsetoid/ap_Q_irreflexive1.con". +inline procedural "cic:/CoRN/model/setoids/Qsetoid/ap_Q_irreflexive1.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Qsetoid/ap_Q_symmetric1.con". +inline procedural "cic:/CoRN/model/setoids/Qsetoid/ap_Q_symmetric1.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Qsetoid/ap_Q_cotransitive1.con". +inline procedural "cic:/CoRN/model/setoids/Qsetoid/ap_Q_cotransitive1.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Qsetoid/ap_Q_tight1.con". +inline procedural "cic:/CoRN/model/setoids/Qsetoid/ap_Q_tight1.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Qsetoid/ap_Q_is_apartness.con". +inline procedural "cic:/CoRN/model/setoids/Qsetoid/ap_Q_is_apartness.con" as definition. -inline procedural "cic:/CoRN/model/setoids/Qsetoid/Q_as_CSetoid.con". +inline procedural "cic:/CoRN/model/setoids/Qsetoid/Q_as_CSetoid.con" as definition. (*#* ***Addition *) -inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qplus_wd.con". +inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qplus_wd.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qplus_strext1.con". +inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qplus_strext1.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qplus_is_bin_fun.con". +inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qplus_is_bin_fun.con" as definition. (*#* It is associative and commutative. *) -inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qplus_is_assoc.con". +inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qplus_is_assoc.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qplus_is_commut1.con". +inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qplus_is_commut1.con" as lemma. (*#* ***Opposite *) -inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qopp_wd.con". +inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qopp_wd.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qopp_strext.con". +inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qopp_strext.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qopp_is_fun.con". +inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qopp_is_fun.con" as definition. (*#* ***Multiplication *) -inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qmult_wd.con". +inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qmult_wd.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qmult_strext1.con". +inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qmult_strext1.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qmult_is_bin_fun.con". +inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qmult_is_bin_fun.con" as definition. (*#* It is associative and commutative. *) -inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qmult_is_assoc.con". +inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qmult_is_assoc.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qmult_is_commut.con". +inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qmult_is_commut.con" as lemma. (*#* ***Less-than *) -inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qlt_strext.con". +inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qlt_strext.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qlt_is_CSetoid_relation.con". +inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qlt_is_CSetoid_relation.con" as definition. diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/setoids/Zsetoid.mma b/helm/software/matita/contribs/CoRN-Procedural/model/setoids/Zsetoid.mma index 80a63ebb1..ea9b92b62 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/setoids/Zsetoid.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/setoids/Zsetoid.mma @@ -26,57 +26,57 @@ include "algebra/CSetoidFun.ma". *** [Z] *) -inline procedural "cic:/CoRN/model/setoids/Zsetoid/ap_Z_irreflexive.con". +inline procedural "cic:/CoRN/model/setoids/Zsetoid/ap_Z_irreflexive.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Zsetoid/ap_Z_symmetric.con". +inline procedural "cic:/CoRN/model/setoids/Zsetoid/ap_Z_symmetric.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Zsetoid/ap_Z_cotransitive.con". +inline procedural "cic:/CoRN/model/setoids/Zsetoid/ap_Z_cotransitive.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Zsetoid/ap_Z_tight.con". +inline procedural "cic:/CoRN/model/setoids/Zsetoid/ap_Z_tight.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Zsetoid/ap_Z_is_apartness.con". +inline procedural "cic:/CoRN/model/setoids/Zsetoid/ap_Z_is_apartness.con" as definition. -inline procedural "cic:/CoRN/model/setoids/Zsetoid/Z_as_CSetoid.con". +inline procedural "cic:/CoRN/model/setoids/Zsetoid/Z_as_CSetoid.con" as definition. (*#* The term [Z_as_CSetoid] is of type [CSetoid]. Hence we have proven that [Z] is a constructive setoid. ***Addition We will prove now that the addition on the integers is a setoid function. *) -inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zplus_wd.con". +inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zplus_wd.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zplus_strext.con". +inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zplus_strext.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zplus_is_bin_fun.con". +inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zplus_is_bin_fun.con" as definition. (*#* What's more: the addition is also associative and commutative. *) -inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zplus_is_assoc.con". +inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zplus_is_assoc.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zplus_is_commut.con". +inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zplus_is_commut.con" as lemma. (*#* ***Opposite Taking the opposite of an integer is a setoid function. *) -inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zopp_wd.con". +inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zopp_wd.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zopp_strext.con". +inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zopp_strext.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zopp_is_fun.con". +inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zopp_is_fun.con" as definition. (*#* ***Multiplication Finally the multiplication is a setoid function and is associative and commutative. *) -inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zmult_wd.con". +inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zmult_wd.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zmult_strext.con". +inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zmult_strext.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zmult_is_bin_fun.con". +inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zmult_is_bin_fun.con" as definition. -inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zmult_is_assoc.con". +inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zmult_is_assoc.con" as lemma. -inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zmult_is_commut.con". +inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zmult_is_commut.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/structures/Npossec.mma b/helm/software/matita/contribs/CoRN-Procedural/model/structures/Npossec.mma index 1a8d0c005..7e292a42d 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/structures/Npossec.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/structures/Npossec.mma @@ -27,9 +27,9 @@ The positive natural numbers have some nice properties. Addition as well as multiplication preserve the feature of being positive. *) -inline procedural "cic:/CoRN/model/structures/Npossec/plus_resp_Npos0.con". +inline procedural "cic:/CoRN/model/structures/Npossec/plus_resp_Npos0.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Npossec/Npos_is_suc.con". +inline procedural "cic:/CoRN/model/structures/Npossec/Npos_is_suc.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Npossec/mult_resp_Npos0.con". +inline procedural "cic:/CoRN/model/structures/Npossec/mult_resp_Npos0.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/structures/Nsec.mma b/helm/software/matita/contribs/CoRN-Procedural/model/structures/Nsec.mma index 65c1bf6a9..a4e44cede 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/structures/Nsec.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/structures/Nsec.mma @@ -30,37 +30,37 @@ We prove some basic lemmas of the natural numbers. A variant of [0_S] from the standard library *) -inline procedural "cic:/CoRN/model/structures/Nsec/S_O.con". +inline procedural "cic:/CoRN/model/structures/Nsec/S_O.con" as lemma. (*#* ***Apartness *) -inline procedural "cic:/CoRN/model/structures/Nsec/ap_nat.con". +inline procedural "cic:/CoRN/model/structures/Nsec/ap_nat.con" as definition. (* NOTATION Infix "{#N}" := ap_nat (no associativity, at level 90). *) -inline procedural "cic:/CoRN/model/structures/Nsec/ap_nat_irreflexive0.con". +inline procedural "cic:/CoRN/model/structures/Nsec/ap_nat_irreflexive0.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Nsec/ap_nat_symmetric0.con". +inline procedural "cic:/CoRN/model/structures/Nsec/ap_nat_symmetric0.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Nsec/ap_nat_cotransitive0.con". +inline procedural "cic:/CoRN/model/structures/Nsec/ap_nat_cotransitive0.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Nsec/ap_nat_tight0.con". +inline procedural "cic:/CoRN/model/structures/Nsec/ap_nat_tight0.con" as lemma. (*#* ***Addition *) -inline procedural "cic:/CoRN/model/structures/Nsec/plus_strext0.con". +inline procedural "cic:/CoRN/model/structures/Nsec/plus_strext0.con" as lemma. (*#* There is no inverse for addition, because every candidate will fail for 2 *) -inline procedural "cic:/CoRN/model/structures/Nsec/no_inverse0.con". +inline procedural "cic:/CoRN/model/structures/Nsec/no_inverse0.con" as lemma. (*#* ***Multiplication *) -inline procedural "cic:/CoRN/model/structures/Nsec/mult_strext0.con". +inline procedural "cic:/CoRN/model/structures/Nsec/mult_strext0.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/structures/Qpossec.mma b/helm/software/matita/contribs/CoRN-Procedural/model/structures/Qpossec.mma index 946c0b922..81d7c1c41 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/structures/Qpossec.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/structures/Qpossec.mma @@ -31,28 +31,28 @@ We will prove some lemmas concerning rationals bigger than 0. One, two and four are all bigger than zero. *) -inline procedural "cic:/CoRN/model/structures/Qpossec/pos_QONE.con". +inline procedural "cic:/CoRN/model/structures/Qpossec/pos_QONE.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Qpossec/pos_QTWO.con". +inline procedural "cic:/CoRN/model/structures/Qpossec/pos_QTWO.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Qpossec/pos_QFOUR.con". +inline procedural "cic:/CoRN/model/structures/Qpossec/pos_QFOUR.con" as lemma. (*#* A positive rational is not zero. *) -inline procedural "cic:/CoRN/model/structures/Qpossec/pos_imp_nonzero.con". +inline procedural "cic:/CoRN/model/structures/Qpossec/pos_imp_nonzero.con" as definition. (*#* ***Multiplication The product of two positive rationals is again positive. *) -inline procedural "cic:/CoRN/model/structures/Qpossec/Qmult_pres_pos0.con". +inline procedural "cic:/CoRN/model/structures/Qpossec/Qmult_pres_pos0.con" as lemma. (*#* ***Inverse The inverse of a positive rational is again positive. *) -inline procedural "cic:/CoRN/model/structures/Qpossec/inv_pres_pos0.con". +inline procedural "cic:/CoRN/model/structures/Qpossec/inv_pres_pos0.con" as lemma. (*#* ***Special multiplication Now we will investigate the function $(x,y) \mapsto xy/2$#(x,y) @@ -60,9 +60,9 @@ Now we will investigate the function $(x,y) \mapsto xy/2$#(x,y) \mapsto 4/x$ #x ↦ 4/x#. *) -inline procedural "cic:/CoRN/model/structures/Qpossec/QTWOpos_is_rht_unit0.con". +inline procedural "cic:/CoRN/model/structures/Qpossec/QTWOpos_is_rht_unit0.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Qpossec/QTWOpos_is_left_unit0.con". +inline procedural "cic:/CoRN/model/structures/Qpossec/QTWOpos_is_left_unit0.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Qpossec/multdiv2_is_inv.con". +inline procedural "cic:/CoRN/model/structures/Qpossec/multdiv2_is_inv.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/structures/Qsec.mma b/helm/software/matita/contribs/CoRN-Procedural/model/structures/Qsec.mma index 2a023a171..396411708 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/structures/Qsec.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/structures/Qsec.mma @@ -50,23 +50,23 @@ Section Q inline procedural "cic:/CoRN/model/structures/Qsec/Q.ind". -inline procedural "cic:/CoRN/model/structures/Qsec/Qeq.con". +inline procedural "cic:/CoRN/model/structures/Qsec/Qeq.con" as definition. -inline procedural "cic:/CoRN/model/structures/Qsec/Qap.con". +inline procedural "cic:/CoRN/model/structures/Qsec/Qap.con" as definition. -inline procedural "cic:/CoRN/model/structures/Qsec/Qlt.con". +inline procedural "cic:/CoRN/model/structures/Qsec/Qlt.con" as definition. -inline procedural "cic:/CoRN/model/structures/Qsec/Qplus.con". +inline procedural "cic:/CoRN/model/structures/Qsec/Qplus.con" as definition. -inline procedural "cic:/CoRN/model/structures/Qsec/Qmult.con". +inline procedural "cic:/CoRN/model/structures/Qsec/Qmult.con" as definition. -inline procedural "cic:/CoRN/model/structures/Qsec/Qopp.con". +inline procedural "cic:/CoRN/model/structures/Qsec/Qopp.con" as definition. -inline procedural "cic:/CoRN/model/structures/Qsec/QZERO.con". +inline procedural "cic:/CoRN/model/structures/Qsec/QZERO.con" as definition. -inline procedural "cic:/CoRN/model/structures/Qsec/QONE.con". +inline procedural "cic:/CoRN/model/structures/Qsec/QONE.con" as definition. -inline procedural "cic:/CoRN/model/structures/Qsec/Qinv.con". +inline procedural "cic:/CoRN/model/structures/Qsec/Qinv.con" as definition. (* UNEXPORTED End Q @@ -99,168 +99,168 @@ Notation "{-Q}" := Qopp (at level 1, left associativity). (*#* ***Constants *) -inline procedural "cic:/CoRN/model/structures/Qsec/QTWO.con". +inline procedural "cic:/CoRN/model/structures/Qsec/QTWO.con" as definition. -inline procedural "cic:/CoRN/model/structures/Qsec/QFOUR.con". +inline procedural "cic:/CoRN/model/structures/Qsec/QFOUR.con" as definition. (*#* ***Equality Here we prove that [QONE] is ##%\emph{%not equal%}%## to [QZERO]: *) -inline procedural "cic:/CoRN/model/structures/Qsec/ONEQ_neq_ZEROQ.con". +inline procedural "cic:/CoRN/model/structures/Qsec/ONEQ_neq_ZEROQ.con" as theorem. -inline procedural "cic:/CoRN/model/structures/Qsec/refl_Qeq.con". +inline procedural "cic:/CoRN/model/structures/Qsec/refl_Qeq.con" as theorem. -inline procedural "cic:/CoRN/model/structures/Qsec/sym_Qeq.con". +inline procedural "cic:/CoRN/model/structures/Qsec/sym_Qeq.con" as theorem. -inline procedural "cic:/CoRN/model/structures/Qsec/trans_Qeq.con". +inline procedural "cic:/CoRN/model/structures/Qsec/trans_Qeq.con" as theorem. (*#* The equality is decidable: *) -inline procedural "cic:/CoRN/model/structures/Qsec/dec_Qeq.con". +inline procedural "cic:/CoRN/model/structures/Qsec/dec_Qeq.con" as theorem. (*#* ***Apartness *) -inline procedural "cic:/CoRN/model/structures/Qsec/Q_non_zero.con". +inline procedural "cic:/CoRN/model/structures/Qsec/Q_non_zero.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Qsec/ap_Q_irreflexive0.con". +inline procedural "cic:/CoRN/model/structures/Qsec/ap_Q_irreflexive0.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Qsec/ap_Q_symmetric0.con". +inline procedural "cic:/CoRN/model/structures/Qsec/ap_Q_symmetric0.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Qsec/ap_Q_cotransitive0.con". +inline procedural "cic:/CoRN/model/structures/Qsec/ap_Q_cotransitive0.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Qsec/ap_Q_tight0.con". +inline procedural "cic:/CoRN/model/structures/Qsec/ap_Q_tight0.con" as lemma. (*#* ***Addition *) -inline procedural "cic:/CoRN/model/structures/Qsec/Qplus_simpl.con". +inline procedural "cic:/CoRN/model/structures/Qsec/Qplus_simpl.con" as theorem. (*#* Addition is associative: *) -inline procedural "cic:/CoRN/model/structures/Qsec/Qplus_assoc.con". +inline procedural "cic:/CoRN/model/structures/Qsec/Qplus_assoc.con" as theorem. (*#* [QZERO] as the neutral element for addition: *) -inline procedural "cic:/CoRN/model/structures/Qsec/QZERO_right.con". +inline procedural "cic:/CoRN/model/structures/Qsec/QZERO_right.con" as theorem. (*#* Commutativity of addition: *) -inline procedural "cic:/CoRN/model/structures/Qsec/Qplus_sym.con". +inline procedural "cic:/CoRN/model/structures/Qsec/Qplus_sym.con" as theorem. -inline procedural "cic:/CoRN/model/structures/Qsec/Qplus_strext0.con". +inline procedural "cic:/CoRN/model/structures/Qsec/Qplus_strext0.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Qsec/ZEROQ_as_rht_unit0.con". +inline procedural "cic:/CoRN/model/structures/Qsec/ZEROQ_as_rht_unit0.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Qsec/ZEROQ_as_lft_unit0.con". +inline procedural "cic:/CoRN/model/structures/Qsec/ZEROQ_as_lft_unit0.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Qsec/Qplus_is_commut0.con". +inline procedural "cic:/CoRN/model/structures/Qsec/Qplus_is_commut0.con" as lemma. (*#* ***Opposite [{-Q}] is a well defined unary operation: *) -inline procedural "cic:/CoRN/model/structures/Qsec/Qopp_simpl.con". +inline procedural "cic:/CoRN/model/structures/Qsec/Qopp_simpl.con" as lemma. (*#* The group equation for [{-Q}] *) -inline procedural "cic:/CoRN/model/structures/Qsec/Qplus_inverse_r.con". +inline procedural "cic:/CoRN/model/structures/Qsec/Qplus_inverse_r.con" as theorem. (*#* ***Multiplication Next we shall prove the properties of multiplication. First we prove that [{*Q}] is well-defined *) -inline procedural "cic:/CoRN/model/structures/Qsec/Qmult_simpl.con". +inline procedural "cic:/CoRN/model/structures/Qsec/Qmult_simpl.con" as theorem. (*#* and it is associative: *) -inline procedural "cic:/CoRN/model/structures/Qsec/Qmult_assoc.con". +inline procedural "cic:/CoRN/model/structures/Qsec/Qmult_assoc.con" as theorem. (*#* [QONE] is the neutral element for multiplication: *) -inline procedural "cic:/CoRN/model/structures/Qsec/Qmult_n_1.con". +inline procedural "cic:/CoRN/model/structures/Qsec/Qmult_n_1.con" as theorem. (*#* The commutativity for [{*Q}]: *) -inline procedural "cic:/CoRN/model/structures/Qsec/Qmult_sym.con". +inline procedural "cic:/CoRN/model/structures/Qsec/Qmult_sym.con" as theorem. -inline procedural "cic:/CoRN/model/structures/Qsec/Qmult_plus_distr_r.con". +inline procedural "cic:/CoRN/model/structures/Qsec/Qmult_plus_distr_r.con" as theorem. (*#* And a property of multiplication which says if [x [~=] Zero] and [xy [=] Zero] then [y [=] Zero]: *) -inline procedural "cic:/CoRN/model/structures/Qsec/Qmult_eq.con". +inline procedural "cic:/CoRN/model/structures/Qsec/Qmult_eq.con" as theorem. -inline procedural "cic:/CoRN/model/structures/Qsec/Qmult_strext0.con". +inline procedural "cic:/CoRN/model/structures/Qsec/Qmult_strext0.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Qsec/nonZero.con". +inline procedural "cic:/CoRN/model/structures/Qsec/nonZero.con" as lemma. (*#* ***Inverse *) -inline procedural "cic:/CoRN/model/structures/Qsec/Qinv_strext.con". +inline procedural "cic:/CoRN/model/structures/Qsec/Qinv_strext.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Qsec/Qinv_is_inv.con". +inline procedural "cic:/CoRN/model/structures/Qsec/Qinv_is_inv.con" as lemma. (*#* ***Less-than *) -inline procedural "cic:/CoRN/model/structures/Qsec/Qlt_wd_right.con". +inline procedural "cic:/CoRN/model/structures/Qsec/Qlt_wd_right.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Qsec/Qlt_wd_left.con". +inline procedural "cic:/CoRN/model/structures/Qsec/Qlt_wd_left.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Qsec/Qlt_eq_gt_dec.con". +inline procedural "cic:/CoRN/model/structures/Qsec/Qlt_eq_gt_dec.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Qsec/Qlt_is_transitive_unfolded.con". +inline procedural "cic:/CoRN/model/structures/Qsec/Qlt_is_transitive_unfolded.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Qsec/Qlt_strext_unfolded.con". +inline procedural "cic:/CoRN/model/structures/Qsec/Qlt_strext_unfolded.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Qsec/Qlt_is_irreflexive_unfolded.con". +inline procedural "cic:/CoRN/model/structures/Qsec/Qlt_is_irreflexive_unfolded.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Qsec/Qlt_is_antisymmetric_unfolded.con". +inline procedural "cic:/CoRN/model/structures/Qsec/Qlt_is_antisymmetric_unfolded.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Qsec/Qplus_resp_Qlt.con". +inline procedural "cic:/CoRN/model/structures/Qsec/Qplus_resp_Qlt.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Qsec/Qmult_resp_pos_Qlt.con". +inline procedural "cic:/CoRN/model/structures/Qsec/Qmult_resp_pos_Qlt.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Qsec/Qlt_gives_apartness.con". +inline procedural "cic:/CoRN/model/structures/Qsec/Qlt_gives_apartness.con" as lemma. (*#* ***Miscellaneous We consider the injection [inject_Z] from [Z] to [Q] as a coercion. *) -inline procedural "cic:/CoRN/model/structures/Qsec/inject_Z.con". +inline procedural "cic:/CoRN/model/structures/Qsec/inject_Z.con" as definition. (* COERCION cic:/matita/CoRN-Procedural/model/structures/Qsec/inject_Z.con *) -inline procedural "cic:/CoRN/model/structures/Qsec/injz_plus.con". +inline procedural "cic:/CoRN/model/structures/Qsec/injz_plus.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Qsec/injZ_One.con". +inline procedural "cic:/CoRN/model/structures/Qsec/injZ_One.con" as lemma. (*#* We can always find a natural number that is bigger than a given rational number. *) -inline procedural "cic:/CoRN/model/structures/Qsec/Q_is_archemaedian0.con". +inline procedural "cic:/CoRN/model/structures/Qsec/Q_is_archemaedian0.con" as theorem. diff --git a/helm/software/matita/contribs/CoRN-Procedural/model/structures/Zsec.mma b/helm/software/matita/contribs/CoRN-Procedural/model/structures/Zsec.mma index 9b8781aa7..b30c4c846 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/model/structures/Zsec.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/model/structures/Zsec.mma @@ -31,7 +31,7 @@ datatype [Z] as defined in [ZArith], in the standard library). We define the apartness as the negation of the Leibniz equality: *) -inline procedural "cic:/CoRN/model/structures/Zsec/ap_Z.con". +inline procedural "cic:/CoRN/model/structures/Zsec/ap_Z.con" as definition. (* NOTATION Infix "{#Z}" := ap_Z (no associativity, at level 90). @@ -40,35 +40,35 @@ Infix "{#Z}" := ap_Z (no associativity, at level 90). (*#* Some properties of apartness: *) -inline procedural "cic:/CoRN/model/structures/Zsec/ap_Z_irreflexive0.con". +inline procedural "cic:/CoRN/model/structures/Zsec/ap_Z_irreflexive0.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Zsec/ap_Z_symmetric0.con". +inline procedural "cic:/CoRN/model/structures/Zsec/ap_Z_symmetric0.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Zsec/ap_Z_cotransitive0.con". +inline procedural "cic:/CoRN/model/structures/Zsec/ap_Z_cotransitive0.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Zsec/ap_Z_tight0.con". +inline procedural "cic:/CoRN/model/structures/Zsec/ap_Z_tight0.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Zsec/ONE_neq_O.con". +inline procedural "cic:/CoRN/model/structures/Zsec/ONE_neq_O.con" as lemma. (*#* ***Addition Some properties of the addition. [Zplus] is also defined in the standard library. *) -inline procedural "cic:/CoRN/model/structures/Zsec/Zplus_wd0.con". +inline procedural "cic:/CoRN/model/structures/Zsec/Zplus_wd0.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Zsec/Zplus_strext0.con". +inline procedural "cic:/CoRN/model/structures/Zsec/Zplus_strext0.con" as lemma. (*#* ***Multiplication The multiplication is extensional: *) -inline procedural "cic:/CoRN/model/structures/Zsec/Zmult_strext0.con". +inline procedural "cic:/CoRN/model/structures/Zsec/Zmult_strext0.con" as lemma. (*#* ***Miscellaneous *) -inline procedural "cic:/CoRN/model/structures/Zsec/Zpos.con". +inline procedural "cic:/CoRN/model/structures/Zsec/Zpos.con" as definition. (* begin hide *) @@ -78,23 +78,23 @@ cic:/Coq/ZArith/BinInt/Z.ind#xpointer(1/1/2) (* end hide *) -inline procedural "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma1.con". +inline procedural "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma1.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma2.con". +inline procedural "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma2.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma3.con". +inline procedural "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma3.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma4.con". +inline procedural "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma4.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma5.con". +inline procedural "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma5.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Zsec/Zpos_pos.con". +inline procedural "cic:/CoRN/model/structures/Zsec/Zpos_pos.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Zsec/Zpos_neg.con". +inline procedural "cic:/CoRN/model/structures/Zsec/Zpos_neg.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Zsec/Zpos_Zsgn.con". +inline procedural "cic:/CoRN/model/structures/Zsec/Zpos_Zsgn.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Zsec/Zpos_Zsgn2.con". +inline procedural "cic:/CoRN/model/structures/Zsec/Zpos_Zsgn2.con" as lemma. -inline procedural "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma5'.con". +inline procedural "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma5'.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/reals/Bridges_LUB.mma b/helm/software/matita/contribs/CoRN-Procedural/reals/Bridges_LUB.mma index 8d4a78b64..70a82cab6 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/Bridges_LUB.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/Bridges_LUB.mma @@ -52,29 +52,29 @@ alias id "OF" = "cic:/CoRN/reals/Bridges_LUB/LUBP/lub_definitions/OF.var". alias id "SS" = "cic:/CoRN/reals/Bridges_LUB/LUBP/lub_definitions/SS.var". -inline procedural "cic:/CoRN/reals/Bridges_LUB/member.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/member.con" as definition. -inline procedural "cic:/CoRN/reals/Bridges_LUB/Pmember.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/Pmember.con" as definition. -inline procedural "cic:/CoRN/reals/Bridges_LUB/is_upper_bound.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/is_upper_bound.con" as definition. -inline procedural "cic:/CoRN/reals/Bridges_LUB/l_u_b.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/l_u_b.con" as definition. -inline procedural "cic:/CoRN/reals/Bridges_LUB/supremum.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/supremum.con" as definition. -inline procedural "cic:/CoRN/reals/Bridges_LUB/Psupremum.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/Psupremum.con" as definition. (* the following definitions are not used in *) (* this file but later we will need them *) -inline procedural "cic:/CoRN/reals/Bridges_LUB/is_lower_bound.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/is_lower_bound.con" as definition. -inline procedural "cic:/CoRN/reals/Bridges_LUB/g_l_b.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/g_l_b.con" as definition. -inline procedural "cic:/CoRN/reals/Bridges_LUB/infimum.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/infimum.con" as definition. -inline procedural "cic:/CoRN/reals/Bridges_LUB/Pinfimum.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/Pinfimum.con" as definition. (* UNEXPORTED End lub_definitions @@ -94,117 +94,117 @@ alias id "bounded_above" = "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequenc alias id "located" = "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/located.var". -inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/s.con" "LUBP__upper_bound_sequence__". +inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/s.con" "LUBP__upper_bound_sequence__" as definition. -inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/Ps.con" "LUBP__upper_bound_sequence__". +inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/Ps.con" "LUBP__upper_bound_sequence__" as definition. -inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/b0.con" "LUBP__upper_bound_sequence__". +inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/b0.con" "LUBP__upper_bound_sequence__" as definition. -inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/Pb0.con" "LUBP__upper_bound_sequence__". +inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/Pb0.con" "LUBP__upper_bound_sequence__" as definition. -inline procedural "cic:/CoRN/reals/Bridges_LUB/b0_is_upper_bound.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/b0_is_upper_bound.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_LUB/s_inhabits_A.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/s_inhabits_A.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/dstart_l.con" "LUBP__upper_bound_sequence__". +inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/dstart_l.con" "LUBP__upper_bound_sequence__" as definition. -inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/dstart_r.con" "LUBP__upper_bound_sequence__". +inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/dstart_r.con" "LUBP__upper_bound_sequence__" as definition. -inline procedural "cic:/CoRN/reals/Bridges_LUB/dl_less_dr.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/dl_less_dr.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_LUB/shrink23d.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/shrink23d.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_LUB/shrink13d.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/shrink13d.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_LUB/shrink24d.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/shrink24d.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_LUB/Real_Interval.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/Real_Interval.con" as definition. -inline procedural "cic:/CoRN/reals/Bridges_LUB/dcotrans_analyze.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/dcotrans_analyze.con" as definition. -inline procedural "cic:/CoRN/reals/Bridges_LUB/dcotrans_analyze_strong.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/dcotrans_analyze_strong.con" as lemma. (* NOTATION Notation "( p , q )" := (pairT p q). *) -inline procedural "cic:/CoRN/reals/Bridges_LUB/dif_cotrans.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/dif_cotrans.con" as definition. -inline procedural "cic:/CoRN/reals/Bridges_LUB/dif_cotrans_strong.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/dif_cotrans_strong.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_LUB/dIntrvl.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/dIntrvl.con" as definition. -inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/U.con" "LUBP__upper_bound_sequence__". +inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/U.con" "LUBP__upper_bound_sequence__" as definition. -inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/V.con" "LUBP__upper_bound_sequence__". +inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/V.con" "LUBP__upper_bound_sequence__" as definition. -inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/W.con" "LUBP__upper_bound_sequence__". +inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/W.con" "LUBP__upper_bound_sequence__" as definition. -inline procedural "cic:/CoRN/reals/Bridges_LUB/delta_dIntrvl.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/delta_dIntrvl.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_LUB/Length_dIntrvl.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/Length_dIntrvl.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_LUB/dIntrvl_inside_l_n.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/dIntrvl_inside_l_n.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_LUB/dIntrvl_inside_r_n.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/dIntrvl_inside_r_n.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_LUB/V_increase.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/V_increase.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_LUB/W_decrease.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/W_decrease.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_LUB/U_m_n_V.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/U_m_n_V.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_LUB/U_m_n_W.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/U_m_n_W.con" as lemma. (* These lemma are *very* similar to those in *) (* Cauchy_rationals_approach_reals.v *) -inline procedural "cic:/CoRN/reals/Bridges_LUB/a_familiar_simple_inequality.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/a_familiar_simple_inequality.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_LUB/U_conversion_rate2.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/U_conversion_rate2.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_LUB/CS_seq_U.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/CS_seq_U.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_LUB/U_as_CauchySeq.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/U_as_CauchySeq.con" as definition. -inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/B.con" "LUBP__upper_bound_sequence__". +inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/B.con" "LUBP__upper_bound_sequence__" as definition. -inline procedural "cic:/CoRN/reals/Bridges_LUB/U_minus_V.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/U_minus_V.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_LUB/U_minus_W.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/U_minus_W.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_LUB/U_V_upper.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/U_V_upper.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_LUB/U_W_lower.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/U_W_lower.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_LUB/AbsSmall_U_V.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/AbsSmall_U_V.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_LUB/AbsSmall_U_W.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/AbsSmall_U_W.con" as lemma. (* Two properties of exponentiation in COrdFields *) -inline procedural "cic:/CoRN/reals/Bridges_LUB/nexp_resp_great_One.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/nexp_resp_great_One.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_LUB/very_weak_binomial.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/very_weak_binomial.con" as lemma. (* A consequence of Archimedean property - *) (* the every basis of definition of e=lim(1+1/n)^n *) -inline procedural "cic:/CoRN/reals/Bridges_LUB/nexp_resp_Two.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/nexp_resp_Two.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_LUB/twisted_archimedean.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/twisted_archimedean.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_LUB/B_limit_V.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/B_limit_V.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_LUB/B_limit_W.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/B_limit_W.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_LUB/W_n_is_upper.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/W_n_is_upper.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_LUB/A_bounds_V_n.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/A_bounds_V_n.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_LUB/cauchy_gives_lub.con". +inline procedural "cic:/CoRN/reals/Bridges_LUB/cauchy_gives_lub.con" as theorem. (* UNEXPORTED End upper_bound_sequence diff --git a/helm/software/matita/contribs/CoRN-Procedural/reals/Bridges_iso.mma b/helm/software/matita/contribs/CoRN-Procedural/reals/Bridges_iso.mma index 91c34862b..38020510b 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/Bridges_iso.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/Bridges_iso.mma @@ -36,7 +36,7 @@ include "reals/Bridges_LUB.ma". (* This lemma comes from lemmas.v of Martijn Oostdijk *) -inline procedural "cic:/CoRN/reals/Bridges_iso/le_witness_informative.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/le_witness_informative.con" as lemma. (* UNEXPORTED Section bridges_axioms_imply_ours @@ -48,15 +48,15 @@ alias id "lubp" = "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/lubp.va alias id "is_Archimedes" = "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/is_Archimedes.var". -inline procedural "cic:/CoRN/reals/Bridges_iso/is_Archimedes'.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/is_Archimedes'.con" as lemma. (* UNEXPORTED Section proofs_in_TCS *) -inline procedural "cic:/CoRN/reals/Bridges_iso/leEq_geEq.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/leEq_geEq.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_iso/glbp.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/glbp.con" as theorem. (* UNEXPORTED Section supremum @@ -64,55 +64,55 @@ Section supremum alias id "P" = "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/supremum/P.var". -inline procedural "cic:/CoRN/reals/Bridges_iso/inequality1.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/inequality1.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_iso/inequality2.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/inequality2.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_iso/inequality3.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/inequality3.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_iso/inequality4.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/inequality4.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_iso/Hum.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/Hum.con" as definition. -inline procedural "cic:/CoRN/reals/Bridges_iso/bound_tk1.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/bound_tk1.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_iso/bound_tk2.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/bound_tk2.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_iso/trick.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/trick.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_iso/trick'.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/trick'.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_iso/up_bound_for_n_element.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/up_bound_for_n_element.con" as theorem. -inline procedural "cic:/CoRN/reals/Bridges_iso/low_bound_for_n_element.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/low_bound_for_n_element.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_iso/saghf.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/saghf.con" as definition. -inline procedural "cic:/CoRN/reals/Bridges_iso/Psaghf.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/Psaghf.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_iso/kaf.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/kaf.con" as definition. -inline procedural "cic:/CoRN/reals/Bridges_iso/Pkaf.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/Pkaf.con" as lemma. alias id "is_finite_P" = "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/supremum/is_finite_P.var". -inline procedural "cic:/CoRN/reals/Bridges_iso/card.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/card.con" as definition. -inline procedural "cic:/CoRN/reals/Bridges_iso/Pcard1.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/Pcard1.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_iso/seq.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/seq.con" as definition. -inline procedural "cic:/CoRN/reals/Bridges_iso/Pseq1.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/Pseq1.con" as definition. -inline procedural "cic:/CoRN/reals/Bridges_iso/Pseq1_unfolded.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/Pseq1_unfolded.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_iso/indeks.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/indeks.con" as definition. -inline procedural "cic:/CoRN/reals/Bridges_iso/Pindeks.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/Pindeks.con" as lemma. alias id "is_onto_seq_P" = "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/supremum/is_onto_seq_P.var". -inline procedural "cic:/CoRN/reals/Bridges_iso/P_is_inhabited.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/P_is_inhabited.con" as lemma. (* Lemma bounded_quantifier:(N:nat;phi,psi:nat->Prop) @@ -183,13 +183,13 @@ Proof. Qed. *) -inline procedural "cic:/CoRN/reals/Bridges_iso/bounded_quantifier_informative.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/bounded_quantifier_informative.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_lemma1a.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_lemma1a.con" as lemma. alias id "P_is_strongly_extensional" = "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/supremum/P_is_strongly_extensional.var". -inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_lemma1b.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_lemma1b.con" as lemma. (* UNEXPORTED End supremum @@ -207,55 +207,55 @@ End supremum Section Every_Cauchy_Sequence_is_bounded *) -inline procedural "cic:/CoRN/reals/Bridges_iso/seq2set.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/seq2set.con" as definition. alias id "g" = "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/Every_Cauchy_Sequence_is_bounded/g.var". -inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/Every_Cauchy_Sequence_is_bounded/g_.con" "bridges_axioms_imply_ours__proofs_in_TCS__Every_Cauchy_Sequence_is_bounded__". +inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/Every_Cauchy_Sequence_is_bounded/g_.con" "bridges_axioms_imply_ours__proofs_in_TCS__Every_Cauchy_Sequence_is_bounded__" as definition. -inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/Every_Cauchy_Sequence_is_bounded/pg.con" "bridges_axioms_imply_ours__proofs_in_TCS__Every_Cauchy_Sequence_is_bounded__". +inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/Every_Cauchy_Sequence_is_bounded/pg.con" "bridges_axioms_imply_ours__proofs_in_TCS__Every_Cauchy_Sequence_is_bounded__" as definition. -inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/Every_Cauchy_Sequence_is_bounded/P.con" "bridges_axioms_imply_ours__proofs_in_TCS__Every_Cauchy_Sequence_is_bounded__". +inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/Every_Cauchy_Sequence_is_bounded/P.con" "bridges_axioms_imply_ours__proofs_in_TCS__Every_Cauchy_Sequence_is_bounded__" as definition. -inline procedural "cic:/CoRN/reals/Bridges_iso/fin_is_fin.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/fin_is_fin.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_iso/card_fin.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/card_fin.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_iso/finite_seq.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/finite_seq.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_lemma2a.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_lemma2a.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_iso/sup.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/sup.con" as definition. -inline procedural "cic:/CoRN/reals/Bridges_iso/Psup.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/Psup.con" as definition. -inline procedural "cic:/CoRN/reals/Bridges_iso/Psup_proj1.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/Psup_proj1.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_iso/Psup_unfolded1.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/Psup_unfolded1.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_iso/Psup_unfolded2.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/Psup_unfolded2.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_lemma2b.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_lemma2b.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_iso/inf.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/inf.con" as definition. -inline procedural "cic:/CoRN/reals/Bridges_iso/Pinf.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/Pinf.con" as definition. -inline procedural "cic:/CoRN/reals/Bridges_iso/Pinf_proj1.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/Pinf_proj1.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_iso/Pinf_unfolded1.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/Pinf_unfolded1.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_iso/Pinf_unfolded2.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/Pinf_unfolded2.con" as lemma. (* I tried very much not to mention this lemma! *) -inline procedural "cic:/CoRN/reals/Bridges_iso/sup_leEq.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/sup_leEq.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_iso/inf_geEq.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/inf_geEq.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_iso/tail_is_Cauchy.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/tail_is_Cauchy.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_iso/tail_seq.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/tail_seq.con" as definition. (* UNEXPORTED End Every_Cauchy_Sequence_is_bounded @@ -263,41 +263,41 @@ End Every_Cauchy_Sequence_is_bounded alias id "g" = "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/g.var". -inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/g_.con" "bridges_axioms_imply_ours__proofs_in_TCS__". +inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/g_.con" "bridges_axioms_imply_ours__proofs_in_TCS__" as definition. -inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/pg.con" "bridges_axioms_imply_ours__proofs_in_TCS__". +inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/pg.con" "bridges_axioms_imply_ours__proofs_in_TCS__" as definition. -inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/sup_tail.con" "bridges_axioms_imply_ours__proofs_in_TCS__". +inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/sup_tail.con" "bridges_axioms_imply_ours__proofs_in_TCS__" as definition. -inline procedural "cic:/CoRN/reals/Bridges_iso/sup_tail_leEq.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/sup_tail_leEq.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_iso/sup_tail_is_Cauchy.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/sup_tail_is_Cauchy.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_iso/sup_tail_as_Cauchy.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/sup_tail_as_Cauchy.con" as definition. -inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/L.con" "bridges_axioms_imply_ours__proofs_in_TCS__". +inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/L.con" "bridges_axioms_imply_ours__proofs_in_TCS__" as definition. -inline procedural "cic:/CoRN/reals/Bridges_iso/sup_tail_decrease.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/sup_tail_decrease.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_iso/L_less_sup_n.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/L_less_sup_n.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_iso/Psup_unfolded2_informative.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/Psup_unfolded2_informative.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_iso/Pinf_unfolded2_informative.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/Pinf_unfolded2_informative.con" as lemma. -inline procedural "cic:/CoRN/reals/Bridges_iso/convergent_subseq.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/convergent_subseq.con" as lemma. (* very elegant proof almost as short as text version! *) -inline procedural "cic:/CoRN/reals/Bridges_iso/lubp_gives_Cauchy.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/lubp_gives_Cauchy.con" as theorem. (* UNEXPORTED End proofs_in_TCS *) -inline procedural "cic:/CoRN/reals/Bridges_iso/Bridges_R_is_CReals.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/Bridges_R_is_CReals.con" as definition. -inline procedural "cic:/CoRN/reals/Bridges_iso/Bridges_R_as_CReals.con". +inline procedural "cic:/CoRN/reals/Bridges_iso/Bridges_R_as_CReals.con" as definition. (* UNEXPORTED End bridges_axioms_imply_ours diff --git a/helm/software/matita/contribs/CoRN-Procedural/reals/CMetricFields.mma b/helm/software/matita/contribs/CoRN-Procedural/reals/CMetricFields.mma index fa6e91b19..db365edae 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/CMetricFields.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/CMetricFields.mma @@ -46,11 +46,11 @@ Notation MAbs := (cmf_abs _). Section basics *) -inline procedural "cic:/CoRN/reals/CMetricFields/MAbs_one.con". +inline procedural "cic:/CoRN/reals/CMetricFields/MAbs_one.con" as lemma. -inline procedural "cic:/CoRN/reals/CMetricFields/Hulp.con". +inline procedural "cic:/CoRN/reals/CMetricFields/Hulp.con" as lemma. -inline procedural "cic:/CoRN/reals/CMetricFields/MAbs_one_recip_one.con". +inline procedural "cic:/CoRN/reals/CMetricFields/MAbs_one_recip_one.con" as lemma. (* end hide *) @@ -69,7 +69,7 @@ alias id "F" = "cic:/CoRN/reals/CMetricFields/CMetric_Field_Cauchy/F.var". %\end{convention}% *) -inline procedural "cic:/CoRN/reals/CMetricFields/MCauchy_prop.con". +inline procedural "cic:/CoRN/reals/CMetricFields/MCauchy_prop.con" as definition. inline procedural "cic:/CoRN/reals/CMetricFields/MCauchySeq.ind". @@ -77,9 +77,9 @@ inline procedural "cic:/CoRN/reals/CMetricFields/MCauchySeq.ind". cic:/matita/CoRN-Procedural/reals/CMetricFields/MCS_seq.con *) -inline procedural "cic:/CoRN/reals/CMetricFields/MseqLimit.con". +inline procedural "cic:/CoRN/reals/CMetricFields/MseqLimit.con" as definition. -inline procedural "cic:/CoRN/reals/CMetricFields/is_MCauchyCompl.con". +inline procedural "cic:/CoRN/reals/CMetricFields/is_MCauchyCompl.con" as definition. (* UNEXPORTED End CMetric_Field_Cauchy diff --git a/helm/software/matita/contribs/CoRN-Procedural/reals/CPoly_Contin.mma b/helm/software/matita/contribs/CoRN-Procedural/reals/CPoly_Contin.mma index 6987ae255..a9e6c784e 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/CPoly_Contin.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/CPoly_Contin.mma @@ -22,11 +22,11 @@ include "CoRN.ma". include "reals/RealFuncts.ma". -inline procedural "cic:/CoRN/reals/CPoly_Contin/plus_op_contin.con". +inline procedural "cic:/CoRN/reals/CPoly_Contin/plus_op_contin.con" as lemma. -inline procedural "cic:/CoRN/reals/CPoly_Contin/mult_op_contin.con". +inline procedural "cic:/CoRN/reals/CPoly_Contin/mult_op_contin.con" as lemma. -inline procedural "cic:/CoRN/reals/CPoly_Contin/linear_op_contin.con". +inline procedural "cic:/CoRN/reals/CPoly_Contin/linear_op_contin.con" as lemma. -inline procedural "cic:/CoRN/reals/CPoly_Contin/cpoly_op_contin.con". +inline procedural "cic:/CoRN/reals/CPoly_Contin/cpoly_op_contin.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/reals/CReals.mma b/helm/software/matita/contribs/CoRN-Procedural/reals/CReals.mma index 036a64173..724ff895a 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/CReals.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/CReals.mma @@ -43,7 +43,7 @@ cic:/matita/CoRN-Procedural/reals/CReals/crl_crr.con (* End_SpecReals *) -inline procedural "cic:/CoRN/reals/CReals/Lim.con". +inline procedural "cic:/CoRN/reals/CReals/Lim.con" as definition. (* UNEXPORTED Implicit Arguments Lim [IR]. diff --git a/helm/software/matita/contribs/CoRN-Procedural/reals/CReals1.mma b/helm/software/matita/contribs/CoRN-Procedural/reals/CReals1.mma index 3b345408d..d3157702c 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/CReals1.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/CReals1.mma @@ -36,20 +36,20 @@ more useful properties about them. The sequence defined by $x_n=\frac2{n+1}$#x(n)=2/(n+1)#. *) -inline procedural "cic:/CoRN/reals/CReals1/twice_inv_seq_Lim.con". +inline procedural "cic:/CoRN/reals/CReals1/twice_inv_seq_Lim.con" as lemma. -inline procedural "cic:/CoRN/reals/CReals1/twice_inv_seq.con". +inline procedural "cic:/CoRN/reals/CReals1/twice_inv_seq.con" as definition. (*#* Next, we prove that the sequence of absolute values of a Cauchy sequence is also Cauchy. *) -inline procedural "cic:/CoRN/reals/CReals1/Cauchy_Lim_abs.con". +inline procedural "cic:/CoRN/reals/CReals1/Cauchy_Lim_abs.con" as lemma. -inline procedural "cic:/CoRN/reals/CReals1/Cauchy_abs.con". +inline procedural "cic:/CoRN/reals/CReals1/Cauchy_abs.con" as lemma. -inline procedural "cic:/CoRN/reals/CReals1/Lim_abs.con". +inline procedural "cic:/CoRN/reals/CReals1/Lim_abs.con" as lemma. (* UNEXPORTED End More_Cauchy_Props @@ -89,21 +89,21 @@ alias id "subseq" = "cic:/CoRN/reals/CReals1/Subsequences/subseq.var". alias id "mon_seq2" = "cic:/CoRN/reals/CReals1/Subsequences/mon_seq2.var". -inline procedural "cic:/CoRN/reals/CReals1/unbnd_f.con". +inline procedural "cic:/CoRN/reals/CReals1/unbnd_f.con" as lemma. (* begin hide *) -inline procedural "cic:/CoRN/reals/CReals1/Subsequences/mon_F'.con" "Subsequences__". +inline procedural "cic:/CoRN/reals/CReals1/Subsequences/mon_F'.con" "Subsequences__" as definition. (* end hide *) -inline procedural "cic:/CoRN/reals/CReals1/conv_subseq_imp_conv_seq.con". +inline procedural "cic:/CoRN/reals/CReals1/conv_subseq_imp_conv_seq.con" as lemma. -inline procedural "cic:/CoRN/reals/CReals1/Cprop2_seq_imp_Cprop2_subseq.con". +inline procedural "cic:/CoRN/reals/CReals1/Cprop2_seq_imp_Cprop2_subseq.con" as lemma. -inline procedural "cic:/CoRN/reals/CReals1/conv_seq_imp_conv_subseq.con". +inline procedural "cic:/CoRN/reals/CReals1/conv_seq_imp_conv_subseq.con" as lemma. -inline procedural "cic:/CoRN/reals/CReals1/Cprop2_subseq_imp_Cprop2_seq.con". +inline procedural "cic:/CoRN/reals/CReals1/Cprop2_subseq_imp_Cprop2_seq.con" as lemma. (* UNEXPORTED End Subsequences @@ -127,9 +127,9 @@ alias id "subseq" = "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/subseq.var". alias id "mon_seq2" = "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/mon_seq2.var". -inline procedural "cic:/CoRN/reals/CReals1/Lim_seq_eq_Lim_subseq.con". +inline procedural "cic:/CoRN/reals/CReals1/Lim_seq_eq_Lim_subseq.con" as lemma. -inline procedural "cic:/CoRN/reals/CReals1/Lim_subseq_eq_Lim_seq.con". +inline procedural "cic:/CoRN/reals/CReals1/Lim_subseq_eq_Lim_seq.con" as lemma. (* UNEXPORTED End Cauchy_Subsequences @@ -144,13 +144,13 @@ Section Properties_of_Exponentiation Finally, we prove that [x[^]n] grows to infinity if [x [>] One]. *) -inline procedural "cic:/CoRN/reals/CReals1/power_big'.con". +inline procedural "cic:/CoRN/reals/CReals1/power_big'.con" as lemma. -inline procedural "cic:/CoRN/reals/CReals1/power_big.con". +inline procedural "cic:/CoRN/reals/CReals1/power_big.con" as lemma. -inline procedural "cic:/CoRN/reals/CReals1/qi_yields_zero.con". +inline procedural "cic:/CoRN/reals/CReals1/qi_yields_zero.con" as lemma. -inline procedural "cic:/CoRN/reals/CReals1/qi_lim_zero.con". +inline procedural "cic:/CoRN/reals/CReals1/qi_lim_zero.con" as lemma. (* UNEXPORTED End Properties_of_Exponentiation @@ -158,9 +158,9 @@ End Properties_of_Exponentiation (*#* *** [IR] has characteristic zero *) -inline procedural "cic:/CoRN/reals/CReals1/char0_IR.con". +inline procedural "cic:/CoRN/reals/CReals1/char0_IR.con" as lemma. -inline procedural "cic:/CoRN/reals/CReals1/poly_apzero_IR.con". +inline procedural "cic:/CoRN/reals/CReals1/poly_apzero_IR.con" as lemma. -inline procedural "cic:/CoRN/reals/CReals1/poly_IR_extensional.con". +inline procedural "cic:/CoRN/reals/CReals1/poly_IR_extensional.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/reals/CSumsReals.mma b/helm/software/matita/contribs/CoRN-Procedural/reals/CSumsReals.mma index ba22c080f..32313cff8 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/CSumsReals.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/CSumsReals.mma @@ -36,13 +36,13 @@ Section Sums_over_Reals alias id "c" = "cic:/CoRN/reals/CSumsReals/Sums_over_Reals/c.var". -inline procedural "cic:/CoRN/reals/CSumsReals/Sum0_c_exp.con". +inline procedural "cic:/CoRN/reals/CSumsReals/Sum0_c_exp.con" as lemma. (* UNEXPORTED Hint Resolve Sum0_c_exp. *) -inline procedural "cic:/CoRN/reals/CSumsReals/Sum_c_exp.con". +inline procedural "cic:/CoRN/reals/CSumsReals/Sum_c_exp.con" as lemma. (* UNEXPORTED Hint Resolve Sum_c_exp. @@ -50,7 +50,7 @@ Hint Resolve Sum_c_exp. (*#* The following formulation is often more useful if [c [<] 1]. *) -inline procedural "cic:/CoRN/reals/CSumsReals/Sum_c_exp'.con". +inline procedural "cic:/CoRN/reals/CSumsReals/Sum_c_exp'.con" as lemma. (* UNEXPORTED Hint Resolve Sum_c_exp'. @@ -64,29 +64,29 @@ End Sums_over_Reals Hint Resolve Sum0_c_exp Sum_c_exp Sum_c_exp': algebra. *) -inline procedural "cic:/CoRN/reals/CSumsReals/diff_is_Sum0.con". +inline procedural "cic:/CoRN/reals/CSumsReals/diff_is_Sum0.con" as lemma. -inline procedural "cic:/CoRN/reals/CSumsReals/diff_is_sum.con". +inline procedural "cic:/CoRN/reals/CSumsReals/diff_is_sum.con" as lemma. -inline procedural "cic:/CoRN/reals/CSumsReals/Sum0_pres_less.con". +inline procedural "cic:/CoRN/reals/CSumsReals/Sum0_pres_less.con" as lemma. -inline procedural "cic:/CoRN/reals/CSumsReals/Sum_pres_less.con". +inline procedural "cic:/CoRN/reals/CSumsReals/Sum_pres_less.con" as lemma. -inline procedural "cic:/CoRN/reals/CSumsReals/Sum_pres_leEq.con". +inline procedural "cic:/CoRN/reals/CSumsReals/Sum_pres_leEq.con" as lemma. -inline procedural "cic:/CoRN/reals/CSumsReals/Sum0_comm_scal.con". +inline procedural "cic:/CoRN/reals/CSumsReals/Sum0_comm_scal.con" as lemma. (* UNEXPORTED Hint Resolve Sum0_comm_scal: algebra. *) -inline procedural "cic:/CoRN/reals/CSumsReals/Sum_comm_scal.con". +inline procedural "cic:/CoRN/reals/CSumsReals/Sum_comm_scal.con" as lemma. -inline procedural "cic:/CoRN/reals/CSumsReals/Sum0_comm_scal'.con". +inline procedural "cic:/CoRN/reals/CSumsReals/Sum0_comm_scal'.con" as lemma. -inline procedural "cic:/CoRN/reals/CSumsReals/Sum_comm_scal'.con". +inline procedural "cic:/CoRN/reals/CSumsReals/Sum_comm_scal'.con" as lemma. -inline procedural "cic:/CoRN/reals/CSumsReals/Sumx_comm_scal'.con". +inline procedural "cic:/CoRN/reals/CSumsReals/Sumx_comm_scal'.con" as lemma. -inline procedural "cic:/CoRN/reals/CSumsReals/Sum2_comm_scal'.con". +inline procedural "cic:/CoRN/reals/CSumsReals/Sum2_comm_scal'.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/reals/CauchySeq.mma b/helm/software/matita/contribs/CoRN-Procedural/reals/CauchySeq.mma index f6dbff62d..16e97d931 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/CauchySeq.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/CauchySeq.mma @@ -75,21 +75,21 @@ Section CReals_axioms (*#* ** [CReals] axioms *) -inline procedural "cic:/CoRN/reals/CauchySeq/CReals_is_CReals.con". +inline procedural "cic:/CoRN/reals/CauchySeq/CReals_is_CReals.con" as lemma. (*#* First properties which follow trivially from the axioms. *) -inline procedural "cic:/CoRN/reals/CauchySeq/Lim_Cauchy.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Lim_Cauchy.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/Archimedes.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Archimedes.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/Archimedes'.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Archimedes'.con" as lemma. (*#* A stronger version, which often comes in useful. *) -inline procedural "cic:/CoRN/reals/CauchySeq/str_Archimedes.con". +inline procedural "cic:/CoRN/reals/CauchySeq/str_Archimedes.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/CauchySeqR.con". +inline procedural "cic:/CoRN/reals/CauchySeq/CauchySeqR.con" as definition. (* UNEXPORTED End CReals_axioms @@ -152,19 +152,19 @@ and [[<=]] being a negative statement, this makes proofs sometimes easier and program extraction much more efficient. *) -inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop1.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop1.con" as definition. -inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop2.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop2.con" as definition. -inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop2.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop2.con" as definition. -inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop3.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop3.con" as definition. -inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop3.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop3.con" as definition. -inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop4.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop4.con" as definition. -inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop4.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop4.con" as definition. (* UNEXPORTED End Cauchy_Defs @@ -178,39 +178,39 @@ Section Inequalities The next lemma is equal to lemma [Lim_Cauchy]. *) -inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_complete.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_complete.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/less_Lim_so_less_seq.con". +inline procedural "cic:/CoRN/reals/CauchySeq/less_Lim_so_less_seq.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/Lim_less_so_seq_less.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Lim_less_so_seq_less.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/Lim_less_Lim_so_seq_less_seq.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Lim_less_Lim_so_seq_less_seq.con" as lemma. (*#* The next lemma follows from [less_Lim_so_less_seq] with [y := (y[+] (Lim seq)) [/]TwoNZ]. *) -inline procedural "cic:/CoRN/reals/CauchySeq/less_Lim_so.con". +inline procedural "cic:/CoRN/reals/CauchySeq/less_Lim_so.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/Lim_less_so.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Lim_less_so.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/leEq_seq_so_leEq_Lim.con". +inline procedural "cic:/CoRN/reals/CauchySeq/leEq_seq_so_leEq_Lim.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/str_leEq_seq_so_leEq_Lim.con". +inline procedural "cic:/CoRN/reals/CauchySeq/str_leEq_seq_so_leEq_Lim.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/Lim_leEq_Lim.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Lim_leEq_Lim.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/seq_leEq_so_Lim_leEq.con". +inline procedural "cic:/CoRN/reals/CauchySeq/seq_leEq_so_Lim_leEq.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/str_seq_leEq_so_Lim_leEq.con". +inline procedural "cic:/CoRN/reals/CauchySeq/str_seq_leEq_so_Lim_leEq.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/Limits_unique.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Limits_unique.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/Lim_wd.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Lim_wd.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/Lim_strext.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Lim_strext.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/Lim_ap_imp_seq_ap.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Lim_ap_imp_seq_ap.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/Lim_ap_imp_seq_ap'.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Lim_ap_imp_seq_ap'.con" as lemma. (* UNEXPORTED End Inequalities @@ -222,47 +222,47 @@ Section Equiv_Cauchy (*#* *** Equivalence of formulations of Cauchy *) -inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop1_prop.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop1_prop.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop2_prop.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop2_prop.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop3_prop2.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop3_prop2.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop3_prop2.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop3_prop2.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop3_prop.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop3_prop.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/Build_CauchySeq1.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Build_CauchySeq1.con" as definition. -inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop4_prop3.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop4_prop3.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop4_prop2.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop4_prop2.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop4_prop3.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop4_prop3.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop4_prop.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop4_prop.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/Build_CauchySeq4.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Build_CauchySeq4.con" as definition. -inline procedural "cic:/CoRN/reals/CauchySeq/Build_CauchySeq4_y.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Build_CauchySeq4_y.con" as definition. -inline procedural "cic:/CoRN/reals/CauchySeq/Lim_CauchySeq4.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Lim_CauchySeq4.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/Build_CauchySeq2.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Build_CauchySeq2.con" as definition. -inline procedural "cic:/CoRN/reals/CauchySeq/Build_CauchySeq2_y.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Build_CauchySeq2_y.con" as definition. -inline procedural "cic:/CoRN/reals/CauchySeq/Lim_CauchySeq2.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Lim_CauchySeq2.con" as lemma. (*#* Well definedness. *) -inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop_wd.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop_wd.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop2_wd.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop2_wd.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/Lim_wd'.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Lim_wd'.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/Lim_unique.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Lim_unique.con" as lemma. (* UNEXPORTED End Equiv_Cauchy @@ -279,33 +279,33 @@ Some of these lemmas are now obsolete, because they were reproved for arbitrary We begin by defining the constant sequence and proving that it is Cauchy with the expected limit. *) -inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_const.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_const.con" as definition. -inline procedural "cic:/CoRN/reals/CauchySeq/Lim_const.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Lim_const.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_plus.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_plus.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_plus.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_plus.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/Lim_plus.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Lim_plus.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_inv.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_inv.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_inv.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_inv.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/Lim_inv.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Lim_inv.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_minus.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_minus.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_minus.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_minus.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/Lim_minus.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Lim_minus.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_mult.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_mult.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_mult.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_mult.con" as lemma. -inline procedural "cic:/CoRN/reals/CauchySeq/Lim_mult.con". +inline procedural "cic:/CoRN/reals/CauchySeq/Lim_mult.con" as lemma. (* UNEXPORTED End Cauchy_props diff --git a/helm/software/matita/contribs/CoRN-Procedural/reals/Cauchy_CReals.mma b/helm/software/matita/contribs/CoRN-Procedural/reals/Cauchy_CReals.mma index dcc8619f3..e26648950 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/Cauchy_CReals.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/Cauchy_CReals.mma @@ -44,53 +44,53 @@ alias id "F" = "cic:/CoRN/reals/Cauchy_CReals/R_CReals/F.var". Notation "'R_COrdField''" := (R_COrdField F). *) -inline procedural "cic:/CoRN/reals/Cauchy_CReals/inject_Q.con". +inline procedural "cic:/CoRN/reals/Cauchy_CReals/inject_Q.con" as definition. -inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_eq.con". +inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_eq.con" as lemma. -inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_plus.con". +inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_plus.con" as lemma. -inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_min.con". +inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_min.con" as lemma. -inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_lt.con". +inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_lt.con" as lemma. -inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_ap.con". +inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_ap.con" as lemma. -inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_cancel_eq.con". +inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_cancel_eq.con" as lemma. -inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_cancel_less.con". +inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_cancel_less.con" as lemma. -inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_le.con". +inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_le.con" as lemma. -inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_cancel_leEq.con". +inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_cancel_leEq.con" as lemma. -inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_cancel_AbsSmall.con". +inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_cancel_AbsSmall.con" as lemma. -inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_One.con". +inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_One.con" as lemma. -inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_nring'.con". +inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_nring'.con" as lemma. -inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_nring.con". +inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_nring.con" as lemma. -inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_mult.con". +inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_mult.con" as lemma. (* UNEXPORTED Opaque R_COrdField. *) -inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_div_three.con". +inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_div_three.con" as lemma. (* UNEXPORTED Transparent R_COrdField. *) -inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_n.con". +inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_n.con" as lemma. -inline procedural "cic:/CoRN/reals/Cauchy_CReals/expand_Q_R.con". +inline procedural "cic:/CoRN/reals/Cauchy_CReals/expand_Q_R.con" as theorem. -inline procedural "cic:/CoRN/reals/Cauchy_CReals/conv_modulus.con". +inline procedural "cic:/CoRN/reals/Cauchy_CReals/conv_modulus.con" as lemma. -inline procedural "cic:/CoRN/reals/Cauchy_CReals/R_CReals/T.con" "R_CReals__". +inline procedural "cic:/CoRN/reals/Cauchy_CReals/R_CReals/T.con" "R_CReals__" as definition. (*#* We now assume our original field is archimedean and prove that the resulting one is, too. @@ -98,35 +98,35 @@ resulting one is, too. alias id "F_is_archemaedian" = "cic:/CoRN/reals/Cauchy_CReals/R_CReals/F_is_archemaedian.var". -inline procedural "cic:/CoRN/reals/Cauchy_CReals/R_is_archemaedian.con". +inline procedural "cic:/CoRN/reals/Cauchy_CReals/R_is_archemaedian.con" as theorem. (* begin hide *) -inline procedural "cic:/CoRN/reals/Cauchy_CReals/R_CReals/PT.con" "R_CReals__". +inline procedural "cic:/CoRN/reals/Cauchy_CReals/R_CReals/PT.con" "R_CReals__" as definition. (* end hide *) -inline procedural "cic:/CoRN/reals/Cauchy_CReals/modulus_property.con". +inline procedural "cic:/CoRN/reals/Cauchy_CReals/modulus_property.con" as lemma. -inline procedural "cic:/CoRN/reals/Cauchy_CReals/modulus_property_2.con". +inline procedural "cic:/CoRN/reals/Cauchy_CReals/modulus_property_2.con" as lemma. -inline procedural "cic:/CoRN/reals/Cauchy_CReals/expand_Q_R_2.con". +inline procedural "cic:/CoRN/reals/Cauchy_CReals/expand_Q_R_2.con" as lemma. -inline procedural "cic:/CoRN/reals/Cauchy_CReals/CS_seq_diagonal.con". +inline procedural "cic:/CoRN/reals/Cauchy_CReals/CS_seq_diagonal.con" as lemma. (*#* ** Cauchy Completeness We can also define a limit operator. *) -inline procedural "cic:/CoRN/reals/Cauchy_CReals/Q_dense_in_R.con". +inline procedural "cic:/CoRN/reals/Cauchy_CReals/Q_dense_in_R.con" as lemma. -inline procedural "cic:/CoRN/reals/Cauchy_CReals/LimR_CauchySeq.con". +inline procedural "cic:/CoRN/reals/Cauchy_CReals/LimR_CauchySeq.con" as definition. -inline procedural "cic:/CoRN/reals/Cauchy_CReals/R_is_complete.con". +inline procedural "cic:/CoRN/reals/Cauchy_CReals/R_is_complete.con" as theorem. -inline procedural "cic:/CoRN/reals/Cauchy_CReals/R_is_CReals.con". +inline procedural "cic:/CoRN/reals/Cauchy_CReals/R_is_CReals.con" as definition. -inline procedural "cic:/CoRN/reals/Cauchy_CReals/R_as_CReals.con". +inline procedural "cic:/CoRN/reals/Cauchy_CReals/R_as_CReals.con" as definition. (* UNEXPORTED End R_CReals diff --git a/helm/software/matita/contribs/CoRN-Procedural/reals/IVT.mma b/helm/software/matita/contribs/CoRN-Procedural/reals/IVT.mma index 1281ce7ff..dba8d459c 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/IVT.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/IVT.mma @@ -49,21 +49,21 @@ alias id "a_b" = "cic:/CoRN/reals/IVT/Nested_Intervals/a_b.var". alias id "b_a" = "cic:/CoRN/reals/IVT/Nested_Intervals/b_a.var". -inline procedural "cic:/CoRN/reals/IVT/a_mon'.con". +inline procedural "cic:/CoRN/reals/IVT/a_mon'.con" as lemma. -inline procedural "cic:/CoRN/reals/IVT/b_mon'.con". +inline procedural "cic:/CoRN/reals/IVT/b_mon'.con" as lemma. -inline procedural "cic:/CoRN/reals/IVT/a_b'.con". +inline procedural "cic:/CoRN/reals/IVT/a_b'.con" as lemma. -inline procedural "cic:/CoRN/reals/IVT/intervals_cauchy.con". +inline procedural "cic:/CoRN/reals/IVT/intervals_cauchy.con" as lemma. (* begin hide *) -inline procedural "cic:/CoRN/reals/IVT/Nested_Intervals/a'.con" "Nested_Intervals__". +inline procedural "cic:/CoRN/reals/IVT/Nested_Intervals/a'.con" "Nested_Intervals__" as definition. (* end hide *) -inline procedural "cic:/CoRN/reals/IVT/Cnested_intervals_limit.con". +inline procedural "cic:/CoRN/reals/IVT/Cnested_intervals_limit.con" as lemma. (*#* %\begin{convention}% Let [f] be a continuous real function. %\end{convention}% @@ -73,9 +73,9 @@ alias id "f" = "cic:/CoRN/reals/IVT/Nested_Intervals/f.var". alias id "f_contin" = "cic:/CoRN/reals/IVT/Nested_Intervals/f_contin.var". -inline procedural "cic:/CoRN/reals/IVT/f_contin_pos.con". +inline procedural "cic:/CoRN/reals/IVT/f_contin_pos.con" as lemma. -inline procedural "cic:/CoRN/reals/IVT/f_contin_neg.con". +inline procedural "cic:/CoRN/reals/IVT/f_contin_neg.con" as lemma. (*#* Assume also that [forall i, f (a i) [<=] Zero [<=] f (b i)]. *) @@ -83,7 +83,7 @@ alias id "f_a" = "cic:/CoRN/reals/IVT/Nested_Intervals/f_a.var". alias id "f_b" = "cic:/CoRN/reals/IVT/Nested_Intervals/f_b.var". -inline procedural "cic:/CoRN/reals/IVT/Cnested_intervals_zero.con". +inline procedural "cic:/CoRN/reals/IVT/Cnested_intervals_zero.con" as lemma. (* UNEXPORTED End Nested_Intervals @@ -116,29 +116,29 @@ alias id "f_b" = "cic:/CoRN/reals/IVT/Bisection/f_b.var". (* begin hide *) -inline procedural "cic:/CoRN/reals/IVT/Bisection/Small.con" "Bisection__". +inline procedural "cic:/CoRN/reals/IVT/Bisection/Small.con" "Bisection__" as definition. -inline procedural "cic:/CoRN/reals/IVT/Bisection/lft.con" "Bisection__". +inline procedural "cic:/CoRN/reals/IVT/Bisection/lft.con" "Bisection__" as definition. -inline procedural "cic:/CoRN/reals/IVT/Bisection/rht.con" "Bisection__". +inline procedural "cic:/CoRN/reals/IVT/Bisection/rht.con" "Bisection__" as definition. (* end hide *) -inline procedural "cic:/CoRN/reals/IVT/a_lft.con". +inline procedural "cic:/CoRN/reals/IVT/a_lft.con" as lemma. -inline procedural "cic:/CoRN/reals/IVT/rht_b.con". +inline procedural "cic:/CoRN/reals/IVT/rht_b.con" as lemma. -inline procedural "cic:/CoRN/reals/IVT/lft_rht.con". +inline procedural "cic:/CoRN/reals/IVT/lft_rht.con" as lemma. -inline procedural "cic:/CoRN/reals/IVT/smaller_lft.con". +inline procedural "cic:/CoRN/reals/IVT/smaller_lft.con" as lemma. -inline procedural "cic:/CoRN/reals/IVT/smaller_rht.con". +inline procedural "cic:/CoRN/reals/IVT/smaller_rht.con" as lemma. (* UNEXPORTED Hint Resolve smaller_lft smaller_rht: algebra. *) -inline procedural "cic:/CoRN/reals/IVT/Cbisect'.con". +inline procedural "cic:/CoRN/reals/IVT/Cbisect'.con" as lemma. (* UNEXPORTED End Bisection @@ -154,17 +154,17 @@ alias id "C_f_apzero_interval" = "cic:/CoRN/reals/IVT/Bisect_Interval/C_f_apzero (* begin hide *) -inline procedural "cic:/CoRN/reals/IVT/Bisect_Interval/Small.con" "Bisect_Interval__". +inline procedural "cic:/CoRN/reals/IVT/Bisect_Interval/Small.con" "Bisect_Interval__" as definition. (* end hide *) inline procedural "cic:/CoRN/reals/IVT/bisect_interval.ind". -inline procedural "cic:/CoRN/reals/IVT/Cbisect_exists.con". +inline procedural "cic:/CoRN/reals/IVT/Cbisect_exists.con" as lemma. -inline procedural "cic:/CoRN/reals/IVT/bisect.con". +inline procedural "cic:/CoRN/reals/IVT/bisect.con" as definition. -inline procedural "cic:/CoRN/reals/IVT/bisect_prop.con". +inline procedural "cic:/CoRN/reals/IVT/bisect_prop.con" as lemma. (* UNEXPORTED End Bisect_Interval @@ -196,25 +196,25 @@ alias id "f_b" = "cic:/CoRN/reals/IVT/IVT_Op/f_b.var". (* begin hide *) -inline procedural "cic:/CoRN/reals/IVT/IVT_Op/Small.con" "IVT_Op__". +inline procedural "cic:/CoRN/reals/IVT/IVT_Op/Small.con" "IVT_Op__" as definition. (* end hide *) -inline procedural "cic:/CoRN/reals/IVT/interval_sequence.con". +inline procedural "cic:/CoRN/reals/IVT/interval_sequence.con" as definition. -inline procedural "cic:/CoRN/reals/IVT/IVT_Op/a_.con" "IVT_Op__". +inline procedural "cic:/CoRN/reals/IVT/IVT_Op/a_.con" "IVT_Op__" as definition. -inline procedural "cic:/CoRN/reals/IVT/IVT_Op/b_.con" "IVT_Op__". +inline procedural "cic:/CoRN/reals/IVT/IVT_Op/b_.con" "IVT_Op__" as definition. -inline procedural "cic:/CoRN/reals/IVT/intervals_smaller.con". +inline procedural "cic:/CoRN/reals/IVT/intervals_smaller.con" as lemma. -inline procedural "cic:/CoRN/reals/IVT/intervals_small''.con". +inline procedural "cic:/CoRN/reals/IVT/intervals_small''.con" as lemma. -inline procedural "cic:/CoRN/reals/IVT/intervals_small'.con". +inline procedural "cic:/CoRN/reals/IVT/intervals_small'.con" as lemma. -inline procedural "cic:/CoRN/reals/IVT/intervals_small.con". +inline procedural "cic:/CoRN/reals/IVT/intervals_small.con" as lemma. -inline procedural "cic:/CoRN/reals/IVT/Civt_op.con". +inline procedural "cic:/CoRN/reals/IVT/Civt_op.con" as lemma. (* UNEXPORTED End IVT_Op @@ -226,7 +226,7 @@ Section IVT_Poly (*#* ** IVT for polynomials *) -inline procedural "cic:/CoRN/reals/IVT/Civt_poly.con". +inline procedural "cic:/CoRN/reals/IVT/Civt_poly.con" as lemma. (* UNEXPORTED End IVT_Poly diff --git a/helm/software/matita/contribs/CoRN-Procedural/reals/Intervals.mma b/helm/software/matita/contribs/CoRN-Procedural/reals/Intervals.mma index e0eb61919..013391089 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/Intervals.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/Intervals.mma @@ -37,7 +37,7 @@ points less or equal than [b] and greater or equal than [a]. We require [a [<=] b], as we want to work only in nonempty intervals. *) -inline procedural "cic:/CoRN/reals/Intervals/compact.con". +inline procedural "cic:/CoRN/reals/Intervals/compact.con" as definition. (*#* %\begin{convention}% Let [a,b : IR] and [Hab : a [<=] b]. @@ -53,26 +53,26 @@ alias id "b" = "cic:/CoRN/reals/Intervals/Intervals/b.var". alias id "Hab" = "cic:/CoRN/reals/Intervals/Intervals/Hab.var". -inline procedural "cic:/CoRN/reals/Intervals/compact_inc_lft.con". +inline procedural "cic:/CoRN/reals/Intervals/compact_inc_lft.con" as lemma. -inline procedural "cic:/CoRN/reals/Intervals/compact_inc_rht.con". +inline procedural "cic:/CoRN/reals/Intervals/compact_inc_rht.con" as lemma. -inline procedural "cic:/CoRN/reals/Intervals/compact_Min_lft.con". +inline procedural "cic:/CoRN/reals/Intervals/compact_Min_lft.con" as lemma. -inline procedural "cic:/CoRN/reals/Intervals/compact_Min_rht.con". +inline procedural "cic:/CoRN/reals/Intervals/compact_Min_rht.con" as lemma. (*#* As we will be interested in taking functions with domain in a compact interval, we want this predicate to be well defined. *) -inline procedural "cic:/CoRN/reals/Intervals/compact_wd.con". +inline procedural "cic:/CoRN/reals/Intervals/compact_wd.con" as lemma. (*#* Also, it will sometimes be necessary to rewrite the endpoints of an interval. *) -inline procedural "cic:/CoRN/reals/Intervals/compact_wd'.con". +inline procedural "cic:/CoRN/reals/Intervals/compact_wd'.con" as lemma. (*#* As we identify subsets with predicates, inclusion is simply implication. @@ -84,7 +84,7 @@ and a well defined predicate [P] included in the domain of [F] and returns the restriction $F|_P$# of F to P#. *) -inline procedural "cic:/CoRN/reals/Intervals/Frestr.con". +inline procedural "cic:/CoRN/reals/Intervals/Frestr.con" as definition. (* UNEXPORTED End Intervals @@ -106,15 +106,15 @@ Notation FRestr := (Frestr (compact_wd _ _ _)). Section More_Intervals *) -inline procedural "cic:/CoRN/reals/Intervals/included_refl'.con". +inline procedural "cic:/CoRN/reals/Intervals/included_refl'.con" as lemma. (*#* We prove some inclusions of compact intervals. *) -inline procedural "cic:/CoRN/reals/Intervals/compact_map1.con". +inline procedural "cic:/CoRN/reals/Intervals/compact_map1.con" as definition. -inline procedural "cic:/CoRN/reals/Intervals/compact_map2.con". +inline procedural "cic:/CoRN/reals/Intervals/compact_map2.con" as definition. -inline procedural "cic:/CoRN/reals/Intervals/compact_map3.con". +inline procedural "cic:/CoRN/reals/Intervals/compact_map3.con" as definition. (* UNEXPORTED End More_Intervals @@ -141,7 +141,7 @@ to come. The definition (equivalent to the classical one) states that Notice the use of lists for quantification. *) -inline procedural "cic:/CoRN/reals/Intervals/totally_bounded.con". +inline procedural "cic:/CoRN/reals/Intervals/totally_bounded.con" as definition. (*#* This definition is classically, but not constructively, equivalent to @@ -151,28 +151,28 @@ that we take the definition of totally bounded to be the relevant one and that we defined compacts as we did. *) -inline procedural "cic:/CoRN/reals/Intervals/compact_is_totally_bounded.con". +inline procedural "cic:/CoRN/reals/Intervals/compact_is_totally_bounded.con" as lemma. (*#* Suprema and infima will be needed throughout; we define them here both for arbitrary subsets of [IR] and for images of functions. *) -inline procedural "cic:/CoRN/reals/Intervals/set_glb_IR.con". +inline procedural "cic:/CoRN/reals/Intervals/set_glb_IR.con" as definition. -inline procedural "cic:/CoRN/reals/Intervals/set_lub_IR.con". +inline procedural "cic:/CoRN/reals/Intervals/set_lub_IR.con" as definition. -inline procedural "cic:/CoRN/reals/Intervals/fun_image.con". +inline procedural "cic:/CoRN/reals/Intervals/fun_image.con" as definition. -inline procedural "cic:/CoRN/reals/Intervals/fun_glb_IR.con". +inline procedural "cic:/CoRN/reals/Intervals/fun_glb_IR.con" as definition. -inline procedural "cic:/CoRN/reals/Intervals/fun_lub_IR.con". +inline procedural "cic:/CoRN/reals/Intervals/fun_lub_IR.con" as definition. (* begin hide *) -inline procedural "cic:/CoRN/reals/Intervals/Totally_Bounded/aux_seq_lub.con" "Totally_Bounded__". +inline procedural "cic:/CoRN/reals/Intervals/Totally_Bounded/aux_seq_lub.con" "Totally_Bounded__" as definition. -inline procedural "cic:/CoRN/reals/Intervals/Totally_Bounded/aux_seq_lub_prop.con" "Totally_Bounded__". +inline procedural "cic:/CoRN/reals/Intervals/Totally_Bounded/aux_seq_lub_prop.con" "Totally_Bounded__" as definition. (* end hide *) @@ -180,17 +180,17 @@ inline procedural "cic:/CoRN/reals/Intervals/Totally_Bounded/aux_seq_lub_prop.co The following are probably the most important results in this section. *) -inline procedural "cic:/CoRN/reals/Intervals/totally_bounded_has_lub.con". +inline procedural "cic:/CoRN/reals/Intervals/totally_bounded_has_lub.con" as lemma. (* begin hide *) -inline procedural "cic:/CoRN/reals/Intervals/Totally_Bounded/aux_seq_glb.con" "Totally_Bounded__". +inline procedural "cic:/CoRN/reals/Intervals/Totally_Bounded/aux_seq_glb.con" "Totally_Bounded__" as definition. -inline procedural "cic:/CoRN/reals/Intervals/Totally_Bounded/aux_seq_glb_prop.con" "Totally_Bounded__". +inline procedural "cic:/CoRN/reals/Intervals/Totally_Bounded/aux_seq_glb_prop.con" "Totally_Bounded__" as definition. (* end hide *) -inline procedural "cic:/CoRN/reals/Intervals/totally_bounded_has_glb.con". +inline procedural "cic:/CoRN/reals/Intervals/totally_bounded_has_glb.con" as lemma. (* UNEXPORTED End Totally_Bounded @@ -208,7 +208,7 @@ and explore some of its properties. The following characterization of inclusion can be very useful: *) -inline procedural "cic:/CoRN/reals/Intervals/included_compact.con". +inline procedural "cic:/CoRN/reals/Intervals/included_compact.con" as lemma. (*#* At several points in our future development of a theory we will need @@ -233,7 +233,7 @@ alias id "Hab" = "cic:/CoRN/reals/Intervals/Compact/Hab.var". (* begin hide *) -inline procedural "cic:/CoRN/reals/Intervals/Compact/I.con" "Compact__". +inline procedural "cic:/CoRN/reals/Intervals/Compact/I.con" "Compact__" as definition. (* end hide *) @@ -247,11 +247,11 @@ alias id "He" = "cic:/CoRN/reals/Intervals/Compact/He.var". We start by finding a natural number [n] such that [(b[-]a) [/] n [<] e]. *) -inline procedural "cic:/CoRN/reals/Intervals/compact_nat.con". +inline procedural "cic:/CoRN/reals/Intervals/compact_nat.con" as definition. (*#* Obviously such an [n] must be greater than zero.*) -inline procedural "cic:/CoRN/reals/Intervals/pos_compact_nat.con". +inline procedural "cic:/CoRN/reals/Intervals/pos_compact_nat.con" as lemma. (*#* We now define a sequence on [n] points in [[a,b]] by @@ -259,25 +259,25 @@ We now define a sequence on [n] points in [[a,b]] by prove that all of its points are really in that interval. *) -inline procedural "cic:/CoRN/reals/Intervals/compact_part.con". +inline procedural "cic:/CoRN/reals/Intervals/compact_part.con" as definition. -inline procedural "cic:/CoRN/reals/Intervals/compact_part_hyp.con". +inline procedural "cic:/CoRN/reals/Intervals/compact_part_hyp.con" as lemma. (*#* This sequence is strictly increasing and each two consecutive points are apart by less than [e].*) -inline procedural "cic:/CoRN/reals/Intervals/compact_less.con". +inline procedural "cic:/CoRN/reals/Intervals/compact_less.con" as lemma. -inline procedural "cic:/CoRN/reals/Intervals/compact_leEq.con". +inline procedural "cic:/CoRN/reals/Intervals/compact_leEq.con" as lemma. (*#* When we proceed to integration, this lemma will also be useful: *) -inline procedural "cic:/CoRN/reals/Intervals/compact_partition_lemma.con". +inline procedural "cic:/CoRN/reals/Intervals/compact_partition_lemma.con" as lemma. (*#* The next lemma provides an upper bound for the distance between two points in an interval: *) -inline procedural "cic:/CoRN/reals/Intervals/compact_elements.con". +inline procedural "cic:/CoRN/reals/Intervals/compact_elements.con" as lemma. (* UNEXPORTED Opaque Min Max. @@ -285,21 +285,21 @@ Opaque Min Max. (*#* The following is a variation on the previous lemma: *) -inline procedural "cic:/CoRN/reals/Intervals/compact_elements'.con". +inline procedural "cic:/CoRN/reals/Intervals/compact_elements'.con" as lemma. (*#* The following lemma is a bit more specific: it shows that we can also estimate the distance from the center of a compact interval to any of its points. *) -inline procedural "cic:/CoRN/reals/Intervals/compact_bnd_AbsIR.con". +inline procedural "cic:/CoRN/reals/Intervals/compact_bnd_AbsIR.con" as lemma. (*#* Finally, two more useful lemmas to prove inclusion of compact intervals. They will be necessary for the definition and proof of the elementary properties of the integral. *) -inline procedural "cic:/CoRN/reals/Intervals/included2_compact.con". +inline procedural "cic:/CoRN/reals/Intervals/included2_compact.con" as lemma. -inline procedural "cic:/CoRN/reals/Intervals/included3_compact.con". +inline procedural "cic:/CoRN/reals/Intervals/included3_compact.con" as lemma. (* UNEXPORTED End Compact diff --git a/helm/software/matita/contribs/CoRN-Procedural/reals/Max_AbsIR.mma b/helm/software/matita/contribs/CoRN-Procedural/reals/Max_AbsIR.mma index c9d3e428c..788a265de 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/Max_AbsIR.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/Max_AbsIR.mma @@ -44,15 +44,15 @@ alias id "x" = "cic:/CoRN/reals/Max_AbsIR/Maximum/Max_function/x.var". alias id "y" = "cic:/CoRN/reals/Max_AbsIR/Maximum/Max_function/y.var". -inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_seq.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_seq.con" as definition. -inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_seq_char.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_seq_char.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/Cauchy_Max_seq.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/Cauchy_Max_seq.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_CauchySeq.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_CauchySeq.con" as definition. -inline procedural "cic:/CoRN/reals/Max_AbsIR/MAX.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/MAX.con" as definition. (*#* Constructively, the elementary properties of the maximum function are: @@ -68,19 +68,19 @@ With strong extensionality, we can make the binary operation [Max]. (So [Max] is [MAX] coupled with some proofs.) *) -inline procedural "cic:/CoRN/reals/Max_AbsIR/lft_leEq_MAX.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/lft_leEq_MAX.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/rht_leEq_MAX.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/rht_leEq_MAX.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/less_MAX_imp.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/less_MAX_imp.con" as lemma. (* UNEXPORTED End Max_function *) -inline procedural "cic:/CoRN/reals/Max_AbsIR/MAX_strext.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/MAX_strext.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/MAX_wd.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/MAX_wd.con" as lemma. (* UNEXPORTED Section properties_of_Max @@ -88,37 +88,37 @@ Section properties_of_Max (*#* *** Maximum *) -inline procedural "cic:/CoRN/reals/Max_AbsIR/Max.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/Max.con" as definition. -inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_wd_unfolded.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_wd_unfolded.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/lft_leEq_Max.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/lft_leEq_Max.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/rht_leEq_Max.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/rht_leEq_Max.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/less_Max_imp.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/less_Max_imp.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_leEq.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_leEq.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_less.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_less.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/equiv_imp_eq_max.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/equiv_imp_eq_max.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_id.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_id.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_comm.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_comm.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/leEq_imp_Max_is_rht.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/leEq_imp_Max_is_rht.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_is_rht_imp_leEq.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_is_rht_imp_leEq.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_minus_eps_leEq.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_minus_eps_leEq.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/max_one_ap_zero.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/max_one_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/pos_max_one.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/pos_max_one.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/x_div_Max_leEq_x.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/x_div_Max_leEq_x.con" as lemma. (* UNEXPORTED End properties_of_Max @@ -142,55 +142,55 @@ The minimum is defined by the formula [Min(x,y) [=] [--]Max( [--]x,[--]y)]. *) -inline procedural "cic:/CoRN/reals/Max_AbsIR/MIN.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/MIN.con" as definition. -inline procedural "cic:/CoRN/reals/Max_AbsIR/MIN_wd.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/MIN_wd.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/MIN_strext.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/MIN_strext.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/Min.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/Min.con" as definition. -inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_wd_unfolded.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_wd_unfolded.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_strext_unfolded.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_strext_unfolded.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_leEq_lft.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_leEq_lft.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_leEq_rht.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_leEq_rht.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_less_imp.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_less_imp.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/leEq_Min.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/leEq_Min.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/less_Min.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/less_Min.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/equiv_imp_eq_min.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/equiv_imp_eq_min.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_id.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_id.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_comm.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_comm.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/leEq_imp_Min_is_lft.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/leEq_imp_Min_is_lft.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_is_lft_imp_leEq.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_is_lft_imp_leEq.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/leEq_Min_plus_eps.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/leEq_Min_plus_eps.con" as lemma. alias id "a" = "cic:/CoRN/reals/Max_AbsIR/Minimum/a.var". alias id "b" = "cic:/CoRN/reals/Max_AbsIR/Minimum/b.var". -inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_leEq_Max.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_leEq_Max.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_leEq_Max'.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_leEq_Max'.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/Min3_leEq_Max3.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/Min3_leEq_Max3.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_less_Max.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_less_Max.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/ap_imp_Min_less_Max.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/ap_imp_Min_less_Max.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_less_Max_imp_ap.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_less_Max_imp_ap.con" as lemma. (* UNEXPORTED End Minimum @@ -206,67 +206,67 @@ Section Absolute (*#* *** Absolute value *) -inline procedural "cic:/CoRN/reals/Max_AbsIR/ABSIR.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/ABSIR.con" as definition. -inline procedural "cic:/CoRN/reals/Max_AbsIR/ABSIR_strext.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/ABSIR_strext.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/ABSIR_wd.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/ABSIR_wd.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR.con" as definition. -inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_wd.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_wd.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_wdl.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_wdl.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_wdr.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_wdr.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIRz_isz.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIRz_isz.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_nonneg.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_nonneg.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_pos.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_pos.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_cancel_ap_zero.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_cancel_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_resp_ap_zero.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_resp_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/leEq_AbsIR.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/leEq_AbsIR.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/inv_leEq_AbsIR.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/inv_leEq_AbsIR.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsSmall_e.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsSmall_e.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsSmall_imp_AbsIR.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsSmall_imp_AbsIR.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_eq_AbsSmall.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_eq_AbsSmall.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_imp_AbsSmall.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_imp_AbsSmall.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsSmall_transitive.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsSmall_transitive.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/zero_less_AbsIR_plus_one.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/zero_less_AbsIR_plus_one.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_inv.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_inv.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_minus.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_minus.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_eq_x.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_eq_x.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_eq_inv_x.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_eq_inv_x.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/less_AbsIR.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/less_AbsIR.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/leEq_distr_AbsIR.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/leEq_distr_AbsIR.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_approach_zero.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_approach_zero.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_eq_zero.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_eq_zero.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/Abs_Max.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/Abs_Max.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_str_bnd.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_str_bnd.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_bnd.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_bnd.con" as lemma. (* UNEXPORTED End Absolute @@ -295,15 +295,15 @@ alias id "G" = "cic:/CoRN/reals/Max_AbsIR/Part_Function_Max/G.var". (* begin hide *) -inline procedural "cic:/CoRN/reals/Max_AbsIR/Part_Function_Max/P.con" "Part_Function_Max__". +inline procedural "cic:/CoRN/reals/Max_AbsIR/Part_Function_Max/P.con" "Part_Function_Max__" as definition. -inline procedural "cic:/CoRN/reals/Max_AbsIR/Part_Function_Max/Q.con" "Part_Function_Max__". +inline procedural "cic:/CoRN/reals/Max_AbsIR/Part_Function_Max/Q.con" "Part_Function_Max__" as definition. (* end hide *) -inline procedural "cic:/CoRN/reals/Max_AbsIR/part_function_Max_strext.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/part_function_Max_strext.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/FMax.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/FMax.con" as definition. (* UNEXPORTED End Part_Function_Max @@ -319,27 +319,27 @@ alias id "G" = "cic:/CoRN/reals/Max_AbsIR/Part_Function_Abs/G.var". (* begin hide *) -inline procedural "cic:/CoRN/reals/Max_AbsIR/Part_Function_Abs/P.con" "Part_Function_Abs__". +inline procedural "cic:/CoRN/reals/Max_AbsIR/Part_Function_Abs/P.con" "Part_Function_Abs__" as definition. -inline procedural "cic:/CoRN/reals/Max_AbsIR/Part_Function_Abs/Q.con" "Part_Function_Abs__". +inline procedural "cic:/CoRN/reals/Max_AbsIR/Part_Function_Abs/Q.con" "Part_Function_Abs__" as definition. (* end hide *) -inline procedural "cic:/CoRN/reals/Max_AbsIR/FMin.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/FMin.con" as definition. -inline procedural "cic:/CoRN/reals/Max_AbsIR/FAbs.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/FAbs.con" as definition. (* UNEXPORTED Opaque Max. *) -inline procedural "cic:/CoRN/reals/Max_AbsIR/FMin_char.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/FMin_char.con" as lemma. (* UNEXPORTED Transparent Max. *) -inline procedural "cic:/CoRN/reals/Max_AbsIR/FAbs_char.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/FAbs_char.con" as lemma. (* UNEXPORTED End Part_Function_Abs @@ -349,9 +349,9 @@ End Part_Function_Abs Hint Resolve FAbs_char: algebra. *) -inline procedural "cic:/CoRN/reals/Max_AbsIR/FAbs_char'.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/FAbs_char'.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/FAbs_nonneg.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/FAbs_nonneg.con" as lemma. (* UNEXPORTED Hint Resolve FAbs_char': algebra. @@ -367,9 +367,9 @@ alias id "G" = "cic:/CoRN/reals/Max_AbsIR/Inclusion/G.var". (* begin hide *) -inline procedural "cic:/CoRN/reals/Max_AbsIR/Inclusion/P.con" "Inclusion__". +inline procedural "cic:/CoRN/reals/Max_AbsIR/Inclusion/P.con" "Inclusion__" as definition. -inline procedural "cic:/CoRN/reals/Max_AbsIR/Inclusion/Q.con" "Inclusion__". +inline procedural "cic:/CoRN/reals/Max_AbsIR/Inclusion/Q.con" "Inclusion__" as definition. (* end hide *) @@ -380,21 +380,21 @@ inline procedural "cic:/CoRN/reals/Max_AbsIR/Inclusion/Q.con" "Inclusion__". alias id "R" = "cic:/CoRN/reals/Max_AbsIR/Inclusion/R.var". -inline procedural "cic:/CoRN/reals/Max_AbsIR/included_FMax.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/included_FMax.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/included_FMax'.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/included_FMax'.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/included_FMax''.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/included_FMax''.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/included_FMin.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/included_FMin.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/included_FMin'.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/included_FMin'.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/included_FMin''.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/included_FMin''.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/included_FAbs.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/included_FAbs.con" as lemma. -inline procedural "cic:/CoRN/reals/Max_AbsIR/included_FAbs'.con". +inline procedural "cic:/CoRN/reals/Max_AbsIR/included_FAbs'.con" as lemma. (* UNEXPORTED End Inclusion diff --git a/helm/software/matita/contribs/CoRN-Procedural/reals/NRootIR.mma b/helm/software/matita/contribs/CoRN-Procedural/reals/NRootIR.mma index 2d9f4e582..c617e2a57 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/NRootIR.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/NRootIR.mma @@ -47,11 +47,11 @@ alias id "c_nonneg" = "cic:/CoRN/reals/NRootIR/NRoot/c_nonneg.var". (* begin hide *) -inline procedural "cic:/CoRN/reals/NRootIR/NRoot/p.con" "NRoot__". +inline procedural "cic:/CoRN/reals/NRootIR/NRoot/p.con" "NRoot__" as definition. (* end hide *) -inline procedural "cic:/CoRN/reals/NRootIR/CnrootIR.con". +inline procedural "cic:/CoRN/reals/NRootIR/CnrootIR.con" as lemma. (* UNEXPORTED End NRoot @@ -73,27 +73,27 @@ prove its main properties: Section Nth_Root *) -inline procedural "cic:/CoRN/reals/NRootIR/nroot.con". +inline procedural "cic:/CoRN/reals/NRootIR/nroot.con" as lemma. -inline procedural "cic:/CoRN/reals/NRootIR/NRoot.con". +inline procedural "cic:/CoRN/reals/NRootIR/NRoot.con" as definition. -inline procedural "cic:/CoRN/reals/NRootIR/NRoot_power.con". +inline procedural "cic:/CoRN/reals/NRootIR/NRoot_power.con" as lemma. (* UNEXPORTED Hint Resolve NRoot_power: algebra. *) -inline procedural "cic:/CoRN/reals/NRootIR/NRoot_nonneg.con". +inline procedural "cic:/CoRN/reals/NRootIR/NRoot_nonneg.con" as lemma. -inline procedural "cic:/CoRN/reals/NRootIR/NRoot_pos.con". +inline procedural "cic:/CoRN/reals/NRootIR/NRoot_pos.con" as lemma. -inline procedural "cic:/CoRN/reals/NRootIR/NRoot_power'.con". +inline procedural "cic:/CoRN/reals/NRootIR/NRoot_power'.con" as lemma. -inline procedural "cic:/CoRN/reals/NRootIR/NRoot_pres_less.con". +inline procedural "cic:/CoRN/reals/NRootIR/NRoot_pres_less.con" as lemma. -inline procedural "cic:/CoRN/reals/NRootIR/NRoot_less_one.con". +inline procedural "cic:/CoRN/reals/NRootIR/NRoot_less_one.con" as lemma. -inline procedural "cic:/CoRN/reals/NRootIR/NRoot_cancel.con". +inline procedural "cic:/CoRN/reals/NRootIR/NRoot_cancel.con" as lemma. (*#* %\begin{convention}% Let [x,y] be nonnegative real numbers. %\end{convention}% *) @@ -106,9 +106,9 @@ alias id "Hx" = "cic:/CoRN/reals/NRootIR/Nth_Root/Hx.var". alias id "Hy" = "cic:/CoRN/reals/NRootIR/Nth_Root/Hy.var". -inline procedural "cic:/CoRN/reals/NRootIR/NRoot_wd.con". +inline procedural "cic:/CoRN/reals/NRootIR/NRoot_wd.con" as lemma. -inline procedural "cic:/CoRN/reals/NRootIR/NRoot_unique.con". +inline procedural "cic:/CoRN/reals/NRootIR/NRoot_unique.con" as lemma. (* UNEXPORTED End Nth_Root @@ -122,7 +122,7 @@ Implicit Arguments NRoot [x n]. Hint Resolve NRoot_power NRoot_power': algebra. *) -inline procedural "cic:/CoRN/reals/NRootIR/NRoot_resp_leEq.con". +inline procedural "cic:/CoRN/reals/NRootIR/NRoot_resp_leEq.con" as lemma. (*#**********************************) @@ -134,41 +134,41 @@ Section Square_root (*#* ** Square root *) -inline procedural "cic:/CoRN/reals/NRootIR/sqrt.con". +inline procedural "cic:/CoRN/reals/NRootIR/sqrt.con" as definition. -inline procedural "cic:/CoRN/reals/NRootIR/sqrt_sqr.con". +inline procedural "cic:/CoRN/reals/NRootIR/sqrt_sqr.con" as lemma. (* UNEXPORTED Hint Resolve sqrt_sqr: algebra. *) -inline procedural "cic:/CoRN/reals/NRootIR/sqrt_nonneg.con". +inline procedural "cic:/CoRN/reals/NRootIR/sqrt_nonneg.con" as lemma. -inline procedural "cic:/CoRN/reals/NRootIR/sqrt_wd.con". +inline procedural "cic:/CoRN/reals/NRootIR/sqrt_wd.con" as lemma. (* UNEXPORTED Hint Resolve sqrt_wd: algebra_c. *) -inline procedural "cic:/CoRN/reals/NRootIR/sqrt_to_nonneg.con". +inline procedural "cic:/CoRN/reals/NRootIR/sqrt_to_nonneg.con" as lemma. -inline procedural "cic:/CoRN/reals/NRootIR/sqrt_to_nonpos.con". +inline procedural "cic:/CoRN/reals/NRootIR/sqrt_to_nonpos.con" as lemma. -inline procedural "cic:/CoRN/reals/NRootIR/sqrt_mult.con". +inline procedural "cic:/CoRN/reals/NRootIR/sqrt_mult.con" as lemma. (* UNEXPORTED Hint Resolve sqrt_mult: algebra. *) -inline procedural "cic:/CoRN/reals/NRootIR/sqrt_mult_wd.con". +inline procedural "cic:/CoRN/reals/NRootIR/sqrt_mult_wd.con" as lemma. -inline procedural "cic:/CoRN/reals/NRootIR/sqrt_less.con". +inline procedural "cic:/CoRN/reals/NRootIR/sqrt_less.con" as lemma. -inline procedural "cic:/CoRN/reals/NRootIR/sqrt_less'.con". +inline procedural "cic:/CoRN/reals/NRootIR/sqrt_less'.con" as lemma. -inline procedural "cic:/CoRN/reals/NRootIR/sqrt_resp_leEq.con". +inline procedural "cic:/CoRN/reals/NRootIR/sqrt_resp_leEq.con" as lemma. -inline procedural "cic:/CoRN/reals/NRootIR/sqrt_resp_less.con". +inline procedural "cic:/CoRN/reals/NRootIR/sqrt_resp_less.con" as lemma. (* UNEXPORTED End Square_root @@ -192,53 +192,53 @@ With the help of square roots, we can prove some more properties of absolute values in [IR]. *) -inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_sqrt_sqr.con". +inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_sqrt_sqr.con" as lemma. (* UNEXPORTED Hint Resolve AbsIR_sqrt_sqr: algebra. *) -inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_resp_mult.con". +inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_resp_mult.con" as lemma. -inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_mult_pos.con". +inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_mult_pos.con" as lemma. -inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_mult_pos'.con". +inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_mult_pos'.con" as lemma. -inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_nexp.con". +inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_nexp.con" as lemma. -inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_nexp_op.con". +inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_nexp_op.con" as lemma. -inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_less_square.con". +inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_less_square.con" as lemma. -inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_leEq_square.con". +inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_leEq_square.con" as lemma. -inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_division.con". +inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_division.con" as lemma. (*#* Some special cases. *) -inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_recip.con". +inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_recip.con" as lemma. -inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_div_two.con". +inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_div_two.con" as lemma. (*#* Cauchy-Schwartz for IR and variants on that subject. *) -inline procedural "cic:/CoRN/reals/NRootIR/triangle_IR.con". +inline procedural "cic:/CoRN/reals/NRootIR/triangle_IR.con" as lemma. -inline procedural "cic:/CoRN/reals/NRootIR/triangle_SumIR.con". +inline procedural "cic:/CoRN/reals/NRootIR/triangle_SumIR.con" as lemma. -inline procedural "cic:/CoRN/reals/NRootIR/triangle_IR_minus.con". +inline procedural "cic:/CoRN/reals/NRootIR/triangle_IR_minus.con" as lemma. -inline procedural "cic:/CoRN/reals/NRootIR/weird_triangleIR.con". +inline procedural "cic:/CoRN/reals/NRootIR/weird_triangleIR.con" as lemma. -inline procedural "cic:/CoRN/reals/NRootIR/triangle_IR_minus'.con". +inline procedural "cic:/CoRN/reals/NRootIR/triangle_IR_minus'.con" as lemma. -inline procedural "cic:/CoRN/reals/NRootIR/triangle_SumxIR.con". +inline procedural "cic:/CoRN/reals/NRootIR/triangle_SumxIR.con" as lemma. -inline procedural "cic:/CoRN/reals/NRootIR/triangle_Sum2IR.con". +inline procedural "cic:/CoRN/reals/NRootIR/triangle_Sum2IR.con" as lemma. -inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_str_bnd_AbsIR.con". +inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_str_bnd_AbsIR.con" as lemma. -inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_bnd_AbsIR.con". +inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_bnd_AbsIR.con" as lemma. (* UNEXPORTED End Absolute_Props @@ -255,11 +255,11 @@ Cauchy sequence that is never zero and whose Limit is not zero is also a Cauchy sequence. *) -inline procedural "cic:/CoRN/reals/NRootIR/Cauchy_Lim_recip.con". +inline procedural "cic:/CoRN/reals/NRootIR/Cauchy_Lim_recip.con" as lemma. -inline procedural "cic:/CoRN/reals/NRootIR/Cauchy_recip.con". +inline procedural "cic:/CoRN/reals/NRootIR/Cauchy_recip.con" as lemma. -inline procedural "cic:/CoRN/reals/NRootIR/Lim_recip.con". +inline procedural "cic:/CoRN/reals/NRootIR/Lim_recip.con" as lemma. (* UNEXPORTED End Consequences diff --git a/helm/software/matita/contribs/CoRN-Procedural/reals/OddPolyRootIR.mma b/helm/software/matita/contribs/CoRN-Procedural/reals/OddPolyRootIR.mma index 2f92f666c..45f932b5a 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/OddPolyRootIR.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/OddPolyRootIR.mma @@ -35,17 +35,17 @@ alias id "R" = "cic:/CoRN/reals/OddPolyRootIR/CPoly_Big/R.var". (* begin hide *) -inline procedural "cic:/CoRN/reals/OddPolyRootIR/CPoly_Big/RX.con" "CPoly_Big__". +inline procedural "cic:/CoRN/reals/OddPolyRootIR/CPoly_Big/RX.con" "CPoly_Big__" as definition. (* end hide *) -inline procedural "cic:/CoRN/reals/OddPolyRootIR/Cbigger.con". +inline procedural "cic:/CoRN/reals/OddPolyRootIR/Cbigger.con" as lemma. -inline procedural "cic:/CoRN/reals/OddPolyRootIR/Ccpoly_big.con". +inline procedural "cic:/CoRN/reals/OddPolyRootIR/Ccpoly_big.con" as lemma. -inline procedural "cic:/CoRN/reals/OddPolyRootIR/cpoly_pos.con". +inline procedural "cic:/CoRN/reals/OddPolyRootIR/cpoly_pos.con" as lemma. -inline procedural "cic:/CoRN/reals/OddPolyRootIR/Ccpoly_pos'.con". +inline procedural "cic:/CoRN/reals/OddPolyRootIR/Ccpoly_pos'.con" as lemma. (* UNEXPORTED End CPoly_Big @@ -64,21 +64,21 @@ alias id "R" = "cic:/CoRN/reals/OddPolyRootIR/Flip_Poly/R.var". (* begin hide *) -inline procedural "cic:/CoRN/reals/OddPolyRootIR/Flip_Poly/RX.con" "Flip_Poly__". +inline procedural "cic:/CoRN/reals/OddPolyRootIR/Flip_Poly/RX.con" "Flip_Poly__" as definition. (* end hide *) -inline procedural "cic:/CoRN/reals/OddPolyRootIR/flip.con". +inline procedural "cic:/CoRN/reals/OddPolyRootIR/flip.con" as definition. -inline procedural "cic:/CoRN/reals/OddPolyRootIR/flip_poly.con". +inline procedural "cic:/CoRN/reals/OddPolyRootIR/flip_poly.con" as lemma. -inline procedural "cic:/CoRN/reals/OddPolyRootIR/flip_coefficient.con". +inline procedural "cic:/CoRN/reals/OddPolyRootIR/flip_coefficient.con" as lemma. (* UNEXPORTED Hint Resolve flip_coefficient: algebra. *) -inline procedural "cic:/CoRN/reals/OddPolyRootIR/flip_odd.con". +inline procedural "cic:/CoRN/reals/OddPolyRootIR/flip_odd.con" as lemma. (* UNEXPORTED End Flip_Poly @@ -101,15 +101,15 @@ alias id "R" = "cic:/CoRN/reals/OddPolyRootIR/OddPoly_Signs/R.var". (* begin hide *) -inline procedural "cic:/CoRN/reals/OddPolyRootIR/OddPoly_Signs/RX.con" "OddPoly_Signs__". +inline procedural "cic:/CoRN/reals/OddPolyRootIR/OddPoly_Signs/RX.con" "OddPoly_Signs__" as definition. (* end hide *) -inline procedural "cic:/CoRN/reals/OddPolyRootIR/oddpoly_pos.con". +inline procedural "cic:/CoRN/reals/OddPolyRootIR/oddpoly_pos.con" as lemma. -inline procedural "cic:/CoRN/reals/OddPolyRootIR/oddpoly_pos'.con". +inline procedural "cic:/CoRN/reals/OddPolyRootIR/oddpoly_pos'.con" as lemma. -inline procedural "cic:/CoRN/reals/OddPolyRootIR/oddpoly_neg.con". +inline procedural "cic:/CoRN/reals/OddPolyRootIR/oddpoly_neg.con" as lemma. (* UNEXPORTED End OddPoly_Signs @@ -129,17 +129,17 @@ alias id "R" = "cic:/CoRN/reals/OddPolyRootIR/Poly_Norm/R.var". (* begin hide *) -inline procedural "cic:/CoRN/reals/OddPolyRootIR/Poly_Norm/RX.con" "Poly_Norm__". +inline procedural "cic:/CoRN/reals/OddPolyRootIR/Poly_Norm/RX.con" "Poly_Norm__" as definition. (* end hide *) -inline procedural "cic:/CoRN/reals/OddPolyRootIR/poly_norm_aux.con". +inline procedural "cic:/CoRN/reals/OddPolyRootIR/poly_norm_aux.con" as lemma. -inline procedural "cic:/CoRN/reals/OddPolyRootIR/poly_norm.con". +inline procedural "cic:/CoRN/reals/OddPolyRootIR/poly_norm.con" as definition. -inline procedural "cic:/CoRN/reals/OddPolyRootIR/poly_norm_monic.con". +inline procedural "cic:/CoRN/reals/OddPolyRootIR/poly_norm_monic.con" as lemma. -inline procedural "cic:/CoRN/reals/OddPolyRootIR/poly_norm_apply.con". +inline procedural "cic:/CoRN/reals/OddPolyRootIR/poly_norm_apply.con" as lemma. (* UNEXPORTED End Poly_Norm @@ -152,11 +152,11 @@ Section OddPoly_Root (*#* ** Roots of polynomials of odd degree Polynomials of odd degree over the reals always have a root. *) -inline procedural "cic:/CoRN/reals/OddPolyRootIR/oddpoly_root'.con". +inline procedural "cic:/CoRN/reals/OddPolyRootIR/oddpoly_root'.con" as lemma. -inline procedural "cic:/CoRN/reals/OddPolyRootIR/oddpoly_root.con". +inline procedural "cic:/CoRN/reals/OddPolyRootIR/oddpoly_root.con" as lemma. -inline procedural "cic:/CoRN/reals/OddPolyRootIR/realpolyn_oddhaszero.con". +inline procedural "cic:/CoRN/reals/OddPolyRootIR/realpolyn_oddhaszero.con" as lemma. (* UNEXPORTED End OddPoly_Root diff --git a/helm/software/matita/contribs/CoRN-Procedural/reals/Q_dense.mma b/helm/software/matita/contribs/CoRN-Procedural/reals/Q_dense.mma index e3f87c84d..6a52158d1 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/Q_dense.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/Q_dense.mma @@ -22,7 +22,7 @@ include "reals/Q_in_CReals.ma". (*#***** Opaque_algebra.v will be loaded in line 151 ******) -inline procedural "cic:/CoRN/reals/Q_dense/or_not_and.con". +inline procedural "cic:/CoRN/reals/Q_dense/or_not_and.con" as lemma. (* UNEXPORTED Section Interval_definition @@ -36,17 +36,17 @@ inline procedural "cic:/CoRN/reals/Q_dense/Interval.ind". cic:/matita/CoRN-Procedural/reals/Q_dense/pair_crr.con *) -inline procedural "cic:/CoRN/reals/Q_dense/Length.con". +inline procedural "cic:/CoRN/reals/Q_dense/Length.con" as definition. (* UNEXPORTED End Interval_definition *) -inline procedural "cic:/CoRN/reals/Q_dense/Rat_Interval.con". +inline procedural "cic:/CoRN/reals/Q_dense/Rat_Interval.con" as definition. (* we have this in Q_COrdField... *) -inline procedural "cic:/CoRN/reals/Q_dense/Qlt_eq_gt_dec'.con". +inline procedural "cic:/CoRN/reals/Q_dense/Qlt_eq_gt_dec'.con" as lemma. (* Lemma ex_informative_on_Q:(P:Q_as_COrdField->Prop)(Ex [q:Q_as_COrdField](P q)) @@ -65,11 +65,11 @@ Section COrdField_extra alias id "OF" = "cic:/CoRN/reals/Q_dense/COrdField_extra/OF.var". -inline procedural "cic:/CoRN/reals/Q_dense/AbsSmall_pos_reflexive.con". +inline procedural "cic:/CoRN/reals/Q_dense/AbsSmall_pos_reflexive.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_dense/AbsSmall_neg_reflexive.con". +inline procedural "cic:/CoRN/reals/Q_dense/AbsSmall_neg_reflexive.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_dense/AbsSmall_subinterval.con". +inline procedural "cic:/CoRN/reals/Q_dense/AbsSmall_subinterval.con" as lemma. (* UNEXPORTED End COrdField_extra @@ -85,81 +85,81 @@ include "tactics/Opaque_algebra.ma". alias id "R1" = "cic:/CoRN/reals/Q_dense/Rational_sequence/R1.var". -inline procedural "cic:/CoRN/reals/Q_dense/start_l.con". +inline procedural "cic:/CoRN/reals/Q_dense/start_l.con" as definition. -inline procedural "cic:/CoRN/reals/Q_dense/start_of_sequence2.con". +inline procedural "cic:/CoRN/reals/Q_dense/start_of_sequence2.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_dense/start_r.con". +inline procedural "cic:/CoRN/reals/Q_dense/start_r.con" as definition. -inline procedural "cic:/CoRN/reals/Q_dense/start_of_sequence_property.con". +inline procedural "cic:/CoRN/reals/Q_dense/start_of_sequence_property.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_dense/l_less_r.con". +inline procedural "cic:/CoRN/reals/Q_dense/l_less_r.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_dense/shrink23.con". +inline procedural "cic:/CoRN/reals/Q_dense/shrink23.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_dense/shrink13.con". +inline procedural "cic:/CoRN/reals/Q_dense/shrink13.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_dense/shrink24.con". +inline procedural "cic:/CoRN/reals/Q_dense/shrink24.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_dense/cotrans_analyze.con". +inline procedural "cic:/CoRN/reals/Q_dense/cotrans_analyze.con" as definition. -inline procedural "cic:/CoRN/reals/Q_dense/cotrans_analyze_strong.con". +inline procedural "cic:/CoRN/reals/Q_dense/cotrans_analyze_strong.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_dense/trichotomy.con". +inline procedural "cic:/CoRN/reals/Q_dense/trichotomy.con" as definition. -inline procedural "cic:/CoRN/reals/Q_dense/trichotomy_strong1.con". +inline procedural "cic:/CoRN/reals/Q_dense/trichotomy_strong1.con" as lemma. (* NOTATION Notation "( A , B )" := (pairT A B). *) -inline procedural "cic:/CoRN/reals/Q_dense/if_cotrans.con". +inline procedural "cic:/CoRN/reals/Q_dense/if_cotrans.con" as definition. -inline procedural "cic:/CoRN/reals/Q_dense/if_cotrans_strong.con". +inline procedural "cic:/CoRN/reals/Q_dense/if_cotrans_strong.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_dense/Intrvl.con". +inline procedural "cic:/CoRN/reals/Q_dense/Intrvl.con" as definition. -inline procedural "cic:/CoRN/reals/Q_dense/G.con". +inline procedural "cic:/CoRN/reals/Q_dense/G.con" as definition. (* UNEXPORTED Opaque Q_as_CField. *) -inline procedural "cic:/CoRN/reals/Q_dense/delta_Intrvl.con". +inline procedural "cic:/CoRN/reals/Q_dense/delta_Intrvl.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_dense/Length_Intrvl.con". +inline procedural "cic:/CoRN/reals/Q_dense/Length_Intrvl.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_dense/Intrvl_inside_l_n.con". +inline procedural "cic:/CoRN/reals/Q_dense/Intrvl_inside_l_n.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_dense/Intrvl_inside_r_n.con". +inline procedural "cic:/CoRN/reals/Q_dense/Intrvl_inside_r_n.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_dense/G_m_n_lower.con". +inline procedural "cic:/CoRN/reals/Q_dense/G_m_n_lower.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_dense/G_m_n_upper.con". +inline procedural "cic:/CoRN/reals/Q_dense/G_m_n_upper.con" as lemma. (* UNEXPORTED Opaque Q_as_COrdField. *) -inline procedural "cic:/CoRN/reals/Q_dense/a_simple_inequality.con". +inline procedural "cic:/CoRN/reals/Q_dense/a_simple_inequality.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_dense/G_conversion_rate2.con". +inline procedural "cic:/CoRN/reals/Q_dense/G_conversion_rate2.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_dense/CS_seq_G.con". +inline procedural "cic:/CoRN/reals/Q_dense/CS_seq_G.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_dense/G_as_CauchySeq.con". +inline procedural "cic:/CoRN/reals/Q_dense/G_as_CauchySeq.con" as definition. -inline procedural "cic:/CoRN/reals/Q_dense/CS_seq_inj_Q_G.con". +inline procedural "cic:/CoRN/reals/Q_dense/CS_seq_inj_Q_G.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_dense/inj_Q_G_as_CauchySeq.con". +inline procedural "cic:/CoRN/reals/Q_dense/inj_Q_G_as_CauchySeq.con" as definition. -inline procedural "cic:/CoRN/reals/Q_dense/x_in_Intrvl_l.con". +inline procedural "cic:/CoRN/reals/Q_dense/x_in_Intrvl_l.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_dense/x_in_Intrvl_r.con". +inline procedural "cic:/CoRN/reals/Q_dense/x_in_Intrvl_r.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_dense/G_conversion_rate_resp_x.con". +inline procedural "cic:/CoRN/reals/Q_dense/G_conversion_rate_resp_x.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_dense/x_is_SeqLimit_G.con". +inline procedural "cic:/CoRN/reals/Q_dense/x_is_SeqLimit_G.con" as lemma. (* UNEXPORTED End Rational_sequence diff --git a/helm/software/matita/contribs/CoRN-Procedural/reals/Q_in_CReals.mma b/helm/software/matita/contribs/CoRN-Procedural/reals/Q_in_CReals.mma index 10196d4a5..f6f152ede 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/Q_in_CReals.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/Q_in_CReals.mma @@ -47,13 +47,13 @@ alias id "R1" = "cic:/CoRN/reals/Q_in_CReals/Rational_sequence_prelogue/R1.var". (* begin hide *) -inline procedural "cic:/CoRN/reals/Q_in_CReals/CReals_is_CReals.con". +inline procedural "cic:/CoRN/reals/Q_in_CReals/CReals_is_CReals.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_in_CReals/Lim_Cauchy.con". +inline procedural "cic:/CoRN/reals/Q_in_CReals/Lim_Cauchy.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_in_CReals/Archimedes.con". +inline procedural "cic:/CoRN/reals/Q_in_CReals/Archimedes.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_in_CReals/Archimedes'.con". +inline procedural "cic:/CoRN/reals/Q_in_CReals/Archimedes'.con" as lemma. (*#**************************************) @@ -70,21 +70,21 @@ cic:/Coq/NArith/BinPos/nat_of_P.con To define the injection we need one elemntary lemma about the denominator: *) -inline procedural "cic:/CoRN/reals/Q_in_CReals/den_is_nonzero.con". +inline procedural "cic:/CoRN/reals/Q_in_CReals/den_is_nonzero.con" as lemma. (*#* And we define the injection in the natural way, using [zring] and [nring]. We call this [inj_Q], in contrast with [inject_Q] defined in [Cauchy_CReals]. *) -inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q.con". +inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q.con" as definition. (*#* Next we need some properties of [nring], on the setoid of natural numbers: *) -inline procedural "cic:/CoRN/reals/Q_in_CReals/nring_strext.con". +inline procedural "cic:/CoRN/reals/Q_in_CReals/nring_strext.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_in_CReals/nring_wd.con". +inline procedural "cic:/CoRN/reals/Q_in_CReals/nring_wd.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_in_CReals/nring_eq.con". +inline procedural "cic:/CoRN/reals/Q_in_CReals/nring_eq.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_in_CReals/nring_leEq.con". +inline procedural "cic:/CoRN/reals/Q_in_CReals/nring_leEq.con" as lemma. (* begin hide *) @@ -96,53 +96,53 @@ Unset Printing Coercions. (*#* Similarly we prove some properties of [zring] on the ring of integers: *) -inline procedural "cic:/CoRN/reals/Q_in_CReals/zring_strext.con". +inline procedural "cic:/CoRN/reals/Q_in_CReals/zring_strext.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_in_CReals/zring_wd.con". +inline procedural "cic:/CoRN/reals/Q_in_CReals/zring_wd.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_in_CReals/zring_less.con". +inline procedural "cic:/CoRN/reals/Q_in_CReals/zring_less.con" as lemma. (*#* Using the above lemmata we prove the basic properties of [inj_Q], i.e.%\% it is a setoid function and preserves the ring operations and oreder operation. *) -inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_strext.con". +inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_strext.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_wd.con". +inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_wd.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_plus.con". +inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_plus.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_mult.con". +inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_mult.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_less.con". +inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_less.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_in_CReals/less_inj_Q.con". +inline procedural "cic:/CoRN/reals/Q_in_CReals/less_inj_Q.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_in_CReals/leEq_inj_Q.con". +inline procedural "cic:/CoRN/reals/Q_in_CReals/leEq_inj_Q.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_leEq.con". +inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_leEq.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_min.con". +inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_min.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_minus.con". +inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_minus.con" as lemma. (*#* Moreover, and as expected, the [AbsSmall] predicate is also preserved under the [inj_Q] *) -inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_AbsSmall.con". +inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_AbsSmall.con" as lemma. -inline procedural "cic:/CoRN/reals/Q_in_CReals/AbsSmall_inj_Q.con". +inline procedural "cic:/CoRN/reals/Q_in_CReals/AbsSmall_inj_Q.con" as lemma. (*#* ** Injection preserves Cauchy property We apply the above lemmata to obtain following theorem, which says that a Cauchy sequence of elemnts of [Q] will be Cauchy in [R1]. *) -inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_Cauchy.con". +inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_Cauchy.con" as theorem. (*#* Furthermore we prove that applying [nring] (which is adding the ring unit [n] times) is the same whether we do it in [Q] or in [R1]: *) -inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_nring.con". +inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_nring.con" as lemma. (*#* ** Injection of [Q] is dense Finally we are able to prove the density of image of [Q] in [R1]. We @@ -155,14 +155,14 @@ because it can be used as an starting point for the typical "interval trisection" argument, which is ubiquitous in constructive analysis. *) -inline procedural "cic:/CoRN/reals/Q_in_CReals/start_of_sequence.con". +inline procedural "cic:/CoRN/reals/Q_in_CReals/start_of_sequence.con" as theorem. (*#* The second version of the density of [Q] in [R1] states that given any positive real number, there is a rational number between it and zero. This lemma can be used to prove the more general fact that there is a rational number between any two real numbers. *) -inline procedural "cic:/CoRN/reals/Q_in_CReals/Q_dense_in_CReals.con". +inline procedural "cic:/CoRN/reals/Q_in_CReals/Q_dense_in_CReals.con" as lemma. (* UNEXPORTED End Rational_sequence_prelogue diff --git a/helm/software/matita/contribs/CoRN-Procedural/reals/R_morphism.mma b/helm/software/matita/contribs/CoRN-Procedural/reals/R_morphism.mma index ac45467d8..1483e4104 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/R_morphism.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/R_morphism.mma @@ -26,7 +26,7 @@ include "reals/CReals.ma". (* This comes from CReals1.v *) -inline procedural "cic:/CoRN/reals/R_morphism/Cauchy_Lim_prop2.con". +inline procedural "cic:/CoRN/reals/R_morphism/Cauchy_Lim_prop2.con" as definition. (* UNEXPORTED Section morphism @@ -54,18 +54,18 @@ alias id "g1" = "cic:/CoRN/reals/R_morphism/morphism/morphism_details/g1.var". alias id "g2" = "cic:/CoRN/reals/R_morphism/morphism/morphism_details/g2.var". -inline procedural "cic:/CoRN/reals/R_morphism/fun_pres_relation.con". +inline procedural "cic:/CoRN/reals/R_morphism/fun_pres_relation.con" as definition. -inline procedural "cic:/CoRN/reals/R_morphism/fun_pres_un_fun.con". +inline procedural "cic:/CoRN/reals/R_morphism/fun_pres_un_fun.con" as definition. -inline procedural "cic:/CoRN/reals/R_morphism/fun_pres_bin_fun.con". +inline procedural "cic:/CoRN/reals/R_morphism/fun_pres_bin_fun.con" as definition. (* Definition fun_pres_partial_fun:=(x:R1;H1:x[#]Zero;H2:(phi x)[#]Zero) (phi (nzinj R1 (i1 (nzpro R1 x H1))))[=](nzinj R2 (i2 (nzpro R2 (phi x) H2))). *) -inline procedural "cic:/CoRN/reals/R_morphism/fun_pres_Lim.con". +inline procedural "cic:/CoRN/reals/R_morphism/fun_pres_Lim.con" as definition. (* UNEXPORTED End morphism_details @@ -86,39 +86,39 @@ Definition Homo_as_CSetoid_fun:= ). *****************) -inline procedural "cic:/CoRN/reals/R_morphism/map_strext_unfolded.con". +inline procedural "cic:/CoRN/reals/R_morphism/map_strext_unfolded.con" as lemma. -inline procedural "cic:/CoRN/reals/R_morphism/map_wd_unfolded.con". +inline procedural "cic:/CoRN/reals/R_morphism/map_wd_unfolded.con" as lemma. -inline procedural "cic:/CoRN/reals/R_morphism/map_pres_less_unfolded.con". +inline procedural "cic:/CoRN/reals/R_morphism/map_pres_less_unfolded.con" as lemma. -inline procedural "cic:/CoRN/reals/R_morphism/map_pres_plus_unfolded.con". +inline procedural "cic:/CoRN/reals/R_morphism/map_pres_plus_unfolded.con" as lemma. -inline procedural "cic:/CoRN/reals/R_morphism/map_pres_mult_unfolded.con". +inline procedural "cic:/CoRN/reals/R_morphism/map_pres_mult_unfolded.con" as lemma. (* Now we start to derive some useful properties of a Homomorphism *) -inline procedural "cic:/CoRN/reals/R_morphism/map_pres_zero.con". +inline procedural "cic:/CoRN/reals/R_morphism/map_pres_zero.con" as lemma. -inline procedural "cic:/CoRN/reals/R_morphism/map_pres_zero_unfolded.con". +inline procedural "cic:/CoRN/reals/R_morphism/map_pres_zero_unfolded.con" as lemma. -inline procedural "cic:/CoRN/reals/R_morphism/map_pres_minus.con". +inline procedural "cic:/CoRN/reals/R_morphism/map_pres_minus.con" as lemma. -inline procedural "cic:/CoRN/reals/R_morphism/map_pres_minus_unfolded.con". +inline procedural "cic:/CoRN/reals/R_morphism/map_pres_minus_unfolded.con" as lemma. -inline procedural "cic:/CoRN/reals/R_morphism/map_pres_apartness.con". +inline procedural "cic:/CoRN/reals/R_morphism/map_pres_apartness.con" as lemma. (* Merely a useful special case *) -inline procedural "cic:/CoRN/reals/R_morphism/map_pres_ap_zero.con". +inline procedural "cic:/CoRN/reals/R_morphism/map_pres_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/reals/R_morphism/map_pres_one.con". +inline procedural "cic:/CoRN/reals/R_morphism/map_pres_one.con" as lemma. -inline procedural "cic:/CoRN/reals/R_morphism/map_pres_one_unfolded.con". +inline procedural "cic:/CoRN/reals/R_morphism/map_pres_one_unfolded.con" as lemma. (* I will not use the following lemma *) -inline procedural "cic:/CoRN/reals/R_morphism/map_pres_inv_unfolded.con". +inline procedural "cic:/CoRN/reals/R_morphism/map_pres_inv_unfolded.con" as lemma. (* UNEXPORTED End morphism @@ -138,19 +138,19 @@ alias id "f" = "cic:/CoRN/reals/R_morphism/composition/f.var". alias id "g" = "cic:/CoRN/reals/R_morphism/composition/g.var". -inline procedural "cic:/CoRN/reals/R_morphism/compose.con". +inline procedural "cic:/CoRN/reals/R_morphism/compose.con" as definition. -inline procedural "cic:/CoRN/reals/R_morphism/compose_strext.con". +inline procedural "cic:/CoRN/reals/R_morphism/compose_strext.con" as lemma. -inline procedural "cic:/CoRN/reals/R_morphism/compose_pres_less.con". +inline procedural "cic:/CoRN/reals/R_morphism/compose_pres_less.con" as lemma. -inline procedural "cic:/CoRN/reals/R_morphism/compose_pres_plus.con". +inline procedural "cic:/CoRN/reals/R_morphism/compose_pres_plus.con" as lemma. -inline procedural "cic:/CoRN/reals/R_morphism/compose_pres_mult.con". +inline procedural "cic:/CoRN/reals/R_morphism/compose_pres_mult.con" as lemma. -inline procedural "cic:/CoRN/reals/R_morphism/compose_pres_Lim.con". +inline procedural "cic:/CoRN/reals/R_morphism/compose_pres_Lim.con" as lemma. -inline procedural "cic:/CoRN/reals/R_morphism/Compose.con". +inline procedural "cic:/CoRN/reals/R_morphism/Compose.con" as definition. (* UNEXPORTED End composition @@ -172,7 +172,7 @@ alias id "R3" = "cic:/CoRN/reals/R_morphism/isomorphism/identity_map/R3.var". alias id "f" = "cic:/CoRN/reals/R_morphism/isomorphism/identity_map/f.var". -inline procedural "cic:/CoRN/reals/R_morphism/map_is_id.con". +inline procedural "cic:/CoRN/reals/R_morphism/map_is_id.con" as definition. (* UNEXPORTED End identity_map @@ -194,7 +194,7 @@ alias id "R2" = "cic:/CoRN/reals/R_morphism/surjective_map/R2.var". alias id "f" = "cic:/CoRN/reals/R_morphism/surjective_map/f.var". -inline procedural "cic:/CoRN/reals/R_morphism/map_is_surjective.con". +inline procedural "cic:/CoRN/reals/R_morphism/map_is_surjective.con" as definition. (* UNEXPORTED End surjective_map @@ -212,7 +212,7 @@ alias id "f" = "cic:/CoRN/reals/R_morphism/simplification/f.var". alias id "H1" = "cic:/CoRN/reals/R_morphism/simplification/H1.var". -inline procedural "cic:/CoRN/reals/R_morphism/f_well_def.con". +inline procedural "cic:/CoRN/reals/R_morphism/f_well_def.con" as lemma. (* UNEXPORTED Section with_less @@ -220,13 +220,13 @@ Section with_less alias id "H2" = "cic:/CoRN/reals/R_morphism/simplification/with_less/H2.var". -inline procedural "cic:/CoRN/reals/R_morphism/less_pres_f.con". +inline procedural "cic:/CoRN/reals/R_morphism/less_pres_f.con" as lemma. -inline procedural "cic:/CoRN/reals/R_morphism/leEq_pres_f.con". +inline procedural "cic:/CoRN/reals/R_morphism/leEq_pres_f.con" as lemma. -inline procedural "cic:/CoRN/reals/R_morphism/f_pres_leEq.con". +inline procedural "cic:/CoRN/reals/R_morphism/f_pres_leEq.con" as lemma. -inline procedural "cic:/CoRN/reals/R_morphism/f_pres_apartness.con". +inline procedural "cic:/CoRN/reals/R_morphism/f_pres_apartness.con" as lemma. (* UNEXPORTED End with_less @@ -238,11 +238,11 @@ Section with_plus alias id "H3" = "cic:/CoRN/reals/R_morphism/simplification/with_plus/H3.var". -inline procedural "cic:/CoRN/reals/R_morphism/f_pres_Zero.con". +inline procedural "cic:/CoRN/reals/R_morphism/f_pres_Zero.con" as lemma. -inline procedural "cic:/CoRN/reals/R_morphism/f_pres_minus.con". +inline procedural "cic:/CoRN/reals/R_morphism/f_pres_minus.con" as lemma. -inline procedural "cic:/CoRN/reals/R_morphism/f_pres_min.con". +inline procedural "cic:/CoRN/reals/R_morphism/f_pres_min.con" as lemma. (* UNEXPORTED End with_plus @@ -256,7 +256,7 @@ alias id "H2" = "cic:/CoRN/reals/R_morphism/simplification/with_plus_less/H2.var alias id "H3" = "cic:/CoRN/reals/R_morphism/simplification/with_plus_less/H3.var". -inline procedural "cic:/CoRN/reals/R_morphism/f_pres_ap_zero.con". +inline procedural "cic:/CoRN/reals/R_morphism/f_pres_ap_zero.con" as lemma. (* UNEXPORTED Section surjectivity_helps @@ -264,7 +264,7 @@ Section surjectivity_helps alias id "f_surj" = "cic:/CoRN/reals/R_morphism/simplification/with_plus_less/surjectivity_helps/f_surj.var". -inline procedural "cic:/CoRN/reals/R_morphism/f_pres_Lim.con". +inline procedural "cic:/CoRN/reals/R_morphism/f_pres_Lim.con" as lemma. (* UNEXPORTED End surjectivity_helps @@ -276,11 +276,11 @@ Section with_mult_plus_less alias id "H4" = "cic:/CoRN/reals/R_morphism/simplification/with_plus_less/with_mult_plus_less/H4.var". -inline procedural "cic:/CoRN/reals/R_morphism/f_pres_one.con". +inline procedural "cic:/CoRN/reals/R_morphism/f_pres_one.con" as lemma. -inline procedural "cic:/CoRN/reals/R_morphism/f_pres_inv.con". +inline procedural "cic:/CoRN/reals/R_morphism/f_pres_inv.con" as lemma. -inline procedural "cic:/CoRN/reals/R_morphism/simplified_Homomorphism.con". +inline procedural "cic:/CoRN/reals/R_morphism/simplified_Homomorphism.con" as definition. (* UNEXPORTED End with_mult_plus_less diff --git a/helm/software/matita/contribs/CoRN-Procedural/reals/RealFuncts.mma b/helm/software/matita/contribs/CoRN-Procedural/reals/RealFuncts.mma index 8ba6e4bb6..fa95a4af1 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/RealFuncts.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/RealFuncts.mma @@ -58,15 +58,15 @@ Intervals like $[a,b]$#[a,b]# are defined for arbitrary reals [a,b] (being $\emptyset$#∅# for [a [>] b]). *) -inline procedural "cic:/CoRN/reals/RealFuncts/Intclr.con". +inline procedural "cic:/CoRN/reals/RealFuncts/Intclr.con" as definition. -inline procedural "cic:/CoRN/reals/RealFuncts/Intolr.con". +inline procedural "cic:/CoRN/reals/RealFuncts/Intolr.con" as definition. -inline procedural "cic:/CoRN/reals/RealFuncts/Intol.con". +inline procedural "cic:/CoRN/reals/RealFuncts/Intol.con" as definition. -inline procedural "cic:/CoRN/reals/RealFuncts/Intcl.con". +inline procedural "cic:/CoRN/reals/RealFuncts/Intcl.con" as definition. -inline procedural "cic:/CoRN/reals/RealFuncts/Intcr.con". +inline procedural "cic:/CoRN/reals/RealFuncts/Intcr.con" as definition. (*#* The limit of [f(x)] as [x] goes to [p = l], for both unary and binary functions: @@ -78,11 +78,11 @@ forall e [>] Zero, exists d [>] Zero, forall (x : IR) ]] *) -inline procedural "cic:/CoRN/reals/RealFuncts/funLim.con". +inline procedural "cic:/CoRN/reals/RealFuncts/funLim.con" as definition. (*#* The definition of limit of [f] in [p] using Cauchy sequences. *) -inline procedural "cic:/CoRN/reals/RealFuncts/funLim_Cauchy.con". +inline procedural "cic:/CoRN/reals/RealFuncts/funLim_Cauchy.con" as definition. (*#* The first definition implies the second one. *) @@ -111,40 +111,40 @@ forall e [>] Zero, exists d [>] Zero, forall (x : IR) ]] *) -inline procedural "cic:/CoRN/reals/RealFuncts/funLim2.con". +inline procedural "cic:/CoRN/reals/RealFuncts/funLim2.con" as definition. (*#* The function [f] is continuous at [p] if the limit of [f(x)] as [x] goes to [p] is [f(p)]. This is the [eps [/] delta] definition. We also give the definition with limits of Cauchy sequences. *) -inline procedural "cic:/CoRN/reals/RealFuncts/continAt.con". +inline procedural "cic:/CoRN/reals/RealFuncts/continAt.con" as definition. -inline procedural "cic:/CoRN/reals/RealFuncts/continAtCauchy.con". +inline procedural "cic:/CoRN/reals/RealFuncts/continAtCauchy.con" as definition. -inline procedural "cic:/CoRN/reals/RealFuncts/continAt2.con". +inline procedural "cic:/CoRN/reals/RealFuncts/continAt2.con" as definition. (* Ax_iom continAt_prop1 :(p:IR)(continAt p)->(continAtCauchy p). *) -inline procedural "cic:/CoRN/reals/RealFuncts/contin.con". +inline procedural "cic:/CoRN/reals/RealFuncts/contin.con" as definition. -inline procedural "cic:/CoRN/reals/RealFuncts/continCauchy.con". +inline procedural "cic:/CoRN/reals/RealFuncts/continCauchy.con" as definition. -inline procedural "cic:/CoRN/reals/RealFuncts/contin2.con". +inline procedural "cic:/CoRN/reals/RealFuncts/contin2.con" as definition. (*#* Continuous on a closed, resp.%\% open, resp.%\% left open, resp.%\% left closed interval *) -inline procedural "cic:/CoRN/reals/RealFuncts/continOnc.con". +inline procedural "cic:/CoRN/reals/RealFuncts/continOnc.con" as definition. -inline procedural "cic:/CoRN/reals/RealFuncts/continOno.con". +inline procedural "cic:/CoRN/reals/RealFuncts/continOno.con" as definition. -inline procedural "cic:/CoRN/reals/RealFuncts/continOnol.con". +inline procedural "cic:/CoRN/reals/RealFuncts/continOnol.con" as definition. -inline procedural "cic:/CoRN/reals/RealFuncts/continOncl.con". +inline procedural "cic:/CoRN/reals/RealFuncts/continOncl.con" as definition. (* Section Sequence_and_function_limits. diff --git a/helm/software/matita/contribs/CoRN-Procedural/reals/RealLists.mma b/helm/software/matita/contribs/CoRN-Procedural/reals/RealLists.mma index 361a72363..090f907d9 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/RealLists.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/RealLists.mma @@ -35,16 +35,16 @@ Notice that some of the properties listed below only make sense in the context w We start by defining maximum and minimum of lists of reals and two membership predicates. The value of these functions for the empty list is arbitrarily set to 0, but it will be irrelevant, as we will never work with empty lists. *) -inline procedural "cic:/CoRN/reals/RealLists/maxlist.con". +inline procedural "cic:/CoRN/reals/RealLists/maxlist.con" as definition. -inline procedural "cic:/CoRN/reals/RealLists/minlist.con". +inline procedural "cic:/CoRN/reals/RealLists/minlist.con" as definition. -inline procedural "cic:/CoRN/reals/RealLists/member.con". +inline procedural "cic:/CoRN/reals/RealLists/member.con" as definition. (*#* Sometimes the length of the list has to be restricted; the next definition provides an easy way to do that. *) -inline procedural "cic:/CoRN/reals/RealLists/length_leEq.con". +inline procedural "cic:/CoRN/reals/RealLists/length_leEq.con" as definition. (*#* Length is preserved by mapping. *) @@ -52,7 +52,7 @@ inline procedural "cic:/CoRN/reals/RealLists/length_leEq.con". Implicit Arguments map [A B]. *) -inline procedural "cic:/CoRN/reals/RealLists/map_pres_length.con". +inline procedural "cic:/CoRN/reals/RealLists/map_pres_length.con" as lemma. (*#* Often we want to map partial functions through a list; this next operator provides a way to do that, and is proved to be correct. *) @@ -61,42 +61,42 @@ Often we want to map partial functions through a list; this next operator provid Implicit Arguments cons [A]. *) -inline procedural "cic:/CoRN/reals/RealLists/map2.con". +inline procedural "cic:/CoRN/reals/RealLists/map2.con" as definition. -inline procedural "cic:/CoRN/reals/RealLists/map2_wd.con". +inline procedural "cic:/CoRN/reals/RealLists/map2_wd.con" as lemma. -inline procedural "cic:/CoRN/reals/RealLists/map2_pres_member.con". +inline procedural "cic:/CoRN/reals/RealLists/map2_pres_member.con" as lemma. (*#* As [maxlist] and [minlist] are generalizations of [Max] and [Min] to finite sets of real numbers, they have the expected properties: *) -inline procedural "cic:/CoRN/reals/RealLists/maxlist_greater.con". +inline procedural "cic:/CoRN/reals/RealLists/maxlist_greater.con" as lemma. (* begin hide *) -inline procedural "cic:/CoRN/reals/RealLists/Lists/maxlist_aux.con" "Lists__". +inline procedural "cic:/CoRN/reals/RealLists/Lists/maxlist_aux.con" "Lists__" as definition. (* end hide *) -inline procedural "cic:/CoRN/reals/RealLists/maxlist_leEq_eps.con". +inline procedural "cic:/CoRN/reals/RealLists/maxlist_leEq_eps.con" as lemma. -inline procedural "cic:/CoRN/reals/RealLists/maxlist_less.con". +inline procedural "cic:/CoRN/reals/RealLists/maxlist_less.con" as lemma. -inline procedural "cic:/CoRN/reals/RealLists/maxlist_leEq.con". +inline procedural "cic:/CoRN/reals/RealLists/maxlist_leEq.con" as lemma. -inline procedural "cic:/CoRN/reals/RealLists/minlist_smaller.con". +inline procedural "cic:/CoRN/reals/RealLists/minlist_smaller.con" as lemma. (* begin hide *) -inline procedural "cic:/CoRN/reals/RealLists/Lists/minlist_aux.con" "Lists__". +inline procedural "cic:/CoRN/reals/RealLists/Lists/minlist_aux.con" "Lists__" as definition. (* end hide *) -inline procedural "cic:/CoRN/reals/RealLists/minlist_leEq_eps.con". +inline procedural "cic:/CoRN/reals/RealLists/minlist_leEq_eps.con" as lemma. -inline procedural "cic:/CoRN/reals/RealLists/less_minlist.con". +inline procedural "cic:/CoRN/reals/RealLists/less_minlist.con" as lemma. -inline procedural "cic:/CoRN/reals/RealLists/leEq_minlist.con". +inline procedural "cic:/CoRN/reals/RealLists/leEq_minlist.con" as lemma. (* UNEXPORTED End Lists diff --git a/helm/software/matita/contribs/CoRN-Procedural/reals/Series.mma b/helm/software/matita/contribs/CoRN-Procedural/reals/Series.mma index 9a898a409..3ad3ce01b 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/Series.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/Series.mma @@ -45,7 +45,7 @@ To each such sequence we can assign a sequence of partial sums. alias id "x" = "cic:/CoRN/reals/Series/Definitions/x.var". -inline procedural "cic:/CoRN/reals/Series/seq_part_sum.con". +inline procedural "cic:/CoRN/reals/Series/seq_part_sum.con" as definition. (*#* For subsequent purposes it will be very useful to be able to write the @@ -53,15 +53,15 @@ difference between two arbitrary elements of the sequence of partial sums as a sum of elements of the original sequence. *) -inline procedural "cic:/CoRN/reals/Series/seq_part_sum_n.con". +inline procedural "cic:/CoRN/reals/Series/seq_part_sum_n.con" as lemma. (*#* A series is convergent iff its sequence of partial Sums is a Cauchy sequence. To each convergent series we can assign a Sum. *) -inline procedural "cic:/CoRN/reals/Series/convergent.con". +inline procedural "cic:/CoRN/reals/Series/convergent.con" as definition. -inline procedural "cic:/CoRN/reals/Series/series_sum.con". +inline procedural "cic:/CoRN/reals/Series/series_sum.con" as definition. (*#* Divergence can be characterized in a positive way, which will sometimes be useful. We thus define divergence of sequences and series and prove the @@ -69,25 +69,25 @@ obvious fact that no sequence can be both convergent and divergent, whether considered either as a sequence or as a series. *) -inline procedural "cic:/CoRN/reals/Series/divergent_seq.con". +inline procedural "cic:/CoRN/reals/Series/divergent_seq.con" as definition. -inline procedural "cic:/CoRN/reals/Series/divergent.con". +inline procedural "cic:/CoRN/reals/Series/divergent.con" as definition. -inline procedural "cic:/CoRN/reals/Series/conv_imp_not_div.con". +inline procedural "cic:/CoRN/reals/Series/conv_imp_not_div.con" as lemma. -inline procedural "cic:/CoRN/reals/Series/div_imp_not_conv.con". +inline procedural "cic:/CoRN/reals/Series/div_imp_not_conv.con" as lemma. -inline procedural "cic:/CoRN/reals/Series/convergent_imp_not_divergent.con". +inline procedural "cic:/CoRN/reals/Series/convergent_imp_not_divergent.con" as lemma. -inline procedural "cic:/CoRN/reals/Series/divergent_imp_not_convergent.con". +inline procedural "cic:/CoRN/reals/Series/divergent_imp_not_convergent.con" as lemma. (*#* Finally we have the well known fact that every convergent series converges to zero as a sequence. *) -inline procedural "cic:/CoRN/reals/Series/series_seq_Lim.con". +inline procedural "cic:/CoRN/reals/Series/series_seq_Lim.con" as lemma. -inline procedural "cic:/CoRN/reals/Series/series_seq_Lim'.con". +inline procedural "cic:/CoRN/reals/Series/series_seq_Lim'.con" as lemma. (* UNEXPORTED End Definitions @@ -101,7 +101,7 @@ alias id "x" = "cic:/CoRN/reals/Series/More_Definitions/x.var". (*#* We also define absolute convergence. *) -inline procedural "cic:/CoRN/reals/Series/abs_convergent.con". +inline procedural "cic:/CoRN/reals/Series/abs_convergent.con" as definition. (* UNEXPORTED End More_Definitions @@ -116,7 +116,7 @@ Section Power_Series Power series are an important special case. *) -inline procedural "cic:/CoRN/reals/Series/power_series.con". +inline procedural "cic:/CoRN/reals/Series/power_series.con" as definition. (*#* Specially important is the case when [c] is a positive real number @@ -133,13 +133,13 @@ alias id "H0c" = "cic:/CoRN/reals/Series/Power_Series/H0c.var". alias id "Hc1" = "cic:/CoRN/reals/Series/Power_Series/Hc1.var". -inline procedural "cic:/CoRN/reals/Series/c_exp_Lim.con". +inline procedural "cic:/CoRN/reals/Series/c_exp_Lim.con" as lemma. -inline procedural "cic:/CoRN/reals/Series/power_series_Lim1.con". +inline procedural "cic:/CoRN/reals/Series/power_series_Lim1.con" as lemma. -inline procedural "cic:/CoRN/reals/Series/power_series_conv.con". +inline procedural "cic:/CoRN/reals/Series/power_series_conv.con" as lemma. -inline procedural "cic:/CoRN/reals/Series/power_series_sum.con". +inline procedural "cic:/CoRN/reals/Series/power_series_sum.con" as lemma. (* UNEXPORTED End Power_Series @@ -155,9 +155,9 @@ Some operations with series preserve convergence. We start by defining the series that is zero everywhere. *) -inline procedural "cic:/CoRN/reals/Series/conv_zero_series.con". +inline procedural "cic:/CoRN/reals/Series/conv_zero_series.con" as lemma. -inline procedural "cic:/CoRN/reals/Series/series_sum_zero.con". +inline procedural "cic:/CoRN/reals/Series/series_sum_zero.con" as lemma. (*#* Next we consider extensionality, as well as the sum and difference of two convergent series. @@ -174,25 +174,25 @@ alias id "convX" = "cic:/CoRN/reals/Series/Operations/convX.var". alias id "convY" = "cic:/CoRN/reals/Series/Operations/convY.var". -inline procedural "cic:/CoRN/reals/Series/convergent_wd.con". +inline procedural "cic:/CoRN/reals/Series/convergent_wd.con" as lemma. -inline procedural "cic:/CoRN/reals/Series/series_sum_wd.con". +inline procedural "cic:/CoRN/reals/Series/series_sum_wd.con" as lemma. -inline procedural "cic:/CoRN/reals/Series/conv_series_plus.con". +inline procedural "cic:/CoRN/reals/Series/conv_series_plus.con" as lemma. -inline procedural "cic:/CoRN/reals/Series/series_sum_plus.con". +inline procedural "cic:/CoRN/reals/Series/series_sum_plus.con" as lemma. -inline procedural "cic:/CoRN/reals/Series/conv_series_minus.con". +inline procedural "cic:/CoRN/reals/Series/conv_series_minus.con" as lemma. -inline procedural "cic:/CoRN/reals/Series/series_sum_minus.con". +inline procedural "cic:/CoRN/reals/Series/series_sum_minus.con" as lemma. (*#* Multiplication by a scalar [c] is also permitted. *) alias id "c" = "cic:/CoRN/reals/Series/Operations/c.var". -inline procedural "cic:/CoRN/reals/Series/conv_series_mult_scal.con". +inline procedural "cic:/CoRN/reals/Series/conv_series_mult_scal.con" as lemma. -inline procedural "cic:/CoRN/reals/Series/series_sum_mult_scal.con". +inline procedural "cic:/CoRN/reals/Series/series_sum_mult_scal.con" as lemma. (* UNEXPORTED End Operations @@ -208,9 +208,9 @@ alias id "convX" = "cic:/CoRN/reals/Series/More_Operations/convX.var". (*#* As a corollary, we get the series of the inverses. *) -inline procedural "cic:/CoRN/reals/Series/conv_series_inv.con". +inline procedural "cic:/CoRN/reals/Series/conv_series_inv.con" as lemma. -inline procedural "cic:/CoRN/reals/Series/series_sum_inv.con". +inline procedural "cic:/CoRN/reals/Series/series_sum_inv.con" as lemma. (* UNEXPORTED End More_Operations @@ -232,15 +232,15 @@ alias id "x" = "cic:/CoRN/reals/Series/Almost_Everywhere/x.var". alias id "y" = "cic:/CoRN/reals/Series/Almost_Everywhere/y.var". -inline procedural "cic:/CoRN/reals/Series/aew_eq.con". +inline procedural "cic:/CoRN/reals/Series/aew_eq.con" as definition. alias id "aew_equal" = "cic:/CoRN/reals/Series/Almost_Everywhere/aew_equal.var". -inline procedural "cic:/CoRN/reals/Series/aew_Cauchy.con". +inline procedural "cic:/CoRN/reals/Series/aew_Cauchy.con" as lemma. -inline procedural "cic:/CoRN/reals/Series/aew_Cauchy2.con". +inline procedural "cic:/CoRN/reals/Series/aew_Cauchy2.con" as lemma. -inline procedural "cic:/CoRN/reals/Series/aew_series_conv.con". +inline procedural "cic:/CoRN/reals/Series/aew_series_conv.con" as lemma. (* UNEXPORTED End Almost_Everywhere @@ -258,7 +258,7 @@ alias id "y" = "cic:/CoRN/reals/Series/Cauchy_Almost_Everywhere/y.var". alias id "aew_equal" = "cic:/CoRN/reals/Series/Cauchy_Almost_Everywhere/aew_equal.var". -inline procedural "cic:/CoRN/reals/Series/aew_Lim.con". +inline procedural "cic:/CoRN/reals/Series/aew_Lim.con" as lemma. (* UNEXPORTED End Cauchy_Almost_Everywhere @@ -280,21 +280,21 @@ alias id "x" = "cic:/CoRN/reals/Series/Convergence_Criteria/x.var". general (but simpler) form. *) -inline procedural "cic:/CoRN/reals/Series/str_comparison.con". +inline procedural "cic:/CoRN/reals/Series/str_comparison.con" as lemma. -inline procedural "cic:/CoRN/reals/Series/comparison.con". +inline procedural "cic:/CoRN/reals/Series/comparison.con" as lemma. (*#* As a corollary, we get that every absolutely convergent series converges. *) -inline procedural "cic:/CoRN/reals/Series/abs_imp_conv.con". +inline procedural "cic:/CoRN/reals/Series/abs_imp_conv.con" as lemma. (*#* Next we have the ratio test, both as a positive and negative result. *) -inline procedural "cic:/CoRN/reals/Series/divergent_crit.con". +inline procedural "cic:/CoRN/reals/Series/divergent_crit.con" as lemma. -inline procedural "cic:/CoRN/reals/Series/tail_series.con". +inline procedural "cic:/CoRN/reals/Series/tail_series.con" as lemma. -inline procedural "cic:/CoRN/reals/Series/join_series.con". +inline procedural "cic:/CoRN/reals/Series/join_series.con" as lemma. (* UNEXPORTED End Convergence_Criteria @@ -306,9 +306,9 @@ Section More_CC alias id "x" = "cic:/CoRN/reals/Series/More_CC/x.var". -inline procedural "cic:/CoRN/reals/Series/ratio_test_conv.con". +inline procedural "cic:/CoRN/reals/Series/ratio_test_conv.con" as lemma. -inline procedural "cic:/CoRN/reals/Series/ratio_test_div.con". +inline procedural "cic:/CoRN/reals/Series/ratio_test_div.con" as lemma. (* UNEXPORTED End More_CC @@ -334,19 +334,19 @@ alias id "mon_x" = "cic:/CoRN/reals/Series/Alternate_Series/mon_x.var". (* begin hide *) -inline procedural "cic:/CoRN/reals/Series/Alternate_Series/y.con" "Alternate_Series__". +inline procedural "cic:/CoRN/reals/Series/Alternate_Series/y.con" "Alternate_Series__" as definition. -inline procedural "cic:/CoRN/reals/Series/Alternate_Series/alternate_lemma1.con" "Alternate_Series__". +inline procedural "cic:/CoRN/reals/Series/Alternate_Series/alternate_lemma1.con" "Alternate_Series__" as definition. -inline procedural "cic:/CoRN/reals/Series/Alternate_Series/alternate_lemma2.con" "Alternate_Series__". +inline procedural "cic:/CoRN/reals/Series/Alternate_Series/alternate_lemma2.con" "Alternate_Series__" as definition. -inline procedural "cic:/CoRN/reals/Series/Alternate_Series/alternate_lemma3.con" "Alternate_Series__". +inline procedural "cic:/CoRN/reals/Series/Alternate_Series/alternate_lemma3.con" "Alternate_Series__" as definition. -inline procedural "cic:/CoRN/reals/Series/Alternate_Series/alternate_lemma4.con" "Alternate_Series__". +inline procedural "cic:/CoRN/reals/Series/Alternate_Series/alternate_lemma4.con" "Alternate_Series__" as definition. (* end hide *) -inline procedural "cic:/CoRN/reals/Series/alternate_series_conv.con". +inline procedural "cic:/CoRN/reals/Series/alternate_series_conv.con" as lemma. (* UNEXPORTED End Alternate_Series @@ -362,17 +362,17 @@ We end this chapter by defining two important numbers in mathematics: [pi] and $e$#e#, both as sums of convergent series. *) -inline procedural "cic:/CoRN/reals/Series/e_series.con". +inline procedural "cic:/CoRN/reals/Series/e_series.con" as definition. -inline procedural "cic:/CoRN/reals/Series/e_series_conv.con". +inline procedural "cic:/CoRN/reals/Series/e_series_conv.con" as lemma. -inline procedural "cic:/CoRN/reals/Series/E.con". +inline procedural "cic:/CoRN/reals/Series/E.con" as definition. -inline procedural "cic:/CoRN/reals/Series/pi_series.con". +inline procedural "cic:/CoRN/reals/Series/pi_series.con" as definition. -inline procedural "cic:/CoRN/reals/Series/pi_series_conv.con". +inline procedural "cic:/CoRN/reals/Series/pi_series_conv.con" as lemma. -inline procedural "cic:/CoRN/reals/Series/pi.con". +inline procedural "cic:/CoRN/reals/Series/pi.con" as definition. (* UNEXPORTED End Important_Numbers diff --git a/helm/software/matita/contribs/CoRN-Procedural/reals/iso_CReals.mma b/helm/software/matita/contribs/CoRN-Procedural/reals/iso_CReals.mma index f2d6c81cd..b15f7a930 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/iso_CReals.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/iso_CReals.mma @@ -25,35 +25,35 @@ include "reals/Q_dense.ma". include "reals/R_morphism.ma". -inline procedural "cic:/CoRN/reals/iso_CReals/less_pres_Lim.con". +inline procedural "cic:/CoRN/reals/iso_CReals/less_pres_Lim.con" as lemma. -inline procedural "cic:/CoRN/reals/iso_CReals/Lim_pres_less.con". +inline procedural "cic:/CoRN/reals/iso_CReals/Lim_pres_less.con" as lemma. -inline procedural "cic:/CoRN/reals/iso_CReals/inj_seq_less.con". +inline procedural "cic:/CoRN/reals/iso_CReals/inj_seq_less.con" as lemma. -inline procedural "cic:/CoRN/reals/iso_CReals/less_inj_seq.con". +inline procedural "cic:/CoRN/reals/iso_CReals/less_inj_seq.con" as lemma. -inline procedural "cic:/CoRN/reals/iso_CReals/SeqLimit_unique.con". +inline procedural "cic:/CoRN/reals/iso_CReals/SeqLimit_unique.con" as theorem. -inline procedural "cic:/CoRN/reals/iso_CReals/Lim_well_def.con". +inline procedural "cic:/CoRN/reals/iso_CReals/Lim_well_def.con" as lemma. -inline procedural "cic:/CoRN/reals/iso_CReals/Lim_one_one.con". +inline procedural "cic:/CoRN/reals/iso_CReals/Lim_one_one.con" as lemma. -inline procedural "cic:/CoRN/reals/iso_CReals/inj_seq_well_def.con". +inline procedural "cic:/CoRN/reals/iso_CReals/inj_seq_well_def.con" as lemma. -inline procedural "cic:/CoRN/reals/iso_CReals/inj_Q_one_one.con". +inline procedural "cic:/CoRN/reals/iso_CReals/inj_Q_one_one.con" as lemma. -inline procedural "cic:/CoRN/reals/iso_CReals/Lim_pres_plus.con". +inline procedural "cic:/CoRN/reals/iso_CReals/Lim_pres_plus.con" as lemma. -inline procedural "cic:/CoRN/reals/iso_CReals/G_pres_plus.con". +inline procedural "cic:/CoRN/reals/iso_CReals/G_pres_plus.con" as lemma. (* This theorem can be avoided but it is interesting *) -inline procedural "cic:/CoRN/reals/iso_CReals/nonarchemaedian_bound_for_Lim.con". +inline procedural "cic:/CoRN/reals/iso_CReals/nonarchemaedian_bound_for_Lim.con" as theorem. -inline procedural "cic:/CoRN/reals/iso_CReals/Lim_pres_mult.con". +inline procedural "cic:/CoRN/reals/iso_CReals/Lim_pres_mult.con" as lemma. -inline procedural "cic:/CoRN/reals/iso_CReals/G_pres_mult.con". +inline procedural "cic:/CoRN/reals/iso_CReals/G_pres_mult.con" as lemma. (* UNEXPORTED Section Concrete_iso_between_Creals @@ -63,57 +63,57 @@ alias id "R1" = "cic:/CoRN/reals/iso_CReals/Concrete_iso_between_Creals/R1.var". alias id "R2" = "cic:/CoRN/reals/iso_CReals/Concrete_iso_between_Creals/R2.var". -inline procedural "cic:/CoRN/reals/iso_CReals/image_Cauchy12.con". +inline procedural "cic:/CoRN/reals/iso_CReals/image_Cauchy12.con" as lemma. -inline procedural "cic:/CoRN/reals/iso_CReals/image_Cauchy21.con". +inline procedural "cic:/CoRN/reals/iso_CReals/image_Cauchy21.con" as lemma. -inline procedural "cic:/CoRN/reals/iso_CReals/image_G_as_CauchySeq12.con". +inline procedural "cic:/CoRN/reals/iso_CReals/image_G_as_CauchySeq12.con" as definition. -inline procedural "cic:/CoRN/reals/iso_CReals/image_G_as_CauchySeq21.con". +inline procedural "cic:/CoRN/reals/iso_CReals/image_G_as_CauchySeq21.con" as definition. -inline procedural "cic:/CoRN/reals/iso_CReals/f12.con". +inline procedural "cic:/CoRN/reals/iso_CReals/f12.con" as definition. -inline procedural "cic:/CoRN/reals/iso_CReals/g21.con". +inline procedural "cic:/CoRN/reals/iso_CReals/g21.con" as definition. (*#****** ISO FROM R1 TO R2 ********) -inline procedural "cic:/CoRN/reals/iso_CReals/f12_is_inverse_g21.con". +inline procedural "cic:/CoRN/reals/iso_CReals/f12_is_inverse_g21.con" as theorem. -inline procedural "cic:/CoRN/reals/iso_CReals/f12_is_surjective.con". +inline procedural "cic:/CoRN/reals/iso_CReals/f12_is_surjective.con" as theorem. -inline procedural "cic:/CoRN/reals/iso_CReals/f12_strong_ext.con". +inline procedural "cic:/CoRN/reals/iso_CReals/f12_strong_ext.con" as theorem. -inline procedural "cic:/CoRN/reals/iso_CReals/f12_pres_less.con". +inline procedural "cic:/CoRN/reals/iso_CReals/f12_pres_less.con" as theorem. -inline procedural "cic:/CoRN/reals/iso_CReals/f12_pres_plus.con". +inline procedural "cic:/CoRN/reals/iso_CReals/f12_pres_plus.con" as theorem. -inline procedural "cic:/CoRN/reals/iso_CReals/f12_pres_mult.con". +inline procedural "cic:/CoRN/reals/iso_CReals/f12_pres_mult.con" as theorem. (*#********* ISO FROM R2 TO R1 **********) -inline procedural "cic:/CoRN/reals/iso_CReals/g21_is_inverse_f12.con". +inline procedural "cic:/CoRN/reals/iso_CReals/g21_is_inverse_f12.con" as theorem. -inline procedural "cic:/CoRN/reals/iso_CReals/g21_is_surjective.con". +inline procedural "cic:/CoRN/reals/iso_CReals/g21_is_surjective.con" as theorem. -inline procedural "cic:/CoRN/reals/iso_CReals/g21_strong_ext.con". +inline procedural "cic:/CoRN/reals/iso_CReals/g21_strong_ext.con" as theorem. -inline procedural "cic:/CoRN/reals/iso_CReals/g21_pres_less.con". +inline procedural "cic:/CoRN/reals/iso_CReals/g21_pres_less.con" as theorem. -inline procedural "cic:/CoRN/reals/iso_CReals/g21_pres_plus.con". +inline procedural "cic:/CoRN/reals/iso_CReals/g21_pres_plus.con" as theorem. -inline procedural "cic:/CoRN/reals/iso_CReals/g21_pres_mult.con". +inline procedural "cic:/CoRN/reals/iso_CReals/g21_pres_mult.con" as theorem. (*#** Building Homomorphisms out of f12 and g21 ***) -inline procedural "cic:/CoRN/reals/iso_CReals/f12_as_Homomorphism.con". +inline procedural "cic:/CoRN/reals/iso_CReals/f12_as_Homomorphism.con" as definition. -inline procedural "cic:/CoRN/reals/iso_CReals/g21_as_Homomorphism.con". +inline procedural "cic:/CoRN/reals/iso_CReals/g21_as_Homomorphism.con" as definition. -inline procedural "cic:/CoRN/reals/iso_CReals/f12_inverse_lft.con". +inline procedural "cic:/CoRN/reals/iso_CReals/f12_inverse_lft.con" as lemma. -inline procedural "cic:/CoRN/reals/iso_CReals/g21_inverse_rht.con". +inline procedural "cic:/CoRN/reals/iso_CReals/g21_inverse_rht.con" as lemma. -inline procedural "cic:/CoRN/reals/iso_CReals/Canonic_Isomorphism_between_CReals.con". +inline procedural "cic:/CoRN/reals/iso_CReals/Canonic_Isomorphism_between_CReals.con" as definition. (* UNEXPORTED End Concrete_iso_between_Creals diff --git a/helm/software/matita/contribs/CoRN-Procedural/tactics/AlgReflection.mma b/helm/software/matita/contribs/CoRN-Procedural/tactics/AlgReflection.mma index 87ed418dc..1f436b320 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/tactics/AlgReflection.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/tactics/AlgReflection.mma @@ -26,27 +26,27 @@ include "algebra/CLogic.ma". Section Syntactic_Expressions *) -inline procedural "cic:/CoRN/tactics/AlgReflection/varindex.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/varindex.con" as definition. -inline procedural "cic:/CoRN/tactics/AlgReflection/pfunindex.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/pfunindex.con" as definition. -inline procedural "cic:/CoRN/tactics/AlgReflection/unopindex.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/unopindex.con" as definition. -inline procedural "cic:/CoRN/tactics/AlgReflection/binopindex.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/binopindex.con" as definition. inline procedural "cic:/CoRN/tactics/AlgReflection/expr.ind". -inline procedural "cic:/CoRN/tactics/AlgReflection/expr_zero.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/expr_zero.con" as definition. -inline procedural "cic:/CoRN/tactics/AlgReflection/expr_one.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/expr_one.con" as definition. -inline procedural "cic:/CoRN/tactics/AlgReflection/expr_nat.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/expr_nat.con" as definition. -inline procedural "cic:/CoRN/tactics/AlgReflection/expr_inv.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/expr_inv.con" as definition. -inline procedural "cic:/CoRN/tactics/AlgReflection/expr_minus.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/expr_minus.con" as definition. -inline procedural "cic:/CoRN/tactics/AlgReflection/expr_power.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/expr_power.con" as definition. (* UNEXPORTED End Syntactic_Expressions @@ -56,57 +56,57 @@ End Syntactic_Expressions Section Normalization_Function *) -inline procedural "cic:/CoRN/tactics/AlgReflection/eq_nat.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/eq_nat.con" as definition. -inline procedural "cic:/CoRN/tactics/AlgReflection/lt_nat.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/lt_nat.con" as definition. -inline procedural "cic:/CoRN/tactics/AlgReflection/le_nat.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/le_nat.con" as definition. -inline procedural "cic:/CoRN/tactics/AlgReflection/eq_int.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/eq_int.con" as definition. -inline procedural "cic:/CoRN/tactics/AlgReflection/lt_int.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/lt_int.con" as definition. -inline procedural "cic:/CoRN/tactics/AlgReflection/le_int.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/le_int.con" as definition. -inline procedural "cic:/CoRN/tactics/AlgReflection/eq_expr.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/eq_expr.con" as definition. -inline procedural "cic:/CoRN/tactics/AlgReflection/lt_expr.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/lt_expr.con" as definition. -inline procedural "cic:/CoRN/tactics/AlgReflection/le_expr.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/le_expr.con" as definition. -inline procedural "cic:/CoRN/tactics/AlgReflection/eq_monom.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/eq_monom.con" as definition. -inline procedural "cic:/CoRN/tactics/AlgReflection/lt_monom.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/lt_monom.con" as definition. -inline procedural "cic:/CoRN/tactics/AlgReflection/MI_mult.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/MI_mult.con" as definition. -inline procedural "cic:/CoRN/tactics/AlgReflection/MV_mult.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/MV_mult.con" as definition. -inline procedural "cic:/CoRN/tactics/AlgReflection/MM_mult.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/MM_mult.con" as definition. -inline procedural "cic:/CoRN/tactics/AlgReflection/MM_plus.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/MM_plus.con" as definition. -inline procedural "cic:/CoRN/tactics/AlgReflection/PM_plus.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/PM_plus.con" as definition. -inline procedural "cic:/CoRN/tactics/AlgReflection/PP_plus.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/PP_plus.con" as definition. -inline procedural "cic:/CoRN/tactics/AlgReflection/PM_mult.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/PM_mult.con" as definition. -inline procedural "cic:/CoRN/tactics/AlgReflection/PP_mult.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/PP_mult.con" as definition. -inline procedural "cic:/CoRN/tactics/AlgReflection/FF_plus.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/FF_plus.con" as definition. -inline procedural "cic:/CoRN/tactics/AlgReflection/FF_mult.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/FF_mult.con" as definition. -inline procedural "cic:/CoRN/tactics/AlgReflection/FF_div.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/FF_div.con" as definition. -inline procedural "cic:/CoRN/tactics/AlgReflection/NormR.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/NormR.con" as definition. -inline procedural "cic:/CoRN/tactics/AlgReflection/NormG.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/NormG.con" as definition. -inline procedural "cic:/CoRN/tactics/AlgReflection/NormF.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/NormF.con" as definition. -inline procedural "cic:/CoRN/tactics/AlgReflection/expr_is_zero.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/expr_is_zero.con" as definition. (* UNEXPORTED End Normalization_Function @@ -116,11 +116,11 @@ End Normalization_Function Section Correctness_Results *) -inline procedural "cic:/CoRN/tactics/AlgReflection/eq_nat_corr.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/eq_nat_corr.con" as lemma. -inline procedural "cic:/CoRN/tactics/AlgReflection/eq_int_corr.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/eq_int_corr.con" as lemma. -inline procedural "cic:/CoRN/tactics/AlgReflection/eq_expr_corr.con". +inline procedural "cic:/CoRN/tactics/AlgReflection/eq_expr_corr.con" as lemma. (* UNEXPORTED End Correctness_Results diff --git a/helm/software/matita/contribs/CoRN-Procedural/tactics/DiffTactics2.mma b/helm/software/matita/contribs/CoRN-Procedural/tactics/DiffTactics2.mma index 3352930be..30fbf96fc 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/tactics/DiffTactics2.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/tactics/DiffTactics2.mma @@ -32,9 +32,9 @@ alias id "b" = "cic:/CoRN/tactics/DiffTactics2/Automatizing_Continuity/b.var". inline procedural "cic:/CoRN/tactics/DiffTactics2/cont_function.ind". -inline procedural "cic:/CoRN/tactics/DiffTactics2/cont_to_pfunct.con". +inline procedural "cic:/CoRN/tactics/DiffTactics2/cont_to_pfunct.con" as definition. -inline procedural "cic:/CoRN/tactics/DiffTactics2/continuous_cont.con". +inline procedural "cic:/CoRN/tactics/DiffTactics2/continuous_cont.con" as lemma. (* UNEXPORTED End Automatizing_Continuity @@ -102,13 +102,13 @@ alias id "b" = "cic:/CoRN/tactics/DiffTactics2/Automatizing_Derivatives/b.var". inline procedural "cic:/CoRN/tactics/DiffTactics2/deriv_function.ind". -inline procedural "cic:/CoRN/tactics/DiffTactics2/deriv_to_pfunct.con". +inline procedural "cic:/CoRN/tactics/DiffTactics2/deriv_to_pfunct.con" as definition. -inline procedural "cic:/CoRN/tactics/DiffTactics2/deriv_deriv.con". +inline procedural "cic:/CoRN/tactics/DiffTactics2/deriv_deriv.con" as definition. -inline procedural "cic:/CoRN/tactics/DiffTactics2/deriv_restr.con". +inline procedural "cic:/CoRN/tactics/DiffTactics2/deriv_restr.con" as lemma. -inline procedural "cic:/CoRN/tactics/DiffTactics2/diffble_restr.con". +inline procedural "cic:/CoRN/tactics/DiffTactics2/diffble_restr.con" as lemma. (* UNEXPORTED End Automatizing_Derivatives diff --git a/helm/software/matita/contribs/CoRN-Procedural/tactics/DiffTactics3.mma b/helm/software/matita/contribs/CoRN-Procedural/tactics/DiffTactics3.mma index 3e2b4f152..01be53402 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/tactics/DiffTactics3.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/tactics/DiffTactics3.mma @@ -43,9 +43,9 @@ inline procedural "cic:/CoRN/tactics/DiffTactics3/symbPF.ind". | ssum : nat->nat->(nat->symbPF)->symbPF *) -inline procedural "cic:/CoRN/tactics/DiffTactics3/symb_to_PartIR.con". +inline procedural "cic:/CoRN/tactics/DiffTactics3/symb_to_PartIR.con" as definition. -inline procedural "cic:/CoRN/tactics/DiffTactics3/symbPF_deriv.con". +inline procedural "cic:/CoRN/tactics/DiffTactics3/symbPF_deriv.con" as definition. (* UNEXPORTED Ltac PartIR_to_symbPF f := diff --git a/helm/software/matita/contribs/CoRN-Procedural/tactics/FieldReflection.mma b/helm/software/matita/contribs/CoRN-Procedural/tactics/FieldReflection.mma index 91e5cd0fc..dae6d3625 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/tactics/FieldReflection.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/tactics/FieldReflection.mma @@ -40,41 +40,41 @@ alias id "pfun" = "cic:/CoRN/tactics/FieldReflection/Field_Interpretation_Functi inline procedural "cic:/CoRN/tactics/FieldReflection/interpF.ind". -inline procedural "cic:/CoRN/tactics/FieldReflection/wfF.con". +inline procedural "cic:/CoRN/tactics/FieldReflection/wfF.con" as definition. inline procedural "cic:/CoRN/tactics/FieldReflection/xexprF.ind". -inline procedural "cic:/CoRN/tactics/FieldReflection/xforgetF.con". +inline procedural "cic:/CoRN/tactics/FieldReflection/xforgetF.con" as definition. -inline procedural "cic:/CoRN/tactics/FieldReflection/xinterpF.con". +inline procedural "cic:/CoRN/tactics/FieldReflection/xinterpF.con" as definition. -inline procedural "cic:/CoRN/tactics/FieldReflection/xexprF2interpF.con". +inline procedural "cic:/CoRN/tactics/FieldReflection/xexprF2interpF.con" as lemma. -inline procedural "cic:/CoRN/tactics/FieldReflection/xexprF_diagram_commutes.con". +inline procedural "cic:/CoRN/tactics/FieldReflection/xexprF_diagram_commutes.con" as definition. -inline procedural "cic:/CoRN/tactics/FieldReflection/xexprF2wfF.con". +inline procedural "cic:/CoRN/tactics/FieldReflection/xexprF2wfF.con" as lemma. inline procedural "cic:/CoRN/tactics/FieldReflection/fexprF.ind". -inline procedural "cic:/CoRN/tactics/FieldReflection/fexprF_var.con". +inline procedural "cic:/CoRN/tactics/FieldReflection/fexprF_var.con" as definition. -inline procedural "cic:/CoRN/tactics/FieldReflection/fexprF_int.con". +inline procedural "cic:/CoRN/tactics/FieldReflection/fexprF_int.con" as definition. -inline procedural "cic:/CoRN/tactics/FieldReflection/fexprF_plus.con". +inline procedural "cic:/CoRN/tactics/FieldReflection/fexprF_plus.con" as definition. -inline procedural "cic:/CoRN/tactics/FieldReflection/fexprF_mult.con". +inline procedural "cic:/CoRN/tactics/FieldReflection/fexprF_mult.con" as definition. -inline procedural "cic:/CoRN/tactics/FieldReflection/fforgetF.con". +inline procedural "cic:/CoRN/tactics/FieldReflection/fforgetF.con" as definition. -inline procedural "cic:/CoRN/tactics/FieldReflection/fexprF2interpF.con". +inline procedural "cic:/CoRN/tactics/FieldReflection/fexprF2interpF.con" as lemma. -inline procedural "cic:/CoRN/tactics/FieldReflection/fexprF2wfF.con". +inline procedural "cic:/CoRN/tactics/FieldReflection/fexprF2wfF.con" as lemma. include "tactics/Opaque_algebra.ma". -inline procedural "cic:/CoRN/tactics/FieldReflection/refl_interpF.con". +inline procedural "cic:/CoRN/tactics/FieldReflection/refl_interpF.con" as lemma. -inline procedural "cic:/CoRN/tactics/FieldReflection/interpF_wd.con". +inline procedural "cic:/CoRN/tactics/FieldReflection/interpF_wd.con" as lemma. (* UNEXPORTED End Field_Interpretation_Function @@ -116,7 +116,7 @@ P: sorted on M, all M's not an I Opaque Zmult. *) -inline procedural "cic:/CoRN/tactics/FieldReflection/MI_mult_corr_F.con". +inline procedural "cic:/CoRN/tactics/FieldReflection/MI_mult_corr_F.con" as lemma. (* UNEXPORTED Transparent Zmult. @@ -126,7 +126,7 @@ Transparent Zmult. Opaque MI_mult. *) -inline procedural "cic:/CoRN/tactics/FieldReflection/MV_mult_corr_F.con". +inline procedural "cic:/CoRN/tactics/FieldReflection/MV_mult_corr_F.con" as lemma. (* UNEXPORTED Transparent MI_mult. @@ -136,7 +136,7 @@ Transparent MI_mult. Opaque MV_mult MI_mult. *) -inline procedural "cic:/CoRN/tactics/FieldReflection/MM_mult_corr_F.con". +inline procedural "cic:/CoRN/tactics/FieldReflection/MM_mult_corr_F.con" as lemma. (* UNEXPORTED Transparent MV_mult MI_mult. @@ -146,7 +146,7 @@ Transparent MV_mult MI_mult. Opaque MV_mult. *) -inline procedural "cic:/CoRN/tactics/FieldReflection/MM_plus_corr_F.con". +inline procedural "cic:/CoRN/tactics/FieldReflection/MM_plus_corr_F.con" as lemma. (* UNEXPORTED Transparent MV_mult. @@ -156,7 +156,7 @@ Transparent MV_mult. Opaque MM_plus. *) -inline procedural "cic:/CoRN/tactics/FieldReflection/PM_plus_corr_F.con". +inline procedural "cic:/CoRN/tactics/FieldReflection/PM_plus_corr_F.con" as lemma. (* UNEXPORTED Transparent MM_plus. @@ -166,7 +166,7 @@ Transparent MM_plus. Opaque PM_plus. *) -inline procedural "cic:/CoRN/tactics/FieldReflection/PP_plus_corr_F.con". +inline procedural "cic:/CoRN/tactics/FieldReflection/PP_plus_corr_F.con" as lemma. (* UNEXPORTED Transparent PM_plus. @@ -176,37 +176,37 @@ Transparent PM_plus. Opaque PM_plus MM_mult MI_mult. *) -inline procedural "cic:/CoRN/tactics/FieldReflection/PM_mult_corr_F.con". +inline procedural "cic:/CoRN/tactics/FieldReflection/PM_mult_corr_F.con" as lemma. (* UNEXPORTED Opaque PM_mult. *) -inline procedural "cic:/CoRN/tactics/FieldReflection/PP_mult_corr_F.con". +inline procedural "cic:/CoRN/tactics/FieldReflection/PP_mult_corr_F.con" as lemma. (* UNEXPORTED Transparent PP_plus PM_mult PP_mult PM_plus MI_mult. *) -inline procedural "cic:/CoRN/tactics/FieldReflection/FF_plus_corr_F.con". +inline procedural "cic:/CoRN/tactics/FieldReflection/FF_plus_corr_F.con" as lemma. -inline procedural "cic:/CoRN/tactics/FieldReflection/FF_mult_corr_F.con". +inline procedural "cic:/CoRN/tactics/FieldReflection/FF_mult_corr_F.con" as lemma. (* UNEXPORTED Transparent FF_div. *) -inline procedural "cic:/CoRN/tactics/FieldReflection/FF_div_corr_F.con". +inline procedural "cic:/CoRN/tactics/FieldReflection/FF_div_corr_F.con" as lemma. -inline procedural "cic:/CoRN/tactics/FieldReflection/NormF_corr.con". +inline procedural "cic:/CoRN/tactics/FieldReflection/NormF_corr.con" as lemma. -inline procedural "cic:/CoRN/tactics/FieldReflection/Norm_wfF.con". +inline procedural "cic:/CoRN/tactics/FieldReflection/Norm_wfF.con" as lemma. -inline procedural "cic:/CoRN/tactics/FieldReflection/expr_is_zero_corr_F.con". +inline procedural "cic:/CoRN/tactics/FieldReflection/expr_is_zero_corr_F.con" as lemma. -inline procedural "cic:/CoRN/tactics/FieldReflection/Tactic_lemma_zero_F.con". +inline procedural "cic:/CoRN/tactics/FieldReflection/Tactic_lemma_zero_F.con" as lemma. -inline procedural "cic:/CoRN/tactics/FieldReflection/Tactic_lemmaF.con". +inline procedural "cic:/CoRN/tactics/FieldReflection/Tactic_lemmaF.con" as lemma. (* UNEXPORTED End Field_NormCorrect diff --git a/helm/software/matita/contribs/CoRN-Procedural/tactics/GroupReflection.mma b/helm/software/matita/contribs/CoRN-Procedural/tactics/GroupReflection.mma index 479e8abbc..bbac139d1 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/tactics/GroupReflection.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/tactics/GroupReflection.mma @@ -40,35 +40,35 @@ alias id "pfun" = "cic:/CoRN/tactics/GroupReflection/Group_Interpretation_Functi inline procedural "cic:/CoRN/tactics/GroupReflection/interpG.ind". -inline procedural "cic:/CoRN/tactics/GroupReflection/wfG.con". +inline procedural "cic:/CoRN/tactics/GroupReflection/wfG.con" as definition. inline procedural "cic:/CoRN/tactics/GroupReflection/xexprG.ind". -inline procedural "cic:/CoRN/tactics/GroupReflection/xforgetG.con". +inline procedural "cic:/CoRN/tactics/GroupReflection/xforgetG.con" as definition. -inline procedural "cic:/CoRN/tactics/GroupReflection/xinterpG.con". +inline procedural "cic:/CoRN/tactics/GroupReflection/xinterpG.con" as definition. -inline procedural "cic:/CoRN/tactics/GroupReflection/xexprG2interpG.con". +inline procedural "cic:/CoRN/tactics/GroupReflection/xexprG2interpG.con" as lemma. -inline procedural "cic:/CoRN/tactics/GroupReflection/xexprG_diagram_commutes.con". +inline procedural "cic:/CoRN/tactics/GroupReflection/xexprG_diagram_commutes.con" as definition. -inline procedural "cic:/CoRN/tactics/GroupReflection/xexprG2wfG.con". +inline procedural "cic:/CoRN/tactics/GroupReflection/xexprG2wfG.con" as lemma. inline procedural "cic:/CoRN/tactics/GroupReflection/fexprG.ind". -inline procedural "cic:/CoRN/tactics/GroupReflection/fexprG_var.con". +inline procedural "cic:/CoRN/tactics/GroupReflection/fexprG_var.con" as definition. -inline procedural "cic:/CoRN/tactics/GroupReflection/fexprG_zero.con". +inline procedural "cic:/CoRN/tactics/GroupReflection/fexprG_zero.con" as definition. -inline procedural "cic:/CoRN/tactics/GroupReflection/fexprG_plus.con". +inline procedural "cic:/CoRN/tactics/GroupReflection/fexprG_plus.con" as definition. -inline procedural "cic:/CoRN/tactics/GroupReflection/fexprG_mult_int.con". +inline procedural "cic:/CoRN/tactics/GroupReflection/fexprG_mult_int.con" as definition. -inline procedural "cic:/CoRN/tactics/GroupReflection/fforgetG.con". +inline procedural "cic:/CoRN/tactics/GroupReflection/fforgetG.con" as definition. -inline procedural "cic:/CoRN/tactics/GroupReflection/fexprG2interp.con". +inline procedural "cic:/CoRN/tactics/GroupReflection/fexprG2interp.con" as lemma. -inline procedural "cic:/CoRN/tactics/GroupReflection/fexprG2wf.con". +inline procedural "cic:/CoRN/tactics/GroupReflection/fexprG2wf.con" as lemma. (* UNEXPORTED Opaque csg_crr. @@ -122,9 +122,9 @@ Opaque cg_inv. Opaque cg_minus. *) -inline procedural "cic:/CoRN/tactics/GroupReflection/refl_interpG.con". +inline procedural "cic:/CoRN/tactics/GroupReflection/refl_interpG.con" as lemma. -inline procedural "cic:/CoRN/tactics/GroupReflection/interpG_wd.con". +inline procedural "cic:/CoRN/tactics/GroupReflection/interpG_wd.con" as lemma. (* UNEXPORTED End Group_Interpretation_Function @@ -162,13 +162,13 @@ M: sorted on V P: sorted on M, all M's not an I *) -inline procedural "cic:/CoRN/tactics/GroupReflection/MI_mult_comm_int.con". +inline procedural "cic:/CoRN/tactics/GroupReflection/MI_mult_comm_int.con" as lemma. (* UNEXPORTED Opaque Zmult. *) -inline procedural "cic:/CoRN/tactics/GroupReflection/MI_mult_corr_G.con". +inline procedural "cic:/CoRN/tactics/GroupReflection/MI_mult_corr_G.con" as lemma. (* UNEXPORTED Transparent Zmult. @@ -178,13 +178,13 @@ Transparent Zmult. Opaque MI_mult. *) -inline procedural "cic:/CoRN/tactics/GroupReflection/MV_mult_corr_G.con". +inline procedural "cic:/CoRN/tactics/GroupReflection/MV_mult_corr_G.con" as lemma. (* UNEXPORTED Opaque MV_mult. *) -inline procedural "cic:/CoRN/tactics/GroupReflection/MM_mult_corr_G.con". +inline procedural "cic:/CoRN/tactics/GroupReflection/MM_mult_corr_G.con" as lemma. (* UNEXPORTED Transparent MV_mult MI_mult. @@ -194,7 +194,7 @@ Transparent MV_mult MI_mult. Opaque MV_mult. *) -inline procedural "cic:/CoRN/tactics/GroupReflection/MM_plus_corr_G.con". +inline procedural "cic:/CoRN/tactics/GroupReflection/MM_plus_corr_G.con" as lemma. (* UNEXPORTED Transparent MV_mult. @@ -204,7 +204,7 @@ Transparent MV_mult. Opaque MM_plus. *) -inline procedural "cic:/CoRN/tactics/GroupReflection/PM_plus_corr_G.con". +inline procedural "cic:/CoRN/tactics/GroupReflection/PM_plus_corr_G.con" as lemma. (* UNEXPORTED Transparent MM_plus. @@ -214,7 +214,7 @@ Transparent MM_plus. Opaque PM_plus. *) -inline procedural "cic:/CoRN/tactics/GroupReflection/PP_plus_corr_G.con". +inline procedural "cic:/CoRN/tactics/GroupReflection/PP_plus_corr_G.con" as lemma. (* UNEXPORTED Transparent PM_plus. @@ -224,17 +224,17 @@ Transparent PM_plus. Opaque PM_plus MM_mult MI_mult. *) -inline procedural "cic:/CoRN/tactics/GroupReflection/PM_mult_corr_G.con". +inline procedural "cic:/CoRN/tactics/GroupReflection/PM_mult_corr_G.con" as lemma. (* UNEXPORTED Opaque PM_mult. *) -inline procedural "cic:/CoRN/tactics/GroupReflection/PP_mult_corr_G.con". +inline procedural "cic:/CoRN/tactics/GroupReflection/PP_mult_corr_G.con" as lemma. -inline procedural "cic:/CoRN/tactics/GroupReflection/NormG_corr_G.con". +inline procedural "cic:/CoRN/tactics/GroupReflection/NormG_corr_G.con" as lemma. -inline procedural "cic:/CoRN/tactics/GroupReflection/Tactic_lemmaG.con". +inline procedural "cic:/CoRN/tactics/GroupReflection/Tactic_lemmaG.con" as lemma. (* UNEXPORTED End Group_NormCorrect diff --git a/helm/software/matita/contribs/CoRN-Procedural/tactics/RingReflection.mma b/helm/software/matita/contribs/CoRN-Procedural/tactics/RingReflection.mma index 1e0fa25dc..4a348ceae 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/tactics/RingReflection.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/tactics/RingReflection.mma @@ -40,35 +40,35 @@ alias id "pfun" = "cic:/CoRN/tactics/RingReflection/Ring_Interpretation_Function inline procedural "cic:/CoRN/tactics/RingReflection/interpR.ind". -inline procedural "cic:/CoRN/tactics/RingReflection/wfR.con". +inline procedural "cic:/CoRN/tactics/RingReflection/wfR.con" as definition. inline procedural "cic:/CoRN/tactics/RingReflection/xexprR.ind". -inline procedural "cic:/CoRN/tactics/RingReflection/xforgetR.con". +inline procedural "cic:/CoRN/tactics/RingReflection/xforgetR.con" as definition. -inline procedural "cic:/CoRN/tactics/RingReflection/xinterpR.con". +inline procedural "cic:/CoRN/tactics/RingReflection/xinterpR.con" as definition. -inline procedural "cic:/CoRN/tactics/RingReflection/xexprR2interpR.con". +inline procedural "cic:/CoRN/tactics/RingReflection/xexprR2interpR.con" as lemma. -inline procedural "cic:/CoRN/tactics/RingReflection/xexprR_diagram_commutes.con". +inline procedural "cic:/CoRN/tactics/RingReflection/xexprR_diagram_commutes.con" as definition. -inline procedural "cic:/CoRN/tactics/RingReflection/xexprR2wfR.con". +inline procedural "cic:/CoRN/tactics/RingReflection/xexprR2wfR.con" as lemma. inline procedural "cic:/CoRN/tactics/RingReflection/fexprR.ind". -inline procedural "cic:/CoRN/tactics/RingReflection/fexprR_var.con". +inline procedural "cic:/CoRN/tactics/RingReflection/fexprR_var.con" as definition. -inline procedural "cic:/CoRN/tactics/RingReflection/fexprR_int.con". +inline procedural "cic:/CoRN/tactics/RingReflection/fexprR_int.con" as definition. -inline procedural "cic:/CoRN/tactics/RingReflection/fexprR_plus.con". +inline procedural "cic:/CoRN/tactics/RingReflection/fexprR_plus.con" as definition. -inline procedural "cic:/CoRN/tactics/RingReflection/fexprR_mult.con". +inline procedural "cic:/CoRN/tactics/RingReflection/fexprR_mult.con" as definition. -inline procedural "cic:/CoRN/tactics/RingReflection/fforgetR.con". +inline procedural "cic:/CoRN/tactics/RingReflection/fforgetR.con" as definition. -inline procedural "cic:/CoRN/tactics/RingReflection/fexprR2interp.con". +inline procedural "cic:/CoRN/tactics/RingReflection/fexprR2interp.con" as lemma. -inline procedural "cic:/CoRN/tactics/RingReflection/fexprR2wf.con". +inline procedural "cic:/CoRN/tactics/RingReflection/fexprR2wf.con" as lemma. (* UNEXPORTED Opaque csg_crr. @@ -138,9 +138,9 @@ Opaque cr_mult. Opaque nexp_op. *) -inline procedural "cic:/CoRN/tactics/RingReflection/refl_interpR.con". +inline procedural "cic:/CoRN/tactics/RingReflection/refl_interpR.con" as lemma. -inline procedural "cic:/CoRN/tactics/RingReflection/interpR_wd.con". +inline procedural "cic:/CoRN/tactics/RingReflection/interpR_wd.con" as lemma. (* UNEXPORTED End Ring_Interpretation_Function @@ -182,7 +182,7 @@ P: sorted on M, all M's not an I Opaque Zmult. *) -inline procedural "cic:/CoRN/tactics/RingReflection/MI_mult_corr_R.con". +inline procedural "cic:/CoRN/tactics/RingReflection/MI_mult_corr_R.con" as lemma. (* UNEXPORTED Transparent Zmult. @@ -192,7 +192,7 @@ Transparent Zmult. Opaque MI_mult. *) -inline procedural "cic:/CoRN/tactics/RingReflection/MV_mult_corr_R.con". +inline procedural "cic:/CoRN/tactics/RingReflection/MV_mult_corr_R.con" as lemma. (* UNEXPORTED Transparent MI_mult. @@ -202,7 +202,7 @@ Transparent MI_mult. Opaque MV_mult MI_mult. *) -inline procedural "cic:/CoRN/tactics/RingReflection/MM_mult_corr_R.con". +inline procedural "cic:/CoRN/tactics/RingReflection/MM_mult_corr_R.con" as lemma. (* UNEXPORTED Transparent MV_mult MI_mult. @@ -212,7 +212,7 @@ Transparent MV_mult MI_mult. Opaque MV_mult. *) -inline procedural "cic:/CoRN/tactics/RingReflection/MM_plus_corr_R.con". +inline procedural "cic:/CoRN/tactics/RingReflection/MM_plus_corr_R.con" as lemma. (* UNEXPORTED Transparent MV_mult. @@ -222,7 +222,7 @@ Transparent MV_mult. Opaque MM_plus. *) -inline procedural "cic:/CoRN/tactics/RingReflection/PM_plus_corr_R.con". +inline procedural "cic:/CoRN/tactics/RingReflection/PM_plus_corr_R.con" as lemma. (* UNEXPORTED Transparent MM_plus. @@ -232,7 +232,7 @@ Transparent MM_plus. Opaque PM_plus. *) -inline procedural "cic:/CoRN/tactics/RingReflection/PP_plus_corr_R.con". +inline procedural "cic:/CoRN/tactics/RingReflection/PP_plus_corr_R.con" as lemma. (* UNEXPORTED Transparent PM_plus. @@ -242,13 +242,13 @@ Transparent PM_plus. Opaque PM_plus MM_mult MI_mult. *) -inline procedural "cic:/CoRN/tactics/RingReflection/PM_mult_corr_R.con". +inline procedural "cic:/CoRN/tactics/RingReflection/PM_mult_corr_R.con" as lemma. (* UNEXPORTED Opaque PM_mult. *) -inline procedural "cic:/CoRN/tactics/RingReflection/PP_mult_corr_R.con". +inline procedural "cic:/CoRN/tactics/RingReflection/PP_mult_corr_R.con" as lemma. (* Transparent PP_plus PM_mult PP_mult PM_plus MI_mult. @@ -310,9 +310,9 @@ Step_final x2. Qed. *) -inline procedural "cic:/CoRN/tactics/RingReflection/NormR_corr.con". +inline procedural "cic:/CoRN/tactics/RingReflection/NormR_corr.con" as lemma. -inline procedural "cic:/CoRN/tactics/RingReflection/Tactic_lemmaR.con". +inline procedural "cic:/CoRN/tactics/RingReflection/Tactic_lemmaR.con" as lemma. (* UNEXPORTED End Ring_NormCorrect diff --git a/helm/software/matita/contribs/CoRN-Procedural/transc/Exponential.mma b/helm/software/matita/contribs/CoRN-Procedural/transc/Exponential.mma index 4115fe187..3f0929d77 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/transc/Exponential.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/transc/Exponential.mma @@ -33,20 +33,20 @@ The main properties of the exponential and logarithmic functions. Exponential is strongly extensional and well defined. *) -inline procedural "cic:/CoRN/transc/Exponential/Exp_strext.con". +inline procedural "cic:/CoRN/transc/Exponential/Exp_strext.con" as lemma. -inline procedural "cic:/CoRN/transc/Exponential/Exp_wd.con". +inline procedural "cic:/CoRN/transc/Exponential/Exp_wd.con" as lemma. (* UNEXPORTED Hint Resolve Exp_wd: algebra. *) -inline procedural "cic:/CoRN/transc/Exponential/Exp_zero.con". +inline procedural "cic:/CoRN/transc/Exponential/Exp_zero.con" as lemma. (*#* $e^1=e$#e1=e#, where [e] was defined a long time ago. *) -inline procedural "cic:/CoRN/transc/Exponential/Exp_one.con". +inline procedural "cic:/CoRN/transc/Exponential/Exp_one.con" as lemma. (* UNEXPORTED Hint Resolve Exp_zero Exp_one: algebra. @@ -56,13 +56,13 @@ Hint Resolve Exp_zero Exp_one: algebra. The exponential function is its own derivative, and continuous. *) -inline procedural "cic:/CoRN/transc/Exponential/Derivative_Exp.con". +inline procedural "cic:/CoRN/transc/Exponential/Derivative_Exp.con" as lemma. (* UNEXPORTED Hint Resolve Derivative_Exp: derivate. *) -inline procedural "cic:/CoRN/transc/Exponential/Continuous_Exp.con". +inline procedural "cic:/CoRN/transc/Exponential/Continuous_Exp.con" as lemma. (* UNEXPORTED Hint Resolve Continuous_Exp: continuous. @@ -72,20 +72,20 @@ Hint Resolve Continuous_Exp: continuous. Negative numbers are projected into the interval [[0,1]]. *) -inline procedural "cic:/CoRN/transc/Exponential/One_less_Exp.con". +inline procedural "cic:/CoRN/transc/Exponential/One_less_Exp.con" as lemma. -inline procedural "cic:/CoRN/transc/Exponential/One_leEq_Exp.con". +inline procedural "cic:/CoRN/transc/Exponential/One_leEq_Exp.con" as lemma. -inline procedural "cic:/CoRN/transc/Exponential/Exp_pos'.con". +inline procedural "cic:/CoRN/transc/Exponential/Exp_pos'.con" as lemma. (*#* Exponential is the unique function which evaluates to 1 at 0 and is its own derivative. *) -inline procedural "cic:/CoRN/transc/Exponential/Exp_unique_lemma.con". +inline procedural "cic:/CoRN/transc/Exponential/Exp_unique_lemma.con" as lemma. -inline procedural "cic:/CoRN/transc/Exponential/Exp_bnd.con". +inline procedural "cic:/CoRN/transc/Exponential/Exp_bnd.con" as lemma. (* UNEXPORTED Opaque Expon. @@ -95,25 +95,25 @@ Opaque Expon. Transparent Expon. *) -inline procedural "cic:/CoRN/transc/Exponential/Exp_unique.con". +inline procedural "cic:/CoRN/transc/Exponential/Exp_unique.con" as lemma. (* UNEXPORTED Opaque Expon. *) -inline procedural "cic:/CoRN/transc/Exponential/Exp_plus_pos.con". +inline procedural "cic:/CoRN/transc/Exponential/Exp_plus_pos.con" as lemma. (*#* The usual rules for computing the exponential of a sum. *) -inline procedural "cic:/CoRN/transc/Exponential/Exp_plus.con". +inline procedural "cic:/CoRN/transc/Exponential/Exp_plus.con" as lemma. (* UNEXPORTED Hint Resolve Exp_plus: algebra. *) -inline procedural "cic:/CoRN/transc/Exponential/Exp_plus'.con". +inline procedural "cic:/CoRN/transc/Exponential/Exp_plus'.con" as lemma. -inline procedural "cic:/CoRN/transc/Exponential/Exp_inv_char.con". +inline procedural "cic:/CoRN/transc/Exponential/Exp_inv_char.con" as lemma. (* UNEXPORTED Hint Resolve Exp_inv_char: algebra. @@ -123,52 +123,52 @@ Hint Resolve Exp_inv_char: algebra. from zero. *) -inline procedural "cic:/CoRN/transc/Exponential/Exp_pos.con". +inline procedural "cic:/CoRN/transc/Exponential/Exp_pos.con" as lemma. -inline procedural "cic:/CoRN/transc/Exponential/Exp_ap_zero.con". +inline procedural "cic:/CoRN/transc/Exponential/Exp_ap_zero.con" as lemma. (*#* And the rules for the exponential of differences. *) -inline procedural "cic:/CoRN/transc/Exponential/Exp_inv.con". +inline procedural "cic:/CoRN/transc/Exponential/Exp_inv.con" as lemma. (* UNEXPORTED Hint Resolve Exp_inv: algebra. *) -inline procedural "cic:/CoRN/transc/Exponential/Exp_minus.con". +inline procedural "cic:/CoRN/transc/Exponential/Exp_minus.con" as lemma. (* UNEXPORTED Hint Resolve Exp_minus: algebra. *) -inline procedural "cic:/CoRN/transc/Exponential/Exp_inv'.con". +inline procedural "cic:/CoRN/transc/Exponential/Exp_inv'.con" as lemma. -inline procedural "cic:/CoRN/transc/Exponential/Exp_minus'.con". +inline procedural "cic:/CoRN/transc/Exponential/Exp_minus'.con" as lemma. (*#* Exponential is a monotonous function. *) -inline procedural "cic:/CoRN/transc/Exponential/Exp_less_One.con". +inline procedural "cic:/CoRN/transc/Exponential/Exp_less_One.con" as lemma. -inline procedural "cic:/CoRN/transc/Exponential/Exp_leEq_One.con". +inline procedural "cic:/CoRN/transc/Exponential/Exp_leEq_One.con" as lemma. -inline procedural "cic:/CoRN/transc/Exponential/Exp_resp_less.con". +inline procedural "cic:/CoRN/transc/Exponential/Exp_resp_less.con" as lemma. -inline procedural "cic:/CoRN/transc/Exponential/Exp_resp_leEq.con". +inline procedural "cic:/CoRN/transc/Exponential/Exp_resp_leEq.con" as lemma. (*#* **Properties of Logarithm The logarithm is a continuous function with derivative [One[/]x]. *) -inline procedural "cic:/CoRN/transc/Exponential/Derivative_Log.con". +inline procedural "cic:/CoRN/transc/Exponential/Derivative_Log.con" as lemma. (* UNEXPORTED Hint Resolve Derivative_Log: derivate. *) -inline procedural "cic:/CoRN/transc/Exponential/Continuous_Log.con". +inline procedural "cic:/CoRN/transc/Exponential/Continuous_Log.con" as lemma. (* UNEXPORTED Hint Resolve Continuous_Log: continuous. @@ -176,7 +176,7 @@ Hint Resolve Continuous_Log: continuous. (*#* Logarithm of [One]. *) -inline procedural "cic:/CoRN/transc/Exponential/Log_one.con". +inline procedural "cic:/CoRN/transc/Exponential/Log_one.con" as lemma. (* UNEXPORTED Hint Resolve Log_one: algebra. @@ -184,9 +184,9 @@ Hint Resolve Log_one: algebra. (*#* The logarithm is (strongly) extensional. *) -inline procedural "cic:/CoRN/transc/Exponential/Log_strext.con". +inline procedural "cic:/CoRN/transc/Exponential/Log_strext.con" as lemma. -inline procedural "cic:/CoRN/transc/Exponential/Log_wd.con". +inline procedural "cic:/CoRN/transc/Exponential/Log_wd.con" as lemma. (* UNEXPORTED Hint Resolve Log_wd: algebra. @@ -202,17 +202,17 @@ Opaque Logarithm. Transparent Logarithm. *) -inline procedural "cic:/CoRN/transc/Exponential/Log_mult.con". +inline procedural "cic:/CoRN/transc/Exponential/Log_mult.con" as lemma. (* UNEXPORTED Hint Resolve Log_mult: algebra. *) -inline procedural "cic:/CoRN/transc/Exponential/Log_mult'.con". +inline procedural "cic:/CoRN/transc/Exponential/Log_mult'.con" as lemma. (*#* A characterization of the domain of the logarithm. *) -inline procedural "cic:/CoRN/transc/Exponential/Log_domain.con". +inline procedural "cic:/CoRN/transc/Exponential/Log_domain.con" as lemma. (* UNEXPORTED Opaque Expon Logarithm. @@ -222,9 +222,9 @@ Opaque Expon Logarithm. numerical and as a functional equation. *) -inline procedural "cic:/CoRN/transc/Exponential/Log_Exp_inv.con". +inline procedural "cic:/CoRN/transc/Exponential/Log_Exp_inv.con" as lemma. -inline procedural "cic:/CoRN/transc/Exponential/Log_Exp.con". +inline procedural "cic:/CoRN/transc/Exponential/Log_Exp.con" as lemma. (* UNEXPORTED Transparent Logarithm. @@ -234,11 +234,11 @@ Transparent Logarithm. Hint Resolve Log_Exp: algebra. *) -inline procedural "cic:/CoRN/transc/Exponential/Exp_Log_lemma.con". +inline procedural "cic:/CoRN/transc/Exponential/Exp_Log_lemma.con" as lemma. (*#* The converse expression. *) -inline procedural "cic:/CoRN/transc/Exponential/Exp_Log.con". +inline procedural "cic:/CoRN/transc/Exponential/Exp_Log.con" as lemma. (* UNEXPORTED Hint Resolve Exp_Log: algebra. @@ -246,9 +246,9 @@ Hint Resolve Exp_Log: algebra. (*#* Exponential and logarithm are injective. *) -inline procedural "cic:/CoRN/transc/Exponential/Exp_cancel.con". +inline procedural "cic:/CoRN/transc/Exponential/Exp_cancel.con" as lemma. -inline procedural "cic:/CoRN/transc/Exponential/Log_cancel.con". +inline procedural "cic:/CoRN/transc/Exponential/Log_cancel.con" as lemma. (* UNEXPORTED Opaque Logarithm. @@ -256,9 +256,9 @@ Opaque Logarithm. (*#* And the final characterization as inverse functions. *) -inline procedural "cic:/CoRN/transc/Exponential/Exp_Log_inv.con". +inline procedural "cic:/CoRN/transc/Exponential/Exp_Log_inv.con" as lemma. -inline procedural "cic:/CoRN/transc/Exponential/Log_E.con". +inline procedural "cic:/CoRN/transc/Exponential/Log_E.con" as lemma. (* UNEXPORTED Hint Resolve Log_E: algebra. @@ -266,43 +266,43 @@ Hint Resolve Log_E: algebra. (*#* Several rules regarding inequalities. *) -inline procedural "cic:/CoRN/transc/Exponential/Log_cancel_less.con". +inline procedural "cic:/CoRN/transc/Exponential/Log_cancel_less.con" as lemma. -inline procedural "cic:/CoRN/transc/Exponential/Log_cancel_leEq.con". +inline procedural "cic:/CoRN/transc/Exponential/Log_cancel_leEq.con" as lemma. -inline procedural "cic:/CoRN/transc/Exponential/Log_resp_less.con". +inline procedural "cic:/CoRN/transc/Exponential/Log_resp_less.con" as lemma. -inline procedural "cic:/CoRN/transc/Exponential/Log_resp_leEq.con". +inline procedural "cic:/CoRN/transc/Exponential/Log_resp_leEq.con" as lemma. -inline procedural "cic:/CoRN/transc/Exponential/Exp_cancel_less.con". +inline procedural "cic:/CoRN/transc/Exponential/Exp_cancel_less.con" as lemma. -inline procedural "cic:/CoRN/transc/Exponential/Exp_cancel_leEq.con". +inline procedural "cic:/CoRN/transc/Exponential/Exp_cancel_leEq.con" as lemma. -inline procedural "cic:/CoRN/transc/Exponential/Log_less_Zero.con". +inline procedural "cic:/CoRN/transc/Exponential/Log_less_Zero.con" as lemma. -inline procedural "cic:/CoRN/transc/Exponential/Log_leEq_Zero.con". +inline procedural "cic:/CoRN/transc/Exponential/Log_leEq_Zero.con" as lemma. -inline procedural "cic:/CoRN/transc/Exponential/Zero_less_Log.con". +inline procedural "cic:/CoRN/transc/Exponential/Zero_less_Log.con" as lemma. -inline procedural "cic:/CoRN/transc/Exponential/Zero_leEq_Log.con". +inline procedural "cic:/CoRN/transc/Exponential/Zero_leEq_Log.con" as lemma. (*#* Finally, rules for logarithm of quotients. *) -inline procedural "cic:/CoRN/transc/Exponential/Log_recip_char.con". +inline procedural "cic:/CoRN/transc/Exponential/Log_recip_char.con" as lemma. -inline procedural "cic:/CoRN/transc/Exponential/Log_recip.con". +inline procedural "cic:/CoRN/transc/Exponential/Log_recip.con" as lemma. (* UNEXPORTED Hint Resolve Log_recip: algebra. *) -inline procedural "cic:/CoRN/transc/Exponential/Log_recip'.con". +inline procedural "cic:/CoRN/transc/Exponential/Log_recip'.con" as lemma. -inline procedural "cic:/CoRN/transc/Exponential/Log_div.con". +inline procedural "cic:/CoRN/transc/Exponential/Log_div.con" as lemma. (* UNEXPORTED Hint Resolve Log_div: algebra. *) -inline procedural "cic:/CoRN/transc/Exponential/Log_div'.con". +inline procedural "cic:/CoRN/transc/Exponential/Log_div'.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/transc/InvTrigonom.mma b/helm/software/matita/contribs/CoRN-Procedural/transc/InvTrigonom.mma index a04a19c37..b09f9b579 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/transc/InvTrigonom.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/transc/InvTrigonom.mma @@ -49,17 +49,17 @@ Arccosine is defined in terms of arcsine by the relation Opaque Sine Cosine Expon Logarithm. *) -inline procedural "cic:/CoRN/transc/InvTrigonom/ArcSin_def_lemma.con". +inline procedural "cic:/CoRN/transc/InvTrigonom/ArcSin_def_lemma.con" as lemma. -inline procedural "cic:/CoRN/transc/InvTrigonom/ArcSin_def_zero.con". +inline procedural "cic:/CoRN/transc/InvTrigonom/ArcSin_def_zero.con" as lemma. -inline procedural "cic:/CoRN/transc/InvTrigonom/ArcSin.con". +inline procedural "cic:/CoRN/transc/InvTrigonom/ArcSin.con" as definition. -inline procedural "cic:/CoRN/transc/InvTrigonom/ArcSin_domain.con". +inline procedural "cic:/CoRN/transc/InvTrigonom/ArcSin_domain.con" as lemma. -inline procedural "cic:/CoRN/transc/InvTrigonom/Continuous_ArcSin.con". +inline procedural "cic:/CoRN/transc/InvTrigonom/Continuous_ArcSin.con" as lemma. -inline procedural "cic:/CoRN/transc/InvTrigonom/Derivative_ArcSin.con". +inline procedural "cic:/CoRN/transc/InvTrigonom/Derivative_ArcSin.con" as lemma. (* UNEXPORTED Hint Resolve Derivative_ArcSin: derivate. @@ -72,28 +72,28 @@ Hint Resolve Continuous_ArcSin: continuous. (*#* ***Arccosine *) -inline procedural "cic:/CoRN/transc/InvTrigonom/ArcCos.con". +inline procedural "cic:/CoRN/transc/InvTrigonom/ArcCos.con" as definition. -inline procedural "cic:/CoRN/transc/InvTrigonom/ArcCos_domain.con". +inline procedural "cic:/CoRN/transc/InvTrigonom/ArcCos_domain.con" as lemma. -inline procedural "cic:/CoRN/transc/InvTrigonom/Continuous_ArcCos.con". +inline procedural "cic:/CoRN/transc/InvTrigonom/Continuous_ArcCos.con" as lemma. -inline procedural "cic:/CoRN/transc/InvTrigonom/Derivative_ArcCos.con". +inline procedural "cic:/CoRN/transc/InvTrigonom/Derivative_ArcCos.con" as lemma. (*#* ***Arctangent *) -inline procedural "cic:/CoRN/transc/InvTrigonom/ArcTan_def_lemma.con". +inline procedural "cic:/CoRN/transc/InvTrigonom/ArcTan_def_lemma.con" as lemma. -inline procedural "cic:/CoRN/transc/InvTrigonom/ArcTang.con". +inline procedural "cic:/CoRN/transc/InvTrigonom/ArcTang.con" as definition. -inline procedural "cic:/CoRN/transc/InvTrigonom/ArcTan_domain.con". +inline procedural "cic:/CoRN/transc/InvTrigonom/ArcTan_domain.con" as lemma. -inline procedural "cic:/CoRN/transc/InvTrigonom/ArcTan.con". +inline procedural "cic:/CoRN/transc/InvTrigonom/ArcTan.con" as definition. -inline procedural "cic:/CoRN/transc/InvTrigonom/Continuous_ArcTan.con". +inline procedural "cic:/CoRN/transc/InvTrigonom/Continuous_ArcTan.con" as lemma. -inline procedural "cic:/CoRN/transc/InvTrigonom/Derivative_ArcTan.con". +inline procedural "cic:/CoRN/transc/InvTrigonom/Derivative_ArcTan.con" as lemma. (* UNEXPORTED Hint Resolve Derivative_ArcCos Derivative_ArcTan: derivate. @@ -114,59 +114,59 @@ We now prove that this functions are in fact inverses to the corresponding trigo ***Sine and Arcsine *) -inline procedural "cic:/CoRN/transc/InvTrigonom/maps_Sin.con". +inline procedural "cic:/CoRN/transc/InvTrigonom/maps_Sin.con" as lemma. -inline procedural "cic:/CoRN/transc/InvTrigonom/ArcSin_Sin_inv.con". +inline procedural "cic:/CoRN/transc/InvTrigonom/ArcSin_Sin_inv.con" as lemma. (* UNEXPORTED Opaque ArcSin. *) -inline procedural "cic:/CoRN/transc/InvTrigonom/ArcSin_Sin.con". +inline procedural "cic:/CoRN/transc/InvTrigonom/ArcSin_Sin.con" as lemma. (* UNEXPORTED Transparent ArcSin. *) -inline procedural "cic:/CoRN/transc/InvTrigonom/ArcSin_range.con". +inline procedural "cic:/CoRN/transc/InvTrigonom/ArcSin_range.con" as lemma. (* UNEXPORTED Transparent ArcSin. *) -inline procedural "cic:/CoRN/transc/InvTrigonom/Sin_ArcSin.con". +inline procedural "cic:/CoRN/transc/InvTrigonom/Sin_ArcSin.con" as lemma. -inline procedural "cic:/CoRN/transc/InvTrigonom/Sin_ArcSin_inv.con". +inline procedural "cic:/CoRN/transc/InvTrigonom/Sin_ArcSin_inv.con" as lemma. -inline procedural "cic:/CoRN/transc/InvTrigonom/ArcSin_resp_leEq.con". +inline procedural "cic:/CoRN/transc/InvTrigonom/ArcSin_resp_leEq.con" as lemma. (*#* ***Cosine and Arcosine *) -inline procedural "cic:/CoRN/transc/InvTrigonom/ArcCos_Cos.con". +inline procedural "cic:/CoRN/transc/InvTrigonom/ArcCos_Cos.con" as lemma. -inline procedural "cic:/CoRN/transc/InvTrigonom/Cos_ArcCos.con". +inline procedural "cic:/CoRN/transc/InvTrigonom/Cos_ArcCos.con" as lemma. -inline procedural "cic:/CoRN/transc/InvTrigonom/ArcCos_Cos_inv.con". +inline procedural "cic:/CoRN/transc/InvTrigonom/ArcCos_Cos_inv.con" as lemma. -inline procedural "cic:/CoRN/transc/InvTrigonom/Cos_ArcCos_inv.con". +inline procedural "cic:/CoRN/transc/InvTrigonom/Cos_ArcCos_inv.con" as lemma. (* UNEXPORTED Opaque ArcSin. *) -inline procedural "cic:/CoRN/transc/InvTrigonom/ArcCos_resp_leEq.con". +inline procedural "cic:/CoRN/transc/InvTrigonom/ArcCos_resp_leEq.con" as lemma. (*#* ***Tangent and Arctangent *) -inline procedural "cic:/CoRN/transc/InvTrigonom/maps_Tan.con". +inline procedural "cic:/CoRN/transc/InvTrigonom/maps_Tan.con" as lemma. (* UNEXPORTED Opaque Tang. *) -inline procedural "cic:/CoRN/transc/InvTrigonom/ArcTan_Tan_inv.con". +inline procedural "cic:/CoRN/transc/InvTrigonom/ArcTan_Tan_inv.con" as lemma. (* UNEXPORTED Transparent Tang. @@ -176,7 +176,7 @@ Transparent Tang. Opaque ArcTang. *) -inline procedural "cic:/CoRN/transc/InvTrigonom/ArcTan_Tan.con". +inline procedural "cic:/CoRN/transc/InvTrigonom/ArcTan_Tan.con" as lemma. (* UNEXPORTED Opaque iprop. @@ -190,7 +190,7 @@ Transparent iprop. Opaque Cos. *) -inline procedural "cic:/CoRN/transc/InvTrigonom/Tan_ilim.con". +inline procedural "cic:/CoRN/transc/InvTrigonom/Tan_ilim.con" as lemma. (* UNEXPORTED Opaque Min. @@ -208,61 +208,61 @@ alias id "x" = "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/x.var". (* begin hide *) -inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min.con" "Inverses__ArcTan_Range__". +inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min.con" "Inverses__ArcTan_Range__" as definition. -inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max.con" "Inverses__ArcTan_Range__". +inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max.con" "Inverses__ArcTan_Range__" as definition. -inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min1.con" "Inverses__ArcTan_Range__". +inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min1.con" "Inverses__ArcTan_Range__" as definition. -inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min2.con" "Inverses__ArcTan_Range__". +inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min2.con" "Inverses__ArcTan_Range__" as definition. -inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min3.con" "Inverses__ArcTan_Range__". +inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min3.con" "Inverses__ArcTan_Range__" as definition. -inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min4.con" "Inverses__ArcTan_Range__". +inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min4.con" "Inverses__ArcTan_Range__" as definition. -inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max1.con" "Inverses__ArcTan_Range__". +inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max1.con" "Inverses__ArcTan_Range__" as definition. -inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max2.con" "Inverses__ArcTan_Range__". +inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max2.con" "Inverses__ArcTan_Range__" as definition. -inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max3.con" "Inverses__ArcTan_Range__". +inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max3.con" "Inverses__ArcTan_Range__" as definition. -inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max4.con" "Inverses__ArcTan_Range__". +inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max4.con" "Inverses__ArcTan_Range__" as definition. -inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min5.con" "Inverses__ArcTan_Range__". +inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min5.con" "Inverses__ArcTan_Range__" as definition. -inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min6.con" "Inverses__ArcTan_Range__". +inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min6.con" "Inverses__ArcTan_Range__" as definition. -inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max5.con" "Inverses__ArcTan_Range__". +inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max5.con" "Inverses__ArcTan_Range__" as definition. -inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max6.con" "Inverses__ArcTan_Range__". +inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max6.con" "Inverses__ArcTan_Range__" as definition. -inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a.con" "Inverses__ArcTan_Range__". +inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a.con" "Inverses__ArcTan_Range__" as definition. -inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a1.con" "Inverses__ArcTan_Range__". +inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a1.con" "Inverses__ArcTan_Range__" as definition. -inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a2.con" "Inverses__ArcTan_Range__". +inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a2.con" "Inverses__ArcTan_Range__" as definition. -inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a3.con" "Inverses__ArcTan_Range__". +inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a3.con" "Inverses__ArcTan_Range__" as definition. -inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a4.con" "Inverses__ArcTan_Range__". +inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a4.con" "Inverses__ArcTan_Range__" as definition. -inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a5.con" "Inverses__ArcTan_Range__". +inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a5.con" "Inverses__ArcTan_Range__" as definition. -inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b.con" "Inverses__ArcTan_Range__". +inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b.con" "Inverses__ArcTan_Range__" as definition. -inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b1.con" "Inverses__ArcTan_Range__". +inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b1.con" "Inverses__ArcTan_Range__" as definition. -inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b2.con" "Inverses__ArcTan_Range__". +inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b2.con" "Inverses__ArcTan_Range__" as definition. -inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b3.con" "Inverses__ArcTan_Range__". +inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b3.con" "Inverses__ArcTan_Range__" as definition. -inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b4.con" "Inverses__ArcTan_Range__". +inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b4.con" "Inverses__ArcTan_Range__" as definition. -inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b5.con" "Inverses__ArcTan_Range__". +inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b5.con" "Inverses__ArcTan_Range__" as definition. -inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/ab.con" "Inverses__ArcTan_Range__". +inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/ab.con" "Inverses__ArcTan_Range__" as definition. -inline procedural "cic:/CoRN/transc/InvTrigonom/ArcTan_range_lemma.con". +inline procedural "cic:/CoRN/transc/InvTrigonom/ArcTan_range_lemma.con" as lemma. (* end hide *) @@ -270,7 +270,7 @@ inline procedural "cic:/CoRN/transc/InvTrigonom/ArcTan_range_lemma.con". Transparent ArcTang. *) -inline procedural "cic:/CoRN/transc/InvTrigonom/ArcTan_range.con". +inline procedural "cic:/CoRN/transc/InvTrigonom/ArcTan_range.con" as lemma. (* UNEXPORTED End ArcTan_Range @@ -280,13 +280,13 @@ End ArcTan_Range Transparent ArcTang. *) -inline procedural "cic:/CoRN/transc/InvTrigonom/Tan_ArcTan.con". +inline procedural "cic:/CoRN/transc/InvTrigonom/Tan_ArcTan.con" as lemma. (* UNEXPORTED Opaque ArcTang. *) -inline procedural "cic:/CoRN/transc/InvTrigonom/Tan_ArcTan_inv.con". +inline procedural "cic:/CoRN/transc/InvTrigonom/Tan_ArcTan_inv.con" as lemma. (* UNEXPORTED End Inverses diff --git a/helm/software/matita/contribs/CoRN-Procedural/transc/Pi.mma b/helm/software/matita/contribs/CoRN-Procedural/transc/Pi.mma index ee9e30e70..e3d6eec67 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/transc/Pi.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/transc/Pi.mma @@ -29,7 +29,7 @@ Section Properties_of_Pi [Pi] is defined as twice the first positive zero of the cosine. In order to do this, we follow the construction described in Bishop 1969, section 7. *) -inline procedural "cic:/CoRN/transc/Pi/pi_seq.con". +inline procedural "cic:/CoRN/transc/Pi/pi_seq.con" as definition. (* UNEXPORTED Opaque Cosine. @@ -41,7 +41,7 @@ Opaque Cosine. Opaque Sine. *) -inline procedural "cic:/CoRN/transc/Pi/pi_seq_lemma.con". +inline procedural "cic:/CoRN/transc/Pi/pi_seq_lemma.con" as lemma. (* end hide *) @@ -51,64 +51,64 @@ This sequence is nonnegative and the cosine of any number between sequence is strictly increasing. *) -inline procedural "cic:/CoRN/transc/Pi/pi_seq_nonneg.con". +inline procedural "cic:/CoRN/transc/Pi/pi_seq_nonneg.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/cos_pi_seq_pos.con". +inline procedural "cic:/CoRN/transc/Pi/cos_pi_seq_pos.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/pi_seq_incr.con". +inline procedural "cic:/CoRN/transc/Pi/pi_seq_incr.con" as lemma. (*#* Trivial---but useful---consequences. *) -inline procedural "cic:/CoRN/transc/Pi/sin_pi_seq_mon.con". +inline procedural "cic:/CoRN/transc/Pi/sin_pi_seq_mon.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/sin_pi_seq_nonneg.con". +inline procedural "cic:/CoRN/transc/Pi/sin_pi_seq_nonneg.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/sin_pi_seq_gt_one.con". +inline procedural "cic:/CoRN/transc/Pi/sin_pi_seq_gt_one.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/cos_pi_seq_mon.con". +inline procedural "cic:/CoRN/transc/Pi/cos_pi_seq_mon.con" as lemma. (* begin hide *) -inline procedural "cic:/CoRN/transc/Pi/pi_seq_gt_one.con". +inline procedural "cic:/CoRN/transc/Pi/pi_seq_gt_one.con" as lemma. (* UNEXPORTED Opaque Sine Cosine. *) -inline procedural "cic:/CoRN/transc/Pi/pi_seq_bnd.con". +inline procedural "cic:/CoRN/transc/Pi/pi_seq_bnd.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/pi_seq_bnd'.con". +inline procedural "cic:/CoRN/transc/Pi/pi_seq_bnd'.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/pi_seq_bnd''.con". +inline procedural "cic:/CoRN/transc/Pi/pi_seq_bnd''.con" as lemma. (* end hide *) (*#* An auxiliary result. *) -inline procedural "cic:/CoRN/transc/Pi/Sin_One_pos.con". +inline procedural "cic:/CoRN/transc/Pi/Sin_One_pos.con" as lemma. (*#* We can now prove that this is a Cauchy sequence. We define [Pi] as twice its limit. *) -inline procedural "cic:/CoRN/transc/Pi/pi_seq_Cauchy.con". +inline procedural "cic:/CoRN/transc/Pi/pi_seq_Cauchy.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/Pi.con". +inline procedural "cic:/CoRN/transc/Pi/Pi.con" as definition. (*#* For $x\in[0,\frac{\pi}2)$#x∈[0,π/2)#, [(Cos x) [>] 0]; $\cos(\frac{pi}2)=0$#cos(π/2)=0#. *) -inline procedural "cic:/CoRN/transc/Pi/pos_cos.con". +inline procedural "cic:/CoRN/transc/Pi/pos_cos.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/Cos_HalfPi.con". +inline procedural "cic:/CoRN/transc/Pi/Cos_HalfPi.con" as lemma. (*#* Convergence to [Pi [/] Two] is increasing; therefore, [Pi] is positive. *) -inline procedural "cic:/CoRN/transc/Pi/HalfPi_gt_pi_seq.con". +inline procedural "cic:/CoRN/transc/Pi/HalfPi_gt_pi_seq.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/pos_Pi.con". +inline procedural "cic:/CoRN/transc/Pi/pos_Pi.con" as lemma. (* UNEXPORTED End Properties_of_Pi @@ -137,45 +137,45 @@ A summary of what is being proved is simply: [PiSolve] will prove any of these inequalities. *) -inline procedural "cic:/CoRN/transc/Pi/pos_HalfPi.con". +inline procedural "cic:/CoRN/transc/Pi/pos_HalfPi.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/pos_QuarterPi.con". +inline procedural "cic:/CoRN/transc/Pi/pos_QuarterPi.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/QuarterPi_less_HalfPi.con". +inline procedural "cic:/CoRN/transc/Pi/QuarterPi_less_HalfPi.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/HalfPi_less_Pi.con". +inline procedural "cic:/CoRN/transc/Pi/HalfPi_less_Pi.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/QuarterPi_less_Pi.con". +inline procedural "cic:/CoRN/transc/Pi/QuarterPi_less_Pi.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/neg_invPi.con". +inline procedural "cic:/CoRN/transc/Pi/neg_invPi.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/neg_invHalfPi.con". +inline procedural "cic:/CoRN/transc/Pi/neg_invHalfPi.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/neg_invQuarterPi.con". +inline procedural "cic:/CoRN/transc/Pi/neg_invQuarterPi.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/invHalfPi_less_invQuarterPi.con". +inline procedural "cic:/CoRN/transc/Pi/invHalfPi_less_invQuarterPi.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/invPi_less_invHalfPi.con". +inline procedural "cic:/CoRN/transc/Pi/invPi_less_invHalfPi.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/invPi_less_invQuarterPi.con". +inline procedural "cic:/CoRN/transc/Pi/invPi_less_invQuarterPi.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/invPi_less_Pi.con". +inline procedural "cic:/CoRN/transc/Pi/invPi_less_Pi.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/invPi_less_HalfPi.con". +inline procedural "cic:/CoRN/transc/Pi/invPi_less_HalfPi.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/invPi_less_QuarterPi.con". +inline procedural "cic:/CoRN/transc/Pi/invPi_less_QuarterPi.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/invHalfPi_less_Pi.con". +inline procedural "cic:/CoRN/transc/Pi/invHalfPi_less_Pi.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/invHalfPi_less_HalfPi.con". +inline procedural "cic:/CoRN/transc/Pi/invHalfPi_less_HalfPi.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/invHalfPi_less_QuarterPi.con". +inline procedural "cic:/CoRN/transc/Pi/invHalfPi_less_QuarterPi.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/invQuarterPi_less_Pi.con". +inline procedural "cic:/CoRN/transc/Pi/invQuarterPi_less_Pi.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/invQuarterPi_less_HalfPi.con". +inline procedural "cic:/CoRN/transc/Pi/invQuarterPi_less_HalfPi.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/invQuarterPi_less_QuarterPi.con". +inline procedural "cic:/CoRN/transc/Pi/invQuarterPi_less_QuarterPi.con" as lemma. (* UNEXPORTED End Pi_and_Order @@ -208,23 +208,23 @@ We now move back to trigonometric identities: sine, cosine and tangent of the double. *) -inline procedural "cic:/CoRN/transc/Pi/Cos_double.con". +inline procedural "cic:/CoRN/transc/Pi/Cos_double.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/Sin_double.con". +inline procedural "cic:/CoRN/transc/Pi/Sin_double.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/Tan_double.con". +inline procedural "cic:/CoRN/transc/Pi/Tan_double.con" as lemma. (* begin hide *) -inline procedural "cic:/CoRN/transc/Pi/sqrt_lemma.con". +inline procedural "cic:/CoRN/transc/Pi/sqrt_lemma.con" as lemma. (* end hide *) (*#* Value of trigonometric functions at [Pi[/]Four]. *) -inline procedural "cic:/CoRN/transc/Pi/Cos_QuarterPi.con". +inline procedural "cic:/CoRN/transc/Pi/Cos_QuarterPi.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/Sin_QuarterPi.con". +inline procedural "cic:/CoRN/transc/Pi/Sin_QuarterPi.con" as lemma. (* UNEXPORTED Hint Resolve Sin_QuarterPi Cos_QuarterPi: algebra. @@ -234,31 +234,31 @@ Hint Resolve Sin_QuarterPi Cos_QuarterPi: algebra. Opaque Sine Cosine. *) -inline procedural "cic:/CoRN/transc/Pi/Tan_QuarterPi.con". +inline procedural "cic:/CoRN/transc/Pi/Tan_QuarterPi.con" as lemma. (*#* Shifting sine and cosine by [Pi[/]Two] and [Pi]. *) -inline procedural "cic:/CoRN/transc/Pi/Sin_HalfPi.con". +inline procedural "cic:/CoRN/transc/Pi/Sin_HalfPi.con" as lemma. (* UNEXPORTED Hint Resolve Sin_HalfPi: algebra. *) -inline procedural "cic:/CoRN/transc/Pi/Sin_plus_HalfPi.con". +inline procedural "cic:/CoRN/transc/Pi/Sin_plus_HalfPi.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/Sin_HalfPi_minus.con". +inline procedural "cic:/CoRN/transc/Pi/Sin_HalfPi_minus.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/Cos_plus_HalfPi.con". +inline procedural "cic:/CoRN/transc/Pi/Cos_plus_HalfPi.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/Cos_HalfPi_minus.con". +inline procedural "cic:/CoRN/transc/Pi/Cos_HalfPi_minus.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/Sin_Pi.con". +inline procedural "cic:/CoRN/transc/Pi/Sin_Pi.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/Cos_Pi.con". +inline procedural "cic:/CoRN/transc/Pi/Cos_Pi.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/Sin_plus_Pi.con". +inline procedural "cic:/CoRN/transc/Pi/Sin_plus_Pi.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/Cos_plus_Pi.con". +inline procedural "cic:/CoRN/transc/Pi/Cos_plus_Pi.con" as lemma. (* UNEXPORTED Hint Resolve Sin_plus_Pi Cos_plus_Pi: algebra. @@ -266,11 +266,11 @@ Hint Resolve Sin_plus_Pi Cos_plus_Pi: algebra. (*#* Sine and cosine have period [Two Pi], tangent has period [Pi]. *) -inline procedural "cic:/CoRN/transc/Pi/Sin_periodic.con". +inline procedural "cic:/CoRN/transc/Pi/Sin_periodic.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/Cos_periodic.con". +inline procedural "cic:/CoRN/transc/Pi/Cos_periodic.con" as lemma. -inline procedural "cic:/CoRN/transc/Pi/Tan_periodic.con". +inline procedural "cic:/CoRN/transc/Pi/Tan_periodic.con" as lemma. (* UNEXPORTED End Sin_And_Cos diff --git a/helm/software/matita/contribs/CoRN-Procedural/transc/PowerSeries.mma b/helm/software/matita/contribs/CoRN-Procedural/transc/PowerSeries.mma index e7c5c6f7d..6a5b62b88 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/transc/PowerSeries.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/transc/PowerSeries.mma @@ -56,7 +56,7 @@ alias id "Hx0" = "cic:/CoRN/transc/PowerSeries/Power_Series/Hx0.var". alias id "a" = "cic:/CoRN/transc/PowerSeries/Power_Series/a.var". -inline procedural "cic:/CoRN/transc/PowerSeries/FPowerSeries.con". +inline procedural "cic:/CoRN/transc/PowerSeries/FPowerSeries.con" as definition. (*#* The most important convergence criterium specifically for power series @@ -67,27 +67,27 @@ is the Dirichlet criterium. alias id "Ha" = "cic:/CoRN/transc/PowerSeries/Power_Series/Ha.var". -inline procedural "cic:/CoRN/transc/PowerSeries/Power_Series/r.con" "Power_Series__". +inline procedural "cic:/CoRN/transc/PowerSeries/Power_Series/r.con" "Power_Series__" as definition. -inline procedural "cic:/CoRN/transc/PowerSeries/Power_Series/Hr.con" "Power_Series__". +inline procedural "cic:/CoRN/transc/PowerSeries/Power_Series/Hr.con" "Power_Series__" as definition. (* end show *) -inline procedural "cic:/CoRN/transc/PowerSeries/Dirichlet_crit.con". +inline procedural "cic:/CoRN/transc/PowerSeries/Dirichlet_crit.con" as lemma. (*#* When defining a function using its Taylor series as a motivation, the following operator can be of use. *) -inline procedural "cic:/CoRN/transc/PowerSeries/FPowerSeries'.con". +inline procedural "cic:/CoRN/transc/PowerSeries/FPowerSeries'.con" as definition. (*#* This function is also continuous and has a good convergence ratio. *) -inline procedural "cic:/CoRN/transc/PowerSeries/FPowerSeries'_cont.con". +inline procedural "cic:/CoRN/transc/PowerSeries/FPowerSeries'_cont.con" as lemma. -inline procedural "cic:/CoRN/transc/PowerSeries/included_FPowerSeries'.con". +inline procedural "cic:/CoRN/transc/PowerSeries/included_FPowerSeries'.con" as lemma. (* begin show *) @@ -95,9 +95,9 @@ alias id "Ha'" = "cic:/CoRN/transc/PowerSeries/Power_Series/Ha'.var". (* end show *) -inline procedural "cic:/CoRN/transc/PowerSeries/FPowerSeries'_conv'.con". +inline procedural "cic:/CoRN/transc/PowerSeries/FPowerSeries'_conv'.con" as lemma. -inline procedural "cic:/CoRN/transc/PowerSeries/FPowerSeries'_conv.con". +inline procedural "cic:/CoRN/transc/PowerSeries/FPowerSeries'_conv.con" as lemma. (* UNEXPORTED End Power_Series @@ -123,9 +123,9 @@ alias id "a" = "cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/a.var". (* begin hide *) -inline procedural "cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/F.con" "More_on_PowerSeries__". +inline procedural "cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/F.con" "More_on_PowerSeries__" as definition. -inline procedural "cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/G.con" "More_on_PowerSeries__". +inline procedural "cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/G.con" "More_on_PowerSeries__" as definition. (* end hide *) @@ -141,7 +141,7 @@ alias id "Hg" = "cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/Hg.var". (*#* We get a comparison test for power series. *) -inline procedural "cic:/CoRN/transc/PowerSeries/FPowerSeries'_comp.con". +inline procedural "cic:/CoRN/transc/PowerSeries/FPowerSeries'_comp.con" as lemma. (*#* And a rule for differentiation. *) @@ -149,7 +149,7 @@ inline procedural "cic:/CoRN/transc/PowerSeries/FPowerSeries'_comp.con". Opaque nring fac. *) -inline procedural "cic:/CoRN/transc/PowerSeries/Derivative_FPowerSeries1'.con". +inline procedural "cic:/CoRN/transc/PowerSeries/Derivative_FPowerSeries1'.con" as lemma. (* UNEXPORTED End More_on_PowerSeries @@ -166,55 +166,55 @@ series, and prove their convergence. Tangent is defined as the quotient of sine over cosine. *) -inline procedural "cic:/CoRN/transc/PowerSeries/Exp_ps.con". +inline procedural "cic:/CoRN/transc/PowerSeries/Exp_ps.con" as definition. -inline procedural "cic:/CoRN/transc/PowerSeries/sin_seq.con". +inline procedural "cic:/CoRN/transc/PowerSeries/sin_seq.con" as definition. -inline procedural "cic:/CoRN/transc/PowerSeries/sin_ps.con". +inline procedural "cic:/CoRN/transc/PowerSeries/sin_ps.con" as definition. -inline procedural "cic:/CoRN/transc/PowerSeries/cos_seq.con". +inline procedural "cic:/CoRN/transc/PowerSeries/cos_seq.con" as definition. -inline procedural "cic:/CoRN/transc/PowerSeries/cos_ps.con". +inline procedural "cic:/CoRN/transc/PowerSeries/cos_ps.con" as definition. -inline procedural "cic:/CoRN/transc/PowerSeries/Exp_conv'.con". +inline procedural "cic:/CoRN/transc/PowerSeries/Exp_conv'.con" as lemma. -inline procedural "cic:/CoRN/transc/PowerSeries/Exp_conv.con". +inline procedural "cic:/CoRN/transc/PowerSeries/Exp_conv.con" as lemma. -inline procedural "cic:/CoRN/transc/PowerSeries/sin_conv.con". +inline procedural "cic:/CoRN/transc/PowerSeries/sin_conv.con" as lemma. -inline procedural "cic:/CoRN/transc/PowerSeries/cos_conv.con". +inline procedural "cic:/CoRN/transc/PowerSeries/cos_conv.con" as lemma. -inline procedural "cic:/CoRN/transc/PowerSeries/Expon.con". +inline procedural "cic:/CoRN/transc/PowerSeries/Expon.con" as definition. -inline procedural "cic:/CoRN/transc/PowerSeries/Sine.con". +inline procedural "cic:/CoRN/transc/PowerSeries/Sine.con" as definition. -inline procedural "cic:/CoRN/transc/PowerSeries/Cosine.con". +inline procedural "cic:/CoRN/transc/PowerSeries/Cosine.con" as definition. -inline procedural "cic:/CoRN/transc/PowerSeries/Tang.con". +inline procedural "cic:/CoRN/transc/PowerSeries/Tang.con" as definition. (*#* Some auxiliary domain results. *) -inline procedural "cic:/CoRN/transc/PowerSeries/Exp_domain.con". +inline procedural "cic:/CoRN/transc/PowerSeries/Exp_domain.con" as lemma. -inline procedural "cic:/CoRN/transc/PowerSeries/sin_domain.con". +inline procedural "cic:/CoRN/transc/PowerSeries/sin_domain.con" as lemma. -inline procedural "cic:/CoRN/transc/PowerSeries/cos_domain.con". +inline procedural "cic:/CoRN/transc/PowerSeries/cos_domain.con" as lemma. -inline procedural "cic:/CoRN/transc/PowerSeries/included_Exp.con". +inline procedural "cic:/CoRN/transc/PowerSeries/included_Exp.con" as lemma. -inline procedural "cic:/CoRN/transc/PowerSeries/included_Sin.con". +inline procedural "cic:/CoRN/transc/PowerSeries/included_Sin.con" as lemma. -inline procedural "cic:/CoRN/transc/PowerSeries/included_Cos.con". +inline procedural "cic:/CoRN/transc/PowerSeries/included_Cos.con" as lemma. (*#* Definition of the logarithm. *) -inline procedural "cic:/CoRN/transc/PowerSeries/log_defn_lemma.con". +inline procedural "cic:/CoRN/transc/PowerSeries/log_defn_lemma.con" as lemma. -inline procedural "cic:/CoRN/transc/PowerSeries/Logarithm.con". +inline procedural "cic:/CoRN/transc/PowerSeries/Logarithm.con" as definition. (* UNEXPORTED End Definitions @@ -228,13 +228,13 @@ Hint Resolve included_Exp included_Sin included_Cos: included. As most of these functions are total, it makes sense to treat them as setoid functions on the reals. In the case of logarithm and tangent, this is not possible; however, we still define some abbreviations for aesthetical reasons. *) -inline procedural "cic:/CoRN/transc/PowerSeries/Exp.con". +inline procedural "cic:/CoRN/transc/PowerSeries/Exp.con" as definition. -inline procedural "cic:/CoRN/transc/PowerSeries/Sin.con". +inline procedural "cic:/CoRN/transc/PowerSeries/Sin.con" as definition. -inline procedural "cic:/CoRN/transc/PowerSeries/Cos.con". +inline procedural "cic:/CoRN/transc/PowerSeries/Cos.con" as definition. -inline procedural "cic:/CoRN/transc/PowerSeries/Log.con". +inline procedural "cic:/CoRN/transc/PowerSeries/Log.con" as definition. -inline procedural "cic:/CoRN/transc/PowerSeries/Tan.con". +inline procedural "cic:/CoRN/transc/PowerSeries/Tan.con" as definition. diff --git a/helm/software/matita/contribs/CoRN-Procedural/transc/RealPowers.mma b/helm/software/matita/contribs/CoRN-Procedural/transc/RealPowers.mma index 0f55d9769..3f16bd0d3 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/transc/RealPowers.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/transc/RealPowers.mma @@ -37,7 +37,7 @@ $x^y=e^{y\times\log(x)}$#xy=ey*log(x)#, whenever [x [>] 0], inspired by the rules for manipulating these expressions. *) -inline procedural "cic:/CoRN/transc/RealPowers/power.con". +inline procedural "cic:/CoRN/transc/RealPowers/power.con" as definition. (* NOTATION Notation "x [!] y [//] Hy" := (power x y Hy) (at level 20). @@ -50,29 +50,29 @@ still has all the good properties of that operation; when [x [=] e] it coincides with the exponential function. *) -inline procedural "cic:/CoRN/transc/RealPowers/power_wd.con". +inline procedural "cic:/CoRN/transc/RealPowers/power_wd.con" as lemma. -inline procedural "cic:/CoRN/transc/RealPowers/power_strext.con". +inline procedural "cic:/CoRN/transc/RealPowers/power_strext.con" as lemma. -inline procedural "cic:/CoRN/transc/RealPowers/power_plus.con". +inline procedural "cic:/CoRN/transc/RealPowers/power_plus.con" as lemma. -inline procedural "cic:/CoRN/transc/RealPowers/power_inv.con". +inline procedural "cic:/CoRN/transc/RealPowers/power_inv.con" as lemma. (* UNEXPORTED Hint Resolve power_wd power_plus power_inv: algebra. *) -inline procedural "cic:/CoRN/transc/RealPowers/power_minus.con". +inline procedural "cic:/CoRN/transc/RealPowers/power_minus.con" as lemma. -inline procedural "cic:/CoRN/transc/RealPowers/power_nat.con". +inline procedural "cic:/CoRN/transc/RealPowers/power_nat.con" as lemma. (* UNEXPORTED Hint Resolve power_minus power_nat: algebra. *) -inline procedural "cic:/CoRN/transc/RealPowers/power_zero.con". +inline procedural "cic:/CoRN/transc/RealPowers/power_zero.con" as lemma. -inline procedural "cic:/CoRN/transc/RealPowers/power_one.con". +inline procedural "cic:/CoRN/transc/RealPowers/power_one.con" as lemma. (* UNEXPORTED Hint Resolve power_zero power_one: algebra. @@ -82,45 +82,45 @@ Hint Resolve power_zero power_one: algebra. Opaque nexp_op. *) -inline procedural "cic:/CoRN/transc/RealPowers/power_int.con". +inline procedural "cic:/CoRN/transc/RealPowers/power_int.con" as lemma. (* UNEXPORTED Hint Resolve power_int: algebra. *) -inline procedural "cic:/CoRN/transc/RealPowers/Exp_power.con". +inline procedural "cic:/CoRN/transc/RealPowers/Exp_power.con" as lemma. -inline procedural "cic:/CoRN/transc/RealPowers/mult_power.con". +inline procedural "cic:/CoRN/transc/RealPowers/mult_power.con" as lemma. -inline procedural "cic:/CoRN/transc/RealPowers/recip_power.con". +inline procedural "cic:/CoRN/transc/RealPowers/recip_power.con" as lemma. (* UNEXPORTED Hint Resolve Exp_power mult_power recip_power: algebra. *) -inline procedural "cic:/CoRN/transc/RealPowers/div_power.con". +inline procedural "cic:/CoRN/transc/RealPowers/div_power.con" as lemma. (* UNEXPORTED Hint Resolve div_power: algebra. *) -inline procedural "cic:/CoRN/transc/RealPowers/power_ap_zero.con". +inline procedural "cic:/CoRN/transc/RealPowers/power_ap_zero.con" as lemma. -inline procedural "cic:/CoRN/transc/RealPowers/power_mult.con". +inline procedural "cic:/CoRN/transc/RealPowers/power_mult.con" as lemma. -inline procedural "cic:/CoRN/transc/RealPowers/power_pos.con". +inline procedural "cic:/CoRN/transc/RealPowers/power_pos.con" as lemma. (* UNEXPORTED Hint Resolve power_mult: algebra. *) -inline procedural "cic:/CoRN/transc/RealPowers/power_recip.con". +inline procedural "cic:/CoRN/transc/RealPowers/power_recip.con" as lemma. (* UNEXPORTED Hint Resolve power_recip: algebra. *) -inline procedural "cic:/CoRN/transc/RealPowers/power_div.con". +inline procedural "cic:/CoRN/transc/RealPowers/power_div.con" as lemma. (* UNEXPORTED Hint Resolve power_div: algebra. @@ -145,11 +145,11 @@ alias id "F" = "cic:/CoRN/transc/RealPowers/Power_Function/F.var". alias id "G" = "cic:/CoRN/transc/RealPowers/Power_Function/G.var". -inline procedural "cic:/CoRN/transc/RealPowers/FPower.con". +inline procedural "cic:/CoRN/transc/RealPowers/FPower.con" as definition. -inline procedural "cic:/CoRN/transc/RealPowers/FPower_domain.con". +inline procedural "cic:/CoRN/transc/RealPowers/FPower_domain.con" as lemma. -inline procedural "cic:/CoRN/transc/RealPowers/Continuous_power.con". +inline procedural "cic:/CoRN/transc/RealPowers/Continuous_power.con" as lemma. (* UNEXPORTED End Power_Function @@ -169,7 +169,7 @@ Opaque Expon Logarithm. (*#* From global continuity we can obviously get local continuity: *) -inline procedural "cic:/CoRN/transc/RealPowers/continuous_I_power.con". +inline procedural "cic:/CoRN/transc/RealPowers/continuous_I_power.con" as lemma. (*#* The rule for differentiation is a must. *) @@ -181,9 +181,9 @@ Transparent Logarithm. Opaque Logarithm. *) -inline procedural "cic:/CoRN/transc/RealPowers/Derivative_power.con". +inline procedural "cic:/CoRN/transc/RealPowers/Derivative_power.con" as lemma. -inline procedural "cic:/CoRN/transc/RealPowers/Diffble_power.con". +inline procedural "cic:/CoRN/transc/RealPowers/Diffble_power.con" as lemma. (* UNEXPORTED End More_on_Power_Function diff --git a/helm/software/matita/contribs/CoRN-Procedural/transc/SinCos.mma b/helm/software/matita/contribs/CoRN-Procedural/transc/SinCos.mma index 3ff87c6c6..149ff39a6 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/transc/SinCos.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/transc/SinCos.mma @@ -30,19 +30,19 @@ Opaque Sine Cosine. (* begin hide *) -inline procedural "cic:/CoRN/transc/SinCos/Sum_and_so_on/F.con" "Sum_and_so_on__". +inline procedural "cic:/CoRN/transc/SinCos/Sum_and_so_on/F.con" "Sum_and_so_on__" as definition. -inline procedural "cic:/CoRN/transc/SinCos/Sum_and_so_on/G.con" "Sum_and_so_on__". +inline procedural "cic:/CoRN/transc/SinCos/Sum_and_so_on/G.con" "Sum_and_so_on__" as definition. -inline procedural "cic:/CoRN/transc/SinCos/Sum_and_so_on/F'.con" "Sum_and_so_on__". +inline procedural "cic:/CoRN/transc/SinCos/Sum_and_so_on/F'.con" "Sum_and_so_on__" as definition. -inline procedural "cic:/CoRN/transc/SinCos/Sum_and_so_on/G'.con" "Sum_and_so_on__". +inline procedural "cic:/CoRN/transc/SinCos/Sum_and_so_on/G'.con" "Sum_and_so_on__" as definition. (* end hide *) -inline procedural "cic:/CoRN/transc/SinCos/Sin_plus.con". +inline procedural "cic:/CoRN/transc/SinCos/Sin_plus.con" as lemma. -inline procedural "cic:/CoRN/transc/SinCos/Cos_plus.con". +inline procedural "cic:/CoRN/transc/SinCos/Cos_plus.con" as lemma. (* UNEXPORTED Opaque Sine Cosine. @@ -54,7 +54,7 @@ Hint Resolve Cos_plus Sin_plus: algebra. (*#* As a corollary we get the rule for the tangent of the sum. *) -inline procedural "cic:/CoRN/transc/SinCos/Tan_plus.con". +inline procedural "cic:/CoRN/transc/SinCos/Tan_plus.con" as lemma. (* UNEXPORTED Transparent Sine Cosine. @@ -62,9 +62,9 @@ Transparent Sine Cosine. (*#* Sine, cosine and tangent of [[--]x]. *) -inline procedural "cic:/CoRN/transc/SinCos/Cos_inv.con". +inline procedural "cic:/CoRN/transc/SinCos/Cos_inv.con" as lemma. -inline procedural "cic:/CoRN/transc/SinCos/Sin_inv.con". +inline procedural "cic:/CoRN/transc/SinCos/Sin_inv.con" as lemma. (* UNEXPORTED Opaque Sine Cosine. @@ -74,7 +74,7 @@ Opaque Sine Cosine. Hint Resolve Cos_inv Sin_inv: algebra. *) -inline procedural "cic:/CoRN/transc/SinCos/Tan_inv.con". +inline procedural "cic:/CoRN/transc/SinCos/Tan_inv.con" as lemma. (* UNEXPORTED Transparent Sine Cosine. @@ -88,7 +88,7 @@ The fundamental formulas of trigonometry: $\cos(x)^2+\sin(x)^2=1$#cos(x)2