From f919cce8d299eab1dda92af4c5b53a8a7ac348af Mon Sep 17 00:00:00 2001 From: Ferruccio Guidi Date: Mon, 25 Aug 2008 10:27:03 +0000 Subject: [PATCH] transcript: bug fix in the generation of axioms variables are now unexported CoRN-Procedural: regenerated and Makefile improved --- .../components/binaries/transcript/grafite.ml | 7 +- .../binaries/transcript/v8Parser.mly | 3 +- .../matita/contribs/CoRN-Procedural/Makefile | 2 +- .../CoRN-Procedural/algebra/Basics.mma | 40 +- .../CoRN-Procedural/algebra/CAbGroups.mma | 68 +++- .../CoRN-Procedural/algebra/CAbMonoids.mma | 20 +- .../CoRN-Procedural/algebra/CFields.mma | 44 ++- .../CoRN-Procedural/algebra/CGroups.mma | 48 ++- .../CoRN-Procedural/algebra/CLogic.mma | 24 +- .../CoRN-Procedural/algebra/CMonoids.mma | 20 +- .../CoRN-Procedural/algebra/COrdAbs.mma | 8 +- .../CoRN-Procedural/algebra/COrdCauchy.mma | 48 ++- .../CoRN-Procedural/algebra/COrdFields.mma | 24 +- .../CoRN-Procedural/algebra/COrdFields2.mma | 16 +- .../CoRN-Procedural/algebra/CPoly_ApZero.mma | 36 +- .../CoRN-Procedural/algebra/CPoly_Degree.mma | 12 +- .../algebra/CPoly_NthCoeff.mma | 8 +- .../CoRN-Procedural/algebra/CPolynomials.mma | 32 +- .../CoRN-Procedural/algebra/CRings.mma | 76 +++- .../CoRN-Procedural/algebra/CSemiGroups.mma | 36 +- .../CoRN-Procedural/algebra/CSetoidFun.mma | 108 +++-- .../CoRN-Procedural/algebra/CSetoidInc.mma | 28 +- .../CoRN-Procedural/algebra/CSetoids.mma | 88 +++-- .../CoRN-Procedural/algebra/CSums.mma | 8 +- .../CoRN-Procedural/algebra/CVectorSpace.mma | 8 +- .../CoRN-Procedural/algebra/Cauchy_COF.mma | 4 +- .../CoRN-Procedural/algebra/Expon.mma | 16 +- .../CoRN-Procedural/algebra/ListType.mma | 36 +- .../CoRN-Procedural/complex/NRootCC.mma | 144 +++++-- .../CoRN-Procedural/devel/loeb/IDA/Ch6.mma | 132 +++++-- .../contribs/CoRN-Procedural/fta/CC_Props.mma | 4 +- .../CoRN-Procedural/fta/CPoly_Contin1.mma | 4 +- .../CoRN-Procedural/fta/CPoly_Rev.mma | 8 +- .../contribs/CoRN-Procedural/fta/FTA.mma | 32 +- .../contribs/CoRN-Procedural/fta/FTAreg.mma | 104 +++-- .../contribs/CoRN-Procedural/fta/KeyLemma.mma | 36 +- .../CoRN-Procedural/fta/KneserLemma.mma | 24 +- .../CoRN-Procedural/fta/MainLemma.mma | 36 +- .../CoRN-Procedural/ftc/COrdLemmas.mma | 24 +- .../CoRN-Procedural/ftc/Composition.mma | 264 +++++++++---- .../CoRN-Procedural/ftc/Continuity.mma | 116 ++++-- .../CoRN-Procedural/ftc/Derivative.mma | 44 ++- .../CoRN-Procedural/ftc/DerivativeOps.mma | 116 ++++-- .../CoRN-Procedural/ftc/Differentiability.mma | 100 +++-- .../contribs/CoRN-Procedural/ftc/FTC.mma | 216 +++++++--- .../CoRN-Procedural/ftc/FunctSequence.mma | 260 +++++++++---- .../CoRN-Procedural/ftc/FunctSeries.mma | 136 +++++-- .../contribs/CoRN-Procedural/ftc/Integral.mma | 212 +++++++--- .../CoRN-Procedural/ftc/IntervalFunct.mma | 68 +++- .../CoRN-Procedural/ftc/MoreFunSeries.mma | 272 +++++++++---- .../CoRN-Procedural/ftc/MoreFunctions.mma | 260 +++++++++---- .../CoRN-Procedural/ftc/MoreIntegrals.mma | 128 ++++-- .../CoRN-Procedural/ftc/MoreIntervals.mma | 24 +- .../CoRN-Procedural/ftc/NthDerivative.mma | 60 ++- .../CoRN-Procedural/ftc/PartFunEquality.mma | 116 ++++-- .../CoRN-Procedural/ftc/PartInterval.mma | 84 +++- .../CoRN-Procedural/ftc/Partitions.mma | 144 +++++-- .../contribs/CoRN-Procedural/ftc/RefLemma.mma | 368 +++++++++++++----- .../CoRN-Procedural/ftc/RefSepRef.mma | 44 ++- .../CoRN-Procedural/ftc/RefSeparated.mma | 92 +++-- .../CoRN-Procedural/ftc/RefSeparating.mma | 68 +++- .../contribs/CoRN-Procedural/ftc/Rolle.mma | 116 ++++-- .../CoRN-Procedural/ftc/StrongIVT.mma | 40 +- .../contribs/CoRN-Procedural/ftc/Taylor.mma | 84 +++- .../CoRN-Procedural/ftc/TaylorLemma.mma | 32 +- .../contribs/CoRN-Procedural/ftc/WeakIVT.mma | 80 +++- .../metrics/CPseudoMSpaces.mma | 16 +- .../CoRN-Procedural/metrics/ContFunctions.mma | 36 +- .../CoRN-Procedural/metrics/IR_CPMSpace.mma | 4 +- .../CoRN-Procedural/reals/Bridges_LUB.mma | 28 +- .../CoRN-Procedural/reals/Bridges_iso.mma | 36 +- .../CoRN-Procedural/reals/CMetricFields.mma | 4 +- .../CoRN-Procedural/reals/CReals1.mma | 56 ++- .../CoRN-Procedural/reals/CSumsReals.mma | 4 +- .../CoRN-Procedural/reals/CauchySeq.mma | 2 +- .../CoRN-Procedural/reals/Cauchy_CReals.mma | 8 +- .../contribs/CoRN-Procedural/reals/IVT.mma | 108 +++-- .../CoRN-Procedural/reals/Intervals.mma | 36 +- .../CoRN-Procedural/reals/Max_AbsIR.mma | 44 ++- .../CoRN-Procedural/reals/NRootIR.mma | 32 +- .../CoRN-Procedural/reals/OddPolyRootIR.mma | 16 +- .../CoRN-Procedural/reals/Q_dense.mma | 12 +- .../CoRN-Procedural/reals/Q_in_CReals.mma | 4 +- .../CoRN-Procedural/reals/R_morphism.mma | 124 ++++-- .../CoRN-Procedural/reals/RealFuncts.mma | 8 +- .../contribs/CoRN-Procedural/reals/Series.mma | 96 +++-- .../CoRN-Procedural/reals/iso_CReals.mma | 8 +- .../CoRN-Procedural/tactics/DiffTactics2.mma | 16 +- .../tactics/FieldReflection.mma | 40 +- .../tactics/GroupReflection.mma | 40 +- .../tactics/RingReflection.mma | 40 +- .../CoRN-Procedural/transc/InvTrigonom.mma | 4 +- .../CoRN-Procedural/transc/PowerSeries.mma | 44 ++- .../CoRN-Procedural/transc/RealPowers.mma | 12 +- .../CoRN-Procedural/transc/TaylorSeries.mma | 104 +++-- 95 files changed, 4456 insertions(+), 1486 deletions(-) diff --git a/helm/software/components/binaries/transcript/grafite.ml b/helm/software/components/binaries/transcript/grafite.ml index 9e634d655..1f9b36866 100644 --- a/helm/software/components/binaries/transcript/grafite.ml +++ b/helm/software/components/binaries/transcript/grafite.ml @@ -97,7 +97,12 @@ let commit kind och items = | 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_unexported och "UNEXPORTED" src +(* FG: we do not export variables because we cook the other object + * let name = UriManager.name_of_uri (UriManager.uri_of_string src) in + * out_alias och name 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/v8Parser.mly b/helm/software/components/binaries/transcript/v8Parser.mly index 969524d22..65372d914 100644 --- a/helm/software/components/binaries/transcript/v8Parser.mly +++ b/helm/software/components/binaries/transcript/v8Parser.mly @@ -35,7 +35,8 @@ let cat x = String.concat " " x let mk_vars local idents = - let map ident = T.Inline (local, T.Var, trim ident, "", None) in + let kind = if local then T.Var else T.Con in + let map ident = T.Inline (local, kind, trim ident, "", None) in List.map map idents let strip2 s = diff --git a/helm/software/matita/contribs/CoRN-Procedural/Makefile b/helm/software/matita/contribs/CoRN-Procedural/Makefile index 8d82928f2..9336c874e 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/Makefile +++ b/helm/software/matita/contribs/CoRN-Procedural/Makefile @@ -39,5 +39,5 @@ clean.ma: $(H)echo no files to clean endif -mma: CoRN.conf.xml +mma: CoRN.conf.xml clean.ma $(H)$(TRANSCRIPT) -C $(BIN) CoRN diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/Basics.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/Basics.mma index 5e862ff9f..2796abc42 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/Basics.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/Basics.mma @@ -224,9 +224,13 @@ inline procedural "cic:/CoRN/algebra/Basics/Zmult_absorb.con" as lemma. Section Well_foundedT *) -alias id "A" = "cic:/CoRN/algebra/Basics/Well_foundedT/A.var". +(* UNEXPORTED +cic:/CoRN/algebra/Basics/Well_foundedT/A.var +*) -alias id "R" = "cic:/CoRN/algebra/Basics/Well_foundedT/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/Basics/Well_foundedT/R.var +*) (*#* The accessibility predicate is defined to be non-informative *) @@ -240,7 +244,9 @@ End Well_foundedT Section AccT *) -alias id "A" = "cic:/CoRN/algebra/Basics/AccT/A.var". +(* UNEXPORTED +cic:/CoRN/algebra/Basics/AccT/A.var +*) inline procedural "cic:/CoRN/algebra/Basics/well_founded.con" as definition. @@ -256,17 +262,25 @@ Implicit Arguments Acc [A]. Section IndT *) -alias id "A" = "cic:/CoRN/algebra/Basics/IndT/A.var". +(* UNEXPORTED +cic:/CoRN/algebra/Basics/IndT/A.var +*) -alias id "R" = "cic:/CoRN/algebra/Basics/IndT/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/Basics/IndT/R.var +*) (* UNEXPORTED Section AccIter *) -alias id "P" = "cic:/CoRN/algebra/Basics/IndT/AccIter/P.var". +(* UNEXPORTED +cic:/CoRN/algebra/Basics/IndT/AccIter/P.var +*) -alias id "F" = "cic:/CoRN/algebra/Basics/IndT/AccIter/F.var". +(* UNEXPORTED +cic:/CoRN/algebra/Basics/IndT/AccIter/F.var +*) inline procedural "cic:/CoRN/algebra/Basics/Acc_inv.con" as lemma. @@ -276,7 +290,9 @@ inline procedural "cic:/CoRN/algebra/Basics/Acc_iter.con" as definition. End AccIter *) -alias id "Rwf" = "cic:/CoRN/algebra/Basics/IndT/Rwf.var". +(* UNEXPORTED +cic:/CoRN/algebra/Basics/IndT/Rwf.var +*) inline procedural "cic:/CoRN/algebra/Basics/well_founded_induction_type.con" as theorem. @@ -288,9 +304,13 @@ End IndT Section InductionT *) -alias id "A" = "cic:/CoRN/algebra/Basics/InductionT/A.var". +(* UNEXPORTED +cic:/CoRN/algebra/Basics/InductionT/A.var +*) -alias id "f" = "cic:/CoRN/algebra/Basics/InductionT/f.var". +(* UNEXPORTED +cic:/CoRN/algebra/Basics/InductionT/f.var +*) inline procedural "cic:/CoRN/algebra/Basics/ltof.con" as definition. diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/CAbGroups.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/CAbGroups.mma index a18d0e3e4..61aa193c9 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/CAbGroups.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/CAbGroups.mma @@ -39,7 +39,9 @@ cic:/matita/CoRN-Procedural/algebra/CAbGroups/cag_crr.con Section AbGroup_Axioms *) -alias id "G" = "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/AbGroup_Axioms/G.var". +(* UNEXPORTED +cic:/CoRN/algebra/CAbGroups/Abelian_Groups/AbGroup_Axioms/G.var +*) (*#* %\begin{convention}% Let [G] be an Abelian Group. @@ -64,15 +66,25 @@ Section SubCAbGroups ** Subgroups of an Abelian Group *) -alias id "G" = "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/G.var". +(* UNEXPORTED +cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/G.var +*) -alias id "P" = "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/P.var". +(* UNEXPORTED +cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/P.var +*) -alias id "Punit" = "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/Punit.var". +(* UNEXPORTED +cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/Punit.var +*) -alias id "op_pres_P" = "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/op_pres_P.var". +(* UNEXPORTED +cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/op_pres_P.var +*) -alias id "inv_pres_P" = "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/inv_pres_P.var". +(* UNEXPORTED +cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/inv_pres_P.var +*) (*#* %\begin{convention}% @@ -103,7 +115,9 @@ Section Various Hint Resolve cag_commutes_unfolded: algebra. *) -alias id "G" = "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/Various/G.var". +(* UNEXPORTED +cic:/CoRN/algebra/CAbGroups/Abelian_Groups/Various/G.var +*) (*#* %\begin{convention}% Let [G] be an Abelian Group. @@ -163,11 +177,17 @@ as a left unit, and a unary setoid function [inv] which inverts elements respective to [plus]. *) -alias id "S" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/S.var". +(* UNEXPORTED +cic:/CoRN/algebra/CAbGroups/Nice_Char/S.var +*) -alias id "unit" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/unit.var". +(* UNEXPORTED +cic:/CoRN/algebra/CAbGroups/Nice_Char/unit.var +*) -alias id "plus" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/plus.var". +(* UNEXPORTED +cic:/CoRN/algebra/CAbGroups/Nice_Char/plus.var +*) (*#* %\begin{convention}% @@ -179,17 +199,29 @@ for [plus] and [(inv x)] is a right-inverse of [x] w.r.t.%\% [plus]. %\end{convention}% *) -alias id "plus_lext" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/plus_lext.var". +(* UNEXPORTED +cic:/CoRN/algebra/CAbGroups/Nice_Char/plus_lext.var +*) -alias id "plus_lunit" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/plus_lunit.var". +(* UNEXPORTED +cic:/CoRN/algebra/CAbGroups/Nice_Char/plus_lunit.var +*) -alias id "plus_comm" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/plus_comm.var". +(* UNEXPORTED +cic:/CoRN/algebra/CAbGroups/Nice_Char/plus_comm.var +*) -alias id "plus_assoc" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/plus_assoc.var". +(* UNEXPORTED +cic:/CoRN/algebra/CAbGroups/Nice_Char/plus_assoc.var +*) -alias id "inv" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/inv.var". +(* UNEXPORTED +cic:/CoRN/algebra/CAbGroups/Nice_Char/inv.var +*) -alias id "inv_inv" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/inv_inv.var". +(* UNEXPORTED +cic:/CoRN/algebra/CAbGroups/Nice_Char/inv_inv.var +*) inline procedural "cic:/CoRN/algebra/CAbGroups/plus_rext.con" as lemma. @@ -222,7 +254,9 @@ For reflection the following is needed; hopefully it is also useful. Section Group_Extras *) -alias id "G" = "cic:/CoRN/algebra/CAbGroups/Group_Extras/G.var". +(* UNEXPORTED +cic:/CoRN/algebra/CAbGroups/Group_Extras/G.var +*) inline procedural "cic:/CoRN/algebra/CAbGroups/nmult.con" as definition. diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/CAbMonoids.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/CAbMonoids.mma index eada9abc4..b1bce8362 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/CAbMonoids.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/CAbMonoids.mma @@ -39,7 +39,9 @@ cic:/matita/CoRN-Procedural/algebra/CAbMonoids/cam_crr.con Section AbMonoid_Axioms *) -alias id "M" = "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/AbMonoid_Axioms/M.var". +(* UNEXPORTED +cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/AbMonoid_Axioms/M.var +*) (*#* %\begin{convention}% Let [M] be an abelian monoid. @@ -64,13 +66,21 @@ Section SubCAbMonoids ** Subgroups of an Abelian Monoid *) -alias id "M" = "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/M.var". +(* UNEXPORTED +cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/M.var +*) -alias id "P" = "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/P.var". +(* UNEXPORTED +cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/P.var +*) -alias id "Punit" = "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/Punit.var". +(* UNEXPORTED +cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/Punit.var +*) -alias id "op_pres_P" = "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/op_pres_P.var". +(* UNEXPORTED +cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/op_pres_P.var +*) (*#* %\begin{convention}% diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/CFields.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/CFields.mma index 9d1245aa9..5cc4834dc 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/CFields.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/CFields.mma @@ -188,7 +188,9 @@ write [e[/] (Snring n)] and [e[/]TwoNZ], [e[/]ThreeNZ] and so on. Section Field_axioms *) -alias id "F" = "cic:/CoRN/algebra/CFields/Field_axioms/F.var". +(* UNEXPORTED +cic:/CoRN/algebra/CFields/Field_axioms/F.var +*) inline procedural "cic:/CoRN/algebra/CFields/CField_is_CField.con" as lemma. @@ -207,7 +209,9 @@ Section Field_basics %\end{convention}% *) -alias id "F" = "cic:/CoRN/algebra/CFields/Field_basics/F.var". +(* UNEXPORTED +cic:/CoRN/algebra/CFields/Field_basics/F.var +*) inline procedural "cic:/CoRN/algebra/CFields/rcpcl_is_inverse_unfolded.con" as lemma. @@ -237,7 +241,9 @@ Section Field_multiplication %\end{convention}% *) -alias id "F" = "cic:/CoRN/algebra/CFields/Field_multiplication/F.var". +(* UNEXPORTED +cic:/CoRN/algebra/CFields/Field_multiplication/F.var +*) inline procedural "cic:/CoRN/algebra/CFields/mult_resp_ap_zero.con" as lemma. @@ -291,7 +297,9 @@ Section Rcpcl_properties %\end{convention}% *) -alias id "F" = "cic:/CoRN/algebra/CFields/Rcpcl_properties/F.var". +(* UNEXPORTED +cic:/CoRN/algebra/CFields/Rcpcl_properties/F.var +*) inline procedural "cic:/CoRN/algebra/CFields/inv_one.con" as lemma. @@ -317,7 +325,9 @@ Section MultipGroup %\end{convention}% *) -alias id "F" = "cic:/CoRN/algebra/CFields/MultipGroup/F.var". +(* UNEXPORTED +cic:/CoRN/algebra/CFields/MultipGroup/F.var +*) (*#* The multiplicative monoid of NonZeros. @@ -350,7 +360,9 @@ In the names of lemmas, we denote [[/]] by [div], and %\end{nameconvention}% *) -alias id "F" = "cic:/CoRN/algebra/CFields/Div_properties/F.var". +(* UNEXPORTED +cic:/CoRN/algebra/CFields/Div_properties/F.var +*) inline procedural "cic:/CoRN/algebra/CFields/div_prop.con" as lemma. @@ -448,7 +460,9 @@ Hint Resolve div_1 div_1' div_1'' div_wd x_div_x x_div_one div_div div_div2 Section Mult_Cancel_Ap_Zero *) -alias id "F" = "cic:/CoRN/algebra/CFields/Mult_Cancel_Ap_Zero/F.var". +(* UNEXPORTED +cic:/CoRN/algebra/CFields/Mult_Cancel_Ap_Zero/F.var +*) inline procedural "cic:/CoRN/algebra/CFields/mult_cancel_ap_zero_lft.con" as lemma. @@ -480,11 +494,17 @@ Let [X] be a Field and [F,G:(PartFunct X)] have domains respectively %\end{convention}% *) -alias id "X" = "cic:/CoRN/algebra/CFields/CField_Ops/X.var". +(* UNEXPORTED +cic:/CoRN/algebra/CFields/CField_Ops/X.var +*) -alias id "F" = "cic:/CoRN/algebra/CFields/CField_Ops/F.var". +(* UNEXPORTED +cic:/CoRN/algebra/CFields/CField_Ops/F.var +*) -alias id "G" = "cic:/CoRN/algebra/CFields/CField_Ops/G.var". +(* UNEXPORTED +cic:/CoRN/algebra/CFields/CField_Ops/G.var +*) (* begin hide *) @@ -543,7 +563,9 @@ End Part_Function_Div %\end{convention}% *) -alias id "R" = "cic:/CoRN/algebra/CFields/CField_Ops/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/CFields/CField_Ops/R.var +*) inline procedural "cic:/CoRN/algebra/CFields/included_FRecip.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/CGroups.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/CGroups.mma index 12594f975..e7cc27955 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/CGroups.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/CGroups.mma @@ -90,7 +90,9 @@ Infix "[-]" := cg_minus (at level 50, left associativity). Section CGroup_axioms *) -alias id "G" = "cic:/CoRN/algebra/CGroups/CGroup_axioms/G.var". +(* UNEXPORTED +cic:/CoRN/algebra/CGroups/CGroup_axioms/G.var +*) inline procedural "cic:/CoRN/algebra/CGroups/cg_inverse.con" as lemma. @@ -109,7 +111,9 @@ General properties of groups. Section CGroup_basics *) -alias id "G" = "cic:/CoRN/algebra/CGroups/CGroup_basics/G.var". +(* UNEXPORTED +cic:/CoRN/algebra/CGroups/CGroup_basics/G.var +*) inline procedural "cic:/CoRN/algebra/CGroups/cg_rht_inv_unfolded.con" as lemma. @@ -191,13 +195,21 @@ inline procedural "cic:/CoRN/algebra/CGroups/x_minus_x.con" as lemma. Section SubCGroups *) -alias id "P" = "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/P.var". +(* UNEXPORTED +cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/P.var +*) -alias id "Punit" = "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/Punit.var". +(* UNEXPORTED +cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/Punit.var +*) -alias id "op_pres_P" = "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/op_pres_P.var". +(* UNEXPORTED +cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/op_pres_P.var +*) -alias id "inv_pres_P" = "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/inv_pres_P.var". +(* UNEXPORTED +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__" as definition. @@ -241,7 +253,9 @@ Hint Resolve cg_minus_wd: algebra_c. Section Assoc_properties *) -alias id "G" = "cic:/CoRN/algebra/CGroups/Assoc_properties/G.var". +(* UNEXPORTED +cic:/CoRN/algebra/CGroups/Assoc_properties/G.var +*) inline procedural "cic:/CoRN/algebra/CGroups/assoc_2.con" as lemma. @@ -271,7 +285,9 @@ Specific properties of apartness. Section cgroups_apartness *) -alias id "G" = "cic:/CoRN/algebra/CGroups/cgroups_apartness/G.var". +(* UNEXPORTED +cic:/CoRN/algebra/CGroups/cgroups_apartness/G.var +*) inline procedural "cic:/CoRN/algebra/CGroups/cg_add_ap_zero.con" as lemma. @@ -322,11 +338,17 @@ by [P] and [Q]. %\end{convention}% *) -alias id "G" = "cic:/CoRN/algebra/CGroups/CGroup_Ops/G.var". +(* UNEXPORTED +cic:/CoRN/algebra/CGroups/CGroup_Ops/G.var +*) -alias id "F" = "cic:/CoRN/algebra/CGroups/CGroup_Ops/F.var". +(* UNEXPORTED +cic:/CoRN/algebra/CGroups/CGroup_Ops/F.var +*) -alias id "F'" = "cic:/CoRN/algebra/CGroups/CGroup_Ops/F'.var". +(* UNEXPORTED +cic:/CoRN/algebra/CGroups/CGroup_Ops/F'.var +*) (* begin hide *) @@ -365,7 +387,9 @@ End Part_Function_Minus %\end{convention}% *) -alias id "R" = "cic:/CoRN/algebra/CGroups/CGroup_Ops/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/CGroups/CGroup_Ops/R.var +*) inline procedural "cic:/CoRN/algebra/CGroups/included_FInv.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/CLogic.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/CLogic.mma index 09a03a9f5..4c77e6b47 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/CLogic.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/CLogic.mma @@ -215,7 +215,9 @@ Section Choice Let [P] be a predicate on $\NN^2$#N times N#. *) -alias id "P" = "cic:/CoRN/algebra/CLogic/Choice/P.var". +(* UNEXPORTED +cic:/CoRN/algebra/CLogic/Choice/P.var +*) inline procedural "cic:/CoRN/algebra/CLogic/choice.con" as lemma. @@ -250,11 +252,15 @@ Similar to Relations.v in Coq's standard library. %\end{convention}% *) -alias id "A" = "cic:/CoRN/algebra/CLogic/CRelation_Definition/A.var". +(* UNEXPORTED +cic:/CoRN/algebra/CLogic/CRelation_Definition/A.var +*) inline procedural "cic:/CoRN/algebra/CLogic/Crelation.con" as definition. -alias id "R" = "cic:/CoRN/algebra/CLogic/CRelation_Definition/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/CLogic/CRelation_Definition/R.var +*) inline procedural "cic:/CoRN/algebra/CLogic/Creflexive.con" as definition. @@ -279,11 +285,15 @@ Analogous. %\end{convention}% *) -alias id "A" = "cic:/CoRN/algebra/CLogic/TRelation_Definition/A.var". +(* UNEXPORTED +cic:/CoRN/algebra/CLogic/TRelation_Definition/A.var +*) inline procedural "cic:/CoRN/algebra/CLogic/Trelation.con" as definition. -alias id "R" = "cic:/CoRN/algebra/CLogic/TRelation_Definition/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/CLogic/TRelation_Definition/R.var +*) inline procedural "cic:/CoRN/algebra/CLogic/Treflexive.con" as definition. @@ -465,7 +475,9 @@ inline procedural "cic:/CoRN/algebra/CLogic/plus_pred_pred_plus.con" as lemma. %\end{convention}% *) -alias id "h" = "cic:/CoRN/algebra/CLogic/Natural_Numbers/h.var". +(* UNEXPORTED +cic:/CoRN/algebra/CLogic/Natural_Numbers/h.var +*) (*#* First we characterize monotonicity by a local condition: if [h(n) < h(n+1)] diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/CMonoids.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/CMonoids.mma index 6d13c1b52..895ecbdf2 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/CMonoids.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/CMonoids.mma @@ -92,7 +92,9 @@ Implicit Arguments nonZeroP [M]. Section CMonoid_axioms *) -alias id "M" = "cic:/CoRN/algebra/CMonoids/CMonoid_axioms/M.var". +(* UNEXPORTED +cic:/CoRN/algebra/CMonoids/CMonoid_axioms/M.var +*) inline procedural "cic:/CoRN/algebra/CMonoids/CMonoid_is_CMonoid.con" as lemma. @@ -114,7 +116,9 @@ End CMonoid_axioms Section CMonoid_basics *) -alias id "M" = "cic:/CoRN/algebra/CMonoids/CMonoid_basics/M.var". +(* UNEXPORTED +cic:/CoRN/algebra/CMonoids/CMonoid_basics/M.var +*) inline procedural "cic:/CoRN/algebra/CMonoids/cm_rht_unit_unfolded.con" as lemma. @@ -149,11 +153,17 @@ Let [P] a predicate on [M] containing [Zero] and closed under [[+]]. Section SubCMonoids *) -alias id "P" = "cic:/CoRN/algebra/CMonoids/CMonoid_basics/SubCMonoids/P.var". +(* UNEXPORTED +cic:/CoRN/algebra/CMonoids/CMonoid_basics/SubCMonoids/P.var +*) -alias id "Punit" = "cic:/CoRN/algebra/CMonoids/CMonoid_basics/SubCMonoids/Punit.var". +(* UNEXPORTED +cic:/CoRN/algebra/CMonoids/CMonoid_basics/SubCMonoids/Punit.var +*) -alias id "op_pres_P" = "cic:/CoRN/algebra/CMonoids/CMonoid_basics/SubCMonoids/op_pres_P.var". +(* UNEXPORTED +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__" as definition. diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/COrdAbs.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/COrdAbs.mma index e3b9709c7..88fc8cb9e 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/COrdAbs.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/COrdAbs.mma @@ -41,7 +41,9 @@ Section AbsSmall_properties %\end{convention}% *) -alias id "R" = "cic:/CoRN/algebra/COrdAbs/AbsSmall_properties/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/COrdAbs/AbsSmall_properties/R.var +*) inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_wdr.con" as lemma. @@ -134,7 +136,9 @@ Section absBig_wd_properties %\end{convention}% *) -alias id "R" = "cic:/CoRN/algebra/COrdAbs/absBig_wd_properties/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/COrdAbs/absBig_wd_properties/R.var +*) inline procedural "cic:/CoRN/algebra/COrdAbs/AbsBig_wdr.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/COrdCauchy.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/COrdCauchy.mma index c9dc0e0cd..e305a697a 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/COrdCauchy.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/COrdCauchy.mma @@ -29,7 +29,9 @@ Section OrdField_Cauchy %\end{convention}% *) -alias id "R" = "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/R.var +*) (* begin hide *) @@ -95,13 +97,21 @@ inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_const.con" as lemma. %\end{convention}% *) -alias id "f" = "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/f.var". +(* UNEXPORTED +cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/f.var +*) -alias id "g" = "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/g.var". +(* UNEXPORTED +cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/g.var +*) -alias id "Hf" = "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/Hf.var". +(* UNEXPORTED +cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/Hf.var +*) -alias id "Hg" = "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/Hg.var". +(* UNEXPORTED +cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/Hg.var +*) inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_plus.con" as lemma. @@ -121,13 +131,21 @@ Let [e] be a postive element of [R] and let [N:nat] be such that from %\end{convention}% *) -alias id "e" = "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/e.var". +(* UNEXPORTED +cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/e.var +*) -alias id "He" = "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/He.var". +(* UNEXPORTED +cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/He.var +*) -alias id "N" = "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/N.var". +(* UNEXPORTED +cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/N.var +*) -alias id "f_bnd" = "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/f_bnd.var". +(* UNEXPORTED +cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/f_bnd.var +*) inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_recip_def.con" as lemma. @@ -154,7 +172,9 @@ inline procedural "cic:/CoRN/algebra/COrdCauchy/maj_upto_eps.con" as lemma. Section Mult_AbsSmall *) -alias id "R" = "cic:/CoRN/algebra/COrdCauchy/Mult_AbsSmall/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/COrdCauchy/Mult_AbsSmall/R.var +*) (*#* ** [AbsSmall] revisited @@ -178,7 +198,9 @@ End Mult_AbsSmall Section Mult_Continuous *) -alias id "R" = "cic:/CoRN/algebra/COrdCauchy/Mult_Continuous/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/COrdCauchy/Mult_Continuous/R.var +*) (*#* ** Multiplication is continuous @@ -214,7 +236,9 @@ characterize them in some way. %\end{convention}% *) -alias id "R" = "cic:/CoRN/algebra/COrdCauchy/Monotonous_functions/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/COrdCauchy/Monotonous_functions/R.var +*) (*#* We begin by characterizing the preservation of less (less or equal) diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/COrdFields.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/COrdFields.mma index 44e978614..19c308f6e 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/COrdFields.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/COrdFields.mma @@ -144,7 +144,9 @@ Let [F] be a field. %\end{convention}% *) -alias id "F" = "cic:/CoRN/algebra/COrdFields/COrdField_axioms/F.var". +(* UNEXPORTED +cic:/CoRN/algebra/COrdFields/COrdField_axioms/F.var +*) inline procedural "cic:/CoRN/algebra/COrdFields/COrdField_is_COrdField.con" as lemma. @@ -195,7 +197,9 @@ Let in the rest of this section (and all subsections) %\end{convention}% *) -alias id "R" = "cic:/CoRN/algebra/COrdFields/OrdField_basics/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/COrdFields/OrdField_basics/R.var +*) inline procedural "cic:/CoRN/algebra/COrdFields/less_imp_ap.con" as lemma. @@ -232,7 +236,9 @@ Section Basic_Properties_of_leEq (*#* ** Basic properties of [ [<=] ] *) -alias id "R" = "cic:/CoRN/algebra/COrdFields/Basic_Properties_of_leEq/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/COrdFields/Basic_Properties_of_leEq/R.var +*) inline procedural "cic:/CoRN/algebra/COrdFields/leEq_wdr.con" as lemma. @@ -288,7 +294,9 @@ and so on. These are elements of [NonZeros], so that we can write e.g.%\% [x[/]TwoNZ]. *) -alias id "R" = "cic:/CoRN/algebra/COrdFields/infinity_of_cordfields/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/COrdFields/infinity_of_cordfields/R.var +*) inline procedural "cic:/CoRN/algebra/COrdFields/pos_one.con" as lemma. @@ -474,7 +482,9 @@ Section consequences_of_infinity *** Consequences of infinity *) -alias id "F" = "cic:/CoRN/algebra/COrdFields/consequences_of_infinity/F.var". +(* UNEXPORTED +cic:/CoRN/algebra/COrdFields/consequences_of_infinity/F.var +*) inline procedural "cic:/CoRN/algebra/COrdFields/square_eq.con" as lemma. @@ -500,7 +510,9 @@ Section Properties_of_Ordering ** Properties of [[<]] *) -alias id "R" = "cic:/CoRN/algebra/COrdFields/Properties_of_Ordering/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/COrdFields/Properties_of_Ordering/R.var +*) (*#* We do not use a special predicate for positivity, diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/COrdFields2.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/COrdFields2.mma index 595d7ef8b..c8436078d 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/COrdFields2.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/COrdFields2.mma @@ -36,7 +36,9 @@ Section Properties_of_leEq %\end{convention}% *) -alias id "R" = "cic:/CoRN/algebra/COrdFields2/Properties_of_leEq/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/COrdFields2/Properties_of_leEq/R.var +*) (* UNEXPORTED Section addition @@ -246,7 +248,9 @@ Section PosP_properties %\end{convention}% *) -alias id "R" = "cic:/CoRN/algebra/COrdFields2/PosP_properties/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/COrdFields2/PosP_properties/R.var +*) (* begin hide *) @@ -310,7 +314,9 @@ Implicit Arguments one_div_succ [R]. Section One_div_succ_properties *) -alias id "R" = "cic:/CoRN/algebra/COrdFields2/One_div_succ_properties/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/COrdFields2/One_div_succ_properties/R.var +*) inline procedural "cic:/CoRN/algebra/COrdFields2/one_div_succ_resp_leEq.con" as lemma. @@ -342,7 +348,9 @@ Let [R] be an ordered field. %\end{convention}% *) -alias id "R" = "cic:/CoRN/algebra/COrdFields2/Half_properties/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/COrdFields2/Half_properties/R.var +*) inline procedural "cic:/CoRN/algebra/COrdFields2/half_1.con" as lemma. 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 362c9e91b..2280e0354 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/CPoly_ApZero.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/CPoly_ApZero.mma @@ -43,17 +43,29 @@ has degree at most [n]. %\end{convention}% *) -alias id "R" = "cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/R.var +*) -alias id "a_" = "cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/a_.var". +(* UNEXPORTED +cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/a_.var +*) -alias id "distinct_a_" = "cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/distinct_a_.var". +(* UNEXPORTED +cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/distinct_a_.var +*) -alias id "f" = "cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/f.var". +(* UNEXPORTED +cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/f.var +*) -alias id "n" = "cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/n.var". +(* UNEXPORTED +cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/n.var +*) -alias id "degree_f" = "cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/degree_f.var". +(* UNEXPORTED +cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/degree_f.var +*) (* begin hide *) @@ -138,11 +150,15 @@ If we are in a field of characteristic zero, the previous result can be strengthened. *) -alias id "R" = "cic:/CoRN/algebra/CPoly_ApZero/Characteristic_zero/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/CPoly_ApZero/Characteristic_zero/R.var +*) (* begin show *) -alias id "H" = "cic:/CoRN/algebra/CPoly_ApZero/Characteristic_zero/H.var". +(* UNEXPORTED +cic:/CoRN/algebra/CPoly_ApZero/Characteristic_zero/H.var +*) (* end show *) @@ -174,7 +190,9 @@ End Characteristic_zero Section Poly_ApZero_Interval *) -alias id "R" = "cic:/CoRN/algebra/CPoly_ApZero/Poly_ApZero_Interval/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/CPoly_ApZero/Poly_ApZero_Interval/R.var +*) (* begin hide *) 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 52272b28e..7d4b693ef 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/CPoly_Degree.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/CPoly_Degree.mma @@ -34,7 +34,9 @@ over [R]. Section Degree_def *) -alias id "R" = "cic:/CoRN/algebra/CPoly_Degree/Degree_def/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/CPoly_Degree/Degree_def/R.var +*) (* begin hide *) @@ -106,7 +108,9 @@ Implicit Arguments lth_of_poly [R]. Section Degree_props *) -alias id "R" = "cic:/CoRN/algebra/CPoly_Degree/Degree_props/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/CPoly_Degree/Degree_props/R.var +*) (* begin hide *) @@ -220,7 +224,9 @@ polynomials over [F]. %\end{convention}% *) -alias id "F" = "cic:/CoRN/algebra/CPoly_Degree/degree_props_Field/F.var". +(* UNEXPORTED +cic:/CoRN/algebra/CPoly_Degree/degree_props_Field/F.var +*) (* begin hide *) 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 b198a9f80..7318a76c3 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/CPoly_NthCoeff.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/CPoly_NthCoeff.mma @@ -33,7 +33,9 @@ polynomials over [R]. Section NthCoeff_def *) -alias id "R" = "cic:/CoRN/algebra/CPoly_NthCoeff/NthCoeff_def/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/CPoly_NthCoeff/NthCoeff_def/R.var +*) (* begin hide *) @@ -113,7 +115,9 @@ Section NthCoeff_props (*#* ** Properties of [nth_coeff] *) -alias id "R" = "cic:/CoRN/algebra/CPoly_NthCoeff/NthCoeff_props/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/CPoly_NthCoeff/NthCoeff_props/R.var +*) (* begin hide *) diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/CPolynomials.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/CPolynomials.mma index 99b2465aa..d3436dfe7 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/CPolynomials.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/CPolynomials.mma @@ -48,7 +48,9 @@ Section CPoly_CRing %\end{convention}% *) -alias id "CR" = "cic:/CoRN/algebra/CPolynomials/CPoly_CRing/CR.var". +(* UNEXPORTED +cic:/CoRN/algebra/CPolynomials/CPoly_CRing/CR.var +*) (*#* The intuition behind the type [cpoly] is the following @@ -352,7 +354,9 @@ elements of the ring. %\end{convention}% *) -alias id "CR" = "cic:/CoRN/algebra/CPolynomials/CPoly_CRing_ctd/CR.var". +(* UNEXPORTED +cic:/CoRN/algebra/CPolynomials/CPoly_CRing_ctd/CR.var +*) (* NOTATION Notation RX := (cpoly_cring CR). @@ -362,13 +366,21 @@ Notation RX := (cpoly_cring CR). Section helpful_section *) -alias id "p" = "cic:/CoRN/algebra/CPolynomials/CPoly_CRing_ctd/helpful_section/p.var". +(* UNEXPORTED +cic:/CoRN/algebra/CPolynomials/CPoly_CRing_ctd/helpful_section/p.var +*) -alias id "q" = "cic:/CoRN/algebra/CPolynomials/CPoly_CRing_ctd/helpful_section/q.var". +(* UNEXPORTED +cic:/CoRN/algebra/CPolynomials/CPoly_CRing_ctd/helpful_section/q.var +*) -alias id "c" = "cic:/CoRN/algebra/CPolynomials/CPoly_CRing_ctd/helpful_section/c.var". +(* UNEXPORTED +cic:/CoRN/algebra/CPolynomials/CPoly_CRing_ctd/helpful_section/c.var +*) -alias id "d" = "cic:/CoRN/algebra/CPolynomials/CPoly_CRing_ctd/helpful_section/d.var". +(* UNEXPORTED +cic:/CoRN/algebra/CPolynomials/CPoly_CRing_ctd/helpful_section/d.var +*) inline procedural "cic:/CoRN/algebra/CPolynomials/linear_eq_zero_.con" as lemma. @@ -472,7 +484,9 @@ Let [R] be a ring and write [RX] for the ring of polynomials over [R]. Section Poly_properties *) -alias id "R" = "cic:/CoRN/algebra/CPolynomials/Poly_properties/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/CPolynomials/Poly_properties/R.var +*) (* NOTATION Notation RX := (cpoly_cring R). @@ -590,7 +604,9 @@ End Poly_properties Section Poly_Prop_Induction *) -alias id "CR" = "cic:/CoRN/algebra/CPolynomials/Poly_Prop_Induction/CR.var". +(* UNEXPORTED +cic:/CoRN/algebra/CPolynomials/Poly_Prop_Induction/CR.var +*) (* NOTATION Notation Cpoly := (cpoly CR). diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/CRings.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/CRings.mma index 96435df75..eab9274bd 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/CRings.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/CRings.mma @@ -124,7 +124,9 @@ Section CRing_axioms %\end{convention}% *) -alias id "R" = "cic:/CoRN/algebra/CRings/CRing_axioms/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/CRings/CRing_axioms/R.var +*) inline procedural "cic:/CoRN/algebra/CRings/CRing_is_CRing.con" as lemma. @@ -163,7 +165,9 @@ Let [R] be a ring. %\end{convention}% *) -alias id "R" = "cic:/CoRN/algebra/CRings/Ring_constructions/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/CRings/Ring_constructions/R.var +*) (*#* The multiplicative monoid of a ring is defined as follows. @@ -187,7 +191,9 @@ Section Ring_unfolded %\end{convention}% *) -alias id "R" = "cic:/CoRN/algebra/CRings/Ring_unfolded/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/CRings/Ring_unfolded/R.var +*) (* begin hide *) @@ -241,7 +247,9 @@ Section Ring_basics %\end{convention}% *) -alias id "R" = "cic:/CoRN/algebra/CRings/Ring_basics/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/CRings/Ring_basics/R.var +*) inline procedural "cic:/CoRN/algebra/CRings/one_ap_zero.con" as lemma. @@ -344,7 +352,9 @@ Let [R] be a ring. %\end{convention}% *) -alias id "R" = "cic:/CoRN/algebra/CRings/exponentiation/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/CRings/exponentiation/R.var +*) (* End_SpecReals *) @@ -384,7 +394,9 @@ Section nat_injection %\end{convention}% *) -alias id "R" = "cic:/CoRN/algebra/CRings/nat_injection/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/CRings/nat_injection/R.var +*) (*#* The injection of Coq natural numbers into a ring is called [nring]. @@ -491,7 +503,9 @@ Let [R] be a ring. %\end{convention}% *) -alias id "R" = "cic:/CoRN/algebra/CRings/int_injection/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/CRings/int_injection/R.var +*) (*#* The injection of Coq integers into a ring is called [zring]. Again, @@ -644,7 +658,9 @@ Section Ring_sums %\end{convention}% *) -alias id "R" = "cic:/CoRN/algebra/CRings/Ring_sums/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/CRings/Ring_sums/R.var +*) (*#* *** Infinite Ring sums @@ -707,7 +723,9 @@ Let [R] be a ring. Section Dist_properties *) -alias id "R" = "cic:/CoRN/algebra/CRings/Dist_properties/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/CRings/Dist_properties/R.var +*) inline procedural "cic:/CoRN/algebra/CRings/dist_1b.con" as lemma. @@ -763,7 +781,9 @@ Let [R] be a ring. Section NExp_properties *) -alias id "R" = "cic:/CoRN/algebra/CRings/NExp_properties/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/CRings/NExp_properties/R.var +*) inline procedural "cic:/CoRN/algebra/CRings/nexp_wd.con" as lemma. @@ -889,11 +909,17 @@ respectively [P] and [Q]. %\end{convention}% *) -alias id "R" = "cic:/CoRN/algebra/CRings/CRing_Ops/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/CRings/CRing_Ops/R.var +*) -alias id "F" = "cic:/CoRN/algebra/CRings/CRing_Ops/F.var". +(* UNEXPORTED +cic:/CoRN/algebra/CRings/CRing_Ops/F.var +*) -alias id "G" = "cic:/CoRN/algebra/CRings/CRing_Ops/G.var". +(* UNEXPORTED +cic:/CoRN/algebra/CRings/CRing_Ops/G.var +*) (* begin hide *) @@ -919,7 +945,9 @@ End Part_Function_Mult Section Part_Function_Nth_Power *) -alias id "n" = "cic:/CoRN/algebra/CRings/CRing_Ops/Part_Function_Nth_Power/n.var". +(* UNEXPORTED +cic:/CoRN/algebra/CRings/CRing_Ops/Part_Function_Nth_Power/n.var +*) inline procedural "cic:/CoRN/algebra/CRings/part_function_nth_strext.con" as lemma. @@ -934,7 +962,9 @@ End Part_Function_Nth_Power %\end{convention}% *) -alias id "R'" = "cic:/CoRN/algebra/CRings/CRing_Ops/R'.var". +(* UNEXPORTED +cic:/CoRN/algebra/CRings/CRing_Ops/R'.var +*) inline procedural "cic:/CoRN/algebra/CRings/included_FMult.con" as lemma. @@ -942,7 +972,9 @@ inline procedural "cic:/CoRN/algebra/CRings/included_FMult'.con" as lemma. inline procedural "cic:/CoRN/algebra/CRings/included_FMult''.con" as lemma. -alias id "n" = "cic:/CoRN/algebra/CRings/CRing_Ops/n.var". +(* UNEXPORTED +cic:/CoRN/algebra/CRings/CRing_Ops/n.var +*) inline procedural "cic:/CoRN/algebra/CRings/included_FNth.con" as lemma. @@ -982,9 +1014,13 @@ Infix "{^}" := Fnth (at level 30, right associativity). Section ScalarMultiplication *) -alias id "R" = "cic:/CoRN/algebra/CRings/ScalarMultiplication/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/CRings/ScalarMultiplication/R.var +*) -alias id "F" = "cic:/CoRN/algebra/CRings/ScalarMultiplication/F.var". +(* UNEXPORTED +cic:/CoRN/algebra/CRings/ScalarMultiplication/F.var +*) (* begin hide *) @@ -992,7 +1028,9 @@ inline procedural "cic:/CoRN/algebra/CRings/ScalarMultiplication/P.con" "ScalarM (* end hide *) -alias id "R'" = "cic:/CoRN/algebra/CRings/ScalarMultiplication/R'.var". +(* UNEXPORTED +cic:/CoRN/algebra/CRings/ScalarMultiplication/R'.var +*) inline procedural "cic:/CoRN/algebra/CRings/included_FScalMult.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/CSemiGroups.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/CSemiGroups.mma index dbbe3f12a..91bf4b7dd 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/CSemiGroups.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/CSemiGroups.mma @@ -66,7 +66,9 @@ The axiomatic properties of a semi group. Section CSemiGroup_axioms *) -alias id "G" = "cic:/CoRN/algebra/CSemiGroups/CSemiGroup_axioms/G.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSemiGroups/CSemiGroup_axioms/G.var +*) inline procedural "cic:/CoRN/algebra/CSemiGroups/CSemiGroup_is_CSemiGroup.con" as lemma. @@ -89,7 +91,9 @@ Let [G] be a semi-group. Section CSemiGroup_basics *) -alias id "G" = "cic:/CoRN/algebra/CSemiGroups/CSemiGroup_basics/G.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSemiGroups/CSemiGroup_basics/G.var +*) (* End_SpecReals *) @@ -121,11 +125,17 @@ At this stage, we will always consider automorphisms; we %{\em %could%}% treat t Section Part_Function_Plus *) -alias id "G" = "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/G.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/G.var +*) -alias id "F" = "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/F.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/F.var +*) -alias id "F'" = "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/F'.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/F'.var +*) (* begin hide *) @@ -144,7 +154,9 @@ inline procedural "cic:/CoRN/algebra/CSemiGroups/Fplus.con" as definition. %\end{convention}% *) -alias id "R" = "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/R.var +*) inline procedural "cic:/CoRN/algebra/CSemiGroups/included_FPlus.con" as lemma. @@ -183,11 +195,17 @@ predicate on the semi-group which is preserved by [[+]]. Section SubCSemiGroups *) -alias id "csg" = "cic:/CoRN/algebra/CSemiGroups/SubCSemiGroups/csg.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSemiGroups/SubCSemiGroups/csg.var +*) -alias id "P" = "cic:/CoRN/algebra/CSemiGroups/SubCSemiGroups/P.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSemiGroups/SubCSemiGroups/P.var +*) -alias id "op_pres_P" = "cic:/CoRN/algebra/CSemiGroups/SubCSemiGroups/op_pres_P.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSemiGroups/SubCSemiGroups/op_pres_P.var +*) inline procedural "cic:/CoRN/algebra/CSemiGroups/SubCSemiGroups/subcrr.con" "SubCSemiGroups__" as definition. diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/CSetoidFun.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/CSetoidFun.mma index 3ec367947..6eebecfb0 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/CSetoidFun.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/CSetoidFun.mma @@ -30,15 +30,25 @@ Let [S1], [S2] and [S3] be setoids, [f] a setoid function from [S1] to [S2], and [g] from [S2] to [S3] in the following definition of composition. *) -alias id "S1" = "cic:/CoRN/algebra/CSetoidFun/unary_function_composition/S1.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoidFun/unary_function_composition/S1.var +*) -alias id "S2" = "cic:/CoRN/algebra/CSetoidFun/unary_function_composition/S2.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoidFun/unary_function_composition/S2.var +*) -alias id "S3" = "cic:/CoRN/algebra/CSetoidFun/unary_function_composition/S3.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoidFun/unary_function_composition/S3.var +*) -alias id "f" = "cic:/CoRN/algebra/CSetoidFun/unary_function_composition/f.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoidFun/unary_function_composition/f.var +*) -alias id "g" = "cic:/CoRN/algebra/CSetoidFun/unary_function_composition/g.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoidFun/unary_function_composition/g.var +*) inline procedural "cic:/CoRN/algebra/CSetoidFun/compose_CSetoid_fun.con" as definition. @@ -79,7 +89,9 @@ End function_projection Section BinProj *) -alias id "S" = "cic:/CoRN/algebra/CSetoidFun/BinProj/S.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoidFun/BinProj/S.var +*) inline procedural "cic:/CoRN/algebra/CSetoidFun/binproj1.con" as definition. @@ -100,11 +112,17 @@ End BinProj Section CombiningOperations *) -alias id "S1" = "cic:/CoRN/algebra/CSetoidFun/CombiningOperations/S1.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoidFun/CombiningOperations/S1.var +*) -alias id "S2" = "cic:/CoRN/algebra/CSetoidFun/CombiningOperations/S2.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoidFun/CombiningOperations/S2.var +*) -alias id "S3" = "cic:/CoRN/algebra/CSetoidFun/CombiningOperations/S3.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoidFun/CombiningOperations/S3.var +*) (*#* In the following definition, we assume [f] is a setoid function from @@ -116,9 +134,13 @@ Then [opOnFun] is the composition [op] after [f]. Section CombiningUnaryOperations *) -alias id "f" = "cic:/CoRN/algebra/CSetoidFun/CombiningOperations/CombiningUnaryOperations/f.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoidFun/CombiningOperations/CombiningUnaryOperations/f.var +*) -alias id "op" = "cic:/CoRN/algebra/CSetoidFun/CombiningOperations/CombiningUnaryOperations/op.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoidFun/CombiningOperations/CombiningUnaryOperations/op.var +*) inline procedural "cic:/CoRN/algebra/CSetoidFun/opOnFun.con" as definition. @@ -171,15 +193,21 @@ welldefinedness. %\end{convention}% *) -alias id "S" = "cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/S.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/S.var +*) (* UNEXPORTED Section Conjunction *) -alias id "P" = "cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Conjunction/P.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Conjunction/P.var +*) -alias id "Q" = "cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Conjunction/Q.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Conjunction/Q.var +*) inline procedural "cic:/CoRN/algebra/CSetoidFun/conjP.con" as definition. @@ -197,9 +225,13 @@ End Conjunction Section Disjunction *) -alias id "P" = "cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Disjunction/P.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Disjunction/P.var +*) -alias id "Q" = "cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Disjunction/Q.var". +(* UNEXPORTED +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). @@ -225,9 +257,13 @@ Section Extension The next definition is a bit tricky, and is useful for choosing among the elements that satisfy a predicate [P] those that also satisfy [R] in the case where [R] is only defined for elements satisfying [P]---consider [R] to be a condition on the image of an object via a function with domain [P]. We chose to call this operation [extension]. *) -alias id "P" = "cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Extension/P.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Extension/P.var +*) -alias id "R" = "cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Extension/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Extension/R.var +*) inline procedural "cic:/CoRN/algebra/CSetoidFun/extend.con" as definition. @@ -370,7 +406,9 @@ Hint Resolve CI: core. Section CSetoid_Ops *) -alias id "S" = "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/S.var". +(* UNEXPORTED +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. @@ -389,7 +427,9 @@ In any setoid we can also define constant functions (one for each element of the %\end{convention}% *) -alias id "c" = "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Const/c.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Const/c.var +*) inline procedural "cic:/CoRN/algebra/CSetoidFun/Fconst.con" as definition. @@ -420,9 +460,13 @@ If we have two setoid functions [F] and [G] we can always compose them. The dom Section Part_Function_Composition *) -alias id "G" = "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Composition/G.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Composition/G.var +*) -alias id "F" = "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Composition/F.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Composition/F.var +*) (* begin hide *) @@ -457,15 +501,25 @@ End CSetoid_Ops Section BinPart_Function_Composition *) -alias id "S1" = "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/S1.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/S1.var +*) -alias id "S2" = "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/S2.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/S2.var +*) -alias id "S3" = "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/S3.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/S3.var +*) -alias id "G" = "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/G.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/G.var +*) -alias id "F" = "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/F.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/F.var +*) (* begin hide *) diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/CSetoidInc.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/CSetoidInc.mma index ed961f468..858921a56 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/CSetoidInc.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/CSetoidInc.mma @@ -30,7 +30,9 @@ Section inclusion Let [S] be a setoid, and [P], [Q], [R] be predicates on [S]. *) -alias id "S" = "cic:/CoRN/algebra/CSetoidInc/inclusion/S.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoidInc/inclusion/S.var +*) inline procedural "cic:/CoRN/algebra/CSetoidInc/included.con" as definition. @@ -38,11 +40,17 @@ inline procedural "cic:/CoRN/algebra/CSetoidInc/included.con" as definition. Section Basics *) -alias id "P" = "cic:/CoRN/algebra/CSetoidInc/inclusion/Basics/P.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoidInc/inclusion/Basics/P.var +*) -alias id "Q" = "cic:/CoRN/algebra/CSetoidInc/inclusion/Basics/Q.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoidInc/inclusion/Basics/Q.var +*) -alias id "R" = "cic:/CoRN/algebra/CSetoidInc/inclusion/Basics/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoidInc/inclusion/Basics/R.var +*) inline procedural "cic:/CoRN/algebra/CSetoidInc/included_refl.con" as lemma. @@ -70,9 +78,13 @@ by [P] and [Q], respectively, the domains of [F] and [G]. %\end{convention}% *) -alias id "F" = "cic:/CoRN/algebra/CSetoidInc/inclusion/F.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoidInc/inclusion/F.var +*) -alias id "G" = "cic:/CoRN/algebra/CSetoidInc/inclusion/G.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoidInc/inclusion/G.var +*) (* begin hide *) @@ -82,7 +94,9 @@ inline procedural "cic:/CoRN/algebra/CSetoidInc/inclusion/Q.con" "inclusion__" a (* end hide *) -alias id "R" = "cic:/CoRN/algebra/CSetoidInc/inclusion/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoidInc/inclusion/R.var +*) inline procedural "cic:/CoRN/algebra/CSetoidInc/included_FComp.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/CSetoids.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/CSetoids.mma index 23107d94a..4bfc7ce4a 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/CSetoids.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/CSetoids.mma @@ -94,7 +94,9 @@ Notice that their type depends on the main logical connective. Section Properties_of_relations *) -alias id "A" = "cic:/CoRN/algebra/CSetoids/Properties_of_relations/A.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoids/Properties_of_relations/A.var +*) inline procedural "cic:/CoRN/algebra/CSetoids/irreflexive.con" as definition. @@ -180,7 +182,9 @@ Let [S] be a setoid. Section CSetoid_axioms *) -alias id "S" = "cic:/CoRN/algebra/CSetoids/CSetoid_axioms/S.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoids/CSetoid_axioms/S.var +*) inline procedural "cic:/CoRN/algebra/CSetoids/CSetoid_is_CSetoid.con" as lemma. @@ -209,7 +213,9 @@ End CSetoid_axioms Section CSetoid_basics *) -alias id "S" = "cic:/CoRN/algebra/CSetoids/CSetoid_basics/S.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoids/CSetoid_basics/S.var +*) (* End_SpecReals *) @@ -348,7 +354,9 @@ on predicates and relations. Section CSetoid_relations_and_predicates *) -alias id "S" = "cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/S.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/S.var +*) (* End_SpecReals *) @@ -364,7 +372,9 @@ At this stage, we consider [CProp]- and [Prop]-valued predicates on setoids. Section CSetoidPredicates *) -alias id "P" = "cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/CSetoidPredicates/P.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/CSetoidPredicates/P.var +*) inline procedural "cic:/CoRN/algebra/CSetoids/pred_strong_ext.con" as definition. @@ -388,7 +398,9 @@ inline procedural "cic:/CoRN/algebra/CSetoids/csp_wd.con" as lemma. Section CSetoidPPredicates *) -alias id "P" = "cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/CSetoidPPredicates/P.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/CSetoidPPredicates/P.var +*) inline procedural "cic:/CoRN/algebra/CSetoids/pred_strong_ext'.con" as definition. @@ -419,7 +431,9 @@ Let [R] be a relation on (the carrier of) [S]. Section CsetoidRelations *) -alias id "R" = "cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/CsetoidRelations/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/CsetoidRelations/R.var +*) inline procedural "cic:/CoRN/algebra/CSetoids/rel_wdr.con" as definition. @@ -464,7 +478,9 @@ Let [R] be a relation on (the carrier of) [S]. Section CCsetoidRelations *) -alias id "R" = "cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/CCsetoidRelations/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/CCsetoidRelations/R.var +*) inline procedural "cic:/CoRN/algebra/CSetoids/Crel_wdr.con" as definition. @@ -551,11 +567,17 @@ First we consider unary functions. *) Section CSetoid_functions *) -alias id "S1" = "cic:/CoRN/algebra/CSetoids/CSetoid_functions/S1.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoids/CSetoid_functions/S1.var +*) -alias id "S2" = "cic:/CoRN/algebra/CSetoids/CSetoid_functions/S2.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoids/CSetoid_functions/S2.var +*) -alias id "S3" = "cic:/CoRN/algebra/CSetoids/CSetoid_functions/S3.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoids/CSetoid_functions/S3.var +*) (* UNEXPORTED Section unary_functions @@ -566,7 +588,9 @@ In the following two definitions, [f] is a function from (the carrier of) [S1] to (the carrier of) [S2]. *) -alias id "f" = "cic:/CoRN/algebra/CSetoids/CSetoid_functions/unary_functions/f.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoids/CSetoid_functions/unary_functions/f.var +*) inline procedural "cic:/CoRN/algebra/CSetoids/fun_wd.con" as definition. @@ -606,7 +630,9 @@ In the following two definitions, [f] is a function from [S1] and [S2] to [S3]. *) -alias id "f" = "cic:/CoRN/algebra/CSetoids/CSetoid_functions/binary_functions/f.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoids/CSetoid_functions/binary_functions/f.var +*) inline procedural "cic:/CoRN/algebra/CSetoids/bin_fun_wd.con" as definition. @@ -673,7 +699,9 @@ Let [S] be a setoid. Section csetoid_inner_ops *) -alias id "S" = "cic:/CoRN/algebra/CSetoids/csetoid_inner_ops/S.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoids/csetoid_inner_ops/S.var +*) (*#* Properties of binary operations *) @@ -797,9 +825,13 @@ Let [S1] and [S2] be setoids. Section csetoid_outer_ops *) -alias id "S1" = "cic:/CoRN/algebra/CSetoids/csetoid_outer_ops/S1.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoids/csetoid_outer_ops/S1.var +*) -alias id "S2" = "cic:/CoRN/algebra/CSetoids/csetoid_outer_ops/S2.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoids/csetoid_outer_ops/S2.var +*) (*#* Well-defined outer operations on a setoid. @@ -847,9 +879,13 @@ Let [S] be a setoid, and [P] a predicate on the carrier of [S]. Section SubCSetoids *) -alias id "S" = "cic:/CoRN/algebra/CSetoids/SubCSetoids/S.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoids/SubCSetoids/S.var +*) -alias id "P" = "cic:/CoRN/algebra/CSetoids/SubCSetoids/P.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoids/SubCSetoids/P.var +*) inline procedural "cic:/CoRN/algebra/CSetoids/subcsetoid_crr.ind". @@ -892,7 +928,9 @@ Let [f] be a unary setoid operation on [S]. Section SubCSetoid_unary_operations *) -alias id "f" = "cic:/CoRN/algebra/CSetoids/SubCSetoids/SubCSetoid_unary_operations/f.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoids/SubCSetoids/SubCSetoid_unary_operations/f.var +*) inline procedural "cic:/CoRN/algebra/CSetoids/un_op_pres_pred.con" as definition. @@ -901,7 +939,9 @@ inline procedural "cic:/CoRN/algebra/CSetoids/un_op_pres_pred.con" as definition Assume [pr:un_op_pres_pred]. %\end{convention}% *) -alias id "pr" = "cic:/CoRN/algebra/CSetoids/SubCSetoids/SubCSetoid_unary_operations/pr.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoids/SubCSetoids/SubCSetoid_unary_operations/pr.var +*) inline procedural "cic:/CoRN/algebra/CSetoids/restr_un_op.con" as definition. @@ -925,7 +965,9 @@ Let [f] be a binary setoid operation on [S]. Section SubCSetoid_binary_operations *) -alias id "f" = "cic:/CoRN/algebra/CSetoids/SubCSetoids/SubCSetoid_binary_operations/f.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoids/SubCSetoids/SubCSetoid_binary_operations/f.var +*) inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_pres_pred.con" as definition. @@ -935,7 +977,9 @@ Assume [bin_op_pres_pred]. %\end{convention}% *) -alias id "pr" = "cic:/CoRN/algebra/CSetoids/SubCSetoids/SubCSetoid_binary_operations/pr.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSetoids/SubCSetoids/SubCSetoid_binary_operations/pr.var +*) inline procedural "cic:/CoRN/algebra/CSetoids/restr_bin_op.con" as definition. diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/CSums.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/CSums.mma index 57ece830d..baf3f4ec3 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/CSums.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/CSums.mma @@ -40,7 +40,9 @@ include "algebra/CAbGroups.ma". Section Sums *) -alias id "G" = "cic:/CoRN/algebra/CSums/Sums/G.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSums/Sums/G.var +*) (* Sum1 and Sum use subtraction *) @@ -217,7 +219,9 @@ often referred to as ``Mengolli Sums''. Section More_Sums *) -alias id "G" = "cic:/CoRN/algebra/CSums/More_Sums/G.var". +(* UNEXPORTED +cic:/CoRN/algebra/CSums/More_Sums/G.var +*) inline procedural "cic:/CoRN/algebra/CSums/Mengolli_Sum.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/CVectorSpace.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/CVectorSpace.mma index 93515c59d..76bf9c59d 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/CVectorSpace.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/CVectorSpace.mma @@ -80,9 +80,13 @@ Let [F] be a fiels and let [V] be a vector space over [F] Section VS_basics *) -alias id "F" = "cic:/CoRN/algebra/CVectorSpace/VS_basics/F.var". +(* UNEXPORTED +cic:/CoRN/algebra/CVectorSpace/VS_basics/F.var +*) -alias id "V" = "cic:/CoRN/algebra/CVectorSpace/VS_basics/V.var". +(* UNEXPORTED +cic:/CoRN/algebra/CVectorSpace/VS_basics/V.var +*) inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_op_zero.con" as lemma. 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 e0beb5018..7cd2bd6ef 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/Cauchy_COF.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/Cauchy_COF.mma @@ -36,7 +36,9 @@ field [F], we can define a new ordered field of Cauchy sequences over [F]. Section Structure *) -alias id "F" = "cic:/CoRN/algebra/Cauchy_COF/Structure/F.var". +(* UNEXPORTED +cic:/CoRN/algebra/Cauchy_COF/Structure/F.var +*) (*#* ** Setoid Structure diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/Expon.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/Expon.mma index a0ed1a5f9..4532bf82d 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/Expon.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/Expon.mma @@ -34,7 +34,9 @@ include "tactics/Transparent_algebra.ma". Section More_Nexp *) -alias id "R" = "cic:/CoRN/algebra/Expon/More_Nexp/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/Expon/More_Nexp/R.var +*) inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_ap_zero.con" as lemma. @@ -97,7 +99,9 @@ Implicit Arguments nexp_resp_ap_zero [R x]. Section Zexp_def *) -alias id "R" = "cic:/CoRN/algebra/Expon/Zexp_def/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/Expon/Zexp_def/R.var +*) (*#* It would be nicer to define [zexp] using [caseZdiff], but we already @@ -127,7 +131,9 @@ Notation "( x [//] Hx ) [^^] n" := (zexp x Hx n) (at level 0). Section Zexp_properties *) -alias id "R" = "cic:/CoRN/algebra/Expon/Zexp_properties/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/Expon/Zexp_properties/R.var +*) inline procedural "cic:/CoRN/algebra/Expon/zexp_zero.con" as lemma. @@ -274,7 +280,9 @@ Hint Resolve zexp_wd: algebra_c. Section Root_Unique *) -alias id "R" = "cic:/CoRN/algebra/Expon/Root_Unique/R.var". +(* UNEXPORTED +cic:/CoRN/algebra/Expon/Root_Unique/R.var +*) inline procedural "cic:/CoRN/algebra/Expon/root_unique.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/algebra/ListType.mma b/helm/software/matita/contribs/CoRN-Procedural/algebra/ListType.mma index 9e83709f4..307bc76e3 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/algebra/ListType.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/algebra/ListType.mma @@ -52,7 +52,9 @@ library of Coq but moved to the Type level. Section List *) -alias id "A" = "cic:/CoRN/algebra/ListType/List/A.var". +(* UNEXPORTED +cic:/CoRN/algebra/ListType/List/A.var +*) inline procedural "cic:/CoRN/algebra/ListType/list.ind". @@ -104,15 +106,25 @@ inline procedural "cic:/CoRN/algebra/ListType/lel.con" as definition. Hint Unfold lel: list. *) -alias id "a" = "cic:/CoRN/algebra/ListType/List/length_order/a.var". +(* UNEXPORTED +cic:/CoRN/algebra/ListType/List/length_order/a.var +*) -alias id "b" = "cic:/CoRN/algebra/ListType/List/length_order/b.var". +(* UNEXPORTED +cic:/CoRN/algebra/ListType/List/length_order/b.var +*) -alias id "l" = "cic:/CoRN/algebra/ListType/List/length_order/l.var". +(* UNEXPORTED +cic:/CoRN/algebra/ListType/List/length_order/l.var +*) -alias id "m" = "cic:/CoRN/algebra/ListType/List/length_order/m.var". +(* UNEXPORTED +cic:/CoRN/algebra/ListType/List/length_order/m.var +*) -alias id "n" = "cic:/CoRN/algebra/ListType/List/length_order/n.var". +(* UNEXPORTED +cic:/CoRN/algebra/ListType/List/length_order/n.var +*) inline procedural "cic:/CoRN/algebra/ListType/lel_refl.con" as lemma. @@ -221,11 +233,17 @@ Implicit Arguments cons [A]. Section Map *) -alias id "A" = "cic:/CoRN/algebra/ListType/Map/A.var". +(* UNEXPORTED +cic:/CoRN/algebra/ListType/Map/A.var +*) -alias id "B" = "cic:/CoRN/algebra/ListType/Map/B.var". +(* UNEXPORTED +cic:/CoRN/algebra/ListType/Map/B.var +*) -alias id "f" = "cic:/CoRN/algebra/ListType/Map/f.var". +(* UNEXPORTED +cic:/CoRN/algebra/ListType/Map/f.var +*) inline procedural "cic:/CoRN/algebra/ListType/map.con" as definition. diff --git a/helm/software/matita/contribs/CoRN-Procedural/complex/NRootCC.mma b/helm/software/matita/contribs/CoRN-Procedural/complex/NRootCC.mma index ddd6b7350..1fa6e5cfe 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/complex/NRootCC.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/complex/NRootCC.mma @@ -107,11 +107,17 @@ Define [c2 := a[^]2[+]b[^]2], [c := sqrt c2], [a'2 := (c[+]a) [*]Half], %\end{convention}% *) -alias id "a" = "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/a.var". +(* UNEXPORTED +cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/a.var +*) -alias id "b" = "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/b.var". +(* UNEXPORTED +cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/b.var +*) -alias id "b_" = "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/b_.var". +(* UNEXPORTED +cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/b_.var +*) (* begin hide *) @@ -196,11 +202,17 @@ Section NRootCC_1_ap_imag %\end{convention}% *) -alias id "a" = "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/a.var". +(* UNEXPORTED +cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/a.var +*) -alias id "b" = "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/b.var". +(* UNEXPORTED +cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/b.var +*) -alias id "a_" = "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/a_.var". +(* UNEXPORTED +cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/a_.var +*) (* begin hide *) @@ -239,13 +251,21 @@ Section NRootCC_2 %\end{convention}% *) -alias id "n" = "cic:/CoRN/complex/NRootCC/NRootCC_2/n.var". +(* UNEXPORTED +cic:/CoRN/complex/NRootCC/NRootCC_2/n.var +*) -alias id "c" = "cic:/CoRN/complex/NRootCC/NRootCC_2/c.var". +(* UNEXPORTED +cic:/CoRN/complex/NRootCC/NRootCC_2/c.var +*) -alias id "z" = "cic:/CoRN/complex/NRootCC/NRootCC_2/z.var". +(* UNEXPORTED +cic:/CoRN/complex/NRootCC/NRootCC_2/z.var +*) -alias id "c_" = "cic:/CoRN/complex/NRootCC/NRootCC_2/c_.var". +(* UNEXPORTED +cic:/CoRN/complex/NRootCC/NRootCC_2/c_.var +*) inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_2'.con" as lemma. @@ -270,13 +290,21 @@ inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a2.con" as lemma. %\end{convention}% *) -alias id "a" = "cic:/CoRN/complex/NRootCC/NRootCC_3/a.var". +(* UNEXPORTED +cic:/CoRN/complex/NRootCC/NRootCC_3/a.var +*) -alias id "b" = "cic:/CoRN/complex/NRootCC/NRootCC_3/b.var". +(* UNEXPORTED +cic:/CoRN/complex/NRootCC/NRootCC_3/b.var +*) -alias id "b_" = "cic:/CoRN/complex/NRootCC/NRootCC_3/b_.var". +(* UNEXPORTED +cic:/CoRN/complex/NRootCC/NRootCC_3/b_.var +*) -alias id "n" = "cic:/CoRN/complex/NRootCC/NRootCC_3/n.var". +(* UNEXPORTED +cic:/CoRN/complex/NRootCC/NRootCC_3/n.var +*) inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_poly''.con" as definition. @@ -349,11 +377,17 @@ Section NRootCC_3' %\end{convention}% *) -alias id "c" = "cic:/CoRN/complex/NRootCC/NRootCC_3'/c.var". +(* UNEXPORTED +cic:/CoRN/complex/NRootCC/NRootCC_3'/c.var +*) -alias id "n" = "cic:/CoRN/complex/NRootCC/NRootCC_3'/n.var". +(* UNEXPORTED +cic:/CoRN/complex/NRootCC/NRootCC_3'/n.var +*) -alias id "n_" = "cic:/CoRN/complex/NRootCC/NRootCC_3'/n_.var". +(* UNEXPORTED +cic:/CoRN/complex/NRootCC/NRootCC_3'/n_.var +*) inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_3'_poly.con" as definition. @@ -379,15 +413,25 @@ Section NRootCC_4_ap_real %\end{convention}% *) -alias id "a" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/a.var". +(* UNEXPORTED +cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/a.var +*) -alias id "b" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/b.var". +(* UNEXPORTED +cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/b.var +*) -alias id "b_" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/b_.var". +(* UNEXPORTED +cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/b_.var +*) -alias id "n" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/n.var". +(* UNEXPORTED +cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/n.var +*) -alias id "n_" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/n_.var". +(* UNEXPORTED +cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/n_.var +*) (* begin hide *) @@ -410,11 +454,17 @@ inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a1.con" as lemma. %\end{convention}% *) -alias id "r2'" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_solutions/r2'.var". +(* UNEXPORTED +cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_solutions/r2'.var +*) -alias id "c2" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_solutions/c2.var". +(* UNEXPORTED +cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_solutions/c2.var +*) -alias id "r2'_" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_solutions/r2'_.var". +(* UNEXPORTED +cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_solutions/r2'_.var +*) (* UNEXPORTED Hint Resolve nrootCC_3': algebra. @@ -437,13 +487,21 @@ and [(y2[*] (r[^] (2) [+]One)) [^]n [=] a[^] (2) [+]b[^] (2)]. %\end{convention}% *) -alias id "r" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/r.var". +(* UNEXPORTED +cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/r.var +*) -alias id "r_property" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/r_property.var". +(* UNEXPORTED +cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/r_property.var +*) -alias id "y2" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/y2.var". +(* UNEXPORTED +cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/y2.var +*) -alias id "y2_property" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/y2_property.var". +(* UNEXPORTED +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" as lemma. @@ -499,15 +557,25 @@ and [(odd n)]; define [c' := (a[+I*]b) [*]II := a'[+I*]b']. %\end{convention}% *) -alias id "a" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/a.var". +(* UNEXPORTED +cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/a.var +*) -alias id "b" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/b.var". +(* UNEXPORTED +cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/b.var +*) -alias id "a_" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/a_.var". +(* UNEXPORTED +cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/a_.var +*) -alias id "n" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/n.var". +(* UNEXPORTED +cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/n.var +*) -alias id "n_" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/n_.var". +(* UNEXPORTED +cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/n_.var +*) (* begin hide *) @@ -556,9 +624,13 @@ Hint Resolve nrCC_5a3: algebra. %\end{convention}% *) -alias id "c" = "cic:/CoRN/complex/NRootCC/NRootCC_5/c.var". +(* UNEXPORTED +cic:/CoRN/complex/NRootCC/NRootCC_5/c.var +*) -alias id "c_" = "cic:/CoRN/complex/NRootCC/NRootCC_5/c_.var". +(* UNEXPORTED +cic:/CoRN/complex/NRootCC/NRootCC_5/c_.var +*) inline procedural "cic:/CoRN/complex/NRootCC/nrCC_5a4.con" as lemma. 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 4e7f837d7..47489e16f 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 @@ -81,13 +81,21 @@ include "model/setoids/Qsetoid.ma". Section p66E2 *) -alias id "X" = "cic:/CoRN/devel/loeb/IDA/Ch6/p66E2/X.var". +(* UNEXPORTED +cic:/CoRN/devel/loeb/IDA/Ch6/p66E2/X.var +*) -alias id "f" = "cic:/CoRN/devel/loeb/IDA/Ch6/p66E2/f.var". +(* UNEXPORTED +cic:/CoRN/devel/loeb/IDA/Ch6/p66E2/f.var +*) -alias id "g" = "cic:/CoRN/devel/loeb/IDA/Ch6/p66E2/g.var". +(* UNEXPORTED +cic:/CoRN/devel/loeb/IDA/Ch6/p66E2/g.var +*) -alias id "h" = "cic:/CoRN/devel/loeb/IDA/Ch6/p66E2/h.var". +(* UNEXPORTED +cic:/CoRN/devel/loeb/IDA/Ch6/p66E2/h.var +*) (* Check comp_as_bin_op.*) @@ -115,7 +123,9 @@ inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/FS_is_CSemiGroup.con" as lemma. Section p66E2b4 *) -alias id "A" = "cic:/CoRN/devel/loeb/IDA/Ch6/p66E2b4/A.var". +(* UNEXPORTED +cic:/CoRN/devel/loeb/IDA/Ch6/p66E2b4/A.var +*) inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/Astar.con" as definition. @@ -171,7 +181,9 @@ inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/is_unit_Z_0.con" as lemma. Section p67R2 *) -alias id "X" = "cic:/CoRN/devel/loeb/IDA/Ch6/p67R2/X.var". +(* UNEXPORTED +cic:/CoRN/devel/loeb/IDA/Ch6/p67R2/X.var +*) inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/is_unit_FS_id.con" as lemma. @@ -299,9 +311,13 @@ include "algebra/CMonoids.ma". Section D9S *) -alias id "M1" = "cic:/CoRN/devel/loeb/IDA/Ch6/D9S/M1.var". +(* UNEXPORTED +cic:/CoRN/devel/loeb/IDA/Ch6/D9S/M1.var +*) -alias id "M2" = "cic:/CoRN/devel/loeb/IDA/Ch6/D9S/M2.var". +(* UNEXPORTED +cic:/CoRN/devel/loeb/IDA/Ch6/D9S/M2.var +*) inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/dprod.con" as definition. @@ -321,9 +337,13 @@ End D9S Section D9M *) -alias id "M1" = "cic:/CoRN/devel/loeb/IDA/Ch6/D9M/M1.var". +(* UNEXPORTED +cic:/CoRN/devel/loeb/IDA/Ch6/D9M/M1.var +*) -alias id "M2" = "cic:/CoRN/devel/loeb/IDA/Ch6/D9M/M2.var". +(* UNEXPORTED +cic:/CoRN/devel/loeb/IDA/Ch6/D9M/M2.var +*) inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/e1e2_is_rht_unit.con" as lemma. @@ -361,15 +381,25 @@ End p69E1 Section Th11 *) -alias id "M" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th11/M.var". +(* UNEXPORTED +cic:/CoRN/devel/loeb/IDA/Ch6/Th11/M.var +*) -alias id "I" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th11/I.var". +(* UNEXPORTED +cic:/CoRN/devel/loeb/IDA/Ch6/Th11/I.var +*) -alias id "C" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th11/C.var". +(* UNEXPORTED +cic:/CoRN/devel/loeb/IDA/Ch6/Th11/C.var +*) -alias id "Cunit" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th11/Cunit.var". +(* UNEXPORTED +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". +(* UNEXPORTED +cic:/CoRN/devel/loeb/IDA/Ch6/Th11/op_pres_C.var +*) inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/K.con" as definition. @@ -387,7 +417,9 @@ End Th11 Section Th12 *) -alias id "A" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th12/A.var". +(* UNEXPORTED +cic:/CoRN/devel/loeb/IDA/Ch6/Th12/A.var +*) inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/nil_is_rht_unit.con" as lemma. @@ -435,9 +467,13 @@ End p70text Section Th13 *) -alias id "M1" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th13/M1.var". +(* UNEXPORTED +cic:/CoRN/devel/loeb/IDA/Ch6/Th13/M1.var +*) -alias id "M2" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th13/M2.var". +(* UNEXPORTED +cic:/CoRN/devel/loeb/IDA/Ch6/Th13/M2.var +*) inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/morphism.con" as definition. @@ -453,15 +489,21 @@ End Th13 Section p71E1 *) -alias id "M" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71E1/M.var". +(* UNEXPORTED +cic:/CoRN/devel/loeb/IDA/Ch6/p71E1/M.var +*) -alias id "c" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71E1/c.var". +(* UNEXPORTED +cic:/CoRN/devel/loeb/IDA/Ch6/p71E1/c.var +*) 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" as definition. -alias id "is_generated_by" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71E1/is_generated_by.var". +(* UNEXPORTED +cic:/CoRN/devel/loeb/IDA/Ch6/p71E1/is_generated_by.var +*) inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/p71E1/f.con" "p71E1__" as definition. @@ -493,7 +535,9 @@ End p71E1' Section p71E2 *) -alias id "A" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2/A.var". +(* UNEXPORTED +cic:/CoRN/devel/loeb/IDA/Ch6/p71E2/A.var +*) inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2/L.con" "p71E2__" as definition. @@ -513,9 +557,13 @@ End p71E2 Section p71R1 *) -alias id "S1" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71R1/S1.var". +(* UNEXPORTED +cic:/CoRN/devel/loeb/IDA/Ch6/p71R1/S1.var +*) -alias id "S2" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71R1/S2.var". +(* UNEXPORTED +cic:/CoRN/devel/loeb/IDA/Ch6/p71R1/S2.var +*) inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/morphism_of_CSemiGroups.con" as definition. @@ -527,7 +575,9 @@ End p71R1 Section p71R2 *) -alias id "M" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71R2/M.var". +(* UNEXPORTED +cic:/CoRN/devel/loeb/IDA/Ch6/p71R2/M.var +*) inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/automorphism.con" as definition. @@ -541,13 +591,21 @@ End p71R2 Section Th14 *) -alias id "M1" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th14/M1.var". +(* UNEXPORTED +cic:/CoRN/devel/loeb/IDA/Ch6/Th14/M1.var +*) -alias id "M2" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th14/M2.var". +(* UNEXPORTED +cic:/CoRN/devel/loeb/IDA/Ch6/Th14/M2.var +*) -alias id "f" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th14/f.var". +(* UNEXPORTED +cic:/CoRN/devel/loeb/IDA/Ch6/Th14/f.var +*) -alias id "isof" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th14/isof.var". +(* UNEXPORTED +cic:/CoRN/devel/loeb/IDA/Ch6/Th14/isof.var +*) inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/iso_imp_bij.con" as lemma. @@ -575,9 +633,13 @@ End p71E2b1 Section p71E2b2 *) -alias id "M1" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2b2/M1.var". +(* UNEXPORTED +cic:/CoRN/devel/loeb/IDA/Ch6/p71E2b2/M1.var +*) -alias id "M2" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2b2/M2.var". +(* UNEXPORTED +cic:/CoRN/devel/loeb/IDA/Ch6/p71E2b2/M2.var +*) inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2b2/f.con" "p71E2b2__" as definition. @@ -595,11 +657,15 @@ End p71E2b2 Section Th15 *) -alias id "M" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th15/M.var". +(* UNEXPORTED +cic:/CoRN/devel/loeb/IDA/Ch6/Th15/M.var +*) 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". +(* UNEXPORTED +cic:/CoRN/devel/loeb/IDA/Ch6/Th15/D.var +*) inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/member.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 9c273c863..d96c21d78 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/fta/CC_Props.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/fta/CC_Props.mma @@ -77,7 +77,9 @@ Section Continuity_for_CC %\end{convention}% *) -alias id "f" = "cic:/CoRN/fta/CC_Props/Continuity_for_CC/f.var". +(* UNEXPORTED +cic:/CoRN/fta/CC_Props/Continuity_for_CC/f.var +*) (* (CSetoid_un_op CC). *) 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 e389d23de..1db8b1ac0 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/fta/CPoly_Contin1.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/fta/CPoly_Contin1.mma @@ -46,7 +46,9 @@ Section CPoly_CC_Continuous %\end{convention}% *) -alias id "g" = "cic:/CoRN/fta/CPoly_Contin1/CPoly_CC_Continuous/g.var". +(* UNEXPORTED +cic:/CoRN/fta/CPoly_Contin1/CPoly_CC_Continuous/g.var +*) inline procedural "cic:/CoRN/fta/CPoly_Contin1/cpoly_CC_contin.con" as lemma. 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 5e31ee33e..c8e7e89fc 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/fta/CPoly_Rev.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/fta/CPoly_Rev.mma @@ -33,7 +33,9 @@ polynomials over this ring. %\end{convention}% *) -alias id "R" = "cic:/CoRN/fta/CPoly_Rev/Monomials/R.var". +(* UNEXPORTED +cic:/CoRN/fta/CPoly_Rev/Monomials/R.var +*) (* begin hide *) @@ -91,7 +93,9 @@ Implicit Arguments monom [R]. Section Poly_Reverse *) -alias id "R" = "cic:/CoRN/fta/CPoly_Rev/Poly_Reverse/R.var". +(* UNEXPORTED +cic:/CoRN/fta/CPoly_Rev/Poly_Reverse/R.var +*) (* begin hide *) diff --git a/helm/software/matita/contribs/CoRN-Procedural/fta/FTA.mma b/helm/software/matita/contribs/CoRN-Procedural/fta/FTA.mma index d8c24667c..6786002fc 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/fta/FTA.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/fta/FTA.mma @@ -32,11 +32,17 @@ degree [(S n)]. Section FTA_reg' *) -alias id "f" = "cic:/CoRN/fta/FTA/FTA_reg'/f.var". +(* UNEXPORTED +cic:/CoRN/fta/FTA/FTA_reg'/f.var +*) -alias id "n" = "cic:/CoRN/fta/FTA/FTA_reg'/n.var". +(* UNEXPORTED +cic:/CoRN/fta/FTA/FTA_reg'/n.var +*) -alias id "f_degree" = "cic:/CoRN/fta/FTA/FTA_reg'/f_degree.var". +(* UNEXPORTED +cic:/CoRN/fta/FTA/FTA_reg'/f_degree.var +*) inline procedural "cic:/CoRN/fta/FTA/FTA_reg'.con" as lemma. @@ -55,15 +61,25 @@ less than or equal to [(S n)] and [c] be a complex number such that Section FTA_1 *) -alias id "f" = "cic:/CoRN/fta/FTA/FTA_1/f.var". +(* UNEXPORTED +cic:/CoRN/fta/FTA/FTA_1/f.var +*) -alias id "n" = "cic:/CoRN/fta/FTA/FTA_1/n.var". +(* UNEXPORTED +cic:/CoRN/fta/FTA/FTA_1/n.var +*) -alias id "f_degree" = "cic:/CoRN/fta/FTA/FTA_1/f_degree.var". +(* UNEXPORTED +cic:/CoRN/fta/FTA/FTA_1/f_degree.var +*) -alias id "c" = "cic:/CoRN/fta/FTA/FTA_1/c.var". +(* UNEXPORTED +cic:/CoRN/fta/FTA/FTA_1/c.var +*) -alias id "f_c" = "cic:/CoRN/fta/FTA/FTA_1/f_c.var". +(* UNEXPORTED +cic:/CoRN/fta/FTA/FTA_1/f_c.var +*) inline procedural "cic:/CoRN/fta/FTA/FTA_1a.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/fta/FTAreg.mma b/helm/software/matita/contribs/CoRN-Procedural/fta/FTAreg.mma index d96c06c8c..8c6d3cbc9 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/fta/FTAreg.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/fta/FTAreg.mma @@ -34,9 +34,13 @@ include "fta/CPoly_Contin1.ma". Section Seq_Exists *) -alias id "n" = "cic:/CoRN/fta/FTAreg/Seq_Exists/n.var". +(* UNEXPORTED +cic:/CoRN/fta/FTAreg/Seq_Exists/n.var +*) -alias id "lt0n" = "cic:/CoRN/fta/FTAreg/Seq_Exists/lt0n.var". +(* UNEXPORTED +cic:/CoRN/fta/FTAreg/Seq_Exists/lt0n.var +*) (*#* %\begin{convention}% Let [qK] be a real between 0 and 1, with @@ -53,21 +57,37 @@ Let [p] be a monic polynomial over the complex numbers with degree Section Kneser_Sequence *) -alias id "qK" = "cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/qK.var". +(* UNEXPORTED +cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/qK.var +*) -alias id "zltq" = "cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/zltq.var". +(* UNEXPORTED +cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/zltq.var +*) -alias id "qlt1" = "cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/qlt1.var". +(* UNEXPORTED +cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/qlt1.var +*) -alias id "q_prop" = "cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/q_prop.var". +(* UNEXPORTED +cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/q_prop.var +*) -alias id "p" = "cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/p.var". +(* UNEXPORTED +cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/p.var +*) -alias id "mp" = "cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/mp.var". +(* UNEXPORTED +cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/mp.var +*) -alias id "c0" = "cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/c0.var". +(* UNEXPORTED +cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/c0.var +*) -alias id "p0ltc0" = "cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/p0ltc0.var". +(* UNEXPORTED +cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/p0ltc0.var +*) inline procedural "cic:/CoRN/fta/FTAreg/Knes_tup.ind". @@ -122,19 +142,33 @@ End Seq_Exists Section N_Exists *) -alias id "n" = "cic:/CoRN/fta/FTAreg/N_Exists/n.var". +(* UNEXPORTED +cic:/CoRN/fta/FTAreg/N_Exists/n.var +*) -alias id "lt0n" = "cic:/CoRN/fta/FTAreg/N_Exists/lt0n.var". +(* UNEXPORTED +cic:/CoRN/fta/FTAreg/N_Exists/lt0n.var +*) -alias id "q" = "cic:/CoRN/fta/FTAreg/N_Exists/q.var". +(* UNEXPORTED +cic:/CoRN/fta/FTAreg/N_Exists/q.var +*) -alias id "zleq" = "cic:/CoRN/fta/FTAreg/N_Exists/zleq.var". +(* UNEXPORTED +cic:/CoRN/fta/FTAreg/N_Exists/zleq.var +*) -alias id "qlt1" = "cic:/CoRN/fta/FTAreg/N_Exists/qlt1.var". +(* UNEXPORTED +cic:/CoRN/fta/FTAreg/N_Exists/qlt1.var +*) -alias id "c" = "cic:/CoRN/fta/FTAreg/N_Exists/c.var". +(* UNEXPORTED +cic:/CoRN/fta/FTAreg/N_Exists/c.var +*) -alias id "zltc" = "cic:/CoRN/fta/FTAreg/N_Exists/zltc.var". +(* UNEXPORTED +cic:/CoRN/fta/FTAreg/N_Exists/zltc.var +*) (* begin hide *) @@ -142,9 +176,13 @@ inline procedural "cic:/CoRN/fta/FTAreg/N_Exists/q_.con" "N_Exists__" as definit (* end hide *) -alias id "e" = "cic:/CoRN/fta/FTAreg/N_Exists/e.var". +(* UNEXPORTED +cic:/CoRN/fta/FTAreg/N_Exists/e.var +*) -alias id "zlte" = "cic:/CoRN/fta/FTAreg/N_Exists/zlte.var". +(* UNEXPORTED +cic:/CoRN/fta/FTAreg/N_Exists/zlte.var +*) inline procedural "cic:/CoRN/fta/FTAreg/N_exists.con" as lemma. @@ -158,19 +196,33 @@ Section Seq_is_CC_CAuchy (*#* ** The Kneser sequence is Cauchy in [CC] *) -alias id "n" = "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/n.var". +(* UNEXPORTED +cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/n.var +*) -alias id "lt0n" = "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/lt0n.var". +(* UNEXPORTED +cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/lt0n.var +*) -alias id "q" = "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/q.var". +(* UNEXPORTED +cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/q.var +*) -alias id "zleq" = "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/zleq.var". +(* UNEXPORTED +cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/zleq.var +*) -alias id "qlt1" = "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/qlt1.var". +(* UNEXPORTED +cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/qlt1.var +*) -alias id "c" = "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/c.var". +(* UNEXPORTED +cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/c.var +*) -alias id "zltc" = "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/zltc.var". +(* UNEXPORTED +cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/zltc.var +*) (*#* %\begin{convention}% Let: - [q_] prove [q[-]One [#] Zero] diff --git a/helm/software/matita/contribs/CoRN-Procedural/fta/KeyLemma.mma b/helm/software/matita/contribs/CoRN-Procedural/fta/KeyLemma.mma index 78240853d..9a43a2dd6 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/fta/KeyLemma.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/fta/KeyLemma.mma @@ -39,23 +39,41 @@ and [eps : IR] such that [(Zero [<] eps)] and [(eps [<=] a_0)]. %\end{convention}% *) -alias id "a" = "cic:/CoRN/fta/KeyLemma/Key_Lemma/a.var". +(* UNEXPORTED +cic:/CoRN/fta/KeyLemma/Key_Lemma/a.var +*) -alias id "n" = "cic:/CoRN/fta/KeyLemma/Key_Lemma/n.var". +(* UNEXPORTED +cic:/CoRN/fta/KeyLemma/Key_Lemma/n.var +*) -alias id "gt_n_0" = "cic:/CoRN/fta/KeyLemma/Key_Lemma/gt_n_0.var". +(* UNEXPORTED +cic:/CoRN/fta/KeyLemma/Key_Lemma/gt_n_0.var +*) -alias id "eps" = "cic:/CoRN/fta/KeyLemma/Key_Lemma/eps.var". +(* UNEXPORTED +cic:/CoRN/fta/KeyLemma/Key_Lemma/eps.var +*) -alias id "eps_pos" = "cic:/CoRN/fta/KeyLemma/Key_Lemma/eps_pos.var". +(* UNEXPORTED +cic:/CoRN/fta/KeyLemma/Key_Lemma/eps_pos.var +*) -alias id "a_nonneg" = "cic:/CoRN/fta/KeyLemma/Key_Lemma/a_nonneg.var". +(* UNEXPORTED +cic:/CoRN/fta/KeyLemma/Key_Lemma/a_nonneg.var +*) -alias id "a_n_1" = "cic:/CoRN/fta/KeyLemma/Key_Lemma/a_n_1.var". +(* UNEXPORTED +cic:/CoRN/fta/KeyLemma/Key_Lemma/a_n_1.var +*) -alias id "a_0" = "cic:/CoRN/fta/KeyLemma/Key_Lemma/a_0.var". +(* UNEXPORTED +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". +(* UNEXPORTED +cic:/CoRN/fta/KeyLemma/Key_Lemma/eps_le_a_0.var +*) inline procedural "cic:/CoRN/fta/KeyLemma/a_0_eps_nonneg.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/fta/KneserLemma.mma b/helm/software/matita/contribs/CoRN-Procedural/fta/KneserLemma.mma index 1d5430cd5..c71f1c248 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/fta/KneserLemma.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/fta/KneserLemma.mma @@ -41,11 +41,17 @@ such that [0 < n], [b_0 := b 0], [b_n := (b n) [=] One] and %\end{convention}% *) -alias id "b" = "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b.var". +(* UNEXPORTED +cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b.var +*) -alias id "n" = "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/n.var". +(* UNEXPORTED +cic:/CoRN/fta/KneserLemma/Kneser_Lemma/n.var +*) -alias id "gt_n_0" = "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/gt_n_0.var". +(* UNEXPORTED +cic:/CoRN/fta/KneserLemma/Kneser_Lemma/gt_n_0.var +*) (* begin hide *) @@ -55,11 +61,17 @@ inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b_n.con" "Kneser_Lemma (* end hide *) -alias id "b_n_1" = "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b_n_1.var". +(* UNEXPORTED +cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b_n_1.var +*) -alias id "c" = "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/c.var". +(* UNEXPORTED +cic:/CoRN/fta/KneserLemma/Kneser_Lemma/c.var +*) -alias id "b_0_lt_c" = "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b_0_lt_c.var". +(* UNEXPORTED +cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b_0_lt_c.var +*) (*#* %\begin{convention}% We define the following local abbreviations: diff --git a/helm/software/matita/contribs/CoRN-Procedural/fta/MainLemma.mma b/helm/software/matita/contribs/CoRN-Procedural/fta/MainLemma.mma index 48a403135..721d471dc 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/fta/MainLemma.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/fta/MainLemma.mma @@ -43,23 +43,41 @@ Let [a : nat->IR], [n : nat], [a_0 : IR] and [eps : IR] such that [0 < n], %\end{convention}% *) -alias id "a" = "cic:/CoRN/fta/MainLemma/Main_Lemma/a.var". +(* UNEXPORTED +cic:/CoRN/fta/MainLemma/Main_Lemma/a.var +*) -alias id "n" = "cic:/CoRN/fta/MainLemma/Main_Lemma/n.var". +(* UNEXPORTED +cic:/CoRN/fta/MainLemma/Main_Lemma/n.var +*) -alias id "gt_n_0" = "cic:/CoRN/fta/MainLemma/Main_Lemma/gt_n_0.var". +(* UNEXPORTED +cic:/CoRN/fta/MainLemma/Main_Lemma/gt_n_0.var +*) -alias id "eps" = "cic:/CoRN/fta/MainLemma/Main_Lemma/eps.var". +(* UNEXPORTED +cic:/CoRN/fta/MainLemma/Main_Lemma/eps.var +*) -alias id "eps_pos" = "cic:/CoRN/fta/MainLemma/Main_Lemma/eps_pos.var". +(* UNEXPORTED +cic:/CoRN/fta/MainLemma/Main_Lemma/eps_pos.var +*) -alias id "a_nonneg" = "cic:/CoRN/fta/MainLemma/Main_Lemma/a_nonneg.var". +(* UNEXPORTED +cic:/CoRN/fta/MainLemma/Main_Lemma/a_nonneg.var +*) -alias id "a_n_1" = "cic:/CoRN/fta/MainLemma/Main_Lemma/a_n_1.var". +(* UNEXPORTED +cic:/CoRN/fta/MainLemma/Main_Lemma/a_n_1.var +*) -alias id "a_0" = "cic:/CoRN/fta/MainLemma/Main_Lemma/a_0.var". +(* UNEXPORTED +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". +(* UNEXPORTED +cic:/CoRN/fta/MainLemma/Main_Lemma/eps_le_a_0.var +*) inline procedural "cic:/CoRN/fta/MainLemma/a_0_pos.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/COrdLemmas.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/COrdLemmas.mma index 51b18daa0..83b34c715 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/COrdLemmas.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/COrdLemmas.mma @@ -37,7 +37,9 @@ the proof that any two partitions with no common point have a common refinement). *) -alias id "F" = "cic:/CoRN/ftc/COrdLemmas/Lemmas/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/COrdLemmas/Lemmas/F.var +*) inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_lt.con" as lemma. @@ -63,13 +65,21 @@ inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_4d.con" as lemma. (* begin hide *) -alias id "f" = "cic:/CoRN/ftc/COrdLemmas/Lemmas/f.var". +(* UNEXPORTED +cic:/CoRN/ftc/COrdLemmas/Lemmas/f.var +*) -alias id "f0" = "cic:/CoRN/ftc/COrdLemmas/Lemmas/f0.var". +(* UNEXPORTED +cic:/CoRN/ftc/COrdLemmas/Lemmas/f0.var +*) -alias id "f_mon" = "cic:/CoRN/ftc/COrdLemmas/Lemmas/f_mon.var". +(* UNEXPORTED +cic:/CoRN/ftc/COrdLemmas/Lemmas/f_mon.var +*) -alias id "h" = "cic:/CoRN/ftc/COrdLemmas/Lemmas/h.var". +(* UNEXPORTED +cic:/CoRN/ftc/COrdLemmas/Lemmas/h.var +*) (* end hide *) @@ -105,7 +115,9 @@ inline procedural "cic:/CoRN/ftc/COrdLemmas/More_Lemmas/f'.con" "More_Lemmas__" (* end hide *) -alias id "F" = "cic:/CoRN/ftc/COrdLemmas/More_Lemmas/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/COrdLemmas/More_Lemmas/F.var +*) (* begin show *) diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/Composition.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/Composition.mma index 7fa209cee..68fda7511 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/Composition.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/Composition.mma @@ -51,21 +51,37 @@ mapped into another compact interval. We define this concept for partial functions, and prove some trivial results. *) -alias id "F" = "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/F.var +*) -alias id "G" = "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/G.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/G.var +*) -alias id "a" = "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/a.var +*) -alias id "b" = "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/Hab.var +*) -alias id "c" = "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/c.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/c.var +*) -alias id "d" = "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/d.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/d.var +*) -alias id "Hcd" = "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/Hcd.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/Hcd.var +*) (* begin hide *) @@ -75,7 +91,9 @@ inline procedural "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/I.con (* begin show *) -alias id "Hf" = "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/Hf.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/Hf.var +*) (* end show *) @@ -83,7 +101,9 @@ inline procedural "cic:/CoRN/ftc/Composition/maps_into_compacts.con" as definiti (* begin show *) -alias id "maps" = "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/maps.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/maps.var +*) (* end show *) @@ -112,29 +132,51 @@ As was the case for division of partial functions, this condition completely characterizes the domain of the composite function. *) -alias id "F" = "cic:/CoRN/ftc/Composition/Mapping/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Mapping/F.var +*) -alias id "G" = "cic:/CoRN/ftc/Composition/Mapping/G.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Mapping/G.var +*) -alias id "a" = "cic:/CoRN/ftc/Composition/Mapping/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Mapping/a.var +*) -alias id "b" = "cic:/CoRN/ftc/Composition/Mapping/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Mapping/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/Composition/Mapping/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Mapping/Hab.var +*) -alias id "c" = "cic:/CoRN/ftc/Composition/Mapping/c.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Mapping/c.var +*) -alias id "d" = "cic:/CoRN/ftc/Composition/Mapping/d.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Mapping/d.var +*) -alias id "Hcd" = "cic:/CoRN/ftc/Composition/Mapping/Hcd.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Mapping/Hcd.var +*) (* begin show *) -alias id "Hf" = "cic:/CoRN/ftc/Composition/Mapping/Hf.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Mapping/Hf.var +*) -alias id "Hg" = "cic:/CoRN/ftc/Composition/Mapping/Hg.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Mapping/Hg.var +*) -alias id "maps" = "cic:/CoRN/ftc/Composition/Mapping/maps.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Mapping/maps.var +*) (* end show *) @@ -153,11 +195,17 @@ Section Interval_Continuity We now prove that the composition of two continuous partial functions is continuous. *) -alias id "a" = "cic:/CoRN/ftc/Composition/Interval_Continuity/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Interval_Continuity/a.var +*) -alias id "b" = "cic:/CoRN/ftc/Composition/Interval_Continuity/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Interval_Continuity/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/Composition/Interval_Continuity/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Interval_Continuity/Hab.var +*) (* begin hide *) @@ -165,23 +213,39 @@ inline procedural "cic:/CoRN/ftc/Composition/Interval_Continuity/I.con" "Interva (* end hide *) -alias id "c" = "cic:/CoRN/ftc/Composition/Interval_Continuity/c.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Interval_Continuity/c.var +*) -alias id "d" = "cic:/CoRN/ftc/Composition/Interval_Continuity/d.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Interval_Continuity/d.var +*) -alias id "Hcd" = "cic:/CoRN/ftc/Composition/Interval_Continuity/Hcd.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Interval_Continuity/Hcd.var +*) -alias id "F" = "cic:/CoRN/ftc/Composition/Interval_Continuity/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Interval_Continuity/F.var +*) -alias id "G" = "cic:/CoRN/ftc/Composition/Interval_Continuity/G.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Interval_Continuity/G.var +*) (* begin show *) -alias id "contF" = "cic:/CoRN/ftc/Composition/Interval_Continuity/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Interval_Continuity/contF.var +*) -alias id "contG" = "cic:/CoRN/ftc/Composition/Interval_Continuity/contG.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Interval_Continuity/contG.var +*) -alias id "Hmap" = "cic:/CoRN/ftc/Composition/Interval_Continuity/Hmap.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Interval_Continuity/Hmap.var +*) (* end show *) @@ -200,25 +264,45 @@ Section Derivative We now work with the derivative relation and prove the chain rule for partial functions. *) -alias id "F" = "cic:/CoRN/ftc/Composition/Derivative/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Derivative/F.var +*) -alias id "F'" = "cic:/CoRN/ftc/Composition/Derivative/F'.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Derivative/F'.var +*) -alias id "G" = "cic:/CoRN/ftc/Composition/Derivative/G.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Derivative/G.var +*) -alias id "G'" = "cic:/CoRN/ftc/Composition/Derivative/G'.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Derivative/G'.var +*) -alias id "a" = "cic:/CoRN/ftc/Composition/Derivative/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Derivative/a.var +*) -alias id "b" = "cic:/CoRN/ftc/Composition/Derivative/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Derivative/b.var +*) -alias id "Hab'" = "cic:/CoRN/ftc/Composition/Derivative/Hab'.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Derivative/Hab'.var +*) -alias id "c" = "cic:/CoRN/ftc/Composition/Derivative/c.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Derivative/c.var +*) -alias id "d" = "cic:/CoRN/ftc/Composition/Derivative/d.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Derivative/d.var +*) -alias id "Hcd'" = "cic:/CoRN/ftc/Composition/Derivative/Hcd'.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Derivative/Hcd'.var +*) (* begin hide *) @@ -232,11 +316,17 @@ inline procedural "cic:/CoRN/ftc/Composition/Derivative/I.con" "Derivative__" as (* begin show *) -alias id "derF" = "cic:/CoRN/ftc/Composition/Derivative/derF.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Derivative/derF.var +*) -alias id "derG" = "cic:/CoRN/ftc/Composition/Derivative/derG.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Derivative/derG.var +*) -alias id "Hmap" = "cic:/CoRN/ftc/Composition/Derivative/Hmap.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Derivative/Hmap.var +*) (* end show *) @@ -265,21 +355,37 @@ Section Differentiability Finally, we move on to differentiability. *) -alias id "F" = "cic:/CoRN/ftc/Composition/Differentiability/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Differentiability/F.var +*) -alias id "G" = "cic:/CoRN/ftc/Composition/Differentiability/G.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Differentiability/G.var +*) -alias id "a" = "cic:/CoRN/ftc/Composition/Differentiability/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Differentiability/a.var +*) -alias id "b" = "cic:/CoRN/ftc/Composition/Differentiability/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Differentiability/b.var +*) -alias id "Hab'" = "cic:/CoRN/ftc/Composition/Differentiability/Hab'.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Differentiability/Hab'.var +*) -alias id "c" = "cic:/CoRN/ftc/Composition/Differentiability/c.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Differentiability/c.var +*) -alias id "d" = "cic:/CoRN/ftc/Composition/Differentiability/d.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Differentiability/d.var +*) -alias id "Hcd'" = "cic:/CoRN/ftc/Composition/Differentiability/Hcd'.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Differentiability/Hcd'.var +*) (* begin hide *) @@ -293,11 +399,17 @@ inline procedural "cic:/CoRN/ftc/Composition/Differentiability/I.con" "Different (* begin show *) -alias id "diffF" = "cic:/CoRN/ftc/Composition/Differentiability/diffF.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Differentiability/diffF.var +*) -alias id "diffG" = "cic:/CoRN/ftc/Composition/Differentiability/diffG.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Differentiability/diffG.var +*) -alias id "Hmap" = "cic:/CoRN/ftc/Composition/Differentiability/Hmap.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Differentiability/Hmap.var +*) (* end show *) @@ -319,13 +431,21 @@ We now generalize this results to arbitrary intervals. We begin by generalizing %\end{convention}% *) -alias id "I" = "cic:/CoRN/ftc/Composition/Generalized_Intervals/I.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Generalized_Intervals/I.var +*) -alias id "J" = "cic:/CoRN/ftc/Composition/Generalized_Intervals/J.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Generalized_Intervals/J.var +*) -alias id "pI" = "cic:/CoRN/ftc/Composition/Generalized_Intervals/pI.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Generalized_Intervals/pI.var +*) -alias id "pJ" = "cic:/CoRN/ftc/Composition/Generalized_Intervals/pJ.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Generalized_Intervals/pJ.var +*) inline procedural "cic:/CoRN/ftc/Composition/maps_compacts_into.con" as definition. @@ -335,17 +455,27 @@ Now everything comes naturally: inline procedural "cic:/CoRN/ftc/Composition/comp_inc_lemma.con" as lemma. -alias id "F" = "cic:/CoRN/ftc/Composition/Generalized_Intervals/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Generalized_Intervals/F.var +*) -alias id "F'" = "cic:/CoRN/ftc/Composition/Generalized_Intervals/F'.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Generalized_Intervals/F'.var +*) -alias id "G" = "cic:/CoRN/ftc/Composition/Generalized_Intervals/G.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Generalized_Intervals/G.var +*) -alias id "G'" = "cic:/CoRN/ftc/Composition/Generalized_Intervals/G'.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Generalized_Intervals/G'.var +*) (* begin show *) -alias id "Hmap" = "cic:/CoRN/ftc/Composition/Generalized_Intervals/Hmap.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Generalized_Intervals/Hmap.var +*) (* end show *) @@ -353,7 +483,9 @@ inline procedural "cic:/CoRN/ftc/Composition/Continuous_comp.con" as lemma. (* begin show *) -alias id "Hmap'" = "cic:/CoRN/ftc/Composition/Generalized_Intervals/Hmap'.var". +(* UNEXPORTED +cic:/CoRN/ftc/Composition/Generalized_Intervals/Hmap'.var +*) (* end show *) diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/Continuity.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/Continuity.mma index ff66216f5..f205054b9 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/Continuity.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/Continuity.mma @@ -52,11 +52,17 @@ respectively [P, Q] and [R]. Here we define continuity and prove some basic properties of continuous functions. *) -alias id "a" = "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/a.var +*) -alias id "b" = "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/Hab.var +*) (* begin hide *) @@ -64,7 +70,9 @@ inline procedural "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/I.con" (* end hide *) -alias id "F" = "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/F.var +*) (* begin hide *) @@ -86,7 +94,9 @@ 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]. *) -alias id "contF" = "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/contF.var +*) (* begin hide *) @@ -171,11 +181,17 @@ Section Local_Results We now state and prove some results about continuous functions. Assume that [I] is included in the domain of both [F] and [G]. *) -alias id "a" = "cic:/CoRN/ftc/Continuity/Local_Results/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/Continuity/Local_Results/a.var +*) -alias id "b" = "cic:/CoRN/ftc/Continuity/Local_Results/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/Continuity/Local_Results/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/Continuity/Local_Results/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/Continuity/Local_Results/Hab.var +*) (* begin hide *) @@ -183,9 +199,13 @@ inline procedural "cic:/CoRN/ftc/Continuity/Local_Results/I.con" "Local_Results_ (* end hide *) -alias id "F" = "cic:/CoRN/ftc/Continuity/Local_Results/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/Continuity/Local_Results/F.var +*) -alias id "G" = "cic:/CoRN/ftc/Continuity/Local_Results/G.var". +(* UNEXPORTED +cic:/CoRN/ftc/Continuity/Local_Results/G.var +*) (* begin hide *) @@ -195,9 +215,13 @@ inline procedural "cic:/CoRN/ftc/Continuity/Local_Results/Q.con" "Local_Results_ (* end hide *) -alias id "incF" = "cic:/CoRN/ftc/Continuity/Local_Results/incF.var". +(* UNEXPORTED +cic:/CoRN/ftc/Continuity/Local_Results/incF.var +*) -alias id "incG" = "cic:/CoRN/ftc/Continuity/Local_Results/incG.var". +(* UNEXPORTED +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. @@ -233,9 +257,13 @@ 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. *) -alias id "contF" = "cic:/CoRN/ftc/Continuity/Local_Results/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/Continuity/Local_Results/contF.var +*) -alias id "contG" = "cic:/CoRN/ftc/Continuity/Local_Results/contG.var". +(* UNEXPORTED +cic:/CoRN/ftc/Continuity/Local_Results/contG.var +*) inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_plus.con" as lemma. @@ -255,9 +283,13 @@ inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_max.con" as lemma. (* begin show *) -alias id "Hg'" = "cic:/CoRN/ftc/Continuity/Local_Results/Hg'.var". +(* UNEXPORTED +cic:/CoRN/ftc/Continuity/Local_Results/Hg'.var +*) -alias id "Hg''" = "cic:/CoRN/ftc/Continuity/Local_Results/Hg''.var". +(* UNEXPORTED +cic:/CoRN/ftc/Continuity/Local_Results/Hg''.var +*) (* end show *) @@ -275,11 +307,17 @@ Hint Resolve contin_imp_inc: included. Section Corolaries *) -alias id "a" = "cic:/CoRN/ftc/Continuity/Corolaries/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/Continuity/Corolaries/a.var +*) -alias id "b" = "cic:/CoRN/ftc/Continuity/Corolaries/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/Continuity/Corolaries/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/Continuity/Corolaries/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/Continuity/Corolaries/Hab.var +*) (* begin hide *) @@ -287,9 +325,13 @@ inline procedural "cic:/CoRN/ftc/Continuity/Corolaries/I.con" "Corolaries__" as (* end hide *) -alias id "F" = "cic:/CoRN/ftc/Continuity/Corolaries/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/Continuity/Corolaries/F.var +*) -alias id "G" = "cic:/CoRN/ftc/Continuity/Corolaries/G.var". +(* UNEXPORTED +cic:/CoRN/ftc/Continuity/Corolaries/G.var +*) (* begin hide *) @@ -299,9 +341,13 @@ inline procedural "cic:/CoRN/ftc/Continuity/Corolaries/Q.con" "Corolaries__" as (* end hide *) -alias id "contF" = "cic:/CoRN/ftc/Continuity/Corolaries/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/Continuity/Corolaries/contF.var +*) -alias id "contG" = "cic:/CoRN/ftc/Continuity/Corolaries/contG.var". +(* UNEXPORTED +cic:/CoRN/ftc/Continuity/Corolaries/contG.var +*) (*#* The corresponding properties for subtraction, division and @@ -320,9 +366,13 @@ inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_min.con" as lemma. inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_abs.con" as lemma. -alias id "Hg'" = "cic:/CoRN/ftc/Continuity/Corolaries/Hg'.var". +(* UNEXPORTED +cic:/CoRN/ftc/Continuity/Corolaries/Hg'.var +*) -alias id "Hg''" = "cic:/CoRN/ftc/Continuity/Corolaries/Hg''.var". +(* UNEXPORTED +cic:/CoRN/ftc/Continuity/Corolaries/Hg''.var +*) inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_div.con" as lemma. @@ -342,13 +392,21 @@ Section Sums We finally prove that the sum of an arbitrary family of continuous functions is still a continuous function. *) -alias id "a" = "cic:/CoRN/ftc/Continuity/Other/Sums/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/Continuity/Other/Sums/a.var +*) -alias id "b" = "cic:/CoRN/ftc/Continuity/Other/Sums/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/Continuity/Other/Sums/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/Continuity/Other/Sums/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/Continuity/Other/Sums/Hab.var +*) -alias id "Hab'" = "cic:/CoRN/ftc/Continuity/Other/Sums/Hab'.var". +(* UNEXPORTED +cic:/CoRN/ftc/Continuity/Other/Sums/Hab'.var +*) (* begin hide *) diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/Derivative.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/Derivative.mma index b593df9de..74c970de4 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/Derivative.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/Derivative.mma @@ -51,11 +51,17 @@ will be partial functions with domains respectively [P, P', Q, Q'] and %\end{convention}% *) -alias id "a" = "cic:/CoRN/ftc/Derivative/Definitions/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/Derivative/Definitions/a.var +*) -alias id "b" = "cic:/CoRN/ftc/Derivative/Definitions/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/Derivative/Definitions/b.var +*) -alias id "Hab'" = "cic:/CoRN/ftc/Derivative/Definitions/Hab'.var". +(* UNEXPORTED +cic:/CoRN/ftc/Derivative/Definitions/Hab'.var +*) (* begin hide *) @@ -65,7 +71,9 @@ inline procedural "cic:/CoRN/ftc/Derivative/Definitions/I.con" "Definitions__" a (* end hide *) -alias id "F" = "cic:/CoRN/ftc/Derivative/Definitions/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/Derivative/Definitions/F.var +*) (* begin hide *) @@ -90,11 +98,17 @@ Section Basic_Properties (*#* **Basic Properties *) -alias id "a" = "cic:/CoRN/ftc/Derivative/Basic_Properties/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/Derivative/Basic_Properties/a.var +*) -alias id "b" = "cic:/CoRN/ftc/Derivative/Basic_Properties/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/Derivative/Basic_Properties/b.var +*) -alias id "Hab'" = "cic:/CoRN/ftc/Derivative/Basic_Properties/Hab'.var". +(* UNEXPORTED +cic:/CoRN/ftc/Derivative/Basic_Properties/Hab'.var +*) (* begin hide *) @@ -116,11 +130,17 @@ inline procedural "cic:/CoRN/ftc/Derivative/Derivative_I_char.con" as lemma. Derivative is a well defined relation; we will make this explicit for both arguments: *) -alias id "F" = "cic:/CoRN/ftc/Derivative/Basic_Properties/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/Derivative/Basic_Properties/F.var +*) -alias id "G" = "cic:/CoRN/ftc/Derivative/Basic_Properties/G.var". +(* UNEXPORTED +cic:/CoRN/ftc/Derivative/Basic_Properties/G.var +*) -alias id "H" = "cic:/CoRN/ftc/Derivative/Basic_Properties/H.var". +(* UNEXPORTED +cic:/CoRN/ftc/Derivative/Basic_Properties/H.var +*) (* begin hide *) @@ -160,7 +180,9 @@ inline procedural "cic:/CoRN/ftc/Derivative/derivative_imp_inc'.con" as lemma. Any function that is or has a derivative is continuous. *) -alias id "Hab''" = "cic:/CoRN/ftc/Derivative/Basic_Properties/Hab''.var". +(* UNEXPORTED +cic:/CoRN/ftc/Derivative/Basic_Properties/Hab''.var +*) inline procedural "cic:/CoRN/ftc/Derivative/deriv_imp_contin'_I.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 2e3636d80..84ded647b 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/DerivativeOps.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/DerivativeOps.mma @@ -36,11 +36,17 @@ context.%}.% We begin with some technical stuff that will be necessary for division. *) -alias id "a" = "cic:/CoRN/ftc/DerivativeOps/Lemmas/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/DerivativeOps/Lemmas/a.var +*) -alias id "b" = "cic:/CoRN/ftc/DerivativeOps/Lemmas/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/DerivativeOps/Lemmas/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/DerivativeOps/Lemmas/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/DerivativeOps/Lemmas/Hab.var +*) (* begin hide *) @@ -48,7 +54,9 @@ inline procedural "cic:/CoRN/ftc/DerivativeOps/Lemmas/I.con" "Lemmas__" as defin (* end hide *) -alias id "F" = "cic:/CoRN/ftc/DerivativeOps/Lemmas/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/DerivativeOps/Lemmas/F.var +*) (* begin hide *) @@ -58,7 +66,9 @@ inline procedural "cic:/CoRN/ftc/DerivativeOps/Lemmas/P.con" "Lemmas__" as defin (* begin show *) -alias id "Fbnd" = "cic:/CoRN/ftc/DerivativeOps/Lemmas/Fbnd.var". +(* UNEXPORTED +cic:/CoRN/ftc/DerivativeOps/Lemmas/Fbnd.var +*) (* end show *) @@ -81,11 +91,17 @@ Section Local_Results We can now derive all the usual rules for deriving constant and identity functions, sums, inverses and products of functions with a known derivative. *) -alias id "a" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/DerivativeOps/Local_Results/a.var +*) -alias id "b" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/DerivativeOps/Local_Results/b.var +*) -alias id "Hab'" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/Hab'.var". +(* UNEXPORTED +cic:/CoRN/ftc/DerivativeOps/Local_Results/Hab'.var +*) (* begin hide *) @@ -99,17 +115,29 @@ inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_const.con" as lemma. inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_id.con" as lemma. -alias id "F" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/DerivativeOps/Local_Results/F.var +*) -alias id "F'" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/F'.var". +(* UNEXPORTED +cic:/CoRN/ftc/DerivativeOps/Local_Results/F'.var +*) -alias id "G" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/G.var". +(* UNEXPORTED +cic:/CoRN/ftc/DerivativeOps/Local_Results/G.var +*) -alias id "G'" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/G'.var". +(* UNEXPORTED +cic:/CoRN/ftc/DerivativeOps/Local_Results/G'.var +*) -alias id "derF" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/derF.var". +(* UNEXPORTED +cic:/CoRN/ftc/DerivativeOps/Local_Results/derF.var +*) -alias id "derG" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/derG.var". +(* UNEXPORTED +cic:/CoRN/ftc/DerivativeOps/Local_Results/derG.var +*) inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_plus.con" as lemma. @@ -123,7 +151,9 @@ As was the case for continuity, the rule for the reciprocal function has a side (* begin show *) -alias id "Fbnd" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/Fbnd.var". +(* UNEXPORTED +cic:/CoRN/ftc/DerivativeOps/Local_Results/Fbnd.var +*) (* end show *) @@ -146,11 +176,17 @@ Hint Resolve Derivative_I_const Derivative_I_id Derivative_I_plus Section Corolaries *) -alias id "a" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/DerivativeOps/Corolaries/a.var +*) -alias id "b" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/DerivativeOps/Corolaries/b.var +*) -alias id "Hab'" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/Hab'.var". +(* UNEXPORTED +cic:/CoRN/ftc/DerivativeOps/Corolaries/Hab'.var +*) (* begin hide *) @@ -160,17 +196,29 @@ inline procedural "cic:/CoRN/ftc/DerivativeOps/Corolaries/I.con" "Corolaries__" (* end hide *) -alias id "F" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/DerivativeOps/Corolaries/F.var +*) -alias id "F'" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/F'.var". +(* UNEXPORTED +cic:/CoRN/ftc/DerivativeOps/Corolaries/F'.var +*) -alias id "G" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/G.var". +(* UNEXPORTED +cic:/CoRN/ftc/DerivativeOps/Corolaries/G.var +*) -alias id "G'" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/G'.var". +(* UNEXPORTED +cic:/CoRN/ftc/DerivativeOps/Corolaries/G'.var +*) -alias id "derF" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/derF.var". +(* UNEXPORTED +cic:/CoRN/ftc/DerivativeOps/Corolaries/derF.var +*) -alias id "derG" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/derG.var". +(* UNEXPORTED +cic:/CoRN/ftc/DerivativeOps/Corolaries/derG.var +*) (*#* From this lemmas the rules for the other algebraic operations follow directly. @@ -182,7 +230,9 @@ inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_scal.con" as lemma. inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_nth.con" as lemma. -alias id "Gbnd" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/Gbnd.var". +(* UNEXPORTED +cic:/CoRN/ftc/DerivativeOps/Corolaries/Gbnd.var +*) inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_div.con" as lemma. @@ -203,13 +253,21 @@ Section Derivative_Sums induction using the constant and addition rules. *) -alias id "a" = "cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/a.var +*) -alias id "b" = "cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/Hab.var +*) -alias id "Hab'" = "cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/Hab'.var". +(* UNEXPORTED +cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/Hab'.var +*) (* begin hide *) diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/Differentiability.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/Differentiability.mma index ad8d9b631..21e0c1ff7 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/Differentiability.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/Differentiability.mma @@ -82,11 +82,17 @@ inline procedural "cic:/CoRN/ftc/Differentiability/included_imp_diffble.con" as A function differentiable in an interval is everywhere defined in that interval. *) -alias id "a" = "cic:/CoRN/ftc/Differentiability/Local_Properties/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/Differentiability/Local_Properties/a.var +*) -alias id "b" = "cic:/CoRN/ftc/Differentiability/Local_Properties/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/Differentiability/Local_Properties/b.var +*) -alias id "Hab'" = "cic:/CoRN/ftc/Differentiability/Local_Properties/Hab'.var". +(* UNEXPORTED +cic:/CoRN/ftc/Differentiability/Local_Properties/Hab'.var +*) (* begin hide *) @@ -120,11 +126,17 @@ Section Operations All the algebraic results carry on. *) -alias id "a" = "cic:/CoRN/ftc/Differentiability/Operations/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/Differentiability/Operations/a.var +*) -alias id "b" = "cic:/CoRN/ftc/Differentiability/Operations/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/Differentiability/Operations/b.var +*) -alias id "Hab'" = "cic:/CoRN/ftc/Differentiability/Operations/Hab'.var". +(* UNEXPORTED +cic:/CoRN/ftc/Differentiability/Operations/Hab'.var +*) (* begin hide *) @@ -150,11 +162,17 @@ End Constants Section Well_Definedness *) -alias id "F" = "cic:/CoRN/ftc/Differentiability/Operations/Well_Definedness/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/Differentiability/Operations/Well_Definedness/F.var +*) -alias id "H" = "cic:/CoRN/ftc/Differentiability/Operations/Well_Definedness/H.var". +(* UNEXPORTED +cic:/CoRN/ftc/Differentiability/Operations/Well_Definedness/H.var +*) -alias id "diffF" = "cic:/CoRN/ftc/Differentiability/Operations/Well_Definedness/diffF.var". +(* UNEXPORTED +cic:/CoRN/ftc/Differentiability/Operations/Well_Definedness/diffF.var +*) inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_wd.con" as lemma. @@ -162,13 +180,21 @@ inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_wd.con" as lemma. End Well_Definedness *) -alias id "F" = "cic:/CoRN/ftc/Differentiability/Operations/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/Differentiability/Operations/F.var +*) -alias id "G" = "cic:/CoRN/ftc/Differentiability/Operations/G.var". +(* UNEXPORTED +cic:/CoRN/ftc/Differentiability/Operations/G.var +*) -alias id "diffF" = "cic:/CoRN/ftc/Differentiability/Operations/diffF.var". +(* UNEXPORTED +cic:/CoRN/ftc/Differentiability/Operations/diffF.var +*) -alias id "diffG" = "cic:/CoRN/ftc/Differentiability/Operations/diffG.var". +(* UNEXPORTED +cic:/CoRN/ftc/Differentiability/Operations/diffG.var +*) inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_plus.con" as lemma. @@ -178,7 +204,9 @@ inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_mult.con" as lemma. (* begin show *) -alias id "Gbnd" = "cic:/CoRN/ftc/Differentiability/Operations/Gbnd.var". +(* UNEXPORTED +cic:/CoRN/ftc/Differentiability/Operations/Gbnd.var +*) (* end show *) @@ -192,11 +220,17 @@ End Operations Section Corollaries *) -alias id "a" = "cic:/CoRN/ftc/Differentiability/Corollaries/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/Differentiability/Corollaries/a.var +*) -alias id "b" = "cic:/CoRN/ftc/Differentiability/Corollaries/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/Differentiability/Corollaries/b.var +*) -alias id "Hab'" = "cic:/CoRN/ftc/Differentiability/Corollaries/Hab'.var". +(* UNEXPORTED +cic:/CoRN/ftc/Differentiability/Corollaries/Hab'.var +*) (* begin hide *) @@ -206,13 +240,21 @@ inline procedural "cic:/CoRN/ftc/Differentiability/Corollaries/I.con" "Corollari (* end hide *) -alias id "F" = "cic:/CoRN/ftc/Differentiability/Corollaries/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/Differentiability/Corollaries/F.var +*) -alias id "G" = "cic:/CoRN/ftc/Differentiability/Corollaries/G.var". +(* UNEXPORTED +cic:/CoRN/ftc/Differentiability/Corollaries/G.var +*) -alias id "diffF" = "cic:/CoRN/ftc/Differentiability/Corollaries/diffF.var". +(* UNEXPORTED +cic:/CoRN/ftc/Differentiability/Corollaries/diffF.var +*) -alias id "diffG" = "cic:/CoRN/ftc/Differentiability/Corollaries/diffG.var". +(* UNEXPORTED +cic:/CoRN/ftc/Differentiability/Corollaries/diffG.var +*) inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_minus.con" as lemma. @@ -220,7 +262,9 @@ inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_scal.con" as lemma. inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_nth.con" as lemma. -alias id "Gbnd" = "cic:/CoRN/ftc/Differentiability/Corollaries/Gbnd.var". +(* UNEXPORTED +cic:/CoRN/ftc/Differentiability/Corollaries/Gbnd.var +*) inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_div.con" as lemma. @@ -237,11 +281,17 @@ Differentiability of families of functions is proved by induction using the constant and addition rules. *) -alias id "a" = "cic:/CoRN/ftc/Differentiability/Other_Properties/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/Differentiability/Other_Properties/a.var +*) -alias id "b" = "cic:/CoRN/ftc/Differentiability/Other_Properties/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/Differentiability/Other_Properties/b.var +*) -alias id "Hab'" = "cic:/CoRN/ftc/Differentiability/Other_Properties/Hab'.var". +(* UNEXPORTED +cic:/CoRN/ftc/Differentiability/Other_Properties/Hab'.var +*) inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_Sum0.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/FTC.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/FTC.mma index 9eee7432c..b7381ac76 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/FTC.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/FTC.mma @@ -49,15 +49,25 @@ and [a] be a point in [I]. %\end{convention}% *) -alias id "I" = "cic:/CoRN/ftc/FTC/Indefinite_Integral/I.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Indefinite_Integral/I.var +*) -alias id "F" = "cic:/CoRN/ftc/FTC/Indefinite_Integral/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Indefinite_Integral/F.var +*) -alias id "contF" = "cic:/CoRN/ftc/FTC/Indefinite_Integral/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Indefinite_Integral/contF.var +*) -alias id "a" = "cic:/CoRN/ftc/FTC/Indefinite_Integral/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Indefinite_Integral/a.var +*) -alias id "Ha" = "cic:/CoRN/ftc/FTC/Indefinite_Integral/Ha.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Indefinite_Integral/Ha.var +*) inline procedural "cic:/CoRN/ftc/FTC/prim_lemma.con" as lemma. @@ -92,15 +102,25 @@ indefinite integral of [F] from [x0]. %\end{convention}% *) -alias id "J" = "cic:/CoRN/ftc/FTC/FTC/J.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/FTC/J.var +*) -alias id "F" = "cic:/CoRN/ftc/FTC/FTC/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/FTC/F.var +*) -alias id "contF" = "cic:/CoRN/ftc/FTC/FTC/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/FTC/contF.var +*) -alias id "x0" = "cic:/CoRN/ftc/FTC/FTC/x0.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/FTC/x0.var +*) -alias id "Hx0" = "cic:/CoRN/ftc/FTC/FTC/Hx0.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/FTC/Hx0.var +*) (* begin hide *) @@ -114,7 +134,9 @@ inline procedural "cic:/CoRN/ftc/FTC/Continuous_prim.con" as lemma. The derivative of [G] is simply [F]. *) -alias id "pJ" = "cic:/CoRN/ftc/FTC/FTC/pJ.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/FTC/pJ.var +*) inline procedural "cic:/CoRN/ftc/FTC/FTC1.con" as theorem. @@ -122,9 +144,13 @@ inline procedural "cic:/CoRN/ftc/FTC/FTC1.con" as theorem. Any other function [G0] with derivative [F] must differ from [G] by a constant. *) -alias id "G0" = "cic:/CoRN/ftc/FTC/FTC/G0.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/FTC/G0.var +*) -alias id "derG0" = "cic:/CoRN/ftc/FTC/FTC/derG0.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/FTC/derG0.var +*) inline procedural "cic:/CoRN/ftc/FTC/FTC2.con" as theorem. @@ -178,15 +204,25 @@ then the sequence of their primitives also converges, and the limit commutes with the indefinite integral. *) -alias id "J" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/J.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/J.var +*) -alias id "f" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/f.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/f.var +*) -alias id "F" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/F.var +*) -alias id "contf" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/contf.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/contf.var +*) -alias id "contF" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/contF.var +*) (* UNEXPORTED Section Compact @@ -202,27 +238,45 @@ continuous in [[a,b]], $x0\in[a,b]$#x0∈[a,b]#; denote by %\end{convention}% *) -alias id "a" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/a.var +*) -alias id "b" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/Hab.var +*) -alias id "contIf" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/contIf.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/contIf.var +*) -alias id "contIF" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/contIF.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/contIF.var +*) (* begin show *) -alias id "convF" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/convF.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/convF.var +*) (* end show *) -alias id "x0" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/x0.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/x0.var +*) -alias id "Hx0" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/Hx0.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/Hx0.var +*) -alias id "Hx0'" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/Hx0'.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/Hx0'.var +*) (* begin hide *) @@ -234,9 +288,13 @@ inline procedural "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/G.con" "Limit (* begin show *) -alias id "contg" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/contg.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/contg.var +*) -alias id "contG" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/contG.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/contG.var +*) (* end show *) @@ -264,13 +322,19 @@ Finally, with [x0, g, G] as before, (* begin show *) -alias id "convF" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/convF.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/convF.var +*) (* end show *) -alias id "x0" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/x0.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/x0.var +*) -alias id "Hx0" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/Hx0.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/Hx0.var +*) (* begin hide *) @@ -280,9 +344,13 @@ inline procedural "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/G.con" "Limit (* end hide *) -alias id "contg" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/contg.var". +(* UNEXPORTED +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". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/contG.var +*) inline procedural "cic:/CoRN/ftc/FTC/fun_lim_seq_integral_IR.con" as lemma. @@ -305,31 +373,57 @@ Similar results hold for the sequence of derivatives of a converging sequence; t %\end{convention}% *) -alias id "J" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/J.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/J.var +*) -alias id "pJ" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/pJ.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/pJ.var +*) -alias id "f" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/f.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/f.var +*) -alias id "g" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/g.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/g.var +*) -alias id "F" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/F.var +*) -alias id "G" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/G.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/G.var +*) -alias id "contf" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/contf.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/contf.var +*) -alias id "contF" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/contF.var +*) -alias id "convF" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/convF.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/convF.var +*) -alias id "contg" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/contg.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/contg.var +*) -alias id "contG" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/contG.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/contG.var +*) -alias id "convG" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/convG.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/convG.var +*) -alias id "derf" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/derf.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/derf.var +*) inline procedural "cic:/CoRN/ftc/FTC/fun_lim_seq_derivative.con" as lemma. @@ -345,23 +439,37 @@ Section Derivative_Series As a very important case of this result, we get a rule for deriving series. *) -alias id "J" = "cic:/CoRN/ftc/FTC/Derivative_Series/J.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Derivative_Series/J.var +*) -alias id "pJ" = "cic:/CoRN/ftc/FTC/Derivative_Series/pJ.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Derivative_Series/pJ.var +*) -alias id "f" = "cic:/CoRN/ftc/FTC/Derivative_Series/f.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Derivative_Series/f.var +*) -alias id "g" = "cic:/CoRN/ftc/FTC/Derivative_Series/g.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Derivative_Series/g.var +*) (* begin show *) -alias id "convF" = "cic:/CoRN/ftc/FTC/Derivative_Series/convF.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Derivative_Series/convF.var +*) -alias id "convG" = "cic:/CoRN/ftc/FTC/Derivative_Series/convG.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Derivative_Series/convG.var +*) (* end show *) -alias id "derF" = "cic:/CoRN/ftc/FTC/Derivative_Series/derF.var". +(* UNEXPORTED +cic:/CoRN/ftc/FTC/Derivative_Series/derF.var +*) inline procedural "cic:/CoRN/ftc/FTC/Derivative_FSeries.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/FunctSequence.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/FunctSequence.mma index 0a3c1ce29..8d5bfb376 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/FunctSequence.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/FunctSequence.mma @@ -50,11 +50,17 @@ be defined. For a discussion on the different notions of convergent see Bishop 1967. *) -alias id "a" = "cic:/CoRN/ftc/FunctSequence/Definitions/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/Definitions/a.var +*) -alias id "b" = "cic:/CoRN/ftc/FunctSequence/Definitions/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/Definitions/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/FunctSequence/Definitions/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/Definitions/Hab.var +*) (* begin hide *) @@ -62,13 +68,21 @@ inline procedural "cic:/CoRN/ftc/FunctSequence/Definitions/I.con" "Definitions__ (* end hide *) -alias id "f" = "cic:/CoRN/ftc/FunctSequence/Definitions/f.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/Definitions/f.var +*) -alias id "F" = "cic:/CoRN/ftc/FunctSequence/Definitions/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/Definitions/F.var +*) -alias id "contf" = "cic:/CoRN/ftc/FunctSequence/Definitions/contf.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/Definitions/contf.var +*) -alias id "contF" = "cic:/CoRN/ftc/FunctSequence/Definitions/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/Definitions/contF.var +*) (* begin hide *) @@ -130,11 +144,17 @@ End Definitions Section More_Definitions *) -alias id "a" = "cic:/CoRN/ftc/FunctSequence/More_Definitions/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/More_Definitions/a.var +*) -alias id "b" = "cic:/CoRN/ftc/FunctSequence/More_Definitions/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/More_Definitions/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/FunctSequence/More_Definitions/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/More_Definitions/Hab.var +*) (* begin hide *) @@ -142,9 +162,13 @@ inline procedural "cic:/CoRN/ftc/FunctSequence/More_Definitions/I.con" "More_Def (* end hide *) -alias id "f" = "cic:/CoRN/ftc/FunctSequence/More_Definitions/f.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/More_Definitions/f.var +*) -alias id "contf" = "cic:/CoRN/ftc/FunctSequence/More_Definitions/contf.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/More_Definitions/contf.var +*) (*#* We can also say that [f] is simply convergent if it converges to some @@ -160,7 +184,9 @@ It is useful to extract the limit as a partial function: (* begin show *) -alias id "H" = "cic:/CoRN/ftc/FunctSequence/More_Definitions/H.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/More_Definitions/H.var +*) (* end show *) @@ -179,11 +205,17 @@ Section Irrelevance_of_Proofs This section contains a number of technical results stating mainly that being a Cauchy sequence or converging to some limit is a property of the sequence itself and independent of the proofs we supply of its continuity or the continuity of its limit. *) -alias id "a" = "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/a.var +*) -alias id "b" = "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/Hab.var +*) (* begin hide *) @@ -191,23 +223,35 @@ inline procedural "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/I.con" "Irr (* end hide *) -alias id "f" = "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/f.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/f.var +*) (* begin show *) -alias id "contf" = "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/contf.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/contf.var +*) -alias id "contf0" = "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/contf0.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/contf0.var +*) (* end show *) -alias id "F" = "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/F.var +*) (* begin show *) -alias id "contF" = "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/contF.var +*) -alias id "contF0" = "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/contF0.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/contF0.var +*) (* end show *) @@ -246,11 +290,17 @@ limit; the limit is a continuous function; and convergence is well defined with respect to functional equality in the interval [[a,b]]. *) -alias id "a" = "cic:/CoRN/ftc/FunctSequence/More_Properties/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/More_Properties/a.var +*) -alias id "b" = "cic:/CoRN/ftc/FunctSequence/More_Properties/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/More_Properties/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/FunctSequence/More_Properties/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/More_Properties/Hab.var +*) (* begin hide *) @@ -258,37 +308,61 @@ inline procedural "cic:/CoRN/ftc/FunctSequence/More_Properties/I.con" "More_Prop (* end hide *) -alias id "f" = "cic:/CoRN/ftc/FunctSequence/More_Properties/f.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/More_Properties/f.var +*) -alias id "g" = "cic:/CoRN/ftc/FunctSequence/More_Properties/g.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/More_Properties/g.var +*) (* begin show *) -alias id "contf" = "cic:/CoRN/ftc/FunctSequence/More_Properties/contf.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/More_Properties/contf.var +*) -alias id "contf0" = "cic:/CoRN/ftc/FunctSequence/More_Properties/contf0.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/More_Properties/contf0.var +*) -alias id "contg" = "cic:/CoRN/ftc/FunctSequence/More_Properties/contg.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/More_Properties/contg.var +*) -alias id "contg0" = "cic:/CoRN/ftc/FunctSequence/More_Properties/contg0.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/More_Properties/contg0.var +*) (* end show *) inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_conv_fun_seq'.con" as lemma. -alias id "F" = "cic:/CoRN/ftc/FunctSequence/More_Properties/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/More_Properties/F.var +*) -alias id "G" = "cic:/CoRN/ftc/FunctSequence/More_Properties/G.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/More_Properties/G.var +*) (* begin show *) -alias id "contF" = "cic:/CoRN/ftc/FunctSequence/More_Properties/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/More_Properties/contF.var +*) -alias id "contF0" = "cic:/CoRN/ftc/FunctSequence/More_Properties/contF0.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/More_Properties/contF0.var +*) -alias id "contG" = "cic:/CoRN/ftc/FunctSequence/More_Properties/contG.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/More_Properties/contG.var +*) -alias id "contG0" = "cic:/CoRN/ftc/FunctSequence/More_Properties/contG0.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/More_Properties/contG0.var +*) (* end show *) @@ -337,11 +411,17 @@ Section Algebraic_Properties We now study how convergence is affected by algebraic operations, and some algebraic properties of the limit function. *) -alias id "a" = "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/a.var +*) -alias id "b" = "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/Hab.var +*) (* begin hide *) @@ -349,13 +429,21 @@ inline procedural "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/I.con" "Alge (* end hide *) -alias id "f" = "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/f.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/f.var +*) -alias id "g" = "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/g.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/g.var +*) -alias id "contf" = "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/contf.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/contf.var +*) -alias id "contg" = "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/contg.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/contg.var +*) (*#* First, the limit function is unique. @@ -374,19 +462,31 @@ inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Cauchy_prop_const.con" as lem We now prove that if two sequences converge than their sum (difference, product) also converge to the sum (difference, product) of their limits. *) -alias id "F" = "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/F.var +*) -alias id "G" = "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/G.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/G.var +*) -alias id "contF" = "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/contF.var +*) -alias id "contG" = "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/contG.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/contG.var +*) (* begin show *) -alias id "convF" = "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/convF.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/convF.var +*) -alias id "convG" = "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/convG.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/convG.var +*) (* end show *) @@ -416,11 +516,17 @@ End Algebraic_Properties Section More_Algebraic_Properties *) -alias id "a" = "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/a.var +*) -alias id "b" = "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/Hab.var +*) (* begin hide *) @@ -428,13 +534,21 @@ inline procedural "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/I.con" (* end hide *) -alias id "f" = "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/f.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/f.var +*) -alias id "g" = "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/g.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/g.var +*) -alias id "contf" = "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/contf.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/contf.var +*) -alias id "contg" = "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/contg.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/contg.var +*) (*#* The same is true if we don't make the limits explicit. @@ -442,9 +556,13 @@ The same is true if we don't make the limits explicit. (* begin hide *) -alias id "Hf" = "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/Hf.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/Hf.var +*) -alias id "Hg" = "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/Hg.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/Hg.var +*) (* end hide *) @@ -468,11 +586,17 @@ End More_Algebraic_Properties Section Still_More_Algebraic_Properties *) -alias id "a" = "cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/a.var +*) -alias id "b" = "cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/Hab.var +*) (* begin hide *) @@ -480,11 +604,17 @@ inline procedural "cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/I (* end hide *) -alias id "f" = "cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/f.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/f.var +*) -alias id "contf" = "cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/contf.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/contf.var +*) -alias id "Hf" = "cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/Hf.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/Hf.var +*) (*#* As a corollary, we get the analogous property for the sequence of algebraic inverse functions. diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/FunctSeries.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/FunctSeries.mma index 49acbf1cf..05ab51726 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/FunctSeries.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/FunctSeries.mma @@ -51,11 +51,17 @@ defined in a compact interval. For this, partial sums are defined and convergence is simply the convergence of the sequence of partial sums. *) -alias id "a" = "cic:/CoRN/ftc/FunctSeries/Definitions/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSeries/Definitions/a.var +*) -alias id "b" = "cic:/CoRN/ftc/FunctSeries/Definitions/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSeries/Definitions/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/Definitions/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSeries/Definitions/Hab.var +*) (* begin hide *) @@ -63,7 +69,9 @@ inline procedural "cic:/CoRN/ftc/FunctSeries/Definitions/I.con" "Definitions__" (* end hide *) -alias id "f" = "cic:/CoRN/ftc/FunctSeries/Definitions/f.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSeries/Definitions/f.var +*) inline procedural "cic:/CoRN/ftc/FunctSeries/fun_seq_part_sum.con" as definition. @@ -85,7 +93,9 @@ the corresponding series. (* begin show *) -alias id "H" = "cic:/CoRN/ftc/FunctSeries/Definitions/H.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSeries/Definitions/H.var +*) (* end show *) @@ -117,13 +127,21 @@ Hint Resolve fun_seq_part_sum_cont: continuous. Section More_Definitions *) -alias id "a" = "cic:/CoRN/ftc/FunctSeries/More_Definitions/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSeries/More_Definitions/a.var +*) -alias id "b" = "cic:/CoRN/ftc/FunctSeries/More_Definitions/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSeries/More_Definitions/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/More_Definitions/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSeries/More_Definitions/Hab.var +*) -alias id "f" = "cic:/CoRN/ftc/FunctSeries/More_Definitions/f.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSeries/More_Definitions/f.var +*) (*#* A series can also be absolutely convergent. *) @@ -142,11 +160,17 @@ Section Operations All of these are analogous to the properties for series of real numbers, so we won't comment much about them. *) -alias id "a" = "cic:/CoRN/ftc/FunctSeries/Operations/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSeries/Operations/a.var +*) -alias id "b" = "cic:/CoRN/ftc/FunctSeries/Operations/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSeries/Operations/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/Operations/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSeries/Operations/Hab.var +*) (* begin hide *) @@ -166,9 +190,13 @@ inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_zero.con" as lemma. (* begin show *) -alias id "f" = "cic:/CoRN/ftc/FunctSeries/Operations/f.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSeries/Operations/f.var +*) -alias id "g" = "cic:/CoRN/ftc/FunctSeries/Operations/g.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSeries/Operations/g.var +*) (* end show *) @@ -176,9 +204,13 @@ inline procedural "cic:/CoRN/ftc/FunctSeries/fun_series_convergent_wd.con" as le (* begin show *) -alias id "convF" = "cic:/CoRN/ftc/FunctSeries/Operations/convF.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSeries/Operations/convF.var +*) -alias id "convG" = "cic:/CoRN/ftc/FunctSeries/Operations/convG.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSeries/Operations/convG.var +*) (* end show *) @@ -197,11 +229,17 @@ inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_min.con" as lemma. %\end{convention}% *) -alias id "c" = "cic:/CoRN/ftc/FunctSeries/Operations/c.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSeries/Operations/c.var +*) -alias id "H" = "cic:/CoRN/ftc/FunctSeries/Operations/H.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSeries/Operations/H.var +*) -alias id "contH" = "cic:/CoRN/ftc/FunctSeries/Operations/contH.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSeries/Operations/contH.var +*) inline procedural "cic:/CoRN/ftc/FunctSeries/conv_fun_series_scal.con" as lemma. @@ -215,11 +253,17 @@ End Operations Section More_Operations *) -alias id "a" = "cic:/CoRN/ftc/FunctSeries/More_Operations/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSeries/More_Operations/a.var +*) -alias id "b" = "cic:/CoRN/ftc/FunctSeries/More_Operations/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSeries/More_Operations/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/More_Operations/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSeries/More_Operations/Hab.var +*) (* begin hide *) @@ -227,9 +271,13 @@ inline procedural "cic:/CoRN/ftc/FunctSeries/More_Operations/I.con" "More_Operat (* end hide *) -alias id "f" = "cic:/CoRN/ftc/FunctSeries/More_Operations/f.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSeries/More_Operations/f.var +*) -alias id "convF" = "cic:/CoRN/ftc/FunctSeries/More_Operations/convF.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSeries/More_Operations/convF.var +*) inline procedural "cic:/CoRN/ftc/FunctSeries/conv_fun_series_inv.con" as lemma. @@ -243,15 +291,25 @@ End More_Operations Section Other_Results *) -alias id "a" = "cic:/CoRN/ftc/FunctSeries/Other_Results/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSeries/Other_Results/a.var +*) -alias id "b" = "cic:/CoRN/ftc/FunctSeries/Other_Results/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSeries/Other_Results/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/Other_Results/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSeries/Other_Results/Hab.var +*) -alias id "f" = "cic:/CoRN/ftc/FunctSeries/Other_Results/f.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSeries/Other_Results/f.var +*) -alias id "convF" = "cic:/CoRN/ftc/FunctSeries/Other_Results/convF.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSeries/Other_Results/convF.var +*) (*#* The following relate the sum series with the limit of the sequence of @@ -286,11 +344,17 @@ Section Convergence_Criteria Most of the convergence criteria for series of real numbers carry over to series of real-valued functions, so again we just present them without comments. *) -alias id "a" = "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/a.var +*) -alias id "b" = "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/Hab.var +*) (* begin hide *) @@ -298,9 +362,13 @@ inline procedural "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/I.con" "Conver (* end hide *) -alias id "f" = "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/f.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/f.var +*) -alias id "contF" = "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/contF.var +*) (* UNEXPORTED Opaque Frestr. diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/Integral.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/Integral.mma index adfac8d02..d482e21b3 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/Integral.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/Integral.mma @@ -57,19 +57,29 @@ continuous functions in [I]. %\end{convention}% *) -alias id "a" = "cic:/CoRN/ftc/Integral/Integral/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Integral/a.var +*) -alias id "b" = "cic:/CoRN/ftc/Integral/Integral/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Integral/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/Integral/Integral/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Integral/Hab.var +*) (* begin hide *) inline procedural "cic:/CoRN/ftc/Integral/Integral/I.con" "Integral__" as definition. -alias id "F" = "cic:/CoRN/ftc/Integral/Integral/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Integral/F.var +*) -alias id "contF" = "cic:/CoRN/ftc/Integral/Integral/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Integral/contF.var +*) inline procedural "cic:/CoRN/ftc/Integral/Integral/contF'.con" "Integral__" as definition. @@ -104,13 +114,21 @@ respecting [P]. %\end{convention}% *) -alias id "n" = "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/n.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Integral/Integral_Thm/n.var +*) -alias id "P" = "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/P.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Integral/Integral_Thm/P.var +*) -alias id "e" = "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/e.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Integral/Integral_Thm/e.var +*) -alias id "He" = "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/He.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Integral/Integral_Thm/He.var +*) (* begin hide *) @@ -118,15 +136,25 @@ inline procedural "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/d.con" "Integral (* end hide *) -alias id "HmeshP" = "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/HmeshP.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Integral/Integral_Thm/HmeshP.var +*) -alias id "fP" = "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/fP.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Integral/Integral_Thm/fP.var +*) -alias id "HfP" = "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/HfP.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Integral/Integral_Thm/HfP.var +*) -alias id "HfP'" = "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/HfP'.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Integral/Integral_Thm/HfP'.var +*) -alias id "incF" = "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/incF.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Integral/Integral_Thm/incF.var +*) inline procedural "cic:/CoRN/ftc/Integral/partition_Sum_conv_integral.con" as lemma. @@ -146,11 +174,17 @@ Section Basic_Properties The usual extensionality and strong extensionality results hold. *) -alias id "a" = "cic:/CoRN/ftc/Integral/Basic_Properties/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/a.var +*) -alias id "b" = "cic:/CoRN/ftc/Integral/Basic_Properties/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/Integral/Basic_Properties/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Hab.var +*) (* begin hide *) @@ -166,13 +200,21 @@ Notation Integral := (integral _ _ Hab). Section Well_Definedness *) -alias id "F" = "cic:/CoRN/ftc/Integral/Basic_Properties/Well_Definedness/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Well_Definedness/F.var +*) -alias id "G" = "cic:/CoRN/ftc/Integral/Basic_Properties/Well_Definedness/G.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Well_Definedness/G.var +*) -alias id "contF" = "cic:/CoRN/ftc/Integral/Basic_Properties/Well_Definedness/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Well_Definedness/contF.var +*) -alias id "contG" = "cic:/CoRN/ftc/Integral/Basic_Properties/Well_Definedness/contG.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Well_Definedness/contG.var +*) inline procedural "cic:/CoRN/ftc/Integral/integral_strext.con" as lemma. @@ -200,13 +242,21 @@ The integral is a linear and monotonous function; in order to prove these facts 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". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity/F.var +*) -alias id "G" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity/G.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity/G.var +*) -alias id "contF" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity/contF.var +*) -alias id "contG" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity/contG.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity/contG.var +*) inline procedural "cic:/CoRN/ftc/Integral/integral_comm_scal.con" as lemma. @@ -226,13 +276,21 @@ End Linearity_and_Monotonicity Section Linearity_and_Monotonicity' *) -alias id "F" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/F.var +*) -alias id "G" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/G.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/G.var +*) -alias id "contF" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/contF.var +*) -alias id "contG" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/contG.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/contG.var +*) (*#* %\begin{convention}% Let [alpha, beta : IR] and assume that @@ -240,9 +298,13 @@ alias id "contG" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monoto %\end{convention}% *) -alias id "alpha" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/alpha.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/alpha.var +*) -alias id "beta" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/beta.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/beta.var +*) (* begin hide *) @@ -250,7 +312,9 @@ inline procedural "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monoton (* end hide *) -alias id "contH" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/contH.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/contH.var +*) inline procedural "cic:/CoRN/ftc/Integral/linear_integral.con" as lemma. @@ -272,13 +336,21 @@ End Linearity_and_Monotonicity' Section Corollaries *) -alias id "F" = "cic:/CoRN/ftc/Integral/Basic_Properties/Corollaries/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Corollaries/F.var +*) -alias id "G" = "cic:/CoRN/ftc/Integral/Basic_Properties/Corollaries/G.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Corollaries/G.var +*) -alias id "contF" = "cic:/CoRN/ftc/Integral/Basic_Properties/Corollaries/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Corollaries/contF.var +*) -alias id "contG" = "cic:/CoRN/ftc/Integral/Basic_Properties/Corollaries/contG.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Corollaries/contG.var +*) (*#* As corollaries we can calculate integrals of group operations applied to functions. @@ -317,19 +389,33 @@ $c\in[a,b]$#c∈[a,b]#. %\end{convention}% *) -alias id "F" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/F.var +*) -alias id "c" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/c.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/c.var +*) -alias id "Hac" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Hac.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Hac.var +*) -alias id "Hcb" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Hcb.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Hcb.var +*) -alias id "Hab'" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Hab'.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Hab'.var +*) -alias id "Hac'" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Hac'.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Hac'.var +*) -alias id "Hcb'" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Hcb'.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Hcb'.var +*) (* UNEXPORTED Section Partition_Join @@ -347,13 +433,21 @@ inequality). %\end{convention}% *) -alias id "n" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/n.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/n.var +*) -alias id "m" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/m.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/m.var +*) -alias id "P" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/P.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/P.var +*) -alias id "Q" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/Q.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/Q.var +*) (* begin hide *) @@ -390,17 +484,29 @@ inline procedural "cic:/CoRN/ftc/Integral/partition_join.con" as definition. %\end{convention}% *) -alias id "fP" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/fP.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/fP.var +*) -alias id "HfP" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/HfP.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/HfP.var +*) -alias id "HfP'" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/HfP'.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/HfP'.var +*) -alias id "fQ" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/fQ.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/fQ.var +*) -alias id "HfQ" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/HfQ.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/HfQ.var +*) -alias id "HfQ'" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/HfQ'.var". +(* UNEXPORTED +cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/HfQ'.var +*) (* begin hide *) diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/IntervalFunct.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/IntervalFunct.mma index 80303c0dd..cf4c9b991 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/IntervalFunct.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/IntervalFunct.mma @@ -45,11 +45,17 @@ type [I -> IR]. %\end{convention}% *) -alias id "a" = "cic:/CoRN/ftc/IntervalFunct/Operations/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/IntervalFunct/Operations/a.var +*) -alias id "b" = "cic:/CoRN/ftc/IntervalFunct/Operations/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/IntervalFunct/Operations/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/IntervalFunct/Operations/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/IntervalFunct/Operations/Hab.var +*) (* begin hide *) @@ -57,9 +63,13 @@ inline procedural "cic:/CoRN/ftc/IntervalFunct/Operations/I.con" "Operations__" (* end hide *) -alias id "f" = "cic:/CoRN/ftc/IntervalFunct/Operations/f.var". +(* UNEXPORTED +cic:/CoRN/ftc/IntervalFunct/Operations/f.var +*) -alias id "g" = "cic:/CoRN/ftc/IntervalFunct/Operations/g.var". +(* UNEXPORTED +cic:/CoRN/ftc/IntervalFunct/Operations/g.var +*) (* UNEXPORTED Section Const @@ -72,7 +82,9 @@ Constant and identity functions are defined. %\end{convention}% *) -alias id "c" = "cic:/CoRN/ftc/IntervalFunct/Operations/Const/c.var". +(* UNEXPORTED +cic:/CoRN/ftc/IntervalFunct/Operations/Const/c.var +*) inline procedural "cic:/CoRN/ftc/IntervalFunct/IConst_strext.con" as lemma. @@ -114,7 +126,9 @@ Section Nth_Power Exponentiation to a natural power [n] is also useful. *) -alias id "n" = "cic:/CoRN/ftc/IntervalFunct/Operations/Nth_Power/n.var". +(* UNEXPORTED +cic:/CoRN/ftc/IntervalFunct/Operations/Nth_Power/n.var +*) inline procedural "cic:/CoRN/ftc/IntervalFunct/INth_strext.con" as lemma. @@ -134,7 +148,9 @@ Section Recip_Div (* begin show *) -alias id "Hg" = "cic:/CoRN/ftc/IntervalFunct/Operations/Recip_Div/Hg.var". +(* UNEXPORTED +cic:/CoRN/ftc/IntervalFunct/Operations/Recip_Div/Hg.var +*) (* end show *) @@ -184,11 +200,17 @@ compact interval [[a',b']], and let [g] be a setoid function of type Section Composition *) -alias id "a" = "cic:/CoRN/ftc/IntervalFunct/Composition/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/IntervalFunct/Composition/a.var +*) -alias id "b" = "cic:/CoRN/ftc/IntervalFunct/Composition/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/IntervalFunct/Composition/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/IntervalFunct/Composition/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/IntervalFunct/Composition/Hab.var +*) (* begin hide *) @@ -196,11 +218,17 @@ inline procedural "cic:/CoRN/ftc/IntervalFunct/Composition/I.con" "Composition__ (* end hide *) -alias id "a'" = "cic:/CoRN/ftc/IntervalFunct/Composition/a'.var". +(* UNEXPORTED +cic:/CoRN/ftc/IntervalFunct/Composition/a'.var +*) -alias id "b'" = "cic:/CoRN/ftc/IntervalFunct/Composition/b'.var". +(* UNEXPORTED +cic:/CoRN/ftc/IntervalFunct/Composition/b'.var +*) -alias id "Hab'" = "cic:/CoRN/ftc/IntervalFunct/Composition/Hab'.var". +(* UNEXPORTED +cic:/CoRN/ftc/IntervalFunct/Composition/Hab'.var +*) (* begin hide *) @@ -208,11 +236,17 @@ inline procedural "cic:/CoRN/ftc/IntervalFunct/Composition/I'.con" "Composition_ (* end hide *) -alias id "f" = "cic:/CoRN/ftc/IntervalFunct/Composition/f.var". +(* UNEXPORTED +cic:/CoRN/ftc/IntervalFunct/Composition/f.var +*) -alias id "g" = "cic:/CoRN/ftc/IntervalFunct/Composition/g.var". +(* UNEXPORTED +cic:/CoRN/ftc/IntervalFunct/Composition/g.var +*) -alias id "Hfg" = "cic:/CoRN/ftc/IntervalFunct/Composition/Hfg.var". +(* UNEXPORTED +cic:/CoRN/ftc/IntervalFunct/Composition/Hfg.var +*) inline procedural "cic:/CoRN/ftc/IntervalFunct/IComp_strext.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/MoreFunSeries.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/MoreFunSeries.mma index 44391b4de..8553850e6 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/MoreFunSeries.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/MoreFunSeries.mma @@ -50,15 +50,25 @@ Some of the definitions do not make sense in this more general setting but the ones which do we simply adapt in the usual way. *) -alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/Definitions/J.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Definitions/J.var +*) -alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/Definitions/f.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Definitions/f.var +*) -alias id "F" = "cic:/CoRN/ftc/MoreFunSeries/Definitions/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Definitions/F.var +*) -alias id "contf" = "cic:/CoRN/ftc/MoreFunSeries/Definitions/contf.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Definitions/contf.var +*) -alias id "contF" = "cic:/CoRN/ftc/MoreFunSeries/Definitions/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Definitions/contF.var +*) inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_IR.con" as definition. @@ -92,15 +102,23 @@ Section More_Definitions Limit is defined and works in the same way as before. *) -alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/More_Definitions/J.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/More_Definitions/J.var +*) -alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/More_Definitions/f.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/More_Definitions/f.var +*) -alias id "contf" = "cic:/CoRN/ftc/MoreFunSeries/More_Definitions/contf.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/More_Definitions/contf.var +*) (* begin show *) -alias id "conv" = "cic:/CoRN/ftc/MoreFunSeries/More_Definitions/conv.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/More_Definitions/conv.var +*) (* end show *) @@ -121,25 +139,39 @@ Section Irrelevance_of_Proofs Proofs are irrelevant as before---they just have to be present. *) -alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/J.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/J.var +*) -alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/f.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/f.var +*) (* begin show *) -alias id "contf" = "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/contf.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/contf.var +*) -alias id "contf0" = "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/contf0.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/contf0.var +*) (* end show *) -alias id "F" = "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/F.var +*) (* begin show *) -alias id "contF" = "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/contF.var +*) -alias id "contF0" = "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/contF0.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/contF0.var +*) (* end show *) @@ -161,39 +193,65 @@ Opaque Cauchy_fun_seq_Lim_IR. Section More_Properties *) -alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/J.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/More_Properties/J.var +*) -alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/f.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/More_Properties/f.var +*) -alias id "g" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/g.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/More_Properties/g.var +*) (* begin show *) -alias id "contf" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contf.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/More_Properties/contf.var +*) -alias id "contf0" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contf0.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/More_Properties/contf0.var +*) -alias id "contg" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contg.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/More_Properties/contg.var +*) -alias id "contg0" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contg0.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/More_Properties/contg0.var +*) (* end show *) 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". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/More_Properties/F.var +*) -alias id "G" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/G.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/More_Properties/G.var +*) (* begin show *) -alias id "contF" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/More_Properties/contF.var +*) -alias id "contF0" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contF0.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/More_Properties/contF0.var +*) -alias id "contG" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contG.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/More_Properties/contG.var +*) -alias id "contG0" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contG0.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/More_Properties/contG0.var +*) (* end show *) @@ -228,15 +286,25 @@ Section Algebraic_Properties Algebraic operations still work well. *) -alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/J.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/J.var +*) -alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/f.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/f.var +*) -alias id "g" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/g.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/g.var +*) -alias id "contf" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/contf.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/contf.var +*) -alias id "contg" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/contg.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/contg.var +*) inline procedural "cic:/CoRN/ftc/MoreFunSeries/FLim_unique_IR.con" as lemma. @@ -246,19 +314,31 @@ inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_const_IR.con" as lemm 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". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/F.var +*) -alias id "G" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/G.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/G.var +*) -alias id "contF" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/contF.var +*) -alias id "contG" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/contG.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/contG.var +*) (* begin show *) -alias id "convF" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/convF.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/convF.var +*) -alias id "convG" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/convG.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/convG.var +*) (* end show *) @@ -280,21 +360,35 @@ Section More_Algebraic_Properties If we work with the limit function things fit in just as well. *) -alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/J.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/J.var +*) -alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/f.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/f.var +*) -alias id "g" = "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/g.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/g.var +*) -alias id "contf" = "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/contf.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/contf.var +*) -alias id "contg" = "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/contg.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/contg.var +*) (* begin show *) -alias id "Hf" = "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/Hf.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/Hf.var +*) -alias id "Hg" = "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/Hg.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/Hg.var +*) (* end show *) @@ -352,9 +446,13 @@ We now consider series of functions defined in arbitrary intervals. Convergence is defined as expected---through convergence in every compact interval. *) -alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/Series_Definitions/J.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Series_Definitions/J.var +*) -alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/Series_Definitions/f.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Series_Definitions/f.var +*) inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_series_convergent_IR.con" as definition. @@ -362,7 +460,9 @@ inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_series_conv_imp_conv_IR.con" (* begin show *) -alias id "H" = "cic:/CoRN/ftc/MoreFunSeries/Series_Definitions/H.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Series_Definitions/H.var +*) (* end show *) @@ -394,9 +494,13 @@ Implicit Arguments FSeries_Sum [J f]. Section More_Series_Definitions *) -alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/More_Series_Definitions/J.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/More_Series_Definitions/J.var +*) -alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/More_Series_Definitions/f.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/More_Series_Definitions/f.var +*) (*#* Absolute convergence still exists. @@ -416,9 +520,13 @@ Section Convergence_Results As before, any series converges to its sum. *) -alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/Convergence_Results/J.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Convergence_Results/J.var +*) -alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/Convergence_Results/f.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Convergence_Results/f.var +*) inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_conv.con" as lemma. @@ -449,7 +557,9 @@ Section Operations Convergence is well defined and preserved by operations. *) -alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/Operations/J.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Operations/J.var +*) inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_const_series_IR.con" as lemma. @@ -459,17 +569,25 @@ inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_zero_fun_series_IR.con" as l inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_zero_IR.con" as lemma. -alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/Operations/f.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Operations/f.var +*) -alias id "g" = "cic:/CoRN/ftc/MoreFunSeries/Operations/g.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Operations/g.var +*) inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_series_convergent_wd_IR.con" as lemma. (* begin show *) -alias id "convF" = "cic:/CoRN/ftc/MoreFunSeries/Operations/convF.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Operations/convF.var +*) -alias id "convG" = "cic:/CoRN/ftc/MoreFunSeries/Operations/convG.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Operations/convG.var +*) (* end show *) @@ -492,11 +610,17 @@ inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_minus.con" as lemma. %\end{convention}% *) -alias id "c" = "cic:/CoRN/ftc/MoreFunSeries/Operations/c.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Operations/c.var +*) -alias id "H" = "cic:/CoRN/ftc/MoreFunSeries/Operations/H.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Operations/H.var +*) -alias id "contH" = "cic:/CoRN/ftc/MoreFunSeries/Operations/contH.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Operations/contH.var +*) inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_scal_conv.con" as lemma. @@ -516,11 +640,17 @@ The most important tests for convergence of series still apply: the comparison test (in both versions) and the ratio test. *) -alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/Convergence_Criteria/J.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Convergence_Criteria/J.var +*) -alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/Convergence_Criteria/f.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Convergence_Criteria/f.var +*) -alias id "contF" = "cic:/CoRN/ftc/MoreFunSeries/Convergence_Criteria/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Convergence_Criteria/contF.var +*) inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_str_comparison_IR.con" as lemma. @@ -547,11 +677,17 @@ $f_i$#fi# and inserting the null function in the first position. This does not affect convergence or the sum of the series. *) -alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/Insert_Series/J.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Insert_Series/J.var +*) -alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/Insert_Series/f.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Insert_Series/f.var +*) -alias id "convF" = "cic:/CoRN/ftc/MoreFunSeries/Insert_Series/convF.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunSeries/Insert_Series/convF.var +*) inline procedural "cic:/CoRN/ftc/MoreFunSeries/insert_series.con" as definition. diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/MoreFunctions.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/MoreFunctions.mma index b90197e3b..89c1d2e1d 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/MoreFunctions.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/MoreFunctions.mma @@ -42,7 +42,9 @@ arbitrary intervals. **Continuity *) -alias id "I" = "cic:/CoRN/ftc/MoreFunctions/Basic_Results/I.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Basic_Results/I.var +*) (*#* Trivial stuff. @@ -55,17 +57,25 @@ inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_imp_inc.con" as lemma. %\end{convention}% *) -alias id "cI" = "cic:/CoRN/ftc/MoreFunctions/Basic_Results/cI.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Basic_Results/cI.var +*) -alias id "F" = "cic:/CoRN/ftc/MoreFunctions/Basic_Results/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Basic_Results/F.var +*) -alias id "contF" = "cic:/CoRN/ftc/MoreFunctions/Basic_Results/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Basic_Results/contF.var +*) inline procedural "cic:/CoRN/ftc/MoreFunctions/continuous_compact.con" as lemma. (* begin show *) -alias id "Hinc" = "cic:/CoRN/ftc/MoreFunctions/Basic_Results/Hinc.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Basic_Results/Hinc.var +*) (* end show *) @@ -91,19 +101,29 @@ Section Other_Results The usual stuff. *) -alias id "I" = "cic:/CoRN/ftc/MoreFunctions/Other_Results/I.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Other_Results/I.var +*) -alias id "F" = "cic:/CoRN/ftc/MoreFunctions/Other_Results/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Other_Results/F.var +*) -alias id "G" = "cic:/CoRN/ftc/MoreFunctions/Other_Results/G.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Other_Results/G.var +*) inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_wd.con" as lemma. (* begin show *) -alias id "contF" = "cic:/CoRN/ftc/MoreFunctions/Other_Results/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Other_Results/contF.var +*) -alias id "contG" = "cic:/CoRN/ftc/MoreFunctions/Other_Results/contG.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Other_Results/contG.var +*) (* end show *) @@ -149,17 +169,29 @@ Hint Immediate included_imp_Continuous Included_imp_Continuous: continuous. Section Corollaries *) -alias id "I" = "cic:/CoRN/ftc/MoreFunctions/Corollaries/I.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Corollaries/I.var +*) -alias id "cI" = "cic:/CoRN/ftc/MoreFunctions/Corollaries/cI.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Corollaries/cI.var +*) -alias id "F" = "cic:/CoRN/ftc/MoreFunctions/Corollaries/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Corollaries/F.var +*) -alias id "G" = "cic:/CoRN/ftc/MoreFunctions/Corollaries/G.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Corollaries/G.var +*) -alias id "contF" = "cic:/CoRN/ftc/MoreFunctions/Corollaries/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Corollaries/contF.var +*) -alias id "contG" = "cic:/CoRN/ftc/MoreFunctions/Corollaries/contG.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Corollaries/contG.var +*) inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_div.con" as lemma. @@ -177,7 +209,9 @@ Hint Resolve Continuous_div: continuous. Section Sums *) -alias id "I" = "cic:/CoRN/ftc/MoreFunctions/Sums/I.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Sums/I.var +*) inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_Sumx.con" as lemma. @@ -186,9 +220,13 @@ inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_Sumx.con" as lemma. %\end{convention}% *) -alias id "f" = "cic:/CoRN/ftc/MoreFunctions/Sums/f.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Sums/f.var +*) -alias id "contF" = "cic:/CoRN/ftc/MoreFunctions/Sums/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Sums/contF.var +*) inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_Sum0.con" as lemma. @@ -214,15 +252,25 @@ Derivative is not that much different. %\end{convention}% *) -alias id "I" = "cic:/CoRN/ftc/MoreFunctions/Basic_Properties/I.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Basic_Properties/I.var +*) -alias id "pI" = "cic:/CoRN/ftc/MoreFunctions/Basic_Properties/pI.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Basic_Properties/pI.var +*) -alias id "F" = "cic:/CoRN/ftc/MoreFunctions/Basic_Properties/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Basic_Properties/F.var +*) -alias id "G" = "cic:/CoRN/ftc/MoreFunctions/Basic_Properties/G.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Basic_Properties/G.var +*) -alias id "H" = "cic:/CoRN/ftc/MoreFunctions/Basic_Properties/H.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Basic_Properties/H.var +*) inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_wdl.con" as lemma. @@ -255,26 +303,42 @@ Hint Immediate Derivative_imp_Continuous Derivative_imp_Continuous': Section More_Results *) -alias id "I" = "cic:/CoRN/ftc/MoreFunctions/More_Results/I.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/More_Results/I.var +*) -alias id "pI" = "cic:/CoRN/ftc/MoreFunctions/More_Results/pI.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/More_Results/pI.var +*) (*#* %\begin{convention}% Assume that [F'] and [G'] are derivatives of [F] and [G], respectively, in [I]. %\end{convention}% *) -alias id "F" = "cic:/CoRN/ftc/MoreFunctions/More_Results/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/More_Results/F.var +*) -alias id "F'" = "cic:/CoRN/ftc/MoreFunctions/More_Results/F'.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/More_Results/F'.var +*) -alias id "G" = "cic:/CoRN/ftc/MoreFunctions/More_Results/G.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/More_Results/G.var +*) -alias id "G'" = "cic:/CoRN/ftc/MoreFunctions/More_Results/G'.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/More_Results/G'.var +*) -alias id "derF" = "cic:/CoRN/ftc/MoreFunctions/More_Results/derF.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/More_Results/derF.var +*) -alias id "derG" = "cic:/CoRN/ftc/MoreFunctions/More_Results/derG.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/More_Results/derG.var +*) inline procedural "cic:/CoRN/ftc/MoreFunctions/included_imp_Derivative.con" as lemma. @@ -306,25 +370,43 @@ End More_Results Section More_Corollaries *) -alias id "I" = "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/I.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/More_Corollaries/I.var +*) -alias id "pI" = "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/pI.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/More_Corollaries/pI.var +*) -alias id "F" = "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/More_Corollaries/F.var +*) -alias id "F'" = "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/F'.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/More_Corollaries/F'.var +*) -alias id "G" = "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/G.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/More_Corollaries/G.var +*) -alias id "G'" = "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/G'.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/More_Corollaries/G'.var +*) -alias id "derF" = "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/derF.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/More_Corollaries/derF.var +*) -alias id "derG" = "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/derG.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/More_Corollaries/derG.var +*) (* begin show *) -alias id "Gbnd" = "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/Gbnd.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/More_Corollaries/Gbnd.var +*) (* end show *) @@ -338,19 +420,29 @@ End More_Corollaries Section More_Sums *) -alias id "I" = "cic:/CoRN/ftc/MoreFunctions/More_Sums/I.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/More_Sums/I.var +*) -alias id "pI" = "cic:/CoRN/ftc/MoreFunctions/More_Sums/pI.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/More_Sums/pI.var +*) inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_Sumx.con" as lemma. (* begin show *) -alias id "f" = "cic:/CoRN/ftc/MoreFunctions/More_Sums/f.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/More_Sums/f.var +*) -alias id "f'" = "cic:/CoRN/ftc/MoreFunctions/More_Sums/f'.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/More_Sums/f'.var +*) -alias id "derF" = "cic:/CoRN/ftc/MoreFunctions/More_Sums/derF.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/More_Sums/derF.var +*) (* end show *) @@ -371,9 +463,13 @@ Section Diffble_Basic_Properties Mutatis mutandis for differentiability. *) -alias id "I" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/I.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/I.var +*) -alias id "pI" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/pI.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/pI.var +*) inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_imp_inc.con" as lemma. @@ -381,13 +477,21 @@ inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_Diffble.con" as le inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_wd.con" as lemma. -alias id "F" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/F.var +*) -alias id "G" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/G.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/G.var +*) -alias id "diffF" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/diffF.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/diffF.var +*) -alias id "diffG" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/diffG.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/diffG.var +*) (*#* %\begin{convention}% Assume [F] and [G] are differentiable in [I]. @@ -428,17 +532,29 @@ Hint Immediate Diffble_imp_inc: included. Section Diffble_Corollaries *) -alias id "I" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/I.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/I.var +*) -alias id "pI" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/pI.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/pI.var +*) -alias id "F" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/F.var +*) -alias id "G" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/G.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/G.var +*) -alias id "diffF" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/diffF.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/diffF.var +*) -alias id "diffG" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/diffG.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/diffG.var +*) inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_div.con" as lemma. @@ -461,9 +577,13 @@ Section Nth_Derivative Higher order derivatives pose more interesting problems. It turns out that it really becomes necessary to generalize our [n_deriv] operator to any interval. *) -alias id "I" = "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/I.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/I.var +*) -alias id "pI" = "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/pI.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/pI.var +*) (* UNEXPORTED Section Definitions @@ -474,11 +594,17 @@ Section Definitions %\end{convention}% *) -alias id "n" = "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Definitions/n.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Definitions/n.var +*) -alias id "F" = "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Definitions/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Definitions/F.var +*) -alias id "diffF" = "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Definitions/diffF.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Definitions/diffF.var +*) inline procedural "cic:/CoRN/ftc/MoreFunctions/N_Deriv_fun.con" as definition. @@ -579,11 +705,15 @@ Section Derivating_Diffble As a special case we get a differentiation operator%\ldots%#...# *) -alias id "F" = "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Derivating_Diffble/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Derivating_Diffble/F.var +*) (* begin show *) -alias id "diffF" = "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Derivating_Diffble/diffF.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Derivating_Diffble/diffF.var +*) (* end show *) diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/MoreIntegrals.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/MoreIntegrals.mma index 26de7113f..5fe1dafc0 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/MoreIntegrals.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/MoreIntegrals.mma @@ -46,11 +46,17 @@ partial functions continuous in [[Min(a,b),Max(a,b)]]. Before we define the new integral we need to some trivial interval inclusions. *) -alias id "a" = "cic:/CoRN/ftc/MoreIntegrals/Lemmas/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntegrals/Lemmas/a.var +*) -alias id "b" = "cic:/CoRN/ftc/MoreIntegrals/Lemmas/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntegrals/Lemmas/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/MoreIntegrals/Lemmas/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntegrals/Lemmas/Hab.var +*) inline procedural "cic:/CoRN/ftc/MoreIntegrals/compact_inc_Min_lft.con" as lemma. @@ -72,15 +78,25 @@ classical definition, and it collapses to the old one in the case [a [<=] b]. *) -alias id "a" = "cic:/CoRN/ftc/MoreIntegrals/Definitions/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntegrals/Definitions/a.var +*) -alias id "b" = "cic:/CoRN/ftc/MoreIntegrals/Definitions/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntegrals/Definitions/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/MoreIntegrals/Definitions/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntegrals/Definitions/Hab.var +*) -alias id "F" = "cic:/CoRN/ftc/MoreIntegrals/Definitions/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntegrals/Definitions/F.var +*) -alias id "HF" = "cic:/CoRN/ftc/MoreIntegrals/Definitions/HF.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntegrals/Definitions/HF.var +*) inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_inc1.con" as lemma. @@ -108,19 +124,33 @@ All our old properties carry over to this new definition---and some new ones, too. We begin with (strong) extensionality. *) -alias id "a" = "cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/a.var +*) -alias id "b" = "cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/Hab.var +*) -alias id "F" = "cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/F.var +*) -alias id "G" = "cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/G.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/G.var +*) -alias id "contF" = "cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/contF.var +*) -alias id "contG" = "cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/contG.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/contG.var +*) inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_strext.con" as lemma. @@ -181,35 +211,59 @@ And now we can prove the addition law for domains with our general operator. %\end{convention}% *) -alias id "a" = "cic:/CoRN/ftc/MoreIntegrals/More_Properties/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntegrals/More_Properties/a.var +*) -alias id "b" = "cic:/CoRN/ftc/MoreIntegrals/More_Properties/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntegrals/More_Properties/b.var +*) -alias id "c" = "cic:/CoRN/ftc/MoreIntegrals/More_Properties/c.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntegrals/More_Properties/c.var +*) (* begin show *) -alias id "Hab'" = "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Hab'.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntegrals/More_Properties/Hab'.var +*) -alias id "Hac'" = "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Hac'.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntegrals/More_Properties/Hac'.var +*) -alias id "Hcb'" = "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Hcb'.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntegrals/More_Properties/Hcb'.var +*) -alias id "Habc'" = "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc'.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc'.var +*) (* end show *) -alias id "F" = "cic:/CoRN/ftc/MoreIntegrals/More_Properties/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntegrals/More_Properties/F.var +*) (* begin show *) -alias id "Hab" = "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntegrals/More_Properties/Hab.var +*) -alias id "Hac" = "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Hac.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntegrals/More_Properties/Hac.var +*) -alias id "Hcb" = "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Hcb.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntegrals/More_Properties/Hcb.var +*) -alias id "Habc" = "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc.var +*) (* end show *) @@ -270,15 +324,25 @@ End More_Properties Section Corollaries *) -alias id "a" = "cic:/CoRN/ftc/MoreIntegrals/Corollaries/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntegrals/Corollaries/a.var +*) -alias id "b" = "cic:/CoRN/ftc/MoreIntegrals/Corollaries/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntegrals/Corollaries/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/MoreIntegrals/Corollaries/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntegrals/Corollaries/Hab.var +*) -alias id "F" = "cic:/CoRN/ftc/MoreIntegrals/Corollaries/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntegrals/Corollaries/F.var +*) -alias id "contF" = "cic:/CoRN/ftc/MoreIntegrals/Corollaries/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntegrals/Corollaries/contF.var +*) (*#* As a corollary, we get the following rule: *) diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/MoreIntervals.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/MoreIntervals.mma index 68c9aeadf..0b92263e6 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/MoreIntervals.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/MoreIntervals.mma @@ -216,13 +216,21 @@ such that [P(x)] holds. %\end{convention}% *) -alias id "P" = "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Single_Compact_Interval/P.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Single_Compact_Interval/P.var +*) -alias id "wdP" = "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Single_Compact_Interval/wdP.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Single_Compact_Interval/wdP.var +*) -alias id "x" = "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Single_Compact_Interval/x.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Single_Compact_Interval/x.var +*) -alias id "Hx" = "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Single_Compact_Interval/Hx.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Single_Compact_Interval/Hx.var +*) inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_single.con" as definition. @@ -389,9 +397,13 @@ previously defined concepts. %\end{convention}% *) -alias id "n" = "cic:/CoRN/ftc/MoreIntervals/Functions/n.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntervals/Functions/n.var +*) -alias id "I" = "cic:/CoRN/ftc/MoreIntervals/Functions/I.var". +(* UNEXPORTED +cic:/CoRN/ftc/MoreIntervals/Functions/I.var +*) inline procedural "cic:/CoRN/ftc/MoreIntervals/Continuous.con" as definition. diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/NthDerivative.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/NthDerivative.mma index 2834afd35..064989e7f 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/NthDerivative.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/NthDerivative.mma @@ -40,11 +40,17 @@ We now study higher order differentiability. We first define what we mean by the derivative of order [n] of a function. *) -alias id "a" = "cic:/CoRN/ftc/NthDerivative/Nth_Derivative/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/NthDerivative/Nth_Derivative/a.var +*) -alias id "b" = "cic:/CoRN/ftc/NthDerivative/Nth_Derivative/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/NthDerivative/Nth_Derivative/b.var +*) -alias id "Hab'" = "cic:/CoRN/ftc/NthDerivative/Nth_Derivative/Hab'.var". +(* UNEXPORTED +cic:/CoRN/ftc/NthDerivative/Nth_Derivative/Hab'.var +*) (* begin hide *) @@ -86,11 +92,17 @@ Section Trivia These are the expected extensionality and uniqueness results. *) -alias id "a" = "cic:/CoRN/ftc/NthDerivative/Trivia/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/NthDerivative/Trivia/a.var +*) -alias id "b" = "cic:/CoRN/ftc/NthDerivative/Trivia/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/NthDerivative/Trivia/b.var +*) -alias id "Hab'" = "cic:/CoRN/ftc/NthDerivative/Trivia/Hab'.var". +(* UNEXPORTED +cic:/CoRN/ftc/NthDerivative/Trivia/Hab'.var +*) (* begin hide *) @@ -124,11 +136,17 @@ the relation of [n] times derivative, but focus rather on the definition of [Diffble_I_n]. *) -alias id "a" = "cic:/CoRN/ftc/NthDerivative/Basic_Results/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/NthDerivative/Basic_Results/a.var +*) -alias id "b" = "cic:/CoRN/ftc/NthDerivative/Basic_Results/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/NthDerivative/Basic_Results/b.var +*) -alias id "Hab'" = "cic:/CoRN/ftc/NthDerivative/Basic_Results/Hab'.var". +(* UNEXPORTED +cic:/CoRN/ftc/NthDerivative/Basic_Results/Hab'.var +*) (* begin hide *) @@ -194,11 +212,17 @@ First order differentiability is just a special case. (* begin show *) -alias id "F" = "cic:/CoRN/ftc/NthDerivative/Basic_Results/aux/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/NthDerivative/Basic_Results/aux/F.var +*) -alias id "diffF" = "cic:/CoRN/ftc/NthDerivative/Basic_Results/aux/diffF.var". +(* UNEXPORTED +cic:/CoRN/ftc/NthDerivative/Basic_Results/aux/diffF.var +*) -alias id "diffFn" = "cic:/CoRN/ftc/NthDerivative/Basic_Results/aux/diffFn.var". +(* UNEXPORTED +cic:/CoRN/ftc/NthDerivative/Basic_Results/aux/diffFn.var +*) (* end show *) @@ -232,11 +256,17 @@ End Basic_Results Section More_Results *) -alias id "a" = "cic:/CoRN/ftc/NthDerivative/More_Results/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/NthDerivative/More_Results/a.var +*) -alias id "b" = "cic:/CoRN/ftc/NthDerivative/More_Results/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/NthDerivative/More_Results/b.var +*) -alias id "Hab'" = "cic:/CoRN/ftc/NthDerivative/More_Results/Hab'.var". +(* UNEXPORTED +cic:/CoRN/ftc/NthDerivative/More_Results/Hab'.var +*) (* begin hide *) diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/PartFunEquality.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/PartFunEquality.mma index eabeadd4b..98b19c4f9 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/PartFunEquality.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/PartFunEquality.mma @@ -85,11 +85,17 @@ by [P] and [Q], respectively, the domains of [F] and [G]. %\end{convention}% *) -alias id "I" = "cic:/CoRN/ftc/PartFunEquality/Equality_Results/I.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartFunEquality/Equality_Results/I.var +*) -alias id "F" = "cic:/CoRN/ftc/PartFunEquality/Equality_Results/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartFunEquality/Equality_Results/F.var +*) -alias id "G" = "cic:/CoRN/ftc/PartFunEquality/Equality_Results/G.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartFunEquality/Equality_Results/G.var +*) (* begin hide *) @@ -99,7 +105,9 @@ inline procedural "cic:/CoRN/ftc/PartFunEquality/Equality_Results/Q.con" "Equali (* end hide *) -alias id "R" = "cic:/CoRN/ftc/PartFunEquality/Equality_Results/R.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartFunEquality/Equality_Results/R.var +*) (*#* We start with two lemmas which make it much easier to prove and use @@ -154,9 +162,13 @@ the domain of [F]. %\end{convention}% *) -alias id "I" = "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Definitions/I.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Definitions/I.var +*) -alias id "F" = "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Definitions/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Definitions/F.var +*) (* begin hide *) @@ -172,7 +184,9 @@ If [F] is bounded away from zero in [I] then [F] is necessarily apart from zero (* begin show *) -alias id "Hf" = "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Definitions/Hf.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Definitions/Hf.var +*) (* end show *) @@ -193,11 +207,17 @@ Boundedness away from zero is preserved through restriction of the set. %\end{convention}% *) -alias id "F" = "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/F.var +*) -alias id "P" = "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/P.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/P.var +*) -alias id "Q" = "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Q.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Q.var +*) inline procedural "cic:/CoRN/ftc/PartFunEquality/included_imp_bnd.con" as lemma. @@ -259,17 +279,25 @@ partial functions. %\end{convention}% *) -alias id "I" = "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/I.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartFunEquality/More_on_Equality/I.var +*) (* UNEXPORTED Section Feq_Equivalence *) -alias id "F" = "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Feq_Equivalence/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Feq_Equivalence/F.var +*) -alias id "G" = "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Feq_Equivalence/G.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Feq_Equivalence/G.var +*) -alias id "H" = "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Feq_Equivalence/H.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Feq_Equivalence/H.var +*) inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_reflexive.con" as lemma. @@ -289,13 +317,21 @@ Section Operations Also it is preserved through application of functional constructors and restriction. *) -alias id "F" = "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Operations/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Operations/F.var +*) -alias id "F'" = "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Operations/F'.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Operations/F'.var +*) -alias id "G" = "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Operations/G.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Operations/G.var +*) -alias id "G'" = "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Operations/G'.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Operations/G'.var +*) inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_plus.con" as lemma. @@ -353,7 +389,9 @@ equality relation. %\end{convention}% *) -alias id "F" = "cic:/CoRN/ftc/PartFunEquality/Nth_Power/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartFunEquality/Nth_Power/F.var +*) (* begin hide *) @@ -361,17 +399,27 @@ inline procedural "cic:/CoRN/ftc/PartFunEquality/Nth_Power/P.con" "Nth_Power__" (* end hide *) -alias id "Q" = "cic:/CoRN/ftc/PartFunEquality/Nth_Power/Q.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartFunEquality/Nth_Power/Q.var +*) -alias id "H" = "cic:/CoRN/ftc/PartFunEquality/Nth_Power/H.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartFunEquality/Nth_Power/H.var +*) -alias id "Hf" = "cic:/CoRN/ftc/PartFunEquality/Nth_Power/Hf.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartFunEquality/Nth_Power/Hf.var +*) inline procedural "cic:/CoRN/ftc/PartFunEquality/FNth_zero.con" as lemma. -alias id "n" = "cic:/CoRN/ftc/PartFunEquality/Nth_Power/n.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartFunEquality/Nth_Power/n.var +*) -alias id "H'" = "cic:/CoRN/ftc/PartFunEquality/Nth_Power/H'.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartFunEquality/Nth_Power/H'.var +*) inline procedural "cic:/CoRN/ftc/PartFunEquality/FNth_mult.con" as lemma. @@ -389,11 +437,17 @@ is included in the domain of [F]. %\end{convention}% *) -alias id "a" = "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/a.var +*) -alias id "b" = "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/Hab.var +*) (* begin hide *) @@ -401,9 +455,13 @@ inline procedural "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/I.con" "Strong (* end hide *) -alias id "F" = "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/F.var +*) -alias id "incF" = "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/incF.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/incF.var +*) inline procedural "cic:/CoRN/ftc/PartFunEquality/FNth_zero'.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/PartInterval.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/PartInterval.mma index 93c906356..6f3197b51 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/PartInterval.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/PartInterval.mma @@ -43,13 +43,21 @@ that [I [=] [a,b]] is included in the domain of [F]. %\end{convention}% *) -alias id "F" = "cic:/CoRN/ftc/PartInterval/Conversion/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartInterval/Conversion/F.var +*) -alias id "a" = "cic:/CoRN/ftc/PartInterval/Conversion/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartInterval/Conversion/a.var +*) -alias id "b" = "cic:/CoRN/ftc/PartInterval/Conversion/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartInterval/Conversion/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/PartInterval/Conversion/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartInterval/Conversion/Hab.var +*) (* begin hide *) @@ -57,7 +65,9 @@ inline procedural "cic:/CoRN/ftc/PartInterval/Conversion/I.con" "Conversion__" a (* end hide *) -alias id "Hf" = "cic:/CoRN/ftc/PartInterval/Conversion/Hf.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartInterval/Conversion/Hf.var +*) inline procedural "cic:/CoRN/ftc/PartInterval/IntPartIR_strext.con" as lemma. @@ -80,11 +90,17 @@ To go the other way around, we simply take a setoid function [f] with domain [[a,b]] and build the corresponding partial function. *) -alias id "a" = "cic:/CoRN/ftc/PartInterval/AntiConversion/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartInterval/AntiConversion/a.var +*) -alias id "b" = "cic:/CoRN/ftc/PartInterval/AntiConversion/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartInterval/AntiConversion/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/PartInterval/AntiConversion/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartInterval/AntiConversion/Hab.var +*) (* begin hide *) @@ -92,7 +108,9 @@ inline procedural "cic:/CoRN/ftc/PartInterval/AntiConversion/I.con" "AntiConvers (* end hide *) -alias id "f" = "cic:/CoRN/ftc/PartInterval/AntiConversion/f.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartInterval/AntiConversion/f.var +*) inline procedural "cic:/CoRN/ftc/PartInterval/PartInt_strext.con" as lemma. @@ -135,17 +153,29 @@ type [I->IR] equal respectively to [F] and [G] in [I]. %\end{convention}% *) -alias id "F" = "cic:/CoRN/ftc/PartInterval/Equivalences/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartInterval/Equivalences/F.var +*) -alias id "G" = "cic:/CoRN/ftc/PartInterval/Equivalences/G.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartInterval/Equivalences/G.var +*) -alias id "a" = "cic:/CoRN/ftc/PartInterval/Equivalences/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartInterval/Equivalences/a.var +*) -alias id "b" = "cic:/CoRN/ftc/PartInterval/Equivalences/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartInterval/Equivalences/b.var +*) -alias id "c" = "cic:/CoRN/ftc/PartInterval/Equivalences/c.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartInterval/Equivalences/c.var +*) -alias id "Hab" = "cic:/CoRN/ftc/PartInterval/Equivalences/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartInterval/Equivalences/Hab.var +*) (* begin hide *) @@ -153,13 +183,21 @@ inline procedural "cic:/CoRN/ftc/PartInterval/Equivalences/I.con" "Equivalences_ (* end hide *) -alias id "f" = "cic:/CoRN/ftc/PartInterval/Equivalences/f.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartInterval/Equivalences/f.var +*) -alias id "g" = "cic:/CoRN/ftc/PartInterval/Equivalences/g.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartInterval/Equivalences/g.var +*) -alias id "Ff" = "cic:/CoRN/ftc/PartInterval/Equivalences/Ff.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartInterval/Equivalences/Ff.var +*) -alias id "Gg" = "cic:/CoRN/ftc/PartInterval/Equivalences/Gg.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartInterval/Equivalences/Gg.var +*) inline procedural "cic:/CoRN/ftc/PartInterval/part_int_const.con" as lemma. @@ -177,9 +215,13 @@ inline procedural "cic:/CoRN/ftc/PartInterval/part_int_nth.con" as lemma. (* begin show *) -alias id "HG" = "cic:/CoRN/ftc/PartInterval/Equivalences/HG.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartInterval/Equivalences/HG.var +*) -alias id "Hg" = "cic:/CoRN/ftc/PartInterval/Equivalences/Hg.var". +(* UNEXPORTED +cic:/CoRN/ftc/PartInterval/Equivalences/Hg.var +*) (* end show *) diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/Partitions.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/Partitions.mma index 5488ba0e7..b4a842480 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/Partitions.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/Partitions.mma @@ -107,19 +107,33 @@ inline procedural "cic:/CoRN/ftc/Partitions/Even_Partition.con" as definition. Section Refinements *) -alias id "a" = "cic:/CoRN/ftc/Partitions/Definitions/Refinements/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/Partitions/Definitions/Refinements/a.var +*) -alias id "b" = "cic:/CoRN/ftc/Partitions/Definitions/Refinements/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/Partitions/Definitions/Refinements/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/Partitions/Definitions/Refinements/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/Partitions/Definitions/Refinements/Hab.var +*) -alias id "m" = "cic:/CoRN/ftc/Partitions/Definitions/Refinements/m.var". +(* UNEXPORTED +cic:/CoRN/ftc/Partitions/Definitions/Refinements/m.var +*) -alias id "n" = "cic:/CoRN/ftc/Partitions/Definitions/Refinements/n.var". +(* UNEXPORTED +cic:/CoRN/ftc/Partitions/Definitions/Refinements/n.var +*) -alias id "P" = "cic:/CoRN/ftc/Partitions/Definitions/Refinements/P.var". +(* UNEXPORTED +cic:/CoRN/ftc/Partitions/Definitions/Refinements/P.var +*) -alias id "Q" = "cic:/CoRN/ftc/Partitions/Definitions/Refinements/Q.var". +(* UNEXPORTED +cic:/CoRN/ftc/Partitions/Definitions/Refinements/Q.var +*) (*#* We now define what it means for a partition [Q] to be a refinement of @@ -165,11 +179,17 @@ We now formalize some trivial and helpful constructions. %\end{convention}% *) -alias id "a" = "cic:/CoRN/ftc/Partitions/Definitions/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/Partitions/Definitions/a.var +*) -alias id "b" = "cic:/CoRN/ftc/Partitions/Definitions/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/Partitions/Definitions/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/Partitions/Definitions/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/Partitions/Definitions/Hab.var +*) (* begin hide *) @@ -190,9 +210,13 @@ partition. %\end{convention}% *) -alias id "m" = "cic:/CoRN/ftc/Partitions/Definitions/Getting_Points/m.var". +(* UNEXPORTED +cic:/CoRN/ftc/Partitions/Definitions/Getting_Points/m.var +*) -alias id "Q" = "cic:/CoRN/ftc/Partitions/Definitions/Getting_Points/Q.var". +(* UNEXPORTED +cic:/CoRN/ftc/Partitions/Definitions/Getting_Points/Q.var +*) inline procedural "cic:/CoRN/ftc/Partitions/Partition_imp_points.con" as definition. @@ -208,9 +232,13 @@ End Getting_Points As a corollary, given any continuous function [F] and a natural number we have an immediate choice of a sum of [F] in [[a,b]]. *) -alias id "F" = "cic:/CoRN/ftc/Partitions/Definitions/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/Partitions/Definitions/F.var +*) -alias id "contF" = "cic:/CoRN/ftc/Partitions/Definitions/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/Partitions/Definitions/contF.var +*) inline procedural "cic:/CoRN/ftc/Partitions/Even_Partition_Sum.con" as definition. @@ -300,9 +328,13 @@ with [n] points. %\end{convention}% *) -alias id "a" = "cic:/CoRN/ftc/Partitions/Lemmas/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/Partitions/Lemmas/a.var +*) -alias id "b" = "cic:/CoRN/ftc/Partitions/Lemmas/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/Partitions/Lemmas/b.var +*) (* begin hide *) @@ -310,11 +342,17 @@ inline procedural "cic:/CoRN/ftc/Partitions/Lemmas/I.con" "Lemmas__" as definiti (* end hide *) -alias id "Hab" = "cic:/CoRN/ftc/Partitions/Lemmas/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/Partitions/Lemmas/Hab.var +*) -alias id "n" = "cic:/CoRN/ftc/Partitions/Lemmas/n.var". +(* UNEXPORTED +cic:/CoRN/ftc/Partitions/Lemmas/n.var +*) -alias id "P" = "cic:/CoRN/ftc/Partitions/Lemmas/P.var". +(* UNEXPORTED +cic:/CoRN/ftc/Partitions/Lemmas/P.var +*) inline procedural "cic:/CoRN/ftc/Partitions/Mesh_lemma.con" as lemma. @@ -348,9 +386,13 @@ inline procedural "cic:/CoRN/ftc/Partitions/even_partition_Mesh.con" as lemma. %\end{convention}% *) -alias id "a" = "cic:/CoRN/ftc/Partitions/Even_Partitions/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/Partitions/Even_Partitions/a.var +*) -alias id "b" = "cic:/CoRN/ftc/Partitions/Even_Partitions/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/Partitions/Even_Partitions/b.var +*) (* begin hide *) @@ -358,7 +400,9 @@ inline procedural "cic:/CoRN/ftc/Partitions/Even_Partitions/I.con" "Even_Partiti (* end hide *) -alias id "Hab" = "cic:/CoRN/ftc/Partitions/Even_Partitions/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/Partitions/Even_Partitions/Hab.var +*) (*#* An interesting property: in a partition, if [ai [<] aj] then [i < j]. @@ -377,13 +421,21 @@ denote by [P] and [Q] the even partitions with, respectively, [m] and Even partitions always have a common refinement. *) -alias id "m" = "cic:/CoRN/ftc/Partitions/Even_Partitions/m.var". +(* UNEXPORTED +cic:/CoRN/ftc/Partitions/Even_Partitions/m.var +*) -alias id "n" = "cic:/CoRN/ftc/Partitions/Even_Partitions/n.var". +(* UNEXPORTED +cic:/CoRN/ftc/Partitions/Even_Partitions/n.var +*) -alias id "Hm" = "cic:/CoRN/ftc/Partitions/Even_Partitions/Hm.var". +(* UNEXPORTED +cic:/CoRN/ftc/Partitions/Even_Partitions/Hm.var +*) -alias id "Hn" = "cic:/CoRN/ftc/Partitions/Even_Partitions/Hn.var". +(* UNEXPORTED +cic:/CoRN/ftc/Partitions/Even_Partitions/Hn.var +*) (* begin hide *) @@ -408,11 +460,17 @@ Section More_Definitions Some auxiliary definitions. A partition is said to be separated if all its points are distinct. *) -alias id "a" = "cic:/CoRN/ftc/Partitions/More_Definitions/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/Partitions/More_Definitions/a.var +*) -alias id "b" = "cic:/CoRN/ftc/Partitions/More_Definitions/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/Partitions/More_Definitions/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/Partitions/More_Definitions/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/Partitions/More_Definitions/Hab.var +*) inline procedural "cic:/CoRN/ftc/Partitions/_Separated.con" as definition. @@ -426,13 +484,21 @@ respectively, [n] and [m] points. %\end{convention}% *) -alias id "n" = "cic:/CoRN/ftc/Partitions/More_Definitions/n.var". +(* UNEXPORTED +cic:/CoRN/ftc/Partitions/More_Definitions/n.var +*) -alias id "m" = "cic:/CoRN/ftc/Partitions/More_Definitions/m.var". +(* UNEXPORTED +cic:/CoRN/ftc/Partitions/More_Definitions/m.var +*) -alias id "P" = "cic:/CoRN/ftc/Partitions/More_Definitions/P.var". +(* UNEXPORTED +cic:/CoRN/ftc/Partitions/More_Definitions/P.var +*) -alias id "Q" = "cic:/CoRN/ftc/Partitions/More_Definitions/Q.var". +(* UNEXPORTED +cic:/CoRN/ftc/Partitions/More_Definitions/Q.var +*) inline procedural "cic:/CoRN/ftc/Partitions/Separated.con" as definition. @@ -452,9 +518,13 @@ Implicit Arguments Separated [a b Hab n m]. Section Sep_Partitions *) -alias id "a" = "cic:/CoRN/ftc/Partitions/Sep_Partitions/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/Partitions/Sep_Partitions/a.var +*) -alias id "b" = "cic:/CoRN/ftc/Partitions/Sep_Partitions/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/Partitions/Sep_Partitions/b.var +*) (* begin hide *) @@ -462,7 +532,9 @@ inline procedural "cic:/CoRN/ftc/Partitions/Sep_Partitions/I.con" "Sep_Partition (* end hide *) -alias id "Hab" = "cic:/CoRN/ftc/Partitions/Sep_Partitions/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/Partitions/Sep_Partitions/Hab.var +*) (*#* The antimesh of a separated partition is always positive. diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/RefLemma.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/RefLemma.mma index 6fa5d117c..932d40d10 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/RefLemma.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/RefLemma.mma @@ -79,11 +79,17 @@ Using the results from these files, we prove our main lemma in several steps %\end{convention}% *) -alias id "a" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/a.var +*) -alias id "b" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Hab.var +*) (* begin hide *) @@ -91,11 +97,17 @@ inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/I.con" "Refinement_Le (* end hide *) -alias id "F" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/F.var +*) -alias id "contF" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/contF.var +*) -alias id "incF" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/incF.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/incF.var +*) (* begin hide *) @@ -122,9 +134,13 @@ respectively. %\end{convention}% *) -alias id "e" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/e.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/e.var +*) -alias id "He" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/He.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/He.var +*) (* begin hide *) @@ -132,29 +148,53 @@ inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemm (* end hide *) -alias id "m" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/m.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/m.var +*) -alias id "n" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/n.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/n.var +*) -alias id "P" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/P.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/P.var +*) -alias id "HMesh" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/HMesh.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/HMesh.var +*) -alias id "Q" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/Q.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/Q.var +*) -alias id "Href" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/Href.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/Href.var +*) -alias id "fP" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/fP.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/fP.var +*) -alias id "HfP" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/HfP.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/HfP.var +*) -alias id "HfP'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/HfP'.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/HfP'.var +*) -alias id "fQ" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/fQ.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/fQ.var +*) -alias id "HfQ" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/HfQ.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/HfQ.var +*) -alias id "HfQ'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/HfQ'.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/HfQ'.var +*) (* begin hide *) @@ -244,29 +284,53 @@ and [R], respectively. %\end{convention}% *) -alias id "n" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/n.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/n.var +*) -alias id "j" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/j.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/j.var +*) -alias id "k" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/k.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/k.var +*) -alias id "P" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/P.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/P.var +*) -alias id "Q" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/Q.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/Q.var +*) -alias id "R" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/R.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/R.var +*) -alias id "HrefP" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HrefP.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HrefP.var +*) -alias id "HrefR" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HrefR.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HrefR.var +*) -alias id "e" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/e.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/e.var +*) -alias id "e'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/e'.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/e'.var +*) -alias id "He" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/He.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/He.var +*) -alias id "He'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/He'.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/He'.var +*) (* begin hide *) @@ -276,21 +340,37 @@ inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lem (* end hide *) -alias id "HMeshP" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HMeshP.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HMeshP.var +*) -alias id "HMeshR" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HMeshR.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HMeshR.var +*) -alias id "fP" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/fP.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/fP.var +*) -alias id "HfP" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HfP.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HfP.var +*) -alias id "HfP'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HfP'.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HfP'.var +*) -alias id "fR" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/fR.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/fR.var +*) -alias id "HfR" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HfR.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HfR.var +*) -alias id "HfR'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HfR'.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HfR'.var +*) inline procedural "cic:/CoRN/ftc/RefLemma/second_refinement_lemma.con" as lemma. @@ -318,21 +398,37 @@ respectively; %\end{convention}% *) -alias id "n" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/n.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/n.var +*) -alias id "m" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/m.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/m.var +*) -alias id "P" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/P.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/P.var +*) -alias id "R" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/R.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/R.var +*) -alias id "e" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/e.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/e.var +*) -alias id "e'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/e'.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/e'.var +*) -alias id "He" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/He.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/He.var +*) -alias id "He'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/He'.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/He'.var +*) (* begin hide *) @@ -342,27 +438,49 @@ inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemm (* end hide *) -alias id "HMeshP" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/HMeshP.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/HMeshP.var +*) -alias id "HMeshR" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/HMeshR.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/HMeshR.var +*) -alias id "fP" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/fP.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/fP.var +*) -alias id "HfP" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/HfP.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/HfP.var +*) -alias id "HfP'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/HfP'.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/HfP'.var +*) -alias id "fR" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/fR.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/fR.var +*) -alias id "HfR" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/HfR.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/HfR.var +*) -alias id "HfR'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/HfR'.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/HfR'.var +*) -alias id "Hab'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/Hab'.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/Hab'.var +*) -alias id "beta" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/beta.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/beta.var +*) -alias id "Hbeta" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/Hbeta.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/Hbeta.var +*) (* begin hide *) @@ -455,21 +573,37 @@ Finally, this is inequality (2.6.7) exactly as stated (same conventions as above) *) -alias id "n" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/n.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/n.var +*) -alias id "m" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/m.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/m.var +*) -alias id "P" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/P.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/P.var +*) -alias id "R" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/R.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/R.var +*) -alias id "e" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/e.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/e.var +*) -alias id "e'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/e'.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/e'.var +*) -alias id "He" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/He.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/He.var +*) -alias id "He'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/He'.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/He'.var +*) (* begin hide *) @@ -479,25 +613,43 @@ inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lem (* end hide *) -alias id "HMeshP" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/HMeshP.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/HMeshP.var +*) -alias id "HMeshR" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/HMeshR.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/HMeshR.var +*) -alias id "fP" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/fP.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/fP.var +*) -alias id "HfP" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/HfP.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/HfP.var +*) -alias id "HfP'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/HfP'.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/HfP'.var +*) -alias id "fR" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/fR.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/fR.var +*) -alias id "HfR" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/HfR.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/HfR.var +*) -alias id "HfR'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/HfR'.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/HfR'.var +*) (* begin show *) -alias id "Hab'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/Hab'.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/Hab'.var +*) (* end show *) @@ -513,21 +665,37 @@ Section Main_Refinement_Lemma (*#* We finish by presenting Theorem 9. *) -alias id "n" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/n.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/n.var +*) -alias id "m" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/m.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/m.var +*) -alias id "P" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/P.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/P.var +*) -alias id "R" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/R.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/R.var +*) -alias id "e" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/e.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/e.var +*) -alias id "e'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/e'.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/e'.var +*) -alias id "He" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/He.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/He.var +*) -alias id "He'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/He'.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/He'.var +*) (* begin hide *) @@ -537,21 +705,37 @@ inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma (* end hide *) -alias id "HMeshP" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HMeshP.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HMeshP.var +*) -alias id "HMeshR" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HMeshR.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HMeshR.var +*) -alias id "fP" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/fP.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/fP.var +*) -alias id "HfP" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HfP.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HfP.var +*) -alias id "HfP'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HfP'.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HfP'.var +*) -alias id "fR" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/fR.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/fR.var +*) -alias id "HfR" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HfR.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HfR.var +*) -alias id "HfR'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HfR'.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HfR'.var +*) inline procedural "cic:/CoRN/ftc/RefLemma/refinement_lemma.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/RefSepRef.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/RefSepRef.mma index a8205ce4c..93c80f65d 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/RefSepRef.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/RefSepRef.mma @@ -28,29 +28,51 @@ include "ftc/Partitions.ma". Section Refining_Separated *) -alias id "a" = "cic:/CoRN/ftc/RefSepRef/Refining_Separated/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSepRef/Refining_Separated/a.var +*) -alias id "b" = "cic:/CoRN/ftc/RefSepRef/Refining_Separated/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSepRef/Refining_Separated/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/RefSepRef/Refining_Separated/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSepRef/Refining_Separated/Hab.var +*) 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". +(* UNEXPORTED +cic:/CoRN/ftc/RefSepRef/Refining_Separated/F.var +*) -alias id "contF" = "cic:/CoRN/ftc/RefSepRef/Refining_Separated/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSepRef/Refining_Separated/contF.var +*) -alias id "incF" = "cic:/CoRN/ftc/RefSepRef/Refining_Separated/incF.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSepRef/Refining_Separated/incF.var +*) -alias id "m" = "cic:/CoRN/ftc/RefSepRef/Refining_Separated/m.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSepRef/Refining_Separated/m.var +*) -alias id "n" = "cic:/CoRN/ftc/RefSepRef/Refining_Separated/n.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSepRef/Refining_Separated/n.var +*) -alias id "P" = "cic:/CoRN/ftc/RefSepRef/Refining_Separated/P.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSepRef/Refining_Separated/P.var +*) -alias id "R" = "cic:/CoRN/ftc/RefSepRef/Refining_Separated/R.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSepRef/Refining_Separated/R.var +*) -alias id "HPR" = "cic:/CoRN/ftc/RefSepRef/Refining_Separated/HPR.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSepRef/Refining_Separated/HPR.var +*) inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_HP.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/RefSeparated.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/RefSeparated.mma index 7d0106093..d74e1bdf7 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/RefSeparated.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/RefSeparated.mma @@ -28,41 +28,71 @@ include "ftc/Partitions.ma". Section Separating__Separated *) -alias id "a" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparated/Separating__Separated/a.var +*) -alias id "b" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparated/Separating__Separated/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparated/Separating__Separated/Hab.var +*) 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". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparated/Separating__Separated/F.var +*) -alias id "contF" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparated/Separating__Separated/contF.var +*) -alias id "incF" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/incF.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparated/Separating__Separated/incF.var +*) -alias id "Hab'" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Hab'.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparated/Separating__Separated/Hab'.var +*) -alias id "m" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/m.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparated/Separating__Separated/m.var +*) -alias id "n" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/n.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparated/Separating__Separated/n.var +*) -alias id "P" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/P.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparated/Separating__Separated/P.var +*) -alias id "R" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/R.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparated/Separating__Separated/R.var +*) -alias id "HP" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/HP.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparated/Separating__Separated/HP.var +*) -alias id "HR" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/HR.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparated/Separating__Separated/HR.var +*) inline procedural "cic:/CoRN/ftc/RefSeparated/RS_pos_n.con" as lemma. inline procedural "cic:/CoRN/ftc/RefSeparated/RS_pos_m.con" as lemma. -alias id "alpha" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/alpha.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparated/Separating__Separated/alpha.var +*) -alias id "Halpha" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Halpha.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparated/Separating__Separated/Halpha.var +*) inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/e.con" "Separating__Separated__" as definition. @@ -76,9 +106,13 @@ inline procedural "cic:/CoRN/ftc/RefSeparated/RS_Hd.con" as lemma. inline procedural "cic:/CoRN/ftc/RefSeparated/RS_Hd'.con" as lemma. -alias id "csi" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/csi.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparated/Separating__Separated/csi.var +*) -alias id "Hcsi" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Hcsi.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparated/Separating__Separated/Hcsi.var +*) inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/M.con" "Separating__Separated__" as definition. @@ -102,9 +136,13 @@ inline procedural "cic:/CoRN/ftc/RefSeparated/RS_delta_pos.con" as lemma. Section Defining_ai' *) -alias id "i" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/i.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/i.var +*) -alias id "Hi" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/Hi.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/Hi.var +*) inline procedural "cic:/CoRN/ftc/RefSeparated/separation_conseq.con" as lemma. @@ -114,9 +152,13 @@ inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai' 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". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/Hi0.var +*) -alias id "Hin" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/Hin.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/Hin.var +*) inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_fun_i.con" as definition. @@ -148,9 +190,13 @@ inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_part.con" as definition. inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_lemma.con" as lemma. -alias id "g" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/g.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparated/Separating__Separated/g.var +*) -alias id "gP" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/gP.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparated/Separating__Separated/gP.var +*) inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_points.con" as definition. diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/RefSeparating.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/RefSeparating.mma index a3d193ec8..c52b72935 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/RefSeparating.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/RefSeparating.mma @@ -28,33 +28,59 @@ include "ftc/Partitions.ma". Section Separating_Partition *) -alias id "a" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparating/Separating_Partition/a.var +*) -alias id "b" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparating/Separating_Partition/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparating/Separating_Partition/Hab.var +*) 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". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparating/Separating_Partition/F.var +*) -alias id "contF" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparating/Separating_Partition/contF.var +*) -alias id "incF" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/incF.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparating/Separating_Partition/incF.var +*) -alias id "Hab'" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/Hab'.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparating/Separating_Partition/Hab'.var +*) -alias id "n" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/n.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparating/Separating_Partition/n.var +*) -alias id "P" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/P.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparating/Separating_Partition/P.var +*) -alias id "alpha" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/alpha.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparating/Separating_Partition/alpha.var +*) -alias id "Halpha" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/Halpha.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparating/Separating_Partition/Halpha.var +*) -alias id "csi" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/csi.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparating/Separating_Partition/csi.var +*) -alias id "Hcsi" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/Hcsi.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparating/Separating_Partition/Hcsi.var +*) inline procedural "cic:/CoRN/ftc/RefSeparating/Separating_Partition/M.con" "Separating_Partition__" as definition. @@ -68,7 +94,9 @@ inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_delta_pos.con" as lemma. inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_delta_csi.con" as lemma. -alias id "Hab''" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/Hab''.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparating/Separating_Partition/Hab''.var +*) inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_lemma.con" as lemma. @@ -132,11 +160,17 @@ inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_mon.con" as lemma. inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_mon_Mesh.con" as lemma. -alias id "g" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/g.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparating/Separating_Partition/g.var +*) -alias id "gP" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/gP.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparating/Separating_Partition/gP.var +*) -alias id "gP'" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/gP'.var". +(* UNEXPORTED +cic:/CoRN/ftc/RefSeparating/Separating_Partition/gP'.var +*) inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_pts.con" as definition. diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/Rolle.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/Rolle.mma index aad4660f4..d9ba2624f 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/Rolle.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/Rolle.mma @@ -40,39 +40,61 @@ We now begin to work with partial functions. We begin by stating and proving Ro (* begin hide *) -alias id "a" = "cic:/CoRN/ftc/Rolle/Rolle/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/Rolle/Rolle/a.var +*) -alias id "b" = "cic:/CoRN/ftc/Rolle/Rolle/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/Rolle/Rolle/b.var +*) -alias id "Hab'" = "cic:/CoRN/ftc/Rolle/Rolle/Hab'.var". +(* UNEXPORTED +cic:/CoRN/ftc/Rolle/Rolle/Hab'.var +*) inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hab.con" "Rolle__" as definition. inline procedural "cic:/CoRN/ftc/Rolle/Rolle/I.con" "Rolle__" as definition. -alias id "F" = "cic:/CoRN/ftc/Rolle/Rolle/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/Rolle/Rolle/F.var +*) -alias id "F'" = "cic:/CoRN/ftc/Rolle/Rolle/F'.var". +(* UNEXPORTED +cic:/CoRN/ftc/Rolle/Rolle/F'.var +*) -alias id "derF" = "cic:/CoRN/ftc/Rolle/Rolle/derF.var". +(* UNEXPORTED +cic:/CoRN/ftc/Rolle/Rolle/derF.var +*) -alias id "Ha" = "cic:/CoRN/ftc/Rolle/Rolle/Ha.var". +(* UNEXPORTED +cic:/CoRN/ftc/Rolle/Rolle/Ha.var +*) -alias id "Hb" = "cic:/CoRN/ftc/Rolle/Rolle/Hb.var". +(* UNEXPORTED +cic:/CoRN/ftc/Rolle/Rolle/Hb.var +*) (* end hide *) (* begin show *) -alias id "Fab" = "cic:/CoRN/ftc/Rolle/Rolle/Fab.var". +(* UNEXPORTED +cic:/CoRN/ftc/Rolle/Rolle/Fab.var +*) (* end show *) (* begin hide *) -alias id "e" = "cic:/CoRN/ftc/Rolle/Rolle/e.var". +(* UNEXPORTED +cic:/CoRN/ftc/Rolle/Rolle/e.var +*) -alias id "He" = "cic:/CoRN/ftc/Rolle/Rolle/He.var". +(* UNEXPORTED +cic:/CoRN/ftc/Rolle/Rolle/He.var +*) inline procedural "cic:/CoRN/ftc/Rolle/Rolle/contF'.con" "Rolle__" as definition. @@ -164,11 +186,17 @@ Section Law_of_the_Mean The following is a simple corollary: *) -alias id "a" = "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/Rolle/Law_of_the_Mean/a.var +*) -alias id "b" = "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/Rolle/Law_of_the_Mean/b.var +*) -alias id "Hab'" = "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/Hab'.var". +(* UNEXPORTED +cic:/CoRN/ftc/Rolle/Law_of_the_Mean/Hab'.var +*) (* begin hide *) @@ -178,17 +206,27 @@ inline procedural "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/I.con" "Law_of_the_Mean__ (* end hide *) -alias id "F" = "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/Rolle/Law_of_the_Mean/F.var +*) -alias id "F'" = "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/F'.var". +(* UNEXPORTED +cic:/CoRN/ftc/Rolle/Law_of_the_Mean/F'.var +*) -alias id "HF" = "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/HF.var". +(* UNEXPORTED +cic:/CoRN/ftc/Rolle/Law_of_the_Mean/HF.var +*) (* begin show *) -alias id "HA" = "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/HA.var". +(* UNEXPORTED +cic:/CoRN/ftc/Rolle/Law_of_the_Mean/HA.var +*) -alias id "HB" = "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/HB.var". +(* UNEXPORTED +cic:/CoRN/ftc/Rolle/Law_of_the_Mean/HB.var +*) (* end show *) @@ -206,11 +244,17 @@ Section Corollaries We can also state these theorems without expliciting the derivative of [F]. *) -alias id "a" = "cic:/CoRN/ftc/Rolle/Corollaries/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/Rolle/Corollaries/a.var +*) -alias id "b" = "cic:/CoRN/ftc/Rolle/Corollaries/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/Rolle/Corollaries/b.var +*) -alias id "Hab'" = "cic:/CoRN/ftc/Rolle/Corollaries/Hab'.var". +(* UNEXPORTED +cic:/CoRN/ftc/Rolle/Corollaries/Hab'.var +*) (* begin hide *) @@ -218,11 +262,15 @@ inline procedural "cic:/CoRN/ftc/Rolle/Corollaries/Hab.con" "Corollaries__" as d (* end hide *) -alias id "F" = "cic:/CoRN/ftc/Rolle/Corollaries/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/Rolle/Corollaries/F.var +*) (* begin show *) -alias id "HF" = "cic:/CoRN/ftc/Rolle/Corollaries/HF.var". +(* UNEXPORTED +cic:/CoRN/ftc/Rolle/Corollaries/HF.var +*) (* end show *) @@ -248,17 +296,27 @@ state it also in this form. %\end{convention}% *) -alias id "I" = "cic:/CoRN/ftc/Rolle/Generalizations/I.var". +(* UNEXPORTED +cic:/CoRN/ftc/Rolle/Generalizations/I.var +*) -alias id "pI" = "cic:/CoRN/ftc/Rolle/Generalizations/pI.var". +(* UNEXPORTED +cic:/CoRN/ftc/Rolle/Generalizations/pI.var +*) -alias id "F" = "cic:/CoRN/ftc/Rolle/Generalizations/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/Rolle/Generalizations/F.var +*) -alias id "F'" = "cic:/CoRN/ftc/Rolle/Generalizations/F'.var". +(* UNEXPORTED +cic:/CoRN/ftc/Rolle/Generalizations/F'.var +*) (* begin show *) -alias id "derF" = "cic:/CoRN/ftc/Rolle/Generalizations/derF.var". +(* UNEXPORTED +cic:/CoRN/ftc/Rolle/Generalizations/derF.var +*) (* end show *) diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/StrongIVT.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/StrongIVT.mma index 536695ff5..c964d748f 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/StrongIVT.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/StrongIVT.mma @@ -34,13 +34,21 @@ part, we will simply do that, repeating the previous construction. The same notations and conventions apply as before. *) -alias id "a" = "cic:/CoRN/ftc/StrongIVT/IVT'/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/StrongIVT/IVT'/a.var +*) -alias id "b" = "cic:/CoRN/ftc/StrongIVT/IVT'/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/StrongIVT/IVT'/b.var +*) -alias id "Hab'" = "cic:/CoRN/ftc/StrongIVT/IVT'/Hab'.var". +(* UNEXPORTED +cic:/CoRN/ftc/StrongIVT/IVT'/Hab'.var +*) -alias id "Hab" = "cic:/CoRN/ftc/StrongIVT/IVT'/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/StrongIVT/IVT'/Hab.var +*) (* begin hide *) @@ -50,9 +58,13 @@ inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/I'.con" "IVT'__" as definition. (* end hide *) -alias id "F" = "cic:/CoRN/ftc/StrongIVT/IVT'/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/StrongIVT/IVT'/F.var +*) -alias id "contF" = "cic:/CoRN/ftc/StrongIVT/IVT'/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/StrongIVT/IVT'/contF.var +*) (* begin hide *) @@ -62,7 +74,9 @@ inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/incF.con" "IVT'__" as definition (* begin show *) -alias id "incrF" = "cic:/CoRN/ftc/StrongIVT/IVT'/incrF.var". +(* UNEXPORTED +cic:/CoRN/ftc/StrongIVT/IVT'/incrF.var +*) (* end show *) @@ -78,11 +92,17 @@ inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/HFab'.con" "IVT'__" as definitio (* begin show *) -alias id "z" = "cic:/CoRN/ftc/StrongIVT/IVT'/z.var". +(* UNEXPORTED +cic:/CoRN/ftc/StrongIVT/IVT'/z.var +*) -alias id "Haz" = "cic:/CoRN/ftc/StrongIVT/IVT'/Haz.var". +(* UNEXPORTED +cic:/CoRN/ftc/StrongIVT/IVT'/Haz.var +*) -alias id "Hzb" = "cic:/CoRN/ftc/StrongIVT/IVT'/Hzb.var". +(* UNEXPORTED +cic:/CoRN/ftc/StrongIVT/IVT'/Hzb.var +*) (* end show *) diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/Taylor.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/Taylor.mma index 56b2057f1..f632a69ad 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/Taylor.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/Taylor.mma @@ -37,11 +37,17 @@ The generalization to arbitrary intervals just needs a few more definitions. %\end{convention}% *) -alias id "I" = "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/I.var". +(* UNEXPORTED +cic:/CoRN/ftc/Taylor/More_Taylor_Defs/I.var +*) -alias id "pI" = "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/pI.var". +(* UNEXPORTED +cic:/CoRN/ftc/Taylor/More_Taylor_Defs/pI.var +*) -alias id "F" = "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/Taylor/More_Taylor_Defs/F.var +*) (* begin show *) @@ -49,13 +55,21 @@ inline procedural "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/deriv_Sn.con" "More_Tay (* end show *) -alias id "a" = "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/Taylor/More_Taylor_Defs/a.var +*) -alias id "b" = "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/Taylor/More_Taylor_Defs/b.var +*) -alias id "Ha" = "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/Ha.var". +(* UNEXPORTED +cic:/CoRN/ftc/Taylor/More_Taylor_Defs/Ha.var +*) -alias id "Hb" = "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/Hb.var". +(* UNEXPORTED +cic:/CoRN/ftc/Taylor/More_Taylor_Defs/Hb.var +*) (* begin show *) @@ -102,33 +116,61 @@ order up to [n] and [F'] be the nth-derivative of [F]. %\end{convention}% *) -alias id "I" = "cic:/CoRN/ftc/Taylor/Taylor_Theorem/I.var". +(* UNEXPORTED +cic:/CoRN/ftc/Taylor/Taylor_Theorem/I.var +*) -alias id "pI" = "cic:/CoRN/ftc/Taylor/Taylor_Theorem/pI.var". +(* UNEXPORTED +cic:/CoRN/ftc/Taylor/Taylor_Theorem/pI.var +*) -alias id "F" = "cic:/CoRN/ftc/Taylor/Taylor_Theorem/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/Taylor/Taylor_Theorem/F.var +*) -alias id "n" = "cic:/CoRN/ftc/Taylor/Taylor_Theorem/n.var". +(* UNEXPORTED +cic:/CoRN/ftc/Taylor/Taylor_Theorem/n.var +*) -alias id "f" = "cic:/CoRN/ftc/Taylor/Taylor_Theorem/f.var". +(* UNEXPORTED +cic:/CoRN/ftc/Taylor/Taylor_Theorem/f.var +*) -alias id "goodF" = "cic:/CoRN/ftc/Taylor/Taylor_Theorem/goodF.var". +(* UNEXPORTED +cic:/CoRN/ftc/Taylor/Taylor_Theorem/goodF.var +*) -alias id "goodF'" = "cic:/CoRN/ftc/Taylor/Taylor_Theorem/goodF'.var". +(* UNEXPORTED +cic:/CoRN/ftc/Taylor/Taylor_Theorem/goodF'.var +*) -alias id "derF" = "cic:/CoRN/ftc/Taylor/Taylor_Theorem/derF.var". +(* UNEXPORTED +cic:/CoRN/ftc/Taylor/Taylor_Theorem/derF.var +*) -alias id "F'" = "cic:/CoRN/ftc/Taylor/Taylor_Theorem/F'.var". +(* UNEXPORTED +cic:/CoRN/ftc/Taylor/Taylor_Theorem/F'.var +*) -alias id "derF'" = "cic:/CoRN/ftc/Taylor/Taylor_Theorem/derF'.var". +(* UNEXPORTED +cic:/CoRN/ftc/Taylor/Taylor_Theorem/derF'.var +*) -alias id "a" = "cic:/CoRN/ftc/Taylor/Taylor_Theorem/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/Taylor/Taylor_Theorem/a.var +*) -alias id "b" = "cic:/CoRN/ftc/Taylor/Taylor_Theorem/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/Taylor/Taylor_Theorem/b.var +*) -alias id "Ha" = "cic:/CoRN/ftc/Taylor/Taylor_Theorem/Ha.var". +(* UNEXPORTED +cic:/CoRN/ftc/Taylor/Taylor_Theorem/Ha.var +*) -alias id "Hb" = "cic:/CoRN/ftc/Taylor/Taylor_Theorem/Hb.var". +(* UNEXPORTED +cic:/CoRN/ftc/Taylor/Taylor_Theorem/Hb.var +*) (* begin show *) diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/TaylorLemma.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/TaylorLemma.mma index 427b0adfb..6f2e56351 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/TaylorLemma.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/TaylorLemma.mma @@ -42,11 +42,17 @@ define the nth order derivative of [F] in the interval [[Min(a,b),Max(a,b)]]. *) -alias id "a" = "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/a.var +*) -alias id "b" = "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/b.var +*) -alias id "Hap" = "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Hap.var". +(* UNEXPORTED +cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Hap.var +*) (* begin hide *) @@ -58,11 +64,17 @@ inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/I.con" "Taylor_Defs__" (* end hide *) -alias id "F" = "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/F.var +*) -alias id "Ha" = "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Ha.var". +(* UNEXPORTED +cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Ha.var +*) -alias id "Hb" = "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Hb.var". +(* UNEXPORTED +cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Hb.var +*) (* begin show *) @@ -286,9 +298,13 @@ Now Taylor's theorem. %\end{convention}% *) -alias id "e" = "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/e.var". +(* UNEXPORTED +cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/e.var +*) -alias id "He" = "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/He.var". +(* UNEXPORTED +cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/He.var +*) (* begin hide *) diff --git a/helm/software/matita/contribs/CoRN-Procedural/ftc/WeakIVT.mma b/helm/software/matita/contribs/CoRN-Procedural/ftc/WeakIVT.mma index b4302f58b..39f0392bd 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/ftc/WeakIVT.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/ftc/WeakIVT.mma @@ -45,11 +45,17 @@ will prove them here. Section Lemma1 *) -alias id "a" = "cic:/CoRN/ftc/WeakIVT/Lemma1/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/WeakIVT/Lemma1/a.var +*) -alias id "b" = "cic:/CoRN/ftc/WeakIVT/Lemma1/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/WeakIVT/Lemma1/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/WeakIVT/Lemma1/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/WeakIVT/Lemma1/Hab.var +*) (* begin hide *) @@ -57,9 +63,13 @@ inline procedural "cic:/CoRN/ftc/WeakIVT/Lemma1/I.con" "Lemma1__" as definition. (* end hide *) -alias id "F" = "cic:/CoRN/ftc/WeakIVT/Lemma1/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/WeakIVT/Lemma1/F.var +*) -alias id "contF" = "cic:/CoRN/ftc/WeakIVT/Lemma1/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/WeakIVT/Lemma1/contF.var +*) (*#* **First Lemmas @@ -82,11 +92,17 @@ End Lemma1 Section Lemma2 *) -alias id "a" = "cic:/CoRN/ftc/WeakIVT/Lemma2/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/WeakIVT/Lemma2/a.var +*) -alias id "b" = "cic:/CoRN/ftc/WeakIVT/Lemma2/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/WeakIVT/Lemma2/b.var +*) -alias id "Hab" = "cic:/CoRN/ftc/WeakIVT/Lemma2/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/WeakIVT/Lemma2/Hab.var +*) (* begin hide *) @@ -94,9 +110,13 @@ inline procedural "cic:/CoRN/ftc/WeakIVT/Lemma2/I.con" "Lemma2__" as definition. (* end hide *) -alias id "F" = "cic:/CoRN/ftc/WeakIVT/Lemma2/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/WeakIVT/Lemma2/F.var +*) -alias id "contF" = "cic:/CoRN/ftc/WeakIVT/Lemma2/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/WeakIVT/Lemma2/contF.var +*) (*#* If [f(b) [<] f(a)], a similar result holds: @@ -120,13 +140,21 @@ these assumptions, we can build two sequences of values which converge to [x0] such that [f(x0) [=] z]. *) -alias id "a" = "cic:/CoRN/ftc/WeakIVT/IVT/a.var". +(* UNEXPORTED +cic:/CoRN/ftc/WeakIVT/IVT/a.var +*) -alias id "b" = "cic:/CoRN/ftc/WeakIVT/IVT/b.var". +(* UNEXPORTED +cic:/CoRN/ftc/WeakIVT/IVT/b.var +*) -alias id "Hab'" = "cic:/CoRN/ftc/WeakIVT/IVT/Hab'.var". +(* UNEXPORTED +cic:/CoRN/ftc/WeakIVT/IVT/Hab'.var +*) -alias id "Hab" = "cic:/CoRN/ftc/WeakIVT/IVT/Hab.var". +(* UNEXPORTED +cic:/CoRN/ftc/WeakIVT/IVT/Hab.var +*) (* begin hide *) @@ -134,9 +162,13 @@ inline procedural "cic:/CoRN/ftc/WeakIVT/IVT/I.con" "IVT__" as definition. (* end hide *) -alias id "F" = "cic:/CoRN/ftc/WeakIVT/IVT/F.var". +(* UNEXPORTED +cic:/CoRN/ftc/WeakIVT/IVT/F.var +*) -alias id "contF" = "cic:/CoRN/ftc/WeakIVT/IVT/contF.var". +(* UNEXPORTED +cic:/CoRN/ftc/WeakIVT/IVT/contF.var +*) (* begin hide *) @@ -146,7 +178,9 @@ inline procedural "cic:/CoRN/ftc/WeakIVT/IVT/incF.con" "IVT__" as definition. (* begin show *) -alias id "incrF" = "cic:/CoRN/ftc/WeakIVT/IVT/incrF.var". +(* UNEXPORTED +cic:/CoRN/ftc/WeakIVT/IVT/incrF.var +*) (* end show *) @@ -162,11 +196,17 @@ inline procedural "cic:/CoRN/ftc/WeakIVT/IVT/HFab'.con" "IVT__" as definition. (* begin show *) -alias id "z" = "cic:/CoRN/ftc/WeakIVT/IVT/z.var". +(* UNEXPORTED +cic:/CoRN/ftc/WeakIVT/IVT/z.var +*) -alias id "Haz" = "cic:/CoRN/ftc/WeakIVT/IVT/Haz.var". +(* UNEXPORTED +cic:/CoRN/ftc/WeakIVT/IVT/Haz.var +*) -alias id "Hzb" = "cic:/CoRN/ftc/WeakIVT/IVT/Hzb.var". +(* UNEXPORTED +cic:/CoRN/ftc/WeakIVT/IVT/Hzb.var +*) (* end show *) diff --git a/helm/software/matita/contribs/CoRN-Procedural/metrics/CPseudoMSpaces.mma b/helm/software/matita/contribs/CoRN-Procedural/metrics/CPseudoMSpaces.mma index 9774f2a62..ec3541174 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/metrics/CPseudoMSpaces.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/metrics/CPseudoMSpaces.mma @@ -33,9 +33,13 @@ Let [A : CSetoid], [d : (CSetoid_bin_fun A A IR)]. %\end{convention}% *) -alias id "A" = "cic:/CoRN/metrics/CPseudoMSpaces/Relations/A.var". +(* UNEXPORTED +cic:/CoRN/metrics/CPseudoMSpaces/Relations/A.var +*) -alias id "d" = "cic:/CoRN/metrics/CPseudoMSpaces/Relations/d.var". +(* UNEXPORTED +cic:/CoRN/metrics/CPseudoMSpaces/Relations/d.var +*) (* UNEXPORTED Set Implicit Arguments. @@ -111,7 +115,9 @@ Let [A] be a pseudo metric space. %\end{convention}% *) -alias id "A" = "cic:/CoRN/metrics/CPseudoMSpaces/PsMS_axioms/A.var". +(* UNEXPORTED +cic:/CoRN/metrics/CPseudoMSpaces/PsMS_axioms/A.var +*) inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/CPsMetricSpace_is_CPsMetricSpace.con" as lemma. @@ -137,7 +143,9 @@ Let [Y] be a pseudo metric space. %\end{convention}% *) -alias id "Y" = "cic:/CoRN/metrics/CPseudoMSpaces/PsMS_basics/Y.var". +(* UNEXPORTED +cic:/CoRN/metrics/CPseudoMSpaces/PsMS_basics/Y.var +*) inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/rev_tri_ineq.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/metrics/ContFunctions.mma b/helm/software/matita/contribs/CoRN-Procedural/metrics/ContFunctions.mma index 1d6d82e96..d60d1d29f 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/metrics/ContFunctions.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/metrics/ContFunctions.mma @@ -30,9 +30,13 @@ Let [A] and [B] be pseudo metric spaces. %\end{convention}% *) -alias id "A" = "cic:/CoRN/metrics/ContFunctions/Continuous_functions/A.var". +(* UNEXPORTED +cic:/CoRN/metrics/ContFunctions/Continuous_functions/A.var +*) -alias id "B" = "cic:/CoRN/metrics/ContFunctions/Continuous_functions/B.var". +(* UNEXPORTED +cic:/CoRN/metrics/ContFunctions/Continuous_functions/B.var +*) (*#* We will look at some notions of continuous functions. @@ -158,9 +162,13 @@ Any constant function is Lipschitz. Hence it is uniformly continuous and continuous. *) -alias id "B" = "cic:/CoRN/metrics/ContFunctions/Constant/B.var". +(* UNEXPORTED +cic:/CoRN/metrics/ContFunctions/Constant/B.var +*) -alias id "X" = "cic:/CoRN/metrics/ContFunctions/Constant/X.var". +(* UNEXPORTED +cic:/CoRN/metrics/ContFunctions/Constant/X.var +*) inline procedural "cic:/CoRN/metrics/ContFunctions/const_fun_is_lipschitz.con" as lemma. @@ -189,15 +197,25 @@ The composition of two Lipschitz/uniformly continous/continuous functions is again Lipschitz/uniformly continuous/continuous. *) -alias id "X" = "cic:/CoRN/metrics/ContFunctions/Composition/X.var". +(* UNEXPORTED +cic:/CoRN/metrics/ContFunctions/Composition/X.var +*) -alias id "B" = "cic:/CoRN/metrics/ContFunctions/Composition/B.var". +(* UNEXPORTED +cic:/CoRN/metrics/ContFunctions/Composition/B.var +*) -alias id "f" = "cic:/CoRN/metrics/ContFunctions/Composition/f.var". +(* UNEXPORTED +cic:/CoRN/metrics/ContFunctions/Composition/f.var +*) -alias id "C" = "cic:/CoRN/metrics/ContFunctions/Composition/C.var". +(* UNEXPORTED +cic:/CoRN/metrics/ContFunctions/Composition/C.var +*) -alias id "g" = "cic:/CoRN/metrics/ContFunctions/Composition/g.var". +(* UNEXPORTED +cic:/CoRN/metrics/ContFunctions/Composition/g.var +*) inline procedural "cic:/CoRN/metrics/ContFunctions/comp_resp_lipschitz.con" as lemma. 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 24e2717f4..189eadee1 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/metrics/IR_CPMSpace.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/metrics/IR_CPMSpace.mma @@ -61,7 +61,9 @@ inline procedural "cic:/CoRN/metrics/IR_CPMSpace/IR_dIR_is_CPsMetricSpace.con" a inline procedural "cic:/CoRN/metrics/IR_CPMSpace/IR_as_CPsMetricSpace.con" as definition. -alias id "X" = "cic:/CoRN/metrics/IR_CPMSpace/Reals/X.var". +(* UNEXPORTED +cic:/CoRN/metrics/IR_CPMSpace/Reals/X.var +*) inline procedural "cic:/CoRN/metrics/IR_CPMSpace/rev_tri_ineq'.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 70a82cab6..69f62c276 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/Bridges_LUB.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/Bridges_LUB.mma @@ -40,7 +40,9 @@ include "algebra/Expon.ma". Section LUBP *) -alias id "R1" = "cic:/CoRN/reals/Bridges_LUB/LUBP/R1.var". +(* UNEXPORTED +cic:/CoRN/reals/Bridges_LUB/LUBP/R1.var +*) (* SUBSECTION ON GENRAL DEFINITIONS *) @@ -48,9 +50,13 @@ alias id "R1" = "cic:/CoRN/reals/Bridges_LUB/LUBP/R1.var". Section lub_definitions *) -alias id "OF" = "cic:/CoRN/reals/Bridges_LUB/LUBP/lub_definitions/OF.var". +(* UNEXPORTED +cic:/CoRN/reals/Bridges_LUB/LUBP/lub_definitions/OF.var +*) -alias id "SS" = "cic:/CoRN/reals/Bridges_LUB/LUBP/lub_definitions/SS.var". +(* UNEXPORTED +cic:/CoRN/reals/Bridges_LUB/LUBP/lub_definitions/SS.var +*) inline procedural "cic:/CoRN/reals/Bridges_LUB/member.con" as definition. @@ -86,13 +92,21 @@ End lub_definitions Section upper_bound_sequence *) -alias id "A" = "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/A.var". +(* UNEXPORTED +cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/A.var +*) -alias id "is_inhabitted" = "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/is_inhabitted.var". +(* UNEXPORTED +cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/is_inhabitted.var +*) -alias id "bounded_above" = "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/bounded_above.var". +(* UNEXPORTED +cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/bounded_above.var +*) -alias id "located" = "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/located.var". +(* UNEXPORTED +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__" as definition. 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 38020510b..9b8cf3b1d 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/Bridges_iso.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/Bridges_iso.mma @@ -42,11 +42,17 @@ inline procedural "cic:/CoRN/reals/Bridges_iso/le_witness_informative.con" as le Section bridges_axioms_imply_ours *) -alias id "OF" = "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/OF.var". +(* UNEXPORTED +cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/OF.var +*) -alias id "lubp" = "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/lubp.var". +(* UNEXPORTED +cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/lubp.var +*) -alias id "is_Archimedes" = "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/is_Archimedes.var". +(* UNEXPORTED +cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/is_Archimedes.var +*) inline procedural "cic:/CoRN/reals/Bridges_iso/is_Archimedes'.con" as lemma. @@ -62,7 +68,9 @@ inline procedural "cic:/CoRN/reals/Bridges_iso/glbp.con" as theorem. Section supremum *) -alias id "P" = "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/supremum/P.var". +(* UNEXPORTED +cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/supremum/P.var +*) inline procedural "cic:/CoRN/reals/Bridges_iso/inequality1.con" as lemma. @@ -94,7 +102,9 @@ inline procedural "cic:/CoRN/reals/Bridges_iso/kaf.con" as definition. 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". +(* UNEXPORTED +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" as definition. @@ -110,7 +120,9 @@ inline procedural "cic:/CoRN/reals/Bridges_iso/indeks.con" as definition. 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". +(* UNEXPORTED +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" as lemma. @@ -187,7 +199,9 @@ inline procedural "cic:/CoRN/reals/Bridges_iso/bounded_quantifier_informative.co 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". +(* UNEXPORTED +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" as lemma. @@ -209,7 +223,9 @@ Section Every_Cauchy_Sequence_is_bounded 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". +(* UNEXPORTED +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__" as definition. @@ -261,7 +277,9 @@ inline procedural "cic:/CoRN/reals/Bridges_iso/tail_seq.con" as definition. End Every_Cauchy_Sequence_is_bounded *) -alias id "g" = "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/g.var". +(* UNEXPORTED +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__" as definition. diff --git a/helm/software/matita/contribs/CoRN-Procedural/reals/CMetricFields.mma b/helm/software/matita/contribs/CoRN-Procedural/reals/CMetricFields.mma index db365edae..4230a8800 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/CMetricFields.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/CMetricFields.mma @@ -62,7 +62,9 @@ End basics Section CMetric_Field_Cauchy *) -alias id "F" = "cic:/CoRN/reals/CMetricFields/CMetric_Field_Cauchy/F.var". +(* UNEXPORTED +cic:/CoRN/reals/CMetricFields/CMetric_Field_Cauchy/F.var +*) (*#* %\begin{convention}% Let [F:CMetricField]. diff --git a/helm/software/matita/contribs/CoRN-Procedural/reals/CReals1.mma b/helm/software/matita/contribs/CoRN-Procedural/reals/CReals1.mma index d3157702c..3fc8a87b8 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/CReals1.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/CReals1.mma @@ -75,19 +75,33 @@ Finally, for some of our results it is important to assume that [seq2] is monotonous. *) -alias id "seq1" = "cic:/CoRN/reals/CReals1/Subsequences/seq1.var". +(* UNEXPORTED +cic:/CoRN/reals/CReals1/Subsequences/seq1.var +*) -alias id "seq2" = "cic:/CoRN/reals/CReals1/Subsequences/seq2.var". +(* UNEXPORTED +cic:/CoRN/reals/CReals1/Subsequences/seq2.var +*) -alias id "f" = "cic:/CoRN/reals/CReals1/Subsequences/f.var". +(* UNEXPORTED +cic:/CoRN/reals/CReals1/Subsequences/f.var +*) -alias id "monF" = "cic:/CoRN/reals/CReals1/Subsequences/monF.var". +(* UNEXPORTED +cic:/CoRN/reals/CReals1/Subsequences/monF.var +*) -alias id "crescF" = "cic:/CoRN/reals/CReals1/Subsequences/crescF.var". +(* UNEXPORTED +cic:/CoRN/reals/CReals1/Subsequences/crescF.var +*) -alias id "subseq" = "cic:/CoRN/reals/CReals1/Subsequences/subseq.var". +(* UNEXPORTED +cic:/CoRN/reals/CReals1/Subsequences/subseq.var +*) -alias id "mon_seq2" = "cic:/CoRN/reals/CReals1/Subsequences/mon_seq2.var". +(* UNEXPORTED +cic:/CoRN/reals/CReals1/Subsequences/mon_seq2.var +*) inline procedural "cic:/CoRN/reals/CReals1/unbnd_f.con" as lemma. @@ -113,19 +127,33 @@ End Subsequences Section Cauchy_Subsequences *) -alias id "seq1" = "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/seq1.var". +(* UNEXPORTED +cic:/CoRN/reals/CReals1/Cauchy_Subsequences/seq1.var +*) -alias id "seq2" = "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/seq2.var". +(* UNEXPORTED +cic:/CoRN/reals/CReals1/Cauchy_Subsequences/seq2.var +*) -alias id "f" = "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/f.var". +(* UNEXPORTED +cic:/CoRN/reals/CReals1/Cauchy_Subsequences/f.var +*) -alias id "monF" = "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/monF.var". +(* UNEXPORTED +cic:/CoRN/reals/CReals1/Cauchy_Subsequences/monF.var +*) -alias id "crescF" = "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/crescF.var". +(* UNEXPORTED +cic:/CoRN/reals/CReals1/Cauchy_Subsequences/crescF.var +*) -alias id "subseq" = "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/subseq.var". +(* UNEXPORTED +cic:/CoRN/reals/CReals1/Cauchy_Subsequences/subseq.var +*) -alias id "mon_seq2" = "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/mon_seq2.var". +(* UNEXPORTED +cic:/CoRN/reals/CReals1/Cauchy_Subsequences/mon_seq2.var +*) inline procedural "cic:/CoRN/reals/CReals1/Lim_seq_eq_Lim_subseq.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 32313cff8..6d3adf12b 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/CSumsReals.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/CSumsReals.mma @@ -34,7 +34,9 @@ $\Sigma_{m\leq i \leq n}~c^k = \frac{c^{n+1}-c^m}{c-1}.$ Section Sums_over_Reals *) -alias id "c" = "cic:/CoRN/reals/CSumsReals/Sums_over_Reals/c.var". +(* UNEXPORTED +cic:/CoRN/reals/CSumsReals/Sums_over_Reals/c.var +*) inline procedural "cic:/CoRN/reals/CSumsReals/Sum0_c_exp.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 16e97d931..d7368566b 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/CauchySeq.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/CauchySeq.mma @@ -41,7 +41,7 @@ Definition IR : CReals := Concrete_R. Opaque IR. *) -alias id "IR" = "cic:/CoRN/reals/CauchySeq/IR.var". +inline procedural "cic:/CoRN/reals/CauchySeq/IR.con". (* NOTATION Notation PartIR := (PartFunct IR). 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 e26648950..0fd1eddc5 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/Cauchy_CReals.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/Cauchy_CReals.mma @@ -38,7 +38,9 @@ We start by showing how to inject the rational numbers in the field of Cauchy se %\end{convention}% *) -alias id "F" = "cic:/CoRN/reals/Cauchy_CReals/R_CReals/F.var". +(* UNEXPORTED +cic:/CoRN/reals/Cauchy_CReals/R_CReals/F.var +*) (* NOTATION Notation "'R_COrdField''" := (R_COrdField F). @@ -96,7 +98,9 @@ inline procedural "cic:/CoRN/reals/Cauchy_CReals/R_CReals/T.con" "R_CReals__" as resulting one is, too. *) -alias id "F_is_archemaedian" = "cic:/CoRN/reals/Cauchy_CReals/R_CReals/F_is_archemaedian.var". +(* UNEXPORTED +cic:/CoRN/reals/Cauchy_CReals/R_CReals/F_is_archemaedian.var +*) inline procedural "cic:/CoRN/reals/Cauchy_CReals/R_is_archemaedian.con" as theorem. diff --git a/helm/software/matita/contribs/CoRN-Procedural/reals/IVT.mma b/helm/software/matita/contribs/CoRN-Procedural/reals/IVT.mma index dba8d459c..b44cbcc44 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/IVT.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/IVT.mma @@ -37,17 +37,29 @@ Section Nested_Intervals %\end{convention}% *) -alias id "a" = "cic:/CoRN/reals/IVT/Nested_Intervals/a.var". +(* UNEXPORTED +cic:/CoRN/reals/IVT/Nested_Intervals/a.var +*) -alias id "b" = "cic:/CoRN/reals/IVT/Nested_Intervals/b.var". +(* UNEXPORTED +cic:/CoRN/reals/IVT/Nested_Intervals/b.var +*) -alias id "a_mon" = "cic:/CoRN/reals/IVT/Nested_Intervals/a_mon.var". +(* UNEXPORTED +cic:/CoRN/reals/IVT/Nested_Intervals/a_mon.var +*) -alias id "b_mon" = "cic:/CoRN/reals/IVT/Nested_Intervals/b_mon.var". +(* UNEXPORTED +cic:/CoRN/reals/IVT/Nested_Intervals/b_mon.var +*) -alias id "a_b" = "cic:/CoRN/reals/IVT/Nested_Intervals/a_b.var". +(* UNEXPORTED +cic:/CoRN/reals/IVT/Nested_Intervals/a_b.var +*) -alias id "b_a" = "cic:/CoRN/reals/IVT/Nested_Intervals/b_a.var". +(* UNEXPORTED +cic:/CoRN/reals/IVT/Nested_Intervals/b_a.var +*) inline procedural "cic:/CoRN/reals/IVT/a_mon'.con" as lemma. @@ -69,9 +81,13 @@ inline procedural "cic:/CoRN/reals/IVT/Cnested_intervals_limit.con" as lemma. %\end{convention}% *) -alias id "f" = "cic:/CoRN/reals/IVT/Nested_Intervals/f.var". +(* UNEXPORTED +cic:/CoRN/reals/IVT/Nested_Intervals/f.var +*) -alias id "f_contin" = "cic:/CoRN/reals/IVT/Nested_Intervals/f_contin.var". +(* UNEXPORTED +cic:/CoRN/reals/IVT/Nested_Intervals/f_contin.var +*) inline procedural "cic:/CoRN/reals/IVT/f_contin_pos.con" as lemma. @@ -79,9 +95,13 @@ inline procedural "cic:/CoRN/reals/IVT/f_contin_neg.con" as lemma. (*#* Assume also that [forall i, f (a i) [<=] Zero [<=] f (b i)]. *) -alias id "f_a" = "cic:/CoRN/reals/IVT/Nested_Intervals/f_a.var". +(* UNEXPORTED +cic:/CoRN/reals/IVT/Nested_Intervals/f_a.var +*) -alias id "f_b" = "cic:/CoRN/reals/IVT/Nested_Intervals/f_b.var". +(* UNEXPORTED +cic:/CoRN/reals/IVT/Nested_Intervals/f_b.var +*) inline procedural "cic:/CoRN/reals/IVT/Cnested_intervals_zero.con" as lemma. @@ -95,19 +115,33 @@ Section Bisection (*#* ** Bissections *) -alias id "f" = "cic:/CoRN/reals/IVT/Bisection/f.var". +(* UNEXPORTED +cic:/CoRN/reals/IVT/Bisection/f.var +*) -alias id "f_apzero_interval" = "cic:/CoRN/reals/IVT/Bisection/f_apzero_interval.var". +(* UNEXPORTED +cic:/CoRN/reals/IVT/Bisection/f_apzero_interval.var +*) -alias id "a" = "cic:/CoRN/reals/IVT/Bisection/a.var". +(* UNEXPORTED +cic:/CoRN/reals/IVT/Bisection/a.var +*) -alias id "b" = "cic:/CoRN/reals/IVT/Bisection/b.var". +(* UNEXPORTED +cic:/CoRN/reals/IVT/Bisection/b.var +*) -alias id "a_b" = "cic:/CoRN/reals/IVT/Bisection/a_b.var". +(* UNEXPORTED +cic:/CoRN/reals/IVT/Bisection/a_b.var +*) -alias id "f_a" = "cic:/CoRN/reals/IVT/Bisection/f_a.var". +(* UNEXPORTED +cic:/CoRN/reals/IVT/Bisection/f_a.var +*) -alias id "f_b" = "cic:/CoRN/reals/IVT/Bisection/f_b.var". +(* UNEXPORTED +cic:/CoRN/reals/IVT/Bisection/f_b.var +*) (*#* %\begin{convention}% Let [Small] denote [Two[/]ThreeNZ], [lft] be [(Two[*]a[+]b) [/]ThreeNZ] and [rht] be [(a[+]Two[*]b) [/]ThreeNZ]. @@ -148,9 +182,13 @@ End Bisection Section Bisect_Interval *) -alias id "f" = "cic:/CoRN/reals/IVT/Bisect_Interval/f.var". +(* UNEXPORTED +cic:/CoRN/reals/IVT/Bisect_Interval/f.var +*) -alias id "C_f_apzero_interval" = "cic:/CoRN/reals/IVT/Bisect_Interval/C_f_apzero_interval.var". +(* UNEXPORTED +cic:/CoRN/reals/IVT/Bisect_Interval/C_f_apzero_interval.var +*) (* begin hide *) @@ -178,21 +216,37 @@ Section IVT_Op Same conventions as before. *) -alias id "f" = "cic:/CoRN/reals/IVT/IVT_Op/f.var". +(* UNEXPORTED +cic:/CoRN/reals/IVT/IVT_Op/f.var +*) -alias id "f_contin" = "cic:/CoRN/reals/IVT/IVT_Op/f_contin.var". +(* UNEXPORTED +cic:/CoRN/reals/IVT/IVT_Op/f_contin.var +*) -alias id "f_apzero_interval" = "cic:/CoRN/reals/IVT/IVT_Op/f_apzero_interval.var". +(* UNEXPORTED +cic:/CoRN/reals/IVT/IVT_Op/f_apzero_interval.var +*) -alias id "a" = "cic:/CoRN/reals/IVT/IVT_Op/a.var". +(* UNEXPORTED +cic:/CoRN/reals/IVT/IVT_Op/a.var +*) -alias id "b" = "cic:/CoRN/reals/IVT/IVT_Op/b.var". +(* UNEXPORTED +cic:/CoRN/reals/IVT/IVT_Op/b.var +*) -alias id "a_b" = "cic:/CoRN/reals/IVT/IVT_Op/a_b.var". +(* UNEXPORTED +cic:/CoRN/reals/IVT/IVT_Op/a_b.var +*) -alias id "f_a" = "cic:/CoRN/reals/IVT/IVT_Op/f_a.var". +(* UNEXPORTED +cic:/CoRN/reals/IVT/IVT_Op/f_a.var +*) -alias id "f_b" = "cic:/CoRN/reals/IVT/IVT_Op/f_b.var". +(* UNEXPORTED +cic:/CoRN/reals/IVT/IVT_Op/f_b.var +*) (* begin hide *) diff --git a/helm/software/matita/contribs/CoRN-Procedural/reals/Intervals.mma b/helm/software/matita/contribs/CoRN-Procedural/reals/Intervals.mma index 013391089..db160770e 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/Intervals.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/Intervals.mma @@ -47,11 +47,17 @@ As expected, both [a] and [b] are members of [[a,b]]. Also they are members of the interval [[Min(a,b),Max(a,b)]]. *) -alias id "a" = "cic:/CoRN/reals/Intervals/Intervals/a.var". +(* UNEXPORTED +cic:/CoRN/reals/Intervals/Intervals/a.var +*) -alias id "b" = "cic:/CoRN/reals/Intervals/Intervals/b.var". +(* UNEXPORTED +cic:/CoRN/reals/Intervals/Intervals/b.var +*) -alias id "Hab" = "cic:/CoRN/reals/Intervals/Intervals/Hab.var". +(* UNEXPORTED +cic:/CoRN/reals/Intervals/Intervals/Hab.var +*) inline procedural "cic:/CoRN/reals/Intervals/compact_inc_lft.con" as lemma. @@ -225,11 +231,17 @@ a positive real number. %\end{convention}% *) -alias id "a" = "cic:/CoRN/reals/Intervals/Compact/a.var". +(* UNEXPORTED +cic:/CoRN/reals/Intervals/Compact/a.var +*) -alias id "b" = "cic:/CoRN/reals/Intervals/Compact/b.var". +(* UNEXPORTED +cic:/CoRN/reals/Intervals/Compact/b.var +*) -alias id "Hab" = "cic:/CoRN/reals/Intervals/Compact/Hab.var". +(* UNEXPORTED +cic:/CoRN/reals/Intervals/Compact/Hab.var +*) (* begin hide *) @@ -237,11 +249,17 @@ inline procedural "cic:/CoRN/reals/Intervals/Compact/I.con" "Compact__" as defin (* end hide *) -alias id "Hab'" = "cic:/CoRN/reals/Intervals/Compact/Hab'.var". +(* UNEXPORTED +cic:/CoRN/reals/Intervals/Compact/Hab'.var +*) -alias id "e" = "cic:/CoRN/reals/Intervals/Compact/e.var". +(* UNEXPORTED +cic:/CoRN/reals/Intervals/Compact/e.var +*) -alias id "He" = "cic:/CoRN/reals/Intervals/Compact/He.var". +(* UNEXPORTED +cic:/CoRN/reals/Intervals/Compact/He.var +*) (*#* We start by finding a natural number [n] such that [(b[-]a) [/] n [<] e]. 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 788a265de..246c4061c 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/Max_AbsIR.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/Max_AbsIR.mma @@ -40,9 +40,13 @@ Let [x] and [y] be reals %\end{convention}% *) -alias id "x" = "cic:/CoRN/reals/Max_AbsIR/Maximum/Max_function/x.var". +(* UNEXPORTED +cic:/CoRN/reals/Max_AbsIR/Maximum/Max_function/x.var +*) -alias id "y" = "cic:/CoRN/reals/Max_AbsIR/Maximum/Max_function/y.var". +(* UNEXPORTED +cic:/CoRN/reals/Max_AbsIR/Maximum/Max_function/y.var +*) inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_seq.con" as definition. @@ -176,9 +180,13 @@ 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" as lemma. -alias id "a" = "cic:/CoRN/reals/Max_AbsIR/Minimum/a.var". +(* UNEXPORTED +cic:/CoRN/reals/Max_AbsIR/Minimum/a.var +*) -alias id "b" = "cic:/CoRN/reals/Max_AbsIR/Minimum/b.var". +(* UNEXPORTED +cic:/CoRN/reals/Max_AbsIR/Minimum/b.var +*) inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_leEq_Max.con" as lemma. @@ -289,9 +297,13 @@ Let [F,G:PartIR] and denote by [P] and [Q] their respective domains. %\end{convention}% *) -alias id "F" = "cic:/CoRN/reals/Max_AbsIR/Part_Function_Max/F.var". +(* UNEXPORTED +cic:/CoRN/reals/Max_AbsIR/Part_Function_Max/F.var +*) -alias id "G" = "cic:/CoRN/reals/Max_AbsIR/Part_Function_Max/G.var". +(* UNEXPORTED +cic:/CoRN/reals/Max_AbsIR/Part_Function_Max/G.var +*) (* begin hide *) @@ -313,9 +325,13 @@ End Part_Function_Max Section Part_Function_Abs *) -alias id "F" = "cic:/CoRN/reals/Max_AbsIR/Part_Function_Abs/F.var". +(* UNEXPORTED +cic:/CoRN/reals/Max_AbsIR/Part_Function_Abs/F.var +*) -alias id "G" = "cic:/CoRN/reals/Max_AbsIR/Part_Function_Abs/G.var". +(* UNEXPORTED +cic:/CoRN/reals/Max_AbsIR/Part_Function_Abs/G.var +*) (* begin hide *) @@ -361,9 +377,13 @@ Hint Resolve FAbs_char': algebra. Section Inclusion *) -alias id "F" = "cic:/CoRN/reals/Max_AbsIR/Inclusion/F.var". +(* UNEXPORTED +cic:/CoRN/reals/Max_AbsIR/Inclusion/F.var +*) -alias id "G" = "cic:/CoRN/reals/Max_AbsIR/Inclusion/G.var". +(* UNEXPORTED +cic:/CoRN/reals/Max_AbsIR/Inclusion/G.var +*) (* begin hide *) @@ -378,7 +398,9 @@ inline procedural "cic:/CoRN/reals/Max_AbsIR/Inclusion/Q.con" "Inclusion__" as d %\end{convention}% *) -alias id "R" = "cic:/CoRN/reals/Max_AbsIR/Inclusion/R.var". +(* UNEXPORTED +cic:/CoRN/reals/Max_AbsIR/Inclusion/R.var +*) inline procedural "cic:/CoRN/reals/Max_AbsIR/included_FMax.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/reals/NRootIR.mma b/helm/software/matita/contribs/CoRN-Procedural/reals/NRootIR.mma index c617e2a57..81dbac168 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/NRootIR.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/NRootIR.mma @@ -37,13 +37,21 @@ Section NRoot %\end{convention}% *) -alias id "n" = "cic:/CoRN/reals/NRootIR/NRoot/n.var". +(* UNEXPORTED +cic:/CoRN/reals/NRootIR/NRoot/n.var +*) -alias id "n_pos" = "cic:/CoRN/reals/NRootIR/NRoot/n_pos.var". +(* UNEXPORTED +cic:/CoRN/reals/NRootIR/NRoot/n_pos.var +*) -alias id "c" = "cic:/CoRN/reals/NRootIR/NRoot/c.var". +(* UNEXPORTED +cic:/CoRN/reals/NRootIR/NRoot/c.var +*) -alias id "c_nonneg" = "cic:/CoRN/reals/NRootIR/NRoot/c_nonneg.var". +(* UNEXPORTED +cic:/CoRN/reals/NRootIR/NRoot/c_nonneg.var +*) (* begin hide *) @@ -98,13 +106,21 @@ inline procedural "cic:/CoRN/reals/NRootIR/NRoot_cancel.con" as lemma. (*#* %\begin{convention}% Let [x,y] be nonnegative real numbers. %\end{convention}% *) -alias id "x" = "cic:/CoRN/reals/NRootIR/Nth_Root/x.var". +(* UNEXPORTED +cic:/CoRN/reals/NRootIR/Nth_Root/x.var +*) -alias id "y" = "cic:/CoRN/reals/NRootIR/Nth_Root/y.var". +(* UNEXPORTED +cic:/CoRN/reals/NRootIR/Nth_Root/y.var +*) -alias id "Hx" = "cic:/CoRN/reals/NRootIR/Nth_Root/Hx.var". +(* UNEXPORTED +cic:/CoRN/reals/NRootIR/Nth_Root/Hx.var +*) -alias id "Hy" = "cic:/CoRN/reals/NRootIR/Nth_Root/Hy.var". +(* UNEXPORTED +cic:/CoRN/reals/NRootIR/Nth_Root/Hy.var +*) inline procedural "cic:/CoRN/reals/NRootIR/NRoot_wd.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/reals/OddPolyRootIR.mma b/helm/software/matita/contribs/CoRN-Procedural/reals/OddPolyRootIR.mma index 45f932b5a..28817e7a1 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/OddPolyRootIR.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/OddPolyRootIR.mma @@ -31,7 +31,9 @@ Section CPoly_Big %\end{convention}% *) -alias id "R" = "cic:/CoRN/reals/OddPolyRootIR/CPoly_Big/R.var". +(* UNEXPORTED +cic:/CoRN/reals/OddPolyRootIR/CPoly_Big/R.var +*) (* begin hide *) @@ -60,7 +62,9 @@ Section Flip_Poly %\end{convention}% *) -alias id "R" = "cic:/CoRN/reals/OddPolyRootIR/Flip_Poly/R.var". +(* UNEXPORTED +cic:/CoRN/reals/OddPolyRootIR/Flip_Poly/R.var +*) (* begin hide *) @@ -97,7 +101,9 @@ Section OddPoly_Signs %\end{convention}% *) -alias id "R" = "cic:/CoRN/reals/OddPolyRootIR/OddPoly_Signs/R.var". +(* UNEXPORTED +cic:/CoRN/reals/OddPolyRootIR/OddPoly_Signs/R.var +*) (* begin hide *) @@ -125,7 +131,9 @@ this field. %\end{convention}% *) -alias id "R" = "cic:/CoRN/reals/OddPolyRootIR/Poly_Norm/R.var". +(* UNEXPORTED +cic:/CoRN/reals/OddPolyRootIR/Poly_Norm/R.var +*) (* begin hide *) 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 6a52158d1..90ba7b7c8 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/Q_dense.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/Q_dense.mma @@ -28,7 +28,9 @@ inline procedural "cic:/CoRN/reals/Q_dense/or_not_and.con" as lemma. Section Interval_definition *) -alias id "OF" = "cic:/CoRN/reals/Q_dense/Interval_definition/OF.var". +(* UNEXPORTED +cic:/CoRN/reals/Q_dense/Interval_definition/OF.var +*) inline procedural "cic:/CoRN/reals/Q_dense/Interval.ind". @@ -63,7 +65,9 @@ Qed. Section COrdField_extra *) -alias id "OF" = "cic:/CoRN/reals/Q_dense/COrdField_extra/OF.var". +(* UNEXPORTED +cic:/CoRN/reals/Q_dense/COrdField_extra/OF.var +*) inline procedural "cic:/CoRN/reals/Q_dense/AbsSmall_pos_reflexive.con" as lemma. @@ -83,7 +87,9 @@ include "tactics/Opaque_algebra.ma". (*#*** WARNING: A file is being loaded *****) -alias id "R1" = "cic:/CoRN/reals/Q_dense/Rational_sequence/R1.var". +(* UNEXPORTED +cic:/CoRN/reals/Q_dense/Rational_sequence/R1.var +*) inline procedural "cic:/CoRN/reals/Q_dense/start_l.con" as definition. 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 f6f152ede..35359504e 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 @@ -41,7 +41,9 @@ Section Rational_sequence_prelogue %\end{convention}% *) -alias id "R1" = "cic:/CoRN/reals/Q_in_CReals/Rational_sequence_prelogue/R1.var". +(* UNEXPORTED +cic:/CoRN/reals/Q_in_CReals/Rational_sequence_prelogue/R1.var +*) (* We clone these proofs from CReals1.v just because there IR is an axiom *) 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 1483e4104..29ad38f24 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/R_morphism.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/R_morphism.mma @@ -32,27 +32,45 @@ inline procedural "cic:/CoRN/reals/R_morphism/Cauchy_Lim_prop2.con" as definitio Section morphism *) -alias id "R1" = "cic:/CoRN/reals/R_morphism/morphism/R1.var". +(* UNEXPORTED +cic:/CoRN/reals/R_morphism/morphism/R1.var +*) -alias id "R2" = "cic:/CoRN/reals/R_morphism/morphism/R2.var". +(* UNEXPORTED +cic:/CoRN/reals/R_morphism/morphism/R2.var +*) (* UNEXPORTED Section morphism_details *) -alias id "phi" = "cic:/CoRN/reals/R_morphism/morphism/morphism_details/phi.var". +(* UNEXPORTED +cic:/CoRN/reals/R_morphism/morphism/morphism_details/phi.var +*) -alias id "p1" = "cic:/CoRN/reals/R_morphism/morphism/morphism_details/p1.var". +(* UNEXPORTED +cic:/CoRN/reals/R_morphism/morphism/morphism_details/p1.var +*) -alias id "p2" = "cic:/CoRN/reals/R_morphism/morphism/morphism_details/p2.var". +(* UNEXPORTED +cic:/CoRN/reals/R_morphism/morphism/morphism_details/p2.var +*) -alias id "f1" = "cic:/CoRN/reals/R_morphism/morphism/morphism_details/f1.var". +(* UNEXPORTED +cic:/CoRN/reals/R_morphism/morphism/morphism_details/f1.var +*) -alias id "f2" = "cic:/CoRN/reals/R_morphism/morphism/morphism_details/f2.var". +(* UNEXPORTED +cic:/CoRN/reals/R_morphism/morphism/morphism_details/f2.var +*) -alias id "g1" = "cic:/CoRN/reals/R_morphism/morphism/morphism_details/g1.var". +(* UNEXPORTED +cic:/CoRN/reals/R_morphism/morphism/morphism_details/g1.var +*) -alias id "g2" = "cic:/CoRN/reals/R_morphism/morphism/morphism_details/g2.var". +(* UNEXPORTED +cic:/CoRN/reals/R_morphism/morphism/morphism_details/g2.var +*) inline procedural "cic:/CoRN/reals/R_morphism/fun_pres_relation.con" as definition. @@ -128,15 +146,25 @@ End morphism Section composition *) -alias id "R1" = "cic:/CoRN/reals/R_morphism/composition/R1.var". +(* UNEXPORTED +cic:/CoRN/reals/R_morphism/composition/R1.var +*) -alias id "R2" = "cic:/CoRN/reals/R_morphism/composition/R2.var". +(* UNEXPORTED +cic:/CoRN/reals/R_morphism/composition/R2.var +*) -alias id "R3" = "cic:/CoRN/reals/R_morphism/composition/R3.var". +(* UNEXPORTED +cic:/CoRN/reals/R_morphism/composition/R3.var +*) -alias id "f" = "cic:/CoRN/reals/R_morphism/composition/f.var". +(* UNEXPORTED +cic:/CoRN/reals/R_morphism/composition/f.var +*) -alias id "g" = "cic:/CoRN/reals/R_morphism/composition/g.var". +(* UNEXPORTED +cic:/CoRN/reals/R_morphism/composition/g.var +*) inline procedural "cic:/CoRN/reals/R_morphism/compose.con" as definition. @@ -160,17 +188,25 @@ End composition Section isomorphism *) -alias id "R1" = "cic:/CoRN/reals/R_morphism/isomorphism/R1.var". +(* UNEXPORTED +cic:/CoRN/reals/R_morphism/isomorphism/R1.var +*) -alias id "R2" = "cic:/CoRN/reals/R_morphism/isomorphism/R2.var". +(* UNEXPORTED +cic:/CoRN/reals/R_morphism/isomorphism/R2.var +*) (* UNEXPORTED Section identity_map *) -alias id "R3" = "cic:/CoRN/reals/R_morphism/isomorphism/identity_map/R3.var". +(* UNEXPORTED +cic:/CoRN/reals/R_morphism/isomorphism/identity_map/R3.var +*) -alias id "f" = "cic:/CoRN/reals/R_morphism/isomorphism/identity_map/f.var". +(* UNEXPORTED +cic:/CoRN/reals/R_morphism/isomorphism/identity_map/f.var +*) inline procedural "cic:/CoRN/reals/R_morphism/map_is_id.con" as definition. @@ -188,11 +224,17 @@ End isomorphism Section surjective_map *) -alias id "R1" = "cic:/CoRN/reals/R_morphism/surjective_map/R1.var". +(* UNEXPORTED +cic:/CoRN/reals/R_morphism/surjective_map/R1.var +*) -alias id "R2" = "cic:/CoRN/reals/R_morphism/surjective_map/R2.var". +(* UNEXPORTED +cic:/CoRN/reals/R_morphism/surjective_map/R2.var +*) -alias id "f" = "cic:/CoRN/reals/R_morphism/surjective_map/f.var". +(* UNEXPORTED +cic:/CoRN/reals/R_morphism/surjective_map/f.var +*) inline procedural "cic:/CoRN/reals/R_morphism/map_is_surjective.con" as definition. @@ -204,13 +246,21 @@ End surjective_map Section simplification *) -alias id "R1" = "cic:/CoRN/reals/R_morphism/simplification/R1.var". +(* UNEXPORTED +cic:/CoRN/reals/R_morphism/simplification/R1.var +*) -alias id "R2" = "cic:/CoRN/reals/R_morphism/simplification/R2.var". +(* UNEXPORTED +cic:/CoRN/reals/R_morphism/simplification/R2.var +*) -alias id "f" = "cic:/CoRN/reals/R_morphism/simplification/f.var". +(* UNEXPORTED +cic:/CoRN/reals/R_morphism/simplification/f.var +*) -alias id "H1" = "cic:/CoRN/reals/R_morphism/simplification/H1.var". +(* UNEXPORTED +cic:/CoRN/reals/R_morphism/simplification/H1.var +*) inline procedural "cic:/CoRN/reals/R_morphism/f_well_def.con" as lemma. @@ -218,7 +268,9 @@ inline procedural "cic:/CoRN/reals/R_morphism/f_well_def.con" as lemma. Section with_less *) -alias id "H2" = "cic:/CoRN/reals/R_morphism/simplification/with_less/H2.var". +(* UNEXPORTED +cic:/CoRN/reals/R_morphism/simplification/with_less/H2.var +*) inline procedural "cic:/CoRN/reals/R_morphism/less_pres_f.con" as lemma. @@ -236,7 +288,9 @@ End with_less Section with_plus *) -alias id "H3" = "cic:/CoRN/reals/R_morphism/simplification/with_plus/H3.var". +(* UNEXPORTED +cic:/CoRN/reals/R_morphism/simplification/with_plus/H3.var +*) inline procedural "cic:/CoRN/reals/R_morphism/f_pres_Zero.con" as lemma. @@ -252,9 +306,13 @@ End with_plus Section with_plus_less *) -alias id "H2" = "cic:/CoRN/reals/R_morphism/simplification/with_plus_less/H2.var". +(* UNEXPORTED +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". +(* UNEXPORTED +cic:/CoRN/reals/R_morphism/simplification/with_plus_less/H3.var +*) inline procedural "cic:/CoRN/reals/R_morphism/f_pres_ap_zero.con" as lemma. @@ -262,7 +320,9 @@ inline procedural "cic:/CoRN/reals/R_morphism/f_pres_ap_zero.con" as lemma. Section surjectivity_helps *) -alias id "f_surj" = "cic:/CoRN/reals/R_morphism/simplification/with_plus_less/surjectivity_helps/f_surj.var". +(* UNEXPORTED +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" as lemma. @@ -274,7 +334,9 @@ End surjectivity_helps Section with_mult_plus_less *) -alias id "H4" = "cic:/CoRN/reals/R_morphism/simplification/with_plus_less/with_mult_plus_less/H4.var". +(* UNEXPORTED +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" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/reals/RealFuncts.mma b/helm/software/matita/contribs/CoRN-Procedural/reals/RealFuncts.mma index fa95a4af1..5a0a65775 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/RealFuncts.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/RealFuncts.mma @@ -39,9 +39,13 @@ Unset Strict Implicit. Section Continuity *) -alias id "f" = "cic:/CoRN/reals/RealFuncts/Continuity/f.var". +(* UNEXPORTED +cic:/CoRN/reals/RealFuncts/Continuity/f.var +*) -alias id "f2" = "cic:/CoRN/reals/RealFuncts/Continuity/f2.var". +(* UNEXPORTED +cic:/CoRN/reals/RealFuncts/Continuity/f2.var +*) (*#* Let [f] be a unary setoid operation on [IR] and diff --git a/helm/software/matita/contribs/CoRN-Procedural/reals/Series.mma b/helm/software/matita/contribs/CoRN-Procedural/reals/Series.mma index 3ad3ce01b..80e034a8d 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/Series.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/Series.mma @@ -43,7 +43,9 @@ To each such sequence we can assign a sequence of partial sums. %\end{convention}% *) -alias id "x" = "cic:/CoRN/reals/Series/Definitions/x.var". +(* UNEXPORTED +cic:/CoRN/reals/Series/Definitions/x.var +*) inline procedural "cic:/CoRN/reals/Series/seq_part_sum.con" as definition. @@ -97,7 +99,9 @@ End Definitions Section More_Definitions *) -alias id "x" = "cic:/CoRN/reals/Series/More_Definitions/x.var". +(* UNEXPORTED +cic:/CoRN/reals/Series/More_Definitions/x.var +*) (*#* We also define absolute convergence. *) @@ -127,11 +131,17 @@ we can also compute its sum. %\end{convention}% *) -alias id "c" = "cic:/CoRN/reals/Series/Power_Series/c.var". +(* UNEXPORTED +cic:/CoRN/reals/Series/Power_Series/c.var +*) -alias id "H0c" = "cic:/CoRN/reals/Series/Power_Series/H0c.var". +(* UNEXPORTED +cic:/CoRN/reals/Series/Power_Series/H0c.var +*) -alias id "Hc1" = "cic:/CoRN/reals/Series/Power_Series/Hc1.var". +(* UNEXPORTED +cic:/CoRN/reals/Series/Power_Series/Hc1.var +*) inline procedural "cic:/CoRN/reals/Series/c_exp_Lim.con" as lemma. @@ -166,13 +176,21 @@ of two convergent series. %\end{convention}% *) -alias id "x" = "cic:/CoRN/reals/Series/Operations/x.var". +(* UNEXPORTED +cic:/CoRN/reals/Series/Operations/x.var +*) -alias id "y" = "cic:/CoRN/reals/Series/Operations/y.var". +(* UNEXPORTED +cic:/CoRN/reals/Series/Operations/y.var +*) -alias id "convX" = "cic:/CoRN/reals/Series/Operations/convX.var". +(* UNEXPORTED +cic:/CoRN/reals/Series/Operations/convX.var +*) -alias id "convY" = "cic:/CoRN/reals/Series/Operations/convY.var". +(* UNEXPORTED +cic:/CoRN/reals/Series/Operations/convY.var +*) inline procedural "cic:/CoRN/reals/Series/convergent_wd.con" as lemma. @@ -188,7 +206,9 @@ 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". +(* UNEXPORTED +cic:/CoRN/reals/Series/Operations/c.var +*) inline procedural "cic:/CoRN/reals/Series/conv_series_mult_scal.con" as lemma. @@ -202,9 +222,13 @@ End Operations Section More_Operations *) -alias id "x" = "cic:/CoRN/reals/Series/More_Operations/x.var". +(* UNEXPORTED +cic:/CoRN/reals/Series/More_Operations/x.var +*) -alias id "convX" = "cic:/CoRN/reals/Series/More_Operations/convX.var". +(* UNEXPORTED +cic:/CoRN/reals/Series/More_Operations/convX.var +*) (*#* As a corollary, we get the series of the inverses. *) @@ -228,13 +252,19 @@ and derive an important corollary for series. Let [x,y : nat->IR] be equal after some natural number. *) -alias id "x" = "cic:/CoRN/reals/Series/Almost_Everywhere/x.var". +(* UNEXPORTED +cic:/CoRN/reals/Series/Almost_Everywhere/x.var +*) -alias id "y" = "cic:/CoRN/reals/Series/Almost_Everywhere/y.var". +(* UNEXPORTED +cic:/CoRN/reals/Series/Almost_Everywhere/y.var +*) inline procedural "cic:/CoRN/reals/Series/aew_eq.con" as definition. -alias id "aew_equal" = "cic:/CoRN/reals/Series/Almost_Everywhere/aew_equal.var". +(* UNEXPORTED +cic:/CoRN/reals/Series/Almost_Everywhere/aew_equal.var +*) inline procedural "cic:/CoRN/reals/Series/aew_Cauchy.con" as lemma. @@ -252,11 +282,17 @@ Section Cauchy_Almost_Everywhere (*#* Suppose furthermore that [x,y] are Cauchy sequences. *) -alias id "x" = "cic:/CoRN/reals/Series/Cauchy_Almost_Everywhere/x.var". +(* UNEXPORTED +cic:/CoRN/reals/Series/Cauchy_Almost_Everywhere/x.var +*) -alias id "y" = "cic:/CoRN/reals/Series/Cauchy_Almost_Everywhere/y.var". +(* UNEXPORTED +cic:/CoRN/reals/Series/Cauchy_Almost_Everywhere/y.var +*) -alias id "aew_equal" = "cic:/CoRN/reals/Series/Cauchy_Almost_Everywhere/aew_equal.var". +(* UNEXPORTED +cic:/CoRN/reals/Series/Cauchy_Almost_Everywhere/aew_equal.var +*) inline procedural "cic:/CoRN/reals/Series/aew_Lim.con" as lemma. @@ -274,7 +310,9 @@ Section Convergence_Criteria %\end{convention}% *) -alias id "x" = "cic:/CoRN/reals/Series/Convergence_Criteria/x.var". +(* UNEXPORTED +cic:/CoRN/reals/Series/Convergence_Criteria/x.var +*) (*#* We include the comparison test for series, both in a strong and in a less general (but simpler) form. @@ -304,7 +342,9 @@ End Convergence_Criteria Section More_CC *) -alias id "x" = "cic:/CoRN/reals/Series/More_CC/x.var". +(* UNEXPORTED +cic:/CoRN/reals/Series/More_CC/x.var +*) inline procedural "cic:/CoRN/reals/Series/ratio_test_conv.con" as lemma. @@ -324,13 +364,21 @@ Alternate series are a special case. Suppose that [x] is nonnegative and decreasing convergent to 0. *) -alias id "x" = "cic:/CoRN/reals/Series/Alternate_Series/x.var". +(* UNEXPORTED +cic:/CoRN/reals/Series/Alternate_Series/x.var +*) -alias id "pos_x" = "cic:/CoRN/reals/Series/Alternate_Series/pos_x.var". +(* UNEXPORTED +cic:/CoRN/reals/Series/Alternate_Series/pos_x.var +*) -alias id "Lim_x" = "cic:/CoRN/reals/Series/Alternate_Series/Lim_x.var". +(* UNEXPORTED +cic:/CoRN/reals/Series/Alternate_Series/Lim_x.var +*) -alias id "mon_x" = "cic:/CoRN/reals/Series/Alternate_Series/mon_x.var". +(* UNEXPORTED +cic:/CoRN/reals/Series/Alternate_Series/mon_x.var +*) (* begin hide *) 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 b15f7a930..c9c314c48 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/reals/iso_CReals.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/reals/iso_CReals.mma @@ -59,9 +59,13 @@ inline procedural "cic:/CoRN/reals/iso_CReals/G_pres_mult.con" as lemma. Section Concrete_iso_between_Creals *) -alias id "R1" = "cic:/CoRN/reals/iso_CReals/Concrete_iso_between_Creals/R1.var". +(* UNEXPORTED +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". +(* UNEXPORTED +cic:/CoRN/reals/iso_CReals/Concrete_iso_between_Creals/R2.var +*) inline procedural "cic:/CoRN/reals/iso_CReals/image_Cauchy12.con" as lemma. diff --git a/helm/software/matita/contribs/CoRN-Procedural/tactics/DiffTactics2.mma b/helm/software/matita/contribs/CoRN-Procedural/tactics/DiffTactics2.mma index 30fbf96fc..52af4558b 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/tactics/DiffTactics2.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/tactics/DiffTactics2.mma @@ -26,9 +26,13 @@ include "ftc/Differentiability.ma". Section Automatizing_Continuity *) -alias id "a" = "cic:/CoRN/tactics/DiffTactics2/Automatizing_Continuity/a.var". +(* UNEXPORTED +cic:/CoRN/tactics/DiffTactics2/Automatizing_Continuity/a.var +*) -alias id "b" = "cic:/CoRN/tactics/DiffTactics2/Automatizing_Continuity/b.var". +(* UNEXPORTED +cic:/CoRN/tactics/DiffTactics2/Automatizing_Continuity/b.var +*) inline procedural "cic:/CoRN/tactics/DiffTactics2/cont_function.ind". @@ -96,9 +100,13 @@ Ltac New_Contin := Section Automatizing_Derivatives *) -alias id "a" = "cic:/CoRN/tactics/DiffTactics2/Automatizing_Derivatives/a.var". +(* UNEXPORTED +cic:/CoRN/tactics/DiffTactics2/Automatizing_Derivatives/a.var +*) -alias id "b" = "cic:/CoRN/tactics/DiffTactics2/Automatizing_Derivatives/b.var". +(* UNEXPORTED +cic:/CoRN/tactics/DiffTactics2/Automatizing_Derivatives/b.var +*) inline procedural "cic:/CoRN/tactics/DiffTactics2/deriv_function.ind". diff --git a/helm/software/matita/contribs/CoRN-Procedural/tactics/FieldReflection.mma b/helm/software/matita/contribs/CoRN-Procedural/tactics/FieldReflection.mma index dae6d3625..5d9a91ef1 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/tactics/FieldReflection.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/tactics/FieldReflection.mma @@ -28,15 +28,25 @@ include "tactics/AlgReflection.ma". Section Field_Interpretation_Function *) -alias id "F" = "cic:/CoRN/tactics/FieldReflection/Field_Interpretation_Function/F.var". +(* UNEXPORTED +cic:/CoRN/tactics/FieldReflection/Field_Interpretation_Function/F.var +*) -alias id "val" = "cic:/CoRN/tactics/FieldReflection/Field_Interpretation_Function/val.var". +(* UNEXPORTED +cic:/CoRN/tactics/FieldReflection/Field_Interpretation_Function/val.var +*) -alias id "unop" = "cic:/CoRN/tactics/FieldReflection/Field_Interpretation_Function/unop.var". +(* UNEXPORTED +cic:/CoRN/tactics/FieldReflection/Field_Interpretation_Function/unop.var +*) -alias id "binop" = "cic:/CoRN/tactics/FieldReflection/Field_Interpretation_Function/binop.var". +(* UNEXPORTED +cic:/CoRN/tactics/FieldReflection/Field_Interpretation_Function/binop.var +*) -alias id "pfun" = "cic:/CoRN/tactics/FieldReflection/Field_Interpretation_Function/pfun.var". +(* UNEXPORTED +cic:/CoRN/tactics/FieldReflection/Field_Interpretation_Function/pfun.var +*) inline procedural "cic:/CoRN/tactics/FieldReflection/interpF.ind". @@ -84,15 +94,25 @@ End Field_Interpretation_Function Section Field_NormCorrect *) -alias id "F" = "cic:/CoRN/tactics/FieldReflection/Field_NormCorrect/F.var". +(* UNEXPORTED +cic:/CoRN/tactics/FieldReflection/Field_NormCorrect/F.var +*) -alias id "val" = "cic:/CoRN/tactics/FieldReflection/Field_NormCorrect/val.var". +(* UNEXPORTED +cic:/CoRN/tactics/FieldReflection/Field_NormCorrect/val.var +*) -alias id "unop" = "cic:/CoRN/tactics/FieldReflection/Field_NormCorrect/unop.var". +(* UNEXPORTED +cic:/CoRN/tactics/FieldReflection/Field_NormCorrect/unop.var +*) -alias id "binop" = "cic:/CoRN/tactics/FieldReflection/Field_NormCorrect/binop.var". +(* UNEXPORTED +cic:/CoRN/tactics/FieldReflection/Field_NormCorrect/binop.var +*) -alias id "pfun" = "cic:/CoRN/tactics/FieldReflection/Field_NormCorrect/pfun.var". +(* UNEXPORTED +cic:/CoRN/tactics/FieldReflection/Field_NormCorrect/pfun.var +*) (* NOTATION Notation II := (interpF F val unop binop pfun). diff --git a/helm/software/matita/contribs/CoRN-Procedural/tactics/GroupReflection.mma b/helm/software/matita/contribs/CoRN-Procedural/tactics/GroupReflection.mma index bbac139d1..0e4cd088a 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/tactics/GroupReflection.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/tactics/GroupReflection.mma @@ -28,15 +28,25 @@ include "tactics/AlgReflection.ma". Section Group_Interpretation_Function *) -alias id "G" = "cic:/CoRN/tactics/GroupReflection/Group_Interpretation_Function/G.var". +(* UNEXPORTED +cic:/CoRN/tactics/GroupReflection/Group_Interpretation_Function/G.var +*) -alias id "val" = "cic:/CoRN/tactics/GroupReflection/Group_Interpretation_Function/val.var". +(* UNEXPORTED +cic:/CoRN/tactics/GroupReflection/Group_Interpretation_Function/val.var +*) -alias id "unop" = "cic:/CoRN/tactics/GroupReflection/Group_Interpretation_Function/unop.var". +(* UNEXPORTED +cic:/CoRN/tactics/GroupReflection/Group_Interpretation_Function/unop.var +*) -alias id "binop" = "cic:/CoRN/tactics/GroupReflection/Group_Interpretation_Function/binop.var". +(* UNEXPORTED +cic:/CoRN/tactics/GroupReflection/Group_Interpretation_Function/binop.var +*) -alias id "pfun" = "cic:/CoRN/tactics/GroupReflection/Group_Interpretation_Function/pfun.var". +(* UNEXPORTED +cic:/CoRN/tactics/GroupReflection/Group_Interpretation_Function/pfun.var +*) inline procedural "cic:/CoRN/tactics/GroupReflection/interpG.ind". @@ -134,15 +144,25 @@ End Group_Interpretation_Function Section Group_NormCorrect *) -alias id "G" = "cic:/CoRN/tactics/GroupReflection/Group_NormCorrect/G.var". +(* UNEXPORTED +cic:/CoRN/tactics/GroupReflection/Group_NormCorrect/G.var +*) -alias id "val" = "cic:/CoRN/tactics/GroupReflection/Group_NormCorrect/val.var". +(* UNEXPORTED +cic:/CoRN/tactics/GroupReflection/Group_NormCorrect/val.var +*) -alias id "unop" = "cic:/CoRN/tactics/GroupReflection/Group_NormCorrect/unop.var". +(* UNEXPORTED +cic:/CoRN/tactics/GroupReflection/Group_NormCorrect/unop.var +*) -alias id "binop" = "cic:/CoRN/tactics/GroupReflection/Group_NormCorrect/binop.var". +(* UNEXPORTED +cic:/CoRN/tactics/GroupReflection/Group_NormCorrect/binop.var +*) -alias id "pfun" = "cic:/CoRN/tactics/GroupReflection/Group_NormCorrect/pfun.var". +(* UNEXPORTED +cic:/CoRN/tactics/GroupReflection/Group_NormCorrect/pfun.var +*) (* NOTATION Notation II := (interpG G val unop binop pfun). diff --git a/helm/software/matita/contribs/CoRN-Procedural/tactics/RingReflection.mma b/helm/software/matita/contribs/CoRN-Procedural/tactics/RingReflection.mma index 4a348ceae..d51f16887 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/tactics/RingReflection.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/tactics/RingReflection.mma @@ -28,15 +28,25 @@ include "tactics/AlgReflection.ma". Section Ring_Interpretation_Function *) -alias id "R" = "cic:/CoRN/tactics/RingReflection/Ring_Interpretation_Function/R.var". +(* UNEXPORTED +cic:/CoRN/tactics/RingReflection/Ring_Interpretation_Function/R.var +*) -alias id "val" = "cic:/CoRN/tactics/RingReflection/Ring_Interpretation_Function/val.var". +(* UNEXPORTED +cic:/CoRN/tactics/RingReflection/Ring_Interpretation_Function/val.var +*) -alias id "unop" = "cic:/CoRN/tactics/RingReflection/Ring_Interpretation_Function/unop.var". +(* UNEXPORTED +cic:/CoRN/tactics/RingReflection/Ring_Interpretation_Function/unop.var +*) -alias id "binop" = "cic:/CoRN/tactics/RingReflection/Ring_Interpretation_Function/binop.var". +(* UNEXPORTED +cic:/CoRN/tactics/RingReflection/Ring_Interpretation_Function/binop.var +*) -alias id "pfun" = "cic:/CoRN/tactics/RingReflection/Ring_Interpretation_Function/pfun.var". +(* UNEXPORTED +cic:/CoRN/tactics/RingReflection/Ring_Interpretation_Function/pfun.var +*) inline procedural "cic:/CoRN/tactics/RingReflection/interpR.ind". @@ -150,15 +160,25 @@ End Ring_Interpretation_Function Section Ring_NormCorrect *) -alias id "R" = "cic:/CoRN/tactics/RingReflection/Ring_NormCorrect/R.var". +(* UNEXPORTED +cic:/CoRN/tactics/RingReflection/Ring_NormCorrect/R.var +*) -alias id "val" = "cic:/CoRN/tactics/RingReflection/Ring_NormCorrect/val.var". +(* UNEXPORTED +cic:/CoRN/tactics/RingReflection/Ring_NormCorrect/val.var +*) -alias id "unop" = "cic:/CoRN/tactics/RingReflection/Ring_NormCorrect/unop.var". +(* UNEXPORTED +cic:/CoRN/tactics/RingReflection/Ring_NormCorrect/unop.var +*) -alias id "binop" = "cic:/CoRN/tactics/RingReflection/Ring_NormCorrect/binop.var". +(* UNEXPORTED +cic:/CoRN/tactics/RingReflection/Ring_NormCorrect/binop.var +*) -alias id "pfun" = "cic:/CoRN/tactics/RingReflection/Ring_NormCorrect/pfun.var". +(* UNEXPORTED +cic:/CoRN/tactics/RingReflection/Ring_NormCorrect/pfun.var +*) (* NOTATION Notation II := (interpR R val unop binop pfun). diff --git a/helm/software/matita/contribs/CoRN-Procedural/transc/InvTrigonom.mma b/helm/software/matita/contribs/CoRN-Procedural/transc/InvTrigonom.mma index b09f9b579..9f138ab7d 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/transc/InvTrigonom.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/transc/InvTrigonom.mma @@ -204,7 +204,9 @@ Transparent Cos. Section ArcTan_Range *) -alias id "x" = "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/x.var". +(* UNEXPORTED +cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/x.var +*) (* begin hide *) diff --git a/helm/software/matita/contribs/CoRN-Procedural/transc/PowerSeries.mma b/helm/software/matita/contribs/CoRN-Procedural/transc/PowerSeries.mma index 6a5b62b88..b91f4a5f3 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/transc/PowerSeries.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/transc/PowerSeries.mma @@ -48,13 +48,21 @@ Let [a : nat -> IR]. %\end{convention}% *) -alias id "J" = "cic:/CoRN/transc/PowerSeries/Power_Series/J.var". +(* UNEXPORTED +cic:/CoRN/transc/PowerSeries/Power_Series/J.var +*) -alias id "x0" = "cic:/CoRN/transc/PowerSeries/Power_Series/x0.var". +(* UNEXPORTED +cic:/CoRN/transc/PowerSeries/Power_Series/x0.var +*) -alias id "Hx0" = "cic:/CoRN/transc/PowerSeries/Power_Series/Hx0.var". +(* UNEXPORTED +cic:/CoRN/transc/PowerSeries/Power_Series/Hx0.var +*) -alias id "a" = "cic:/CoRN/transc/PowerSeries/Power_Series/a.var". +(* UNEXPORTED +cic:/CoRN/transc/PowerSeries/Power_Series/a.var +*) inline procedural "cic:/CoRN/transc/PowerSeries/FPowerSeries.con" as definition. @@ -65,7 +73,9 @@ is the Dirichlet criterium. (* begin show *) -alias id "Ha" = "cic:/CoRN/transc/PowerSeries/Power_Series/Ha.var". +(* UNEXPORTED +cic:/CoRN/transc/PowerSeries/Power_Series/Ha.var +*) inline procedural "cic:/CoRN/transc/PowerSeries/Power_Series/r.con" "Power_Series__" as definition. @@ -91,7 +101,9 @@ inline procedural "cic:/CoRN/transc/PowerSeries/included_FPowerSeries'.con" as l (* begin show *) -alias id "Ha'" = "cic:/CoRN/transc/PowerSeries/Power_Series/Ha'.var". +(* UNEXPORTED +cic:/CoRN/transc/PowerSeries/Power_Series/Ha'.var +*) (* end show *) @@ -117,9 +129,13 @@ respectively by [a] and by [fun n => (a (S n))]. %\end{convention}% *) -alias id "x0" = "cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/x0.var". +(* UNEXPORTED +cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/x0.var +*) -alias id "a" = "cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/a.var". +(* UNEXPORTED +cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/a.var +*) (* begin hide *) @@ -131,11 +147,17 @@ inline procedural "cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/G.con" "More (* begin show *) -alias id "Hf" = "cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/Hf.var". +(* UNEXPORTED +cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/Hf.var +*) -alias id "Hf'" = "cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/Hf'.var". +(* UNEXPORTED +cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/Hf'.var +*) -alias id "Hg" = "cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/Hg.var". +(* UNEXPORTED +cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/Hg.var +*) (* end show *) diff --git a/helm/software/matita/contribs/CoRN-Procedural/transc/RealPowers.mma b/helm/software/matita/contribs/CoRN-Procedural/transc/RealPowers.mma index 3f16bd0d3..dc2701e1f 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/transc/RealPowers.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/transc/RealPowers.mma @@ -139,11 +139,17 @@ on partial functions which preserves continuity. %\end{convention}% *) -alias id "J" = "cic:/CoRN/transc/RealPowers/Power_Function/J.var". +(* UNEXPORTED +cic:/CoRN/transc/RealPowers/Power_Function/J.var +*) -alias id "F" = "cic:/CoRN/transc/RealPowers/Power_Function/F.var". +(* UNEXPORTED +cic:/CoRN/transc/RealPowers/Power_Function/F.var +*) -alias id "G" = "cic:/CoRN/transc/RealPowers/Power_Function/G.var". +(* UNEXPORTED +cic:/CoRN/transc/RealPowers/Power_Function/G.var +*) inline procedural "cic:/CoRN/transc/RealPowers/FPower.con" as definition. diff --git a/helm/software/matita/contribs/CoRN-Procedural/transc/TaylorSeries.mma b/helm/software/matita/contribs/CoRN-Procedural/transc/TaylorSeries.mma index 38f2d2aee..2a5f1e016 100644 --- a/helm/software/matita/contribs/CoRN-Procedural/transc/TaylorSeries.mma +++ b/helm/software/matita/contribs/CoRN-Procedural/transc/TaylorSeries.mma @@ -41,17 +41,29 @@ point of [J]. Section Definitions *) -alias id "J" = "cic:/CoRN/transc/TaylorSeries/Definitions/J.var". +(* UNEXPORTED +cic:/CoRN/transc/TaylorSeries/Definitions/J.var +*) -alias id "pJ" = "cic:/CoRN/transc/TaylorSeries/Definitions/pJ.var". +(* UNEXPORTED +cic:/CoRN/transc/TaylorSeries/Definitions/pJ.var +*) -alias id "F" = "cic:/CoRN/transc/TaylorSeries/Definitions/F.var". +(* UNEXPORTED +cic:/CoRN/transc/TaylorSeries/Definitions/F.var +*) -alias id "diffF" = "cic:/CoRN/transc/TaylorSeries/Definitions/diffF.var". +(* UNEXPORTED +cic:/CoRN/transc/TaylorSeries/Definitions/diffF.var +*) -alias id "a" = "cic:/CoRN/transc/TaylorSeries/Definitions/a.var". +(* UNEXPORTED +cic:/CoRN/transc/TaylorSeries/Definitions/a.var +*) -alias id "Ha" = "cic:/CoRN/transc/TaylorSeries/Definitions/Ha.var". +(* UNEXPORTED +cic:/CoRN/transc/TaylorSeries/Definitions/Ha.var +*) inline procedural "cic:/CoRN/transc/TaylorSeries/Taylor_Series'.con" as definition. @@ -61,9 +73,13 @@ derivatives of [F]. %\end{convention}% *) -alias id "f" = "cic:/CoRN/transc/TaylorSeries/Definitions/f.var". +(* UNEXPORTED +cic:/CoRN/transc/TaylorSeries/Definitions/f.var +*) -alias id "derF" = "cic:/CoRN/transc/TaylorSeries/Definitions/derF.var". +(* UNEXPORTED +cic:/CoRN/transc/TaylorSeries/Definitions/derF.var +*) inline procedural "cic:/CoRN/transc/TaylorSeries/Taylor_Series.con" as definition. @@ -93,17 +109,29 @@ derivatives of [F] that guarantees convergence of its Taylor series to [F]. *) -alias id "H" = "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/H.var". +(* UNEXPORTED +cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/H.var +*) -alias id "F" = "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/F.var". +(* UNEXPORTED +cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/F.var +*) -alias id "a" = "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/a.var". +(* UNEXPORTED +cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/a.var +*) -alias id "Ha" = "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/Ha.var". +(* UNEXPORTED +cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/Ha.var +*) -alias id "f" = "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/f.var". +(* UNEXPORTED +cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/f.var +*) -alias id "derF" = "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/derF.var". +(* UNEXPORTED +cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/derF.var +*) inline procedural "cic:/CoRN/transc/TaylorSeries/Taylor_Series_imp_cont.con" as lemma. @@ -113,7 +141,9 @@ inline procedural "cic:/CoRN/transc/TaylorSeries/Taylor_bnd.con" as definition. (* begin show *) -alias id "bndf" = "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/bndf.var". +(* UNEXPORTED +cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/bndf.var +*) (* end show *) @@ -171,7 +201,9 @@ will separately assume convergence. (* begin show *) -alias id "Hf" = "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/Hf.var". +(* UNEXPORTED +cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/Hf.var +*) (* end show *) @@ -218,27 +250,47 @@ provided that their derivatives coincide at a given point and their Taylor series converge to themselves. *) -alias id "F" = "cic:/CoRN/transc/TaylorSeries/Other_Results/F.var". +(* UNEXPORTED +cic:/CoRN/transc/TaylorSeries/Other_Results/F.var +*) -alias id "G" = "cic:/CoRN/transc/TaylorSeries/Other_Results/G.var". +(* UNEXPORTED +cic:/CoRN/transc/TaylorSeries/Other_Results/G.var +*) -alias id "a" = "cic:/CoRN/transc/TaylorSeries/Other_Results/a.var". +(* UNEXPORTED +cic:/CoRN/transc/TaylorSeries/Other_Results/a.var +*) -alias id "f" = "cic:/CoRN/transc/TaylorSeries/Other_Results/f.var". +(* UNEXPORTED +cic:/CoRN/transc/TaylorSeries/Other_Results/f.var +*) -alias id "g" = "cic:/CoRN/transc/TaylorSeries/Other_Results/g.var". +(* UNEXPORTED +cic:/CoRN/transc/TaylorSeries/Other_Results/g.var +*) -alias id "derF" = "cic:/CoRN/transc/TaylorSeries/Other_Results/derF.var". +(* UNEXPORTED +cic:/CoRN/transc/TaylorSeries/Other_Results/derF.var +*) -alias id "derG" = "cic:/CoRN/transc/TaylorSeries/Other_Results/derG.var". +(* UNEXPORTED +cic:/CoRN/transc/TaylorSeries/Other_Results/derG.var +*) -alias id "bndf" = "cic:/CoRN/transc/TaylorSeries/Other_Results/bndf.var". +(* UNEXPORTED +cic:/CoRN/transc/TaylorSeries/Other_Results/bndf.var +*) -alias id "bndg" = "cic:/CoRN/transc/TaylorSeries/Other_Results/bndg.var". +(* UNEXPORTED +cic:/CoRN/transc/TaylorSeries/Other_Results/bndg.var +*) (* begin show *) -alias id "Heq" = "cic:/CoRN/transc/TaylorSeries/Other_Results/Heq.var". +(* UNEXPORTED +cic:/CoRN/transc/TaylorSeries/Other_Results/Heq.var +*) (* end show *) -- 2.39.2