From: Ferruccio Guidi Date: Wed, 29 Nov 2006 17:29:53 +0000 (+0000) Subject: - new library/logic/coimplication.ma uses new decompose tactic X-Git-Tag: make_still_working~6623 X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=5e01cba364607e7937aec2e359c34f049bb0f108;p=helm.git - new library/logic/coimplication.ma uses new decompose tactic - matitaScript.ml: new parameter of inline tactic now ignored - CoRN-Decl: regenerated with local objects handled correctly --- diff --git a/helm/software/matita/contribs/CoRN-Decl/algebra/Basics.ma b/helm/software/matita/contribs/CoRN-Decl/algebra/Basics.ma index 5d9ba4c2e..865a3061d 100644 --- a/helm/software/matita/contribs/CoRN-Decl/algebra/Basics.ma +++ b/helm/software/matita/contribs/CoRN-Decl/algebra/Basics.ma @@ -221,31 +221,31 @@ inline "cic:/CoRN/algebra/Basics/Zgt_not_eq.con". inline "cic:/CoRN/algebra/Basics/Zmult_absorb.con". (* UNEXPORTED -Section Well_foundedT. +Section Well_foundedT *) -inline "cic:/CoRN/algebra/Basics/A.var". +inline "cic:/CoRN/algebra/Basics/Well_foundedT/A.var" "Well_foundedT__". -inline "cic:/CoRN/algebra/Basics/R.var". +inline "cic:/CoRN/algebra/Basics/Well_foundedT/R.var" "Well_foundedT__". (*#* The accessibility predicate is defined to be non-informative *) inline "cic:/CoRN/algebra/Basics/Acc.ind". (* UNEXPORTED -End Well_foundedT. +End Well_foundedT *) (* UNEXPORTED -Section AccT. +Section AccT *) -inline "cic:/CoRN/algebra/Basics/A.var". +inline "cic:/CoRN/algebra/Basics/AccT/A.var" "AccT__". inline "cic:/CoRN/algebra/Basics/well_founded.con". (* UNEXPORTED -End AccT. +End AccT *) (* UNEXPORTED @@ -253,44 +253,44 @@ Implicit Arguments Acc [A]. *) (* UNEXPORTED -Section IndT. +Section IndT *) -inline "cic:/CoRN/algebra/Basics/A.var". +inline "cic:/CoRN/algebra/Basics/IndT/A.var" "IndT__". -inline "cic:/CoRN/algebra/Basics/R.var". +inline "cic:/CoRN/algebra/Basics/IndT/R.var" "IndT__". (* UNEXPORTED -Section AccIter. +Section AccIter *) -inline "cic:/CoRN/algebra/Basics/P.var". +inline "cic:/CoRN/algebra/Basics/IndT/AccIter/P.var" "IndT__AccIter__". -inline "cic:/CoRN/algebra/Basics/F.var". +inline "cic:/CoRN/algebra/Basics/IndT/AccIter/F.var" "IndT__AccIter__". inline "cic:/CoRN/algebra/Basics/Acc_inv.con". inline "cic:/CoRN/algebra/Basics/Acc_iter.con". (* UNEXPORTED -End AccIter. +End AccIter *) -inline "cic:/CoRN/algebra/Basics/Rwf.var". +inline "cic:/CoRN/algebra/Basics/IndT/Rwf.var" "IndT__". inline "cic:/CoRN/algebra/Basics/well_founded_induction_type.con". (* UNEXPORTED -End IndT. +End IndT *) (* UNEXPORTED -Section InductionT. +Section InductionT *) -inline "cic:/CoRN/algebra/Basics/A.var". +inline "cic:/CoRN/algebra/Basics/InductionT/A.var" "InductionT__". -inline "cic:/CoRN/algebra/Basics/f.var". +inline "cic:/CoRN/algebra/Basics/InductionT/f.var" "InductionT__". inline "cic:/CoRN/algebra/Basics/ltof.con". @@ -299,16 +299,16 @@ inline "cic:/CoRN/algebra/Basics/well_founded_ltof.con". inline "cic:/CoRN/algebra/Basics/induction_ltof2T.con". (* UNEXPORTED -End InductionT. +End InductionT *) (* UNEXPORTED -Section InductionTT. +Section InductionTT *) inline "cic:/CoRN/algebra/Basics/lt_wf_rect.con". (* UNEXPORTED -End InductionTT. +End InductionTT *) diff --git a/helm/software/matita/contribs/CoRN-Decl/algebra/CAbGroups.ma b/helm/software/matita/contribs/CoRN-Decl/algebra/CAbGroups.ma index c603a3517..23bebc427 100644 --- a/helm/software/matita/contribs/CoRN-Decl/algebra/CAbGroups.ma +++ b/helm/software/matita/contribs/CoRN-Decl/algebra/CAbGroups.ma @@ -21,7 +21,7 @@ include "CoRN.ma". include "algebra/CGroups.ma". (* UNEXPORTED -Section Abelian_Groups. +Section Abelian_Groups *) (*#* @@ -36,10 +36,10 @@ inline "cic:/CoRN/algebra/CAbGroups/CAbGroup.ind". coercion cic:/matita/CoRN-Decl/algebra/CAbGroups/cag_crr.con 0 (* compounds *). (* UNEXPORTED -Section AbGroup_Axioms. +Section AbGroup_Axioms *) -inline "cic:/CoRN/algebra/CAbGroups/G.var". +inline "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/AbGroup_Axioms/G.var" "Abelian_Groups__AbGroup_Axioms__". (*#* %\begin{convention}% Let [G] be an Abelian Group. @@ -53,26 +53,26 @@ inline "cic:/CoRN/algebra/CAbGroups/cag_commutes.con". inline "cic:/CoRN/algebra/CAbGroups/cag_commutes_unfolded.con". (* UNEXPORTED -End AbGroup_Axioms. +End AbGroup_Axioms *) (* UNEXPORTED -Section SubCAbGroups. +Section SubCAbGroups *) (*#* ** Subgroups of an Abelian Group *) -inline "cic:/CoRN/algebra/CAbGroups/G.var". +inline "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/G.var" "Abelian_Groups__SubCAbGroups__". -inline "cic:/CoRN/algebra/CAbGroups/P.var". +inline "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/P.var" "Abelian_Groups__SubCAbGroups__". -inline "cic:/CoRN/algebra/CAbGroups/Punit.var". +inline "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/Punit.var" "Abelian_Groups__SubCAbGroups__". -inline "cic:/CoRN/algebra/CAbGroups/op_pres_P.var". +inline "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/op_pres_P.var" "Abelian_Groups__SubCAbGroups__". -inline "cic:/CoRN/algebra/CAbGroups/inv_pres_P.var". +inline "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/inv_pres_P.var" "Abelian_Groups__SubCAbGroups__". (*#* %\begin{convention}% @@ -81,18 +81,18 @@ that contains [Zero] and is closed under [[+]] and [[--]]. %\end{convention}% *) -inline "cic:/CoRN/algebra/CAbGroups/subcrr.con". +inline "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/subcrr.con" "Abelian_Groups__SubCAbGroups__". inline "cic:/CoRN/algebra/CAbGroups/isabgrp_scrr.con". inline "cic:/CoRN/algebra/CAbGroups/Build_SubCAbGroup.con". (* UNEXPORTED -End SubCAbGroups. +End SubCAbGroups *) (* UNEXPORTED -Section Various. +Section Various *) (*#* @@ -103,7 +103,7 @@ Section Various. Hint Resolve cag_commutes_unfolded: algebra. *) -inline "cic:/CoRN/algebra/CAbGroups/G.var". +inline "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/Various/G.var" "Abelian_Groups__Various__". (*#* %\begin{convention}% Let [G] be an Abelian Group. @@ -127,11 +127,11 @@ inline "cic:/CoRN/algebra/CAbGroups/cag_ap_cancel_lft.con". inline "cic:/CoRN/algebra/CAbGroups/plus_cancel_ap_lft.con". (* UNEXPORTED -End Various. +End Various *) (* UNEXPORTED -End Abelian_Groups. +End Abelian_Groups *) (* UNEXPORTED @@ -143,7 +143,7 @@ Hint Resolve cag_op_inv assoc_1 zero_minus minus_plus op_lft_resp_ap: algebra. *) (* UNEXPORTED -Section Nice_Char. +Section Nice_Char *) (*#* @@ -163,11 +163,11 @@ as a left unit, and a unary setoid function [inv] which inverts elements respective to [plus]. *) -inline "cic:/CoRN/algebra/CAbGroups/S.var". +inline "cic:/CoRN/algebra/CAbGroups/Nice_Char/S.var" "Nice_Char__". -inline "cic:/CoRN/algebra/CAbGroups/unit.var". +inline "cic:/CoRN/algebra/CAbGroups/Nice_Char/unit.var" "Nice_Char__". -inline "cic:/CoRN/algebra/CAbGroups/plus.var". +inline "cic:/CoRN/algebra/CAbGroups/Nice_Char/plus.var" "Nice_Char__". (*#* %\begin{convention}% @@ -179,17 +179,17 @@ for [plus] and [(inv x)] is a right-inverse of [x] w.r.t.%\% [plus]. %\end{convention}% *) -inline "cic:/CoRN/algebra/CAbGroups/plus_lext.var". +inline "cic:/CoRN/algebra/CAbGroups/Nice_Char/plus_lext.var" "Nice_Char__". -inline "cic:/CoRN/algebra/CAbGroups/plus_lunit.var". +inline "cic:/CoRN/algebra/CAbGroups/Nice_Char/plus_lunit.var" "Nice_Char__". -inline "cic:/CoRN/algebra/CAbGroups/plus_comm.var". +inline "cic:/CoRN/algebra/CAbGroups/Nice_Char/plus_comm.var" "Nice_Char__". -inline "cic:/CoRN/algebra/CAbGroups/plus_assoc.var". +inline "cic:/CoRN/algebra/CAbGroups/Nice_Char/plus_assoc.var" "Nice_Char__". -inline "cic:/CoRN/algebra/CAbGroups/inv.var". +inline "cic:/CoRN/algebra/CAbGroups/Nice_Char/inv.var" "Nice_Char__". -inline "cic:/CoRN/algebra/CAbGroups/inv_inv.var". +inline "cic:/CoRN/algebra/CAbGroups/Nice_Char/inv_inv.var" "Nice_Char__". inline "cic:/CoRN/algebra/CAbGroups/plus_rext.con". @@ -210,7 +210,7 @@ inline "cic:/CoRN/algebra/CAbGroups/Build_CGroup'.con". inline "cic:/CoRN/algebra/CAbGroups/Build_CAbGroup'.con". (* UNEXPORTED -End Nice_Char. +End Nice_Char *) (*#* ** Iteration @@ -219,10 +219,10 @@ For reflection the following is needed; hopefully it is also useful. *) (* UNEXPORTED -Section Group_Extras. +Section Group_Extras *) -inline "cic:/CoRN/algebra/CAbGroups/G.var". +inline "cic:/CoRN/algebra/CAbGroups/Group_Extras/G.var" "Group_Extras__". inline "cic:/CoRN/algebra/CAbGroups/nmult.con". @@ -285,7 +285,7 @@ inline "cic:/CoRN/algebra/CAbGroups/zmult_mult.con". inline "cic:/CoRN/algebra/CAbGroups/zmult_plus'.con". (* UNEXPORTED -End Group_Extras. +End Group_Extras *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/algebra/CAbMonoids.ma b/helm/software/matita/contribs/CoRN-Decl/algebra/CAbMonoids.ma index de11ce21a..7f31fc103 100644 --- a/helm/software/matita/contribs/CoRN-Decl/algebra/CAbMonoids.ma +++ b/helm/software/matita/contribs/CoRN-Decl/algebra/CAbMonoids.ma @@ -21,7 +21,7 @@ include "CoRN.ma". include "algebra/CMonoids.ma". (* UNEXPORTED -Section Abelian_Monoids. +Section Abelian_Monoids *) (*#* @@ -36,10 +36,10 @@ inline "cic:/CoRN/algebra/CAbMonoids/CAbMonoid.ind". coercion cic:/matita/CoRN-Decl/algebra/CAbMonoids/cam_crr.con 0 (* compounds *). (* UNEXPORTED -Section AbMonoid_Axioms. +Section AbMonoid_Axioms *) -inline "cic:/CoRN/algebra/CAbMonoids/M.var". +inline "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/AbMonoid_Axioms/M.var" "Abelian_Monoids__AbMonoid_Axioms__". (*#* %\begin{convention}% Let [M] be an abelian monoid. @@ -53,24 +53,24 @@ inline "cic:/CoRN/algebra/CAbMonoids/cam_commutes.con". inline "cic:/CoRN/algebra/CAbMonoids/cam_commutes_unfolded.con". (* UNEXPORTED -End AbMonoid_Axioms. +End AbMonoid_Axioms *) (* UNEXPORTED -Section SubCAbMonoids. +Section SubCAbMonoids *) (*#* ** Subgroups of an Abelian Monoid *) -inline "cic:/CoRN/algebra/CAbMonoids/M.var". +inline "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/M.var" "Abelian_Monoids__SubCAbMonoids__". -inline "cic:/CoRN/algebra/CAbMonoids/P.var". +inline "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/P.var" "Abelian_Monoids__SubCAbMonoids__". -inline "cic:/CoRN/algebra/CAbMonoids/Punit.var". +inline "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/Punit.var" "Abelian_Monoids__SubCAbMonoids__". -inline "cic:/CoRN/algebra/CAbMonoids/op_pres_P.var". +inline "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/op_pres_P.var" "Abelian_Monoids__SubCAbMonoids__". (*#* %\begin{convention}% @@ -79,18 +79,18 @@ that contains [Zero] and is closed under [[+]] and [[--]]. %\end{convention}% *) -inline "cic:/CoRN/algebra/CAbMonoids/subcrr.con". +inline "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/subcrr.con" "Abelian_Monoids__SubCAbMonoids__". inline "cic:/CoRN/algebra/CAbMonoids/isabgrp_scrr.con". inline "cic:/CoRN/algebra/CAbMonoids/Build_SubCAbMonoid.con". (* UNEXPORTED -End SubCAbMonoids. +End SubCAbMonoids *) (* UNEXPORTED -End Abelian_Monoids. +End Abelian_Monoids *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/algebra/CFields.ma b/helm/software/matita/contribs/CoRN-Decl/algebra/CFields.ma index 9b216e081..2daac721e 100644 --- a/helm/software/matita/contribs/CoRN-Decl/algebra/CFields.ma +++ b/helm/software/matita/contribs/CoRN-Decl/algebra/CFields.ma @@ -185,21 +185,21 @@ write [e[/] (Snring n)] and [e[/]TwoNZ], [e[/]ThreeNZ] and so on. *) (* UNEXPORTED -Section Field_axioms. +Section Field_axioms *) -inline "cic:/CoRN/algebra/CFields/F.var". +inline "cic:/CoRN/algebra/CFields/Field_axioms/F.var" "Field_axioms__". inline "cic:/CoRN/algebra/CFields/CField_is_CField.con". inline "cic:/CoRN/algebra/CFields/rcpcl_is_inverse.con". (* UNEXPORTED -End Field_axioms. +End Field_axioms *) (* UNEXPORTED -Section Field_basics. +Section Field_basics *) (*#* ** Field basics @@ -207,7 +207,7 @@ Section Field_basics. %\end{convention}% *) -inline "cic:/CoRN/algebra/CFields/F.var". +inline "cic:/CoRN/algebra/CFields/Field_basics/F.var" "Field_basics__". inline "cic:/CoRN/algebra/CFields/rcpcl_is_inverse_unfolded.con". @@ -220,7 +220,7 @@ Hint Resolve field_mult_inv: algebra. inline "cic:/CoRN/algebra/CFields/field_mult_inv_op.con". (* UNEXPORTED -End Field_basics. +End Field_basics *) (* UNEXPORTED @@ -228,7 +228,7 @@ Hint Resolve field_mult_inv field_mult_inv_op: algebra. *) (* UNEXPORTED -Section Field_multiplication. +Section Field_multiplication *) (*#* @@ -237,7 +237,7 @@ Section Field_multiplication. %\end{convention}% *) -inline "cic:/CoRN/algebra/CFields/F.var". +inline "cic:/CoRN/algebra/CFields/Field_multiplication/F.var" "Field_multiplication__". inline "cic:/CoRN/algebra/CFields/mult_resp_ap_zero.con". @@ -262,11 +262,11 @@ inline "cic:/CoRN/algebra/CFields/square_eq_weak.con". inline "cic:/CoRN/algebra/CFields/cond_square_eq.con". (* UNEXPORTED -End Field_multiplication. +End Field_multiplication *) (* UNEXPORTED -Section x_square. +Section x_square *) inline "cic:/CoRN/algebra/CFields/x_xminone.con". @@ -274,7 +274,7 @@ inline "cic:/CoRN/algebra/CFields/x_xminone.con". inline "cic:/CoRN/algebra/CFields/square_id.con". (* UNEXPORTED -End x_square. +End x_square *) (* UNEXPORTED @@ -282,7 +282,7 @@ Hint Resolve mult_resp_ap_zero: algebra. *) (* UNEXPORTED -Section Rcpcl_properties. +Section Rcpcl_properties *) (*#* @@ -291,7 +291,7 @@ Section Rcpcl_properties. %\end{convention}% *) -inline "cic:/CoRN/algebra/CFields/F.var". +inline "cic:/CoRN/algebra/CFields/Rcpcl_properties/F.var" "Rcpcl_properties__". inline "cic:/CoRN/algebra/CFields/inv_one.con". @@ -304,11 +304,11 @@ inline "cic:/CoRN/algebra/CFields/f_rcpcl_resp_ap_zero.con". inline "cic:/CoRN/algebra/CFields/f_rcpcl_f_rcpcl.con". (* UNEXPORTED -End Rcpcl_properties. +End Rcpcl_properties *) (* UNEXPORTED -Section MultipGroup. +Section MultipGroup *) (*#* @@ -317,7 +317,7 @@ Section MultipGroup. %\end{convention}% *) -inline "cic:/CoRN/algebra/CFields/F.var". +inline "cic:/CoRN/algebra/CFields/MultipGroup/F.var" "MultipGroup__". (*#* The multiplicative monoid of NonZeros. @@ -332,11 +332,11 @@ inline "cic:/CoRN/algebra/CFields/plus_nonzeros_eq_mult_dom.con". inline "cic:/CoRN/algebra/CFields/cfield_to_mult_cgroup.con". (* UNEXPORTED -End MultipGroup. +End MultipGroup *) (* UNEXPORTED -Section Div_properties. +Section Div_properties *) (*#* @@ -350,7 +350,7 @@ In the names of lemmas, we denote [[/]] by [div], and %\end{nameconvention}% *) -inline "cic:/CoRN/algebra/CFields/F.var". +inline "cic:/CoRN/algebra/CFields/Div_properties/F.var" "Div_properties__". inline "cic:/CoRN/algebra/CFields/div_prop.con". @@ -429,7 +429,7 @@ inline "cic:/CoRN/algebra/CFields/eq_div.con". inline "cic:/CoRN/algebra/CFields/div_strext.con". (* UNEXPORTED -End Div_properties. +End Div_properties *) (* UNEXPORTED @@ -445,10 +445,10 @@ Hint Resolve div_1 div_1' div_1'' div_wd x_div_x x_div_one div_div div_div2 *) (* UNEXPORTED -Section Mult_Cancel_Ap_Zero. +Section Mult_Cancel_Ap_Zero *) -inline "cic:/CoRN/algebra/CFields/F.var". +inline "cic:/CoRN/algebra/CFields/Mult_Cancel_Ap_Zero/F.var" "Mult_Cancel_Ap_Zero__". inline "cic:/CoRN/algebra/CFields/mult_cancel_ap_zero_lft.con". @@ -459,11 +459,11 @@ inline "cic:/CoRN/algebra/CFields/recip_ap_zero.con". inline "cic:/CoRN/algebra/CFields/recip_resp_ap.con". (* UNEXPORTED -End Mult_Cancel_Ap_Zero. +End Mult_Cancel_Ap_Zero *) (* UNEXPORTED -Section CField_Ops. +Section CField_Ops *) (*#* @@ -480,31 +480,31 @@ Let [X] be a Field and [F,G:(PartFunct X)] have domains respectively %\end{convention}% *) -inline "cic:/CoRN/algebra/CFields/X.var". +inline "cic:/CoRN/algebra/CFields/CField_Ops/X.var" "CField_Ops__". -inline "cic:/CoRN/algebra/CFields/F.var". +inline "cic:/CoRN/algebra/CFields/CField_Ops/F.var" "CField_Ops__". -inline "cic:/CoRN/algebra/CFields/G.var". +inline "cic:/CoRN/algebra/CFields/CField_Ops/G.var" "CField_Ops__". (* begin hide *) -inline "cic:/CoRN/algebra/CFields/P.con". +inline "cic:/CoRN/algebra/CFields/CField_Ops/P.con" "CField_Ops__". -inline "cic:/CoRN/algebra/CFields/Q.con". +inline "cic:/CoRN/algebra/CFields/CField_Ops/Q.con" "CField_Ops__". (* end hide *) (* UNEXPORTED -Section Part_Function_Recip. +Section Part_Function_Recip *) (*#* Some auxiliary notions are helpful in defining the domain. *) -inline "cic:/CoRN/algebra/CFields/R.con". +inline "cic:/CoRN/algebra/CFields/CField_Ops/Part_Function_Recip/R.con" "CField_Ops__Part_Function_Recip__". -inline "cic:/CoRN/algebra/CFields/Ext2R.con". +inline "cic:/CoRN/algebra/CFields/CField_Ops/Part_Function_Recip/Ext2R.con" "CField_Ops__Part_Function_Recip__". inline "cic:/CoRN/algebra/CFields/part_function_recip_strext.con". @@ -513,20 +513,20 @@ inline "cic:/CoRN/algebra/CFields/part_function_recip_pred_wd.con". inline "cic:/CoRN/algebra/CFields/Frecip.con". (* UNEXPORTED -End Part_Function_Recip. +End Part_Function_Recip *) (* UNEXPORTED -Section Part_Function_Div. +Section Part_Function_Div *) (*#* For division things work out almost in the same way. *) -inline "cic:/CoRN/algebra/CFields/R.con". +inline "cic:/CoRN/algebra/CFields/CField_Ops/Part_Function_Div/R.con" "CField_Ops__Part_Function_Div__". -inline "cic:/CoRN/algebra/CFields/Ext2R.con". +inline "cic:/CoRN/algebra/CFields/CField_Ops/Part_Function_Div/Ext2R.con" "CField_Ops__Part_Function_Div__". inline "cic:/CoRN/algebra/CFields/part_function_div_strext.con". @@ -535,7 +535,7 @@ inline "cic:/CoRN/algebra/CFields/part_function_div_pred_wd.con". inline "cic:/CoRN/algebra/CFields/Fdiv.con". (* UNEXPORTED -End Part_Function_Div. +End Part_Function_Div *) (*#* @@ -543,7 +543,7 @@ End Part_Function_Div. %\end{convention}% *) -inline "cic:/CoRN/algebra/CFields/R.var". +inline "cic:/CoRN/algebra/CFields/CField_Ops/R.var" "CField_Ops__". inline "cic:/CoRN/algebra/CFields/included_FRecip.con". @@ -556,7 +556,7 @@ inline "cic:/CoRN/algebra/CFields/included_FDiv'.con". inline "cic:/CoRN/algebra/CFields/included_FDiv''.con". (* UNEXPORTED -End CField_Ops. +End CField_Ops *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/algebra/CGroups.ma b/helm/software/matita/contribs/CoRN-Decl/algebra/CGroups.ma index 6e644810b..232c258e5 100644 --- a/helm/software/matita/contribs/CoRN-Decl/algebra/CGroups.ma +++ b/helm/software/matita/contribs/CoRN-Decl/algebra/CGroups.ma @@ -87,15 +87,15 @@ Infix "[-]" := cg_minus (at level 50, left associativity). *) (* UNEXPORTED -Section CGroup_axioms. +Section CGroup_axioms *) -inline "cic:/CoRN/algebra/CGroups/G.var". +inline "cic:/CoRN/algebra/CGroups/CGroup_axioms/G.var" "CGroup_axioms__". inline "cic:/CoRN/algebra/CGroups/cg_inverse.con". (* UNEXPORTED -End CGroup_axioms. +End CGroup_axioms *) (*#* @@ -106,10 +106,10 @@ General properties of groups. *) (* UNEXPORTED -Section CGroup_basics. +Section CGroup_basics *) -inline "cic:/CoRN/algebra/CGroups/G.var". +inline "cic:/CoRN/algebra/CGroups/CGroup_basics/G.var" "CGroup_basics__". inline "cic:/CoRN/algebra/CGroups/cg_rht_inv_unfolded.con". @@ -188,31 +188,31 @@ inline "cic:/CoRN/algebra/CGroups/x_minus_x.con". *) (* UNEXPORTED -Section SubCGroups. +Section SubCGroups *) -inline "cic:/CoRN/algebra/CGroups/P.var". +inline "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/P.var" "CGroup_basics__SubCGroups__". -inline "cic:/CoRN/algebra/CGroups/Punit.var". +inline "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/Punit.var" "CGroup_basics__SubCGroups__". -inline "cic:/CoRN/algebra/CGroups/op_pres_P.var". +inline "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/op_pres_P.var" "CGroup_basics__SubCGroups__". -inline "cic:/CoRN/algebra/CGroups/inv_pres_P.var". +inline "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/inv_pres_P.var" "CGroup_basics__SubCGroups__". -inline "cic:/CoRN/algebra/CGroups/subcrr.con". +inline "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/subcrr.con" "CGroup_basics__SubCGroups__". -inline "cic:/CoRN/algebra/CGroups/subinv.con". +inline "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/subinv.con" "CGroup_basics__SubCGroups__". inline "cic:/CoRN/algebra/CGroups/isgrp_scrr.con". inline "cic:/CoRN/algebra/CGroups/Build_SubCGroup.con". (* UNEXPORTED -End SubCGroups. +End SubCGroups *) (* UNEXPORTED -End CGroup_basics. +End CGroup_basics *) (* UNEXPORTED @@ -238,10 +238,10 @@ Hint Resolve cg_minus_wd: algebra_c. *) (* UNEXPORTED -Section Assoc_properties. +Section Assoc_properties *) -inline "cic:/CoRN/algebra/CGroups/G.var". +inline "cic:/CoRN/algebra/CGroups/Assoc_properties/G.var" "Assoc_properties__". inline "cic:/CoRN/algebra/CGroups/assoc_2.con". @@ -252,7 +252,7 @@ inline "cic:/CoRN/algebra/CGroups/cg_cancel_mixed.con". inline "cic:/CoRN/algebra/CGroups/plus_resp_eq.con". (* UNEXPORTED -End Assoc_properties. +End Assoc_properties *) (* UNEXPORTED @@ -268,10 +268,10 @@ Specific properties of apartness. *) (* UNEXPORTED -Section cgroups_apartness. +Section cgroups_apartness *) -inline "cic:/CoRN/algebra/CGroups/G.var". +inline "cic:/CoRN/algebra/CGroups/cgroups_apartness/G.var" "cgroups_apartness__". inline "cic:/CoRN/algebra/CGroups/cg_add_ap_zero.con". @@ -296,7 +296,7 @@ inline "cic:/CoRN/algebra/CGroups/minus_resp_ap_lft.con". inline "cic:/CoRN/algebra/CGroups/minus_cancel_ap_rht.con". (* UNEXPORTED -End cgroups_apartness. +End cgroups_apartness *) (* UNEXPORTED @@ -308,7 +308,7 @@ Hint Resolve minus_ap_zero zero_minus_apart inv_resp_ap_zero: algebra. *) (* UNEXPORTED -Section CGroup_Ops. +Section CGroup_Ops *) (*#* @@ -322,22 +322,22 @@ by [P] and [Q]. %\end{convention}% *) -inline "cic:/CoRN/algebra/CGroups/G.var". +inline "cic:/CoRN/algebra/CGroups/CGroup_Ops/G.var" "CGroup_Ops__". -inline "cic:/CoRN/algebra/CGroups/F.var". +inline "cic:/CoRN/algebra/CGroups/CGroup_Ops/F.var" "CGroup_Ops__". -inline "cic:/CoRN/algebra/CGroups/F'.var". +inline "cic:/CoRN/algebra/CGroups/CGroup_Ops/F'.var" "CGroup_Ops__". (* begin hide *) -inline "cic:/CoRN/algebra/CGroups/P.con". +inline "cic:/CoRN/algebra/CGroups/CGroup_Ops/P.con" "CGroup_Ops__". -inline "cic:/CoRN/algebra/CGroups/Q.con". +inline "cic:/CoRN/algebra/CGroups/CGroup_Ops/Q.con" "CGroup_Ops__". (* end hide *) (* UNEXPORTED -Section Part_Function_Inv. +Section Part_Function_Inv *) inline "cic:/CoRN/algebra/CGroups/part_function_inv_strext.con". @@ -345,11 +345,11 @@ inline "cic:/CoRN/algebra/CGroups/part_function_inv_strext.con". inline "cic:/CoRN/algebra/CGroups/Finv.con". (* UNEXPORTED -End Part_Function_Inv. +End Part_Function_Inv *) (* UNEXPORTED -Section Part_Function_Minus. +Section Part_Function_Minus *) inline "cic:/CoRN/algebra/CGroups/part_function_minus_strext.con". @@ -357,7 +357,7 @@ inline "cic:/CoRN/algebra/CGroups/part_function_minus_strext.con". inline "cic:/CoRN/algebra/CGroups/Fminus.con". (* UNEXPORTED -End Part_Function_Minus. +End Part_Function_Minus *) (*#* @@ -365,7 +365,7 @@ End Part_Function_Minus. %\end{convention}% *) -inline "cic:/CoRN/algebra/CGroups/R.var". +inline "cic:/CoRN/algebra/CGroups/CGroup_Ops/R.var" "CGroup_Ops__". inline "cic:/CoRN/algebra/CGroups/included_FInv.con". @@ -378,7 +378,7 @@ inline "cic:/CoRN/algebra/CGroups/included_FMinus'.con". inline "cic:/CoRN/algebra/CGroups/included_FMinus''.con". (* UNEXPORTED -End CGroup_Ops. +End CGroup_Ops *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/algebra/CLogic.ma b/helm/software/matita/contribs/CoRN-Decl/algebra/CLogic.ma index f0ec034f3..d0799ff30 100644 --- a/helm/software/matita/contribs/CoRN-Decl/algebra/CLogic.ma +++ b/helm/software/matita/contribs/CoRN-Decl/algebra/CLogic.ma @@ -81,7 +81,7 @@ version. inline "cic:/CoRN/algebra/CLogic/CProp.con". (* UNEXPORTED -Section Basics. +Section Basics *) (*#* ** Basics @@ -154,7 +154,7 @@ Hint Resolve Iff_trans Iff_sym Iff_refl Iff_right Iff_left Iff_imp_imp : algebra *) (* UNEXPORTED -End Basics. +End Basics *) (* begin hide *) @@ -210,23 +210,23 @@ Hint Resolve CI CAnd_intro Cinleft Cinright existT exist2T: core. *) (* UNEXPORTED -Section Choice. +Section Choice *) (* **Choice Let [P] be a predicate on $\NN^2$#N times N#. *) -inline "cic:/CoRN/algebra/CLogic/P.var". +inline "cic:/CoRN/algebra/CLogic/Choice/P.var" "Choice__". inline "cic:/CoRN/algebra/CLogic/choice.con". (* UNEXPORTED -End Choice. +End Choice *) (* UNEXPORTED -Section Logical_Remarks. +Section Logical_Remarks *) (*#* We prove a few logical results which are helpful to have as lemmas @@ -238,11 +238,11 @@ inline "cic:/CoRN/algebra/CLogic/CNot_Not_or.con". inline "cic:/CoRN/algebra/CLogic/CdeMorgan_ex_all.con". (* UNEXPORTED -End Logical_Remarks. +End Logical_Remarks *) (* UNEXPORTED -Section CRelation_Definition. +Section CRelation_Definition *) (*#* ** [CProp]-valued Relations @@ -252,11 +252,11 @@ Similar to Relations.v in Coq's standard library. %\end{convention}% *) -inline "cic:/CoRN/algebra/CLogic/A.var". +inline "cic:/CoRN/algebra/CLogic/CRelation_Definition/A.var" "CRelation_Definition__". inline "cic:/CoRN/algebra/CLogic/Crelation.con". -inline "cic:/CoRN/algebra/CLogic/R.var". +inline "cic:/CoRN/algebra/CLogic/CRelation_Definition/R.var" "CRelation_Definition__". inline "cic:/CoRN/algebra/CLogic/Creflexive.con". @@ -267,11 +267,11 @@ inline "cic:/CoRN/algebra/CLogic/Csymmetric.con". inline "cic:/CoRN/algebra/CLogic/Cequiv.con". (* UNEXPORTED -End CRelation_Definition. +End CRelation_Definition *) (* UNEXPORTED -Section TRelation_Definition. +Section TRelation_Definition *) (*#* ** [Prop]-valued Relations @@ -281,11 +281,11 @@ Analogous. %\end{convention}% *) -inline "cic:/CoRN/algebra/CLogic/A.var". +inline "cic:/CoRN/algebra/CLogic/TRelation_Definition/A.var" "TRelation_Definition__". inline "cic:/CoRN/algebra/CLogic/Trelation.con". -inline "cic:/CoRN/algebra/CLogic/R.var". +inline "cic:/CoRN/algebra/CLogic/TRelation_Definition/R.var" "TRelation_Definition__". inline "cic:/CoRN/algebra/CLogic/Treflexive.con". @@ -296,13 +296,13 @@ inline "cic:/CoRN/algebra/CLogic/Tsymmetric.con". inline "cic:/CoRN/algebra/CLogic/Tequiv.con". (* UNEXPORTED -End TRelation_Definition. +End TRelation_Definition *) inline "cic:/CoRN/algebra/CLogic/eqs.ind". (* UNEXPORTED -Section le_odd. +Section le_odd *) (*#* ** The relation [le], [lt], [odd] and [even] in [CProp] @@ -349,11 +349,11 @@ inline "cic:/CoRN/algebra/CLogic/to_Codd.con". inline "cic:/CoRN/algebra/CLogic/to_Ceven.con". (* UNEXPORTED -End le_odd. +End le_odd *) (* UNEXPORTED -Section Misc. +Section Misc *) (*#* **Miscellaneous @@ -372,7 +372,7 @@ inline "cic:/CoRN/algebra/CLogic/not_r_sum_rec.con". inline "cic:/CoRN/algebra/CLogic/not_l_sum_rec.con". (* UNEXPORTED -End Misc. +End Misc *) (*#* **Results about the natural numbers @@ -397,7 +397,7 @@ Implicit Arguments nat_less_n_pred' [n]. *) (* UNEXPORTED -Section Odd_and_Even. +Section Odd_and_Even *) (*#* @@ -416,7 +416,7 @@ inline "cic:/CoRN/algebra/CLogic/even_or_odd_plus.con". inline "cic:/CoRN/algebra/CLogic/even_or_odd_plus_gt.con". (* UNEXPORTED -End Odd_and_Even. +End Odd_and_Even *) (* UNEXPORTED @@ -428,7 +428,7 @@ Hint Resolve toCle: core. *) (* UNEXPORTED -Section Natural_Numbers. +Section Natural_Numbers *) (*#* **Algebraic Properties @@ -467,7 +467,7 @@ inline "cic:/CoRN/algebra/CLogic/plus_pred_pred_plus.con". %\end{convention}% *) -inline "cic:/CoRN/algebra/CLogic/h.var". +inline "cic:/CoRN/algebra/CLogic/Natural_Numbers/h.var" "Natural_Numbers__". (*#* First we characterize monotonicity by a local condition: if [h(n) < h(n+1)] @@ -499,7 +499,7 @@ inline "cic:/CoRN/algebra/CLogic/mon_fun_covers.con". inline "cic:/CoRN/algebra/CLogic/weird_mon_covers.con". (* UNEXPORTED -End Natural_Numbers. +End Natural_Numbers *) (*#* @@ -509,7 +509,7 @@ Useful for the Fundamental Theorem of Algebra. inline "cic:/CoRN/algebra/CLogic/kseq_prop.con". (* UNEXPORTED -Section Predicates_to_CProp. +Section Predicates_to_CProp *) (*#* **Logical Properties @@ -539,11 +539,11 @@ inline "cic:/CoRN/algebra/CLogic/finite_or_elim.con". inline "cic:/CoRN/algebra/CLogic/str_finite_or_elim.con". (* UNEXPORTED -End Predicates_to_CProp. +End Predicates_to_CProp *) (* UNEXPORTED -Section Predicates_to_Prop. +Section Predicates_to_Prop *) (*#* Finally, analogous results for [Prop]-valued predicates are presented for @@ -559,7 +559,7 @@ inline "cic:/CoRN/algebra/CLogic/nat_complete_double_ind.con". inline "cic:/CoRN/algebra/CLogic/four_ind.con". (* UNEXPORTED -End Predicates_to_Prop. +End Predicates_to_Prop *) (*#* **Integers diff --git a/helm/software/matita/contribs/CoRN-Decl/algebra/CMonoids.ma b/helm/software/matita/contribs/CoRN-Decl/algebra/CMonoids.ma index 825673c2b..f5d746e6a 100644 --- a/helm/software/matita/contribs/CoRN-Decl/algebra/CMonoids.ma +++ b/helm/software/matita/contribs/CoRN-Decl/algebra/CMonoids.ma @@ -89,10 +89,10 @@ Implicit Arguments nonZeroP [M]. *) (* UNEXPORTED -Section CMonoid_axioms. +Section CMonoid_axioms *) -inline "cic:/CoRN/algebra/CMonoids/M.var". +inline "cic:/CoRN/algebra/CMonoids/CMonoid_axioms/M.var" "CMonoid_axioms__". inline "cic:/CoRN/algebra/CMonoids/CMonoid_is_CMonoid.con". @@ -101,7 +101,7 @@ inline "cic:/CoRN/algebra/CMonoids/cm_rht_unit.con". inline "cic:/CoRN/algebra/CMonoids/cm_lft_unit.con". (* UNEXPORTED -End CMonoid_axioms. +End CMonoid_axioms *) (*#* @@ -111,10 +111,10 @@ End CMonoid_axioms. *) (* UNEXPORTED -Section CMonoid_basics. +Section CMonoid_basics *) -inline "cic:/CoRN/algebra/CMonoids/M.var". +inline "cic:/CoRN/algebra/CMonoids/CMonoid_basics/M.var" "CMonoid_basics__". inline "cic:/CoRN/algebra/CMonoids/cm_rht_unit_unfolded.con". @@ -146,27 +146,27 @@ Let [P] a predicate on [M] containing [Zero] and closed under [[+]]. *) (* UNEXPORTED -Section SubCMonoids. +Section SubCMonoids *) -inline "cic:/CoRN/algebra/CMonoids/P.var". +inline "cic:/CoRN/algebra/CMonoids/CMonoid_basics/SubCMonoids/P.var" "CMonoid_basics__SubCMonoids__". -inline "cic:/CoRN/algebra/CMonoids/Punit.var". +inline "cic:/CoRN/algebra/CMonoids/CMonoid_basics/SubCMonoids/Punit.var" "CMonoid_basics__SubCMonoids__". -inline "cic:/CoRN/algebra/CMonoids/op_pres_P.var". +inline "cic:/CoRN/algebra/CMonoids/CMonoid_basics/SubCMonoids/op_pres_P.var" "CMonoid_basics__SubCMonoids__". -inline "cic:/CoRN/algebra/CMonoids/subcrr.con". +inline "cic:/CoRN/algebra/CMonoids/CMonoid_basics/SubCMonoids/subcrr.con" "CMonoid_basics__SubCMonoids__". inline "cic:/CoRN/algebra/CMonoids/ismon_scrr.con". inline "cic:/CoRN/algebra/CMonoids/Build_SubCMonoid.con". (* UNEXPORTED -End SubCMonoids. +End SubCMonoids *) (* UNEXPORTED -End CMonoid_basics. +End CMonoid_basics *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/algebra/COrdAbs.ma b/helm/software/matita/contribs/CoRN-Decl/algebra/COrdAbs.ma index 44d4f7d7a..b8901d261 100644 --- a/helm/software/matita/contribs/CoRN-Decl/algebra/COrdAbs.ma +++ b/helm/software/matita/contribs/CoRN-Decl/algebra/COrdAbs.ma @@ -35,7 +35,7 @@ Implicit Arguments AbsSmall [R]. (* End_SpecReals *) (* UNEXPORTED -Section AbsSmall_properties. +Section AbsSmall_properties *) (*#* @@ -43,7 +43,7 @@ Section AbsSmall_properties. %\end{convention}% *) -inline "cic:/CoRN/algebra/COrdAbs/R.var". +inline "cic:/CoRN/algebra/COrdAbs/AbsSmall_properties/R.var" "AbsSmall_properties__". inline "cic:/CoRN/algebra/COrdAbs/AbsSmall_wdr.con". @@ -106,7 +106,7 @@ inline "cic:/CoRN/algebra/COrdAbs/AbsSmall_cancel_mult.con". inline "cic:/CoRN/algebra/COrdAbs/AbsSmall_approach_zero.con". (* UNEXPORTED -End AbsSmall_properties. +End AbsSmall_properties *) (* UNEXPORTED @@ -128,7 +128,7 @@ Notation AbsBig := (absBig _). inline "cic:/CoRN/algebra/COrdAbs/AbsBigSmall_minus.con". (* UNEXPORTED -Section absBig_wd_properties. +Section absBig_wd_properties *) (*#* @@ -136,7 +136,7 @@ Section absBig_wd_properties. %\end{convention}% *) -inline "cic:/CoRN/algebra/COrdAbs/R.var". +inline "cic:/CoRN/algebra/COrdAbs/absBig_wd_properties/R.var" "absBig_wd_properties__". inline "cic:/CoRN/algebra/COrdAbs/AbsBig_wdr.con". @@ -147,7 +147,7 @@ inline "cic:/CoRN/algebra/COrdAbs/AbsBig_wdr_unfolded.con". inline "cic:/CoRN/algebra/COrdAbs/AbsBig_wdl_unfolded.con". (* UNEXPORTED -End absBig_wd_properties. +End absBig_wd_properties *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/algebra/COrdCauchy.ma b/helm/software/matita/contribs/CoRN-Decl/algebra/COrdCauchy.ma index 70c46d57a..9cfd863a7 100644 --- a/helm/software/matita/contribs/CoRN-Decl/algebra/COrdCauchy.ma +++ b/helm/software/matita/contribs/CoRN-Decl/algebra/COrdCauchy.ma @@ -23,7 +23,7 @@ include "algebra/COrdAbs.ma". (* Begin_SpecReals *) (* UNEXPORTED -Section OrdField_Cauchy. +Section OrdField_Cauchy *) (*#* **Cauchy sequences @@ -31,7 +31,7 @@ Section OrdField_Cauchy. %\end{convention}% *) -inline "cic:/CoRN/algebra/COrdCauchy/R.var". +inline "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/R.var" "OrdField_Cauchy__". (* begin hide *) @@ -95,13 +95,13 @@ inline "cic:/CoRN/algebra/COrdCauchy/CS_seq_const.con". %\end{convention}% *) -inline "cic:/CoRN/algebra/COrdCauchy/f.var". +inline "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/f.var" "OrdField_Cauchy__". -inline "cic:/CoRN/algebra/COrdCauchy/g.var". +inline "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/g.var" "OrdField_Cauchy__". -inline "cic:/CoRN/algebra/COrdCauchy/Hf.var". +inline "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/Hf.var" "OrdField_Cauchy__". -inline "cic:/CoRN/algebra/COrdCauchy/Hg.var". +inline "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/Hg.var" "OrdField_Cauchy__". inline "cic:/CoRN/algebra/COrdCauchy/CS_seq_plus.con". @@ -121,13 +121,13 @@ Let [e] be a postive element of [R] and let [N:nat] be such that from %\end{convention}% *) -inline "cic:/CoRN/algebra/COrdCauchy/e.var". +inline "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/e.var" "OrdField_Cauchy__". -inline "cic:/CoRN/algebra/COrdCauchy/He.var". +inline "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/He.var" "OrdField_Cauchy__". -inline "cic:/CoRN/algebra/COrdCauchy/N.var". +inline "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/N.var" "OrdField_Cauchy__". -inline "cic:/CoRN/algebra/COrdCauchy/f_bnd.var". +inline "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/f_bnd.var" "OrdField_Cauchy__". inline "cic:/CoRN/algebra/COrdCauchy/CS_seq_recip_def.con". @@ -136,7 +136,7 @@ inline "cic:/CoRN/algebra/COrdCauchy/CS_seq_recip_seq.con". inline "cic:/CoRN/algebra/COrdCauchy/CS_seq_recip.con". (* UNEXPORTED -End OrdField_Cauchy. +End OrdField_Cauchy *) (* UNEXPORTED @@ -151,10 +151,10 @@ well here anyway. inline "cic:/CoRN/algebra/COrdCauchy/maj_upto_eps.con". (* UNEXPORTED -Section Mult_AbsSmall. +Section Mult_AbsSmall *) -inline "cic:/CoRN/algebra/COrdCauchy/R.var". +inline "cic:/CoRN/algebra/COrdCauchy/Mult_AbsSmall/R.var" "Mult_AbsSmall__". (*#* ** [AbsSmall] revisited @@ -171,14 +171,14 @@ inline "cic:/CoRN/algebra/COrdCauchy/mult_AbsSmall_lft.con". inline "cic:/CoRN/algebra/COrdCauchy/mult_AbsSmall.con". (* UNEXPORTED -End Mult_AbsSmall. +End Mult_AbsSmall *) (* UNEXPORTED -Section Mult_Continuous. +Section Mult_Continuous *) -inline "cic:/CoRN/algebra/COrdCauchy/R.var". +inline "cic:/CoRN/algebra/COrdCauchy/Mult_Continuous/R.var" "Mult_Continuous__". (*#* ** Multiplication is continuous @@ -197,11 +197,11 @@ inline "cic:/CoRN/algebra/COrdCauchy/mult_contin.con". inline "cic:/CoRN/algebra/COrdCauchy/plus_contin.con". (* UNEXPORTED -End Mult_Continuous. +End Mult_Continuous *) (* UNEXPORTED -Section Monotonous_functions. +Section Monotonous_functions *) (*#* @@ -214,7 +214,7 @@ characterize them in some way. %\end{convention}% *) -inline "cic:/CoRN/algebra/COrdCauchy/R.var". +inline "cic:/CoRN/algebra/COrdCauchy/Monotonous_functions/R.var" "Monotonous_functions__". (*#* We begin by characterizing the preservation of less (less or equal) @@ -279,6 +279,6 @@ A similar result for %{\em %partial%}% functions. inline "cic:/CoRN/algebra/COrdCauchy/part_mon_imp_mon'.con". (* UNEXPORTED -End Monotonous_functions. +End Monotonous_functions *) diff --git a/helm/software/matita/contribs/CoRN-Decl/algebra/COrdFields.ma b/helm/software/matita/contribs/CoRN-Decl/algebra/COrdFields.ma index dd9b0c82d..a85dc1128 100644 --- a/helm/software/matita/contribs/CoRN-Decl/algebra/COrdFields.ma +++ b/helm/software/matita/contribs/CoRN-Decl/algebra/COrdFields.ma @@ -134,7 +134,7 @@ Infix "[<=]" := leEq (at level 70, no associativity). *) (* UNEXPORTED -Section COrdField_axioms. +Section COrdField_axioms *) (*#* @@ -144,7 +144,7 @@ Let [F] be a field. %\end{convention}% *) -inline "cic:/CoRN/algebra/COrdFields/F.var". +inline "cic:/CoRN/algebra/COrdFields/COrdField_axioms/F.var" "COrdField_axioms__". inline "cic:/CoRN/algebra/COrdFields/COrdField_is_COrdField.con". @@ -169,7 +169,7 @@ inline "cic:/CoRN/algebra/COrdFields/less_wdr.con". inline "cic:/CoRN/algebra/COrdFields/less_wdl.con". (* UNEXPORTED -End COrdField_axioms. +End COrdField_axioms *) (* UNEXPORTED @@ -181,7 +181,7 @@ Declare Right Step less_wdr. *) (* UNEXPORTED -Section OrdField_basics. +Section OrdField_basics *) (*#* @@ -195,7 +195,7 @@ Let in the rest of this section (and all subsections) %\end{convention}% *) -inline "cic:/CoRN/algebra/COrdFields/R.var". +inline "cic:/CoRN/algebra/COrdFields/OrdField_basics/R.var" "OrdField_basics__". inline "cic:/CoRN/algebra/COrdFields/less_imp_ap.con". @@ -218,13 +218,13 @@ inline "cic:/CoRN/algebra/COrdFields/pos_ap_zero.con". inline "cic:/CoRN/algebra/COrdFields/leEq_not_eq.con". (* UNEXPORTED -End OrdField_basics. +End OrdField_basics *) (*#**********************************) (* UNEXPORTED -Section Basic_Properties_of_leEq. +Section Basic_Properties_of_leEq *) (*#**********************************) @@ -232,7 +232,7 @@ Section Basic_Properties_of_leEq. (*#* ** Basic properties of [ [<=] ] *) -inline "cic:/CoRN/algebra/COrdFields/R.var". +inline "cic:/CoRN/algebra/COrdFields/Basic_Properties_of_leEq/R.var" "Basic_Properties_of_leEq__". inline "cic:/CoRN/algebra/COrdFields/leEq_wdr.con". @@ -263,7 +263,7 @@ inline "cic:/CoRN/algebra/COrdFields/leEq_transitive.con". inline "cic:/CoRN/algebra/COrdFields/less_leEq.con". (* UNEXPORTED -End Basic_Properties_of_leEq. +End Basic_Properties_of_leEq *) (* UNEXPORTED @@ -275,7 +275,7 @@ Declare Right Step leEq_wdr. *) (* UNEXPORTED -Section infinity_of_cordfields. +Section infinity_of_cordfields *) (*#* @@ -288,7 +288,7 @@ and so on. These are elements of [NonZeros], so that we can write e.g.%\% [x[/]TwoNZ]. *) -inline "cic:/CoRN/algebra/COrdFields/R.var". +inline "cic:/CoRN/algebra/COrdFields/infinity_of_cordfields/R.var" "infinity_of_cordfields__". inline "cic:/CoRN/algebra/COrdFields/pos_one.con". @@ -319,7 +319,7 @@ inline "cic:/CoRN/algebra/COrdFields/nring_fac_ap_zero.con". include "tactics/Opaque_algebra.ma". (* UNEXPORTED -Section up_to_four. +Section up_to_four *) (*#* @@ -361,11 +361,11 @@ inline "cic:/CoRN/algebra/COrdFields/three_ap_zero.con". inline "cic:/CoRN/algebra/COrdFields/four_ap_zero.con". (* UNEXPORTED -End up_to_four. +End up_to_four *) (* UNEXPORTED -Section More_than_four. +Section More_than_four *) (*#* *** Properties of some other numbers *) @@ -403,11 +403,11 @@ inline "cic:/CoRN/algebra/COrdFields/twentyfour_ap_zero.con". inline "cic:/CoRN/algebra/COrdFields/fortyeight_ap_zero.con". (* UNEXPORTED -End More_than_four. +End More_than_four *) (* UNEXPORTED -End infinity_of_cordfields. +End infinity_of_cordfields *) (* UNEXPORTED @@ -467,14 +467,14 @@ Notation " x [/]FortyEightNZ" := (x[/] FortyEight[//]fortyeight_ap_zero _) (at l *) (* UNEXPORTED -Section consequences_of_infinity. +Section consequences_of_infinity *) (*#* *** Consequences of infinity *) -inline "cic:/CoRN/algebra/COrdFields/F.var". +inline "cic:/CoRN/algebra/COrdFields/consequences_of_infinity/F.var" "consequences_of_infinity__". inline "cic:/CoRN/algebra/COrdFields/square_eq.con". @@ -485,13 +485,13 @@ Ordered fields have characteristic zero. inline "cic:/CoRN/algebra/COrdFields/char0_OrdField.con". (* UNEXPORTED -End consequences_of_infinity. +End consequences_of_infinity *) (*#**********************************) (* UNEXPORTED -Section Properties_of_Ordering. +Section Properties_of_Ordering *) (*#**********************************) @@ -500,7 +500,7 @@ Section Properties_of_Ordering. ** Properties of [[<]] *) -inline "cic:/CoRN/algebra/COrdFields/R.var". +inline "cic:/CoRN/algebra/COrdFields/Properties_of_Ordering/R.var" "Properties_of_Ordering__". (*#* We do not use a special predicate for positivity, @@ -511,7 +511,7 @@ Reasons: it is more natural; in ordinary mathematics we also write [Zero [<] x] *) (* UNEXPORTED -Section addition. +Section addition *) (*#* @@ -593,11 +593,11 @@ inline "cic:/CoRN/algebra/COrdFields/shift_zero_less_minus'.con". inline "cic:/CoRN/algebra/COrdFields/qltone.con". (* UNEXPORTED -End addition. +End addition *) (* UNEXPORTED -Section multiplication. +Section multiplication *) (*#* @@ -702,11 +702,11 @@ inline "cic:/CoRN/algebra/COrdFields/pos_div_twentyfour.con". inline "cic:/CoRN/algebra/COrdFields/pos_div_fortyeight.con". (* UNEXPORTED -End multiplication. +End multiplication *) (* UNEXPORTED -Section misc. +Section misc *) (*#* @@ -734,10 +734,10 @@ inline "cic:/CoRN/algebra/COrdFields/positive_Sumx.con". inline "cic:/CoRN/algebra/COrdFields/negative_Sumx.con". (* UNEXPORTED -End misc. +End misc *) (* UNEXPORTED -End Properties_of_Ordering. +End Properties_of_Ordering *) diff --git a/helm/software/matita/contribs/CoRN-Decl/algebra/COrdFields2.ma b/helm/software/matita/contribs/CoRN-Decl/algebra/COrdFields2.ma index 59b5d94ee..3671078fa 100644 --- a/helm/software/matita/contribs/CoRN-Decl/algebra/COrdFields2.ma +++ b/helm/software/matita/contribs/CoRN-Decl/algebra/COrdFields2.ma @@ -27,7 +27,7 @@ include "algebra/COrdFields.ma". (*#**********************************) (* UNEXPORTED -Section Properties_of_leEq. +Section Properties_of_leEq *) (*#**********************************) @@ -38,10 +38,10 @@ Section Properties_of_leEq. %\end{convention}% *) -inline "cic:/CoRN/algebra/COrdFields2/R.var". +inline "cic:/CoRN/algebra/COrdFields2/Properties_of_leEq/R.var" "Properties_of_leEq__". (* UNEXPORTED -Section addition. +Section addition *) (*#* @@ -105,11 +105,11 @@ inline "cic:/CoRN/algebra/COrdFields2/shift_zero_leEq_minus.con". inline "cic:/CoRN/algebra/COrdFields2/shift_zero_leEq_minus'.con". (* UNEXPORTED -End addition. +End addition *) (* UNEXPORTED -Section multiplication. +Section multiplication *) (*#* @@ -171,11 +171,11 @@ inline "cic:/CoRN/algebra/COrdFields2/nonneg_div_four.con". inline "cic:/CoRN/algebra/COrdFields2/nonneg_div_four'.con". (* UNEXPORTED -End multiplication. +End multiplication *) (* UNEXPORTED -Section misc. +Section misc *) (*#* @@ -225,19 +225,19 @@ inline "cic:/CoRN/algebra/COrdFields2/approach_zero.con". inline "cic:/CoRN/algebra/COrdFields2/approach_zero_weak.con". (* UNEXPORTED -End misc. +End misc *) inline "cic:/CoRN/algebra/COrdFields2/equal_less_leEq.con". (* UNEXPORTED -End Properties_of_leEq. +End Properties_of_leEq *) (*#**********************************) (* UNEXPORTED -Section PosP_properties. +Section PosP_properties *) (*#**********************************) @@ -248,7 +248,7 @@ Section PosP_properties. %\end{convention}% *) -inline "cic:/CoRN/algebra/COrdFields2/R.var". +inline "cic:/CoRN/algebra/COrdFields2/PosP_properties/R.var" "PosP_properties__". (* begin hide *) @@ -289,7 +289,7 @@ inline "cic:/CoRN/algebra/COrdFields2/square_eq_pos.con". inline "cic:/CoRN/algebra/COrdFields2/square_eq_neg.con". (* UNEXPORTED -End PosP_properties. +End PosP_properties *) (* UNEXPORTED @@ -309,10 +309,10 @@ Implicit Arguments one_div_succ [R]. *) (* UNEXPORTED -Section One_div_succ_properties. +Section One_div_succ_properties *) -inline "cic:/CoRN/algebra/COrdFields2/R.var". +inline "cic:/CoRN/algebra/COrdFields2/One_div_succ_properties/R.var" "One_div_succ_properties__". inline "cic:/CoRN/algebra/COrdFields2/one_div_succ_resp_leEq.con". @@ -321,7 +321,7 @@ inline "cic:/CoRN/algebra/COrdFields2/one_div_succ_pos.con". inline "cic:/CoRN/algebra/COrdFields2/one_div_succ_resp_less.con". (* UNEXPORTED -End One_div_succ_properties. +End One_div_succ_properties *) (*#* @@ -335,7 +335,7 @@ Implicit Arguments Half [R]. *) (* UNEXPORTED -Section Half_properties. +Section Half_properties *) (*#* @@ -344,7 +344,7 @@ Let [R] be an ordered field. %\end{convention}% *) -inline "cic:/CoRN/algebra/COrdFields2/R.var". +inline "cic:/CoRN/algebra/COrdFields2/Half_properties/R.var" "Half_properties__". inline "cic:/CoRN/algebra/COrdFields2/half_1.con". @@ -363,7 +363,7 @@ inline "cic:/CoRN/algebra/COrdFields2/half_lt1.con". inline "cic:/CoRN/algebra/COrdFields2/half_3.con". (* UNEXPORTED -End Half_properties. +End Half_properties *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/algebra/CPoly_ApZero.ma b/helm/software/matita/contribs/CoRN-Decl/algebra/CPoly_ApZero.ma index fd7835ba5..5878f1663 100644 --- a/helm/software/matita/contribs/CoRN-Decl/algebra/CPoly_ApZero.ma +++ b/helm/software/matita/contribs/CoRN-Decl/algebra/CPoly_ApZero.ma @@ -33,7 +33,7 @@ Implicit Arguments distinct1 [A]. *) (* UNEXPORTED -Section Poly_Representation. +Section Poly_Representation *) (*#* @@ -45,17 +45,17 @@ has degree at most [n]. %\end{convention}% *) -inline "cic:/CoRN/algebra/CPoly_ApZero/R.var". +inline "cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/R.var" "Poly_Representation__". -inline "cic:/CoRN/algebra/CPoly_ApZero/a_.var". +inline "cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/a_.var" "Poly_Representation__". -inline "cic:/CoRN/algebra/CPoly_ApZero/distinct_a_.var". +inline "cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/distinct_a_.var" "Poly_Representation__". -inline "cic:/CoRN/algebra/CPoly_ApZero/f.var". +inline "cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/f.var" "Poly_Representation__". -inline "cic:/CoRN/algebra/CPoly_ApZero/n.var". +inline "cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/n.var" "Poly_Representation__". -inline "cic:/CoRN/algebra/CPoly_ApZero/degree_f.var". +inline "cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/degree_f.var" "Poly_Representation__". (* begin hide *) @@ -128,11 +128,11 @@ Hint Resolve poly_representation: algebra. inline "cic:/CoRN/algebra/CPoly_ApZero/Cpoly_choose_apzero.con". (* UNEXPORTED -End Poly_Representation. +End Poly_Representation *) (* UNEXPORTED -Section Characteristic_zero. +Section Characteristic_zero *) (*#* @@ -140,11 +140,11 @@ If we are in a field of characteristic zero, the previous result can be strengthened. *) -inline "cic:/CoRN/algebra/CPoly_ApZero/R.var". +inline "cic:/CoRN/algebra/CPoly_ApZero/Characteristic_zero/R.var" "Characteristic_zero__". (* begin show *) -inline "cic:/CoRN/algebra/CPoly_ApZero/H.var". +inline "cic:/CoRN/algebra/CPoly_ApZero/Characteristic_zero/H.var" "Characteristic_zero__". (* end show *) @@ -165,7 +165,7 @@ Also, in this situation polynomials are extensional functions. inline "cic:/CoRN/algebra/CPoly_ApZero/poly_extensional.con". (* UNEXPORTED -End Characteristic_zero. +End Characteristic_zero *) (*#* @@ -173,10 +173,10 @@ End Characteristic_zero. *) (* UNEXPORTED -Section Poly_ApZero_Interval. +Section Poly_ApZero_Interval *) -inline "cic:/CoRN/algebra/CPoly_ApZero/R.var". +inline "cic:/CoRN/algebra/CPoly_ApZero/Poly_ApZero_Interval/R.var" "Poly_ApZero_Interval__". (* begin hide *) @@ -189,6 +189,6 @@ Notation RX := (cpoly_cring R). inline "cic:/CoRN/algebra/CPoly_ApZero/Cpoly_apzero_interval.con". (* UNEXPORTED -End Poly_ApZero_Interval. +End Poly_ApZero_Interval *) diff --git a/helm/software/matita/contribs/CoRN-Decl/algebra/CPoly_Degree.ma b/helm/software/matita/contribs/CoRN-Decl/algebra/CPoly_Degree.ma index 038c3f3c4..55a65deeb 100644 --- a/helm/software/matita/contribs/CoRN-Decl/algebra/CPoly_Degree.ma +++ b/helm/software/matita/contribs/CoRN-Decl/algebra/CPoly_Degree.ma @@ -33,10 +33,10 @@ over [R]. *) (* UNEXPORTED -Section Degree_def. +Section Degree_def *) -inline "cic:/CoRN/algebra/CPoly_Degree/R.var". +inline "cic:/CoRN/algebra/CPoly_Degree/Degree_def/R.var" "Degree_def__". (* begin hide *) @@ -85,7 +85,7 @@ inline "cic:/CoRN/algebra/CPoly_Degree/even_cpoly.con". inline "cic:/CoRN/algebra/CPoly_Degree/regular.con". (* UNEXPORTED -End Degree_def. +End Degree_def *) (* UNEXPORTED @@ -105,10 +105,10 @@ Implicit Arguments lth_of_poly [R]. *) (* UNEXPORTED -Section Degree_props. +Section Degree_props *) -inline "cic:/CoRN/algebra/CPoly_Degree/R.var". +inline "cic:/CoRN/algebra/CPoly_Degree/Degree_props/R.var" "Degree_props__". (* begin hide *) @@ -201,7 +201,7 @@ inline "cic:/CoRN/algebra/CPoly_Degree/monic_one.con". inline "cic:/CoRN/algebra/CPoly_Degree/monic_apzero.con". (* UNEXPORTED -End Degree_props. +End Degree_props *) (* UNEXPORTED @@ -213,7 +213,7 @@ Hint Resolve degree_mult_aux: algebra. *) (* UNEXPORTED -Section degree_props_Field. +Section degree_props_Field *) (*#* ** Degrees of polynomials over a field @@ -222,7 +222,7 @@ polynomials over [F]. %\end{convention}% *) -inline "cic:/CoRN/algebra/CPoly_Degree/F.var". +inline "cic:/CoRN/algebra/CPoly_Degree/degree_props_Field/F.var" "degree_props_Field__". (* begin hide *) @@ -241,6 +241,6 @@ inline "cic:/CoRN/algebra/CPoly_Degree/degree_le_mult_imp.con". inline "cic:/CoRN/algebra/CPoly_Degree/degree_mult_imp.con". (* UNEXPORTED -End degree_props_Field. +End degree_props_Field *) diff --git a/helm/software/matita/contribs/CoRN-Decl/algebra/CPoly_NthCoeff.ma b/helm/software/matita/contribs/CoRN-Decl/algebra/CPoly_NthCoeff.ma index ae0db8884..6e51655a7 100644 --- a/helm/software/matita/contribs/CoRN-Decl/algebra/CPoly_NthCoeff.ma +++ b/helm/software/matita/contribs/CoRN-Decl/algebra/CPoly_NthCoeff.ma @@ -32,10 +32,10 @@ polynomials over [R]. *) (* UNEXPORTED -Section NthCoeff_def. +Section NthCoeff_def *) -inline "cic:/CoRN/algebra/CPoly_NthCoeff/R.var". +inline "cic:/CoRN/algebra/CPoly_NthCoeff/NthCoeff_def/R.var" "NthCoeff_def__". (* begin hide *) @@ -94,7 +94,7 @@ The [cpoly_zero] case should be [c [=] Zero] in order to be extensional. inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_S.con". (* UNEXPORTED -End NthCoeff_def. +End NthCoeff_def *) (* UNEXPORTED @@ -110,12 +110,12 @@ Hint Resolve nth_coeff_wd: algebra_c. *) (* UNEXPORTED -Section NthCoeff_props. +Section NthCoeff_props *) (*#* ** Properties of [nth_coeff] *) -inline "cic:/CoRN/algebra/CPoly_NthCoeff/R.var". +inline "cic:/CoRN/algebra/CPoly_NthCoeff/NthCoeff_props/R.var" "NthCoeff_props__". (* begin hide *) @@ -187,7 +187,7 @@ inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_nexp_neq.con". inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_mult.con". (* UNEXPORTED -End NthCoeff_props. +End NthCoeff_props *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/algebra/CPolynomials.ma b/helm/software/matita/contribs/CoRN-Decl/algebra/CPolynomials.ma index ce31278d6..033a79f4d 100644 --- a/helm/software/matita/contribs/CoRN-Decl/algebra/CPolynomials.ma +++ b/helm/software/matita/contribs/CoRN-Decl/algebra/CPolynomials.ma @@ -42,7 +42,7 @@ equality and induction of polynomials. *) (* UNEXPORTED -Section CPoly_CRing. +Section CPoly_CRing *) (*#* @@ -50,7 +50,7 @@ Section CPoly_CRing. %\end{convention}% *) -inline "cic:/CoRN/algebra/CPolynomials/CR.var". +inline "cic:/CoRN/algebra/CPolynomials/CPoly_CRing/CR.var" "CPoly_CRing__". (*#* The intuition behind the type [cpoly] is the following @@ -119,9 +119,9 @@ the most basic properties of equality and apartness in terms of these generators. *) -inline "cic:/CoRN/algebra/CPolynomials/cpoly_zero_cs.con". +inline "cic:/CoRN/algebra/CPolynomials/CPoly_CRing/cpoly_zero_cs.con" "CPoly_CRing__". -inline "cic:/CoRN/algebra/CPolynomials/cpoly_linear_cs.con". +inline "cic:/CoRN/algebra/CPolynomials/CPoly_CRing/cpoly_linear_cs.con" "CPoly_CRing__". inline "cic:/CoRN/algebra/CPolynomials/Ccpoly_ind_cs.con". @@ -318,7 +318,7 @@ inline "cic:/CoRN/algebra/CPolynomials/cpoly_x_minus_c_strext.con". inline "cic:/CoRN/algebra/CPolynomials/cpoly_x_minus_c_wd.con". (* UNEXPORTED -End CPoly_CRing. +End CPoly_CRing *) (* UNEXPORTED @@ -344,7 +344,7 @@ Infix "[+X*]" := cpoly_linear_fun' (at level 50, left associativity). *) (* UNEXPORTED -Section CPoly_CRing_ctd. +Section CPoly_CRing_ctd *) (*#* @@ -354,23 +354,23 @@ elements of the ring. %\end{convention}% *) -inline "cic:/CoRN/algebra/CPolynomials/CR.var". +inline "cic:/CoRN/algebra/CPolynomials/CPoly_CRing_ctd/CR.var" "CPoly_CRing_ctd__". (* NOTATION Notation RX := (cpoly_cring CR). *) (* UNEXPORTED -Section helpful_section. +Section helpful_section *) -inline "cic:/CoRN/algebra/CPolynomials/p.var". +inline "cic:/CoRN/algebra/CPolynomials/CPoly_CRing_ctd/helpful_section/p.var" "CPoly_CRing_ctd__helpful_section__". -inline "cic:/CoRN/algebra/CPolynomials/q.var". +inline "cic:/CoRN/algebra/CPolynomials/CPoly_CRing_ctd/helpful_section/q.var" "CPoly_CRing_ctd__helpful_section__". -inline "cic:/CoRN/algebra/CPolynomials/c.var". +inline "cic:/CoRN/algebra/CPolynomials/CPoly_CRing_ctd/helpful_section/c.var" "CPoly_CRing_ctd__helpful_section__". -inline "cic:/CoRN/algebra/CPolynomials/d.var". +inline "cic:/CoRN/algebra/CPolynomials/CPoly_CRing_ctd/helpful_section/d.var" "CPoly_CRing_ctd__helpful_section__". inline "cic:/CoRN/algebra/CPolynomials/linear_eq_zero_.con". @@ -403,7 +403,7 @@ inline "cic:/CoRN/algebra/CPolynomials/_linear_ap_linear.con". inline "cic:/CoRN/algebra/CPolynomials/linear_ap_linear.con". (* UNEXPORTED -End helpful_section. +End helpful_section *) inline "cic:/CoRN/algebra/CPolynomials/Ccpoly_induc.con". @@ -443,7 +443,7 @@ inline "cic:/CoRN/algebra/CPolynomials/cpoly_apply_wd.con". inline "cic:/CoRN/algebra/CPolynomials/cpoly_apply_fun.con". (* UNEXPORTED -End CPoly_CRing_ctd. +End CPoly_CRing_ctd *) (*#* @@ -471,10 +471,10 @@ Let [R] be a ring and write [RX] for the ring of polynomials over [R]. *) (* UNEXPORTED -Section Poly_properties. +Section Poly_properties *) -inline "cic:/CoRN/algebra/CPolynomials/R.var". +inline "cic:/CoRN/algebra/CPolynomials/Poly_properties/R.var" "Poly_properties__". (* NOTATION Notation RX := (cpoly_cring R). @@ -582,17 +582,17 @@ inline "cic:/CoRN/algebra/CPolynomials/Sum0_cpoly_ap.con". inline "cic:/CoRN/algebra/CPolynomials/Sum_cpoly_ap.con". (* UNEXPORTED -End Poly_properties. +End Poly_properties *) (*#* ** Induction properties of polynomials for [Prop] *) (* UNEXPORTED -Section Poly_Prop_Induction. +Section Poly_Prop_Induction *) -inline "cic:/CoRN/algebra/CPolynomials/CR.var". +inline "cic:/CoRN/algebra/CPolynomials/Poly_Prop_Induction/CR.var" "Poly_Prop_Induction__". (* NOTATION Notation Cpoly := (cpoly CR). @@ -613,7 +613,7 @@ Notation Cpoly_cring := (cpoly_cring CR). inline "cic:/CoRN/algebra/CPolynomials/cpoly_double_ind.con". (* UNEXPORTED -End Poly_Prop_Induction. +End Poly_Prop_Induction *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/algebra/CRings.ma b/helm/software/matita/contribs/CoRN-Decl/algebra/CRings.ma index 4a79f1220..64f84532b 100644 --- a/helm/software/matita/contribs/CoRN-Decl/algebra/CRings.ma +++ b/helm/software/matita/contribs/CoRN-Decl/algebra/CRings.ma @@ -115,7 +115,7 @@ Infix "[*]" := cr_mult (at level 40, left associativity). *) (* UNEXPORTED -Section CRing_axioms. +Section CRing_axioms *) (*#* @@ -124,7 +124,7 @@ Section CRing_axioms. %\end{convention}% *) -inline "cic:/CoRN/algebra/CRings/R.var". +inline "cic:/CoRN/algebra/CRings/CRing_axioms/R.var" "CRing_axioms__". inline "cic:/CoRN/algebra/CRings/CRing_is_CRing.con". @@ -149,11 +149,11 @@ inline "cic:/CoRN/algebra/CRings/mult_wdr.con". (* Begin_SpecReals *) (* UNEXPORTED -End CRing_axioms. +End CRing_axioms *) (* UNEXPORTED -Section Ring_constructions. +Section Ring_constructions *) (*#* @@ -163,7 +163,7 @@ Let [R] be a ring. %\end{convention}% *) -inline "cic:/CoRN/algebra/CRings/R.var". +inline "cic:/CoRN/algebra/CRings/Ring_constructions/R.var" "Ring_constructions__". (*#* The multiplicative monoid of a ring is defined as follows. @@ -172,13 +172,13 @@ The multiplicative monoid of a ring is defined as follows. inline "cic:/CoRN/algebra/CRings/Build_multCMonoid.con". (* UNEXPORTED -End Ring_constructions. +End Ring_constructions *) (* End_SpecReals *) (* UNEXPORTED -Section Ring_unfolded. +Section Ring_unfolded *) (*#* @@ -187,11 +187,11 @@ Section Ring_unfolded. %\end{convention}% *) -inline "cic:/CoRN/algebra/CRings/R.var". +inline "cic:/CoRN/algebra/CRings/Ring_unfolded/R.var" "Ring_unfolded__". (* begin hide *) -inline "cic:/CoRN/algebra/CRings/mmR.con". +inline "cic:/CoRN/algebra/CRings/Ring_unfolded/mmR.con" "Ring_unfolded__". (* end hide *) @@ -216,7 +216,7 @@ Hint Resolve ring_dist_unfolded: algebra. inline "cic:/CoRN/algebra/CRings/ring_distl_unfolded.con". (* UNEXPORTED -End Ring_unfolded. +End Ring_unfolded *) (* UNEXPORTED @@ -232,7 +232,7 @@ Hint Resolve ring_dist_unfolded ring_distl_unfolded: algebra. *) (* UNEXPORTED -Section Ring_basics. +Section Ring_basics *) (*#* @@ -241,7 +241,7 @@ Section Ring_basics. %\end{convention}% *) -inline "cic:/CoRN/algebra/CRings/R.var". +inline "cic:/CoRN/algebra/CRings/Ring_basics/R.var" "Ring_basics__". inline "cic:/CoRN/algebra/CRings/one_ap_zero.con". @@ -302,7 +302,7 @@ Hint Resolve ring_distl_minus: algebra. *) (* UNEXPORTED -End Ring_basics. +End Ring_basics *) (* UNEXPORTED @@ -334,7 +334,7 @@ especially geared towards CReals. *) (* UNEXPORTED -Section exponentiation. +Section exponentiation *) (*#* @@ -344,7 +344,7 @@ Let [R] be a ring. %\end{convention}% *) -inline "cic:/CoRN/algebra/CRings/R.var". +inline "cic:/CoRN/algebra/CRings/exponentiation/R.var" "exponentiation__". (* End_SpecReals *) @@ -359,7 +359,7 @@ inline "cic:/CoRN/algebra/CRings/nexp_op.con". (* Begin_SpecReals *) (* UNEXPORTED -End exponentiation. +End exponentiation *) (* End_SpecReals *) @@ -375,7 +375,7 @@ Implicit Arguments nexp_op [R]. (* Begin_SpecReals *) (* UNEXPORTED -Section nat_injection. +Section nat_injection *) (*#* @@ -384,7 +384,7 @@ Section nat_injection. %\end{convention}% *) -inline "cic:/CoRN/algebra/CRings/R.var". +inline "cic:/CoRN/algebra/CRings/nat_injection/R.var" "nat_injection__". (*#* The injection of Coq natural numbers into a ring is called [nring]. @@ -405,7 +405,7 @@ inline "cic:/CoRN/algebra/CRings/nring_comm_mult.con". (* Begin_SpecReals *) (* UNEXPORTED -End nat_injection. +End nat_injection *) (* End_SpecReals *) @@ -481,7 +481,7 @@ In a ring of characteristic zero, [nring] is really an injection. inline "cic:/CoRN/algebra/CRings/nring_different.con". (* UNEXPORTED -Section int_injection. +Section int_injection *) (*#* @@ -491,7 +491,7 @@ Let [R] be a ring. %\end{convention}% *) -inline "cic:/CoRN/algebra/CRings/R.var". +inline "cic:/CoRN/algebra/CRings/int_injection/R.var" "int_injection__". (*#* The injection of Coq integers into a ring is called [zring]. Again, @@ -621,7 +621,7 @@ inline "cic:/CoRN/algebra/CRings/zring_one.con". inline "cic:/CoRN/algebra/CRings/zring_inv_one.con". (* UNEXPORTED -End int_injection. +End int_injection *) (* UNEXPORTED @@ -635,7 +635,7 @@ Hint Resolve pring_convert zring_zero zring_diff zring_plus_nat zring_inv_nat *) (* UNEXPORTED -Section Ring_sums. +Section Ring_sums *) (*#* @@ -644,14 +644,14 @@ Section Ring_sums. %\end{convention}% *) -inline "cic:/CoRN/algebra/CRings/R.var". +inline "cic:/CoRN/algebra/CRings/Ring_sums/R.var" "Ring_sums__". (*#* *** Infinite Ring sums *) (* UNEXPORTED -Section infinite_ring_sums. +Section infinite_ring_sums *) inline "cic:/CoRN/algebra/CRings/Sum_upto.con". @@ -670,11 +670,11 @@ inline "cic:/CoRN/algebra/CRings/seq_from.con". inline "cic:/CoRN/algebra/CRings/Sum_from_upto_alt.con". (* UNEXPORTED -End infinite_ring_sums. +End infinite_ring_sums *) (* UNEXPORTED -Section ring_sums_over_lists. +Section ring_sums_over_lists *) (*#* *** Ring Sums over Lists @@ -689,11 +689,11 @@ inline "cic:/CoRN/algebra/CRings/list_sum_upto_O.con". inline "cic:/CoRN/algebra/CRings/List_Sum_from_upto.con". (* UNEXPORTED -End ring_sums_over_lists. +End ring_sums_over_lists *) (* UNEXPORTED -End Ring_sums. +End Ring_sums *) (*#* @@ -704,10 +704,10 @@ Let [R] be a ring. *) (* UNEXPORTED -Section Dist_properties. +Section Dist_properties *) -inline "cic:/CoRN/algebra/CRings/R.var". +inline "cic:/CoRN/algebra/CRings/Dist_properties/R.var" "Dist_properties__". inline "cic:/CoRN/algebra/CRings/dist_1b.con". @@ -744,7 +744,7 @@ inline "cic:/CoRN/algebra/CRings/mult_distr_sum_rht.con". inline "cic:/CoRN/algebra/CRings/sumx_const.con". (* UNEXPORTED -End Dist_properties. +End Dist_properties *) (* UNEXPORTED @@ -760,10 +760,10 @@ Let [R] be a ring. *) (* UNEXPORTED -Section NExp_properties. +Section NExp_properties *) -inline "cic:/CoRN/algebra/CRings/R.var". +inline "cic:/CoRN/algebra/CRings/NExp_properties/R.var" "NExp_properties__". inline "cic:/CoRN/algebra/CRings/nexp_wd.con". @@ -864,7 +864,7 @@ Hint Resolve nexp_funny': algebra. *) (* UNEXPORTED -End NExp_properties. +End NExp_properties *) (* UNEXPORTED @@ -875,7 +875,7 @@ Hint Resolve nexp_wd nexp_Sn nexp_plus one_nexp mult_nexp nexp_mult zero_nexp *) (* UNEXPORTED -Section CRing_Ops. +Section CRing_Ops *) (*#* @@ -889,22 +889,22 @@ respectively [P] and [Q]. %\end{convention}% *) -inline "cic:/CoRN/algebra/CRings/R.var". +inline "cic:/CoRN/algebra/CRings/CRing_Ops/R.var" "CRing_Ops__". -inline "cic:/CoRN/algebra/CRings/F.var". +inline "cic:/CoRN/algebra/CRings/CRing_Ops/F.var" "CRing_Ops__". -inline "cic:/CoRN/algebra/CRings/G.var". +inline "cic:/CoRN/algebra/CRings/CRing_Ops/G.var" "CRing_Ops__". (* begin hide *) -inline "cic:/CoRN/algebra/CRings/P.con". +inline "cic:/CoRN/algebra/CRings/CRing_Ops/P.con" "CRing_Ops__". -inline "cic:/CoRN/algebra/CRings/Q.con". +inline "cic:/CoRN/algebra/CRings/CRing_Ops/Q.con" "CRing_Ops__". (* end hide *) (* UNEXPORTED -Section Part_Function_Mult. +Section Part_Function_Mult *) inline "cic:/CoRN/algebra/CRings/part_function_mult_strext.con". @@ -912,21 +912,21 @@ inline "cic:/CoRN/algebra/CRings/part_function_mult_strext.con". inline "cic:/CoRN/algebra/CRings/Fmult.con". (* UNEXPORTED -End Part_Function_Mult. +End Part_Function_Mult *) (* UNEXPORTED -Section Part_Function_Nth_Power. +Section Part_Function_Nth_Power *) -inline "cic:/CoRN/algebra/CRings/n.var". +inline "cic:/CoRN/algebra/CRings/CRing_Ops/Part_Function_Nth_Power/n.var" "CRing_Ops__Part_Function_Nth_Power__". inline "cic:/CoRN/algebra/CRings/part_function_nth_strext.con". inline "cic:/CoRN/algebra/CRings/Fnth.con". (* UNEXPORTED -End Part_Function_Nth_Power. +End Part_Function_Nth_Power *) (*#* @@ -934,7 +934,7 @@ End Part_Function_Nth_Power. %\end{convention}% *) -inline "cic:/CoRN/algebra/CRings/R'.var". +inline "cic:/CoRN/algebra/CRings/CRing_Ops/R'.var" "CRing_Ops__". inline "cic:/CoRN/algebra/CRings/included_FMult.con". @@ -942,14 +942,14 @@ inline "cic:/CoRN/algebra/CRings/included_FMult'.con". inline "cic:/CoRN/algebra/CRings/included_FMult''.con". -inline "cic:/CoRN/algebra/CRings/n.var". +inline "cic:/CoRN/algebra/CRings/CRing_Ops/n.var" "CRing_Ops__". inline "cic:/CoRN/algebra/CRings/included_FNth.con". inline "cic:/CoRN/algebra/CRings/included_FNth'.con". (* UNEXPORTED -End CRing_Ops. +End CRing_Ops *) inline "cic:/CoRN/algebra/CRings/Fscalmult.con". @@ -979,27 +979,27 @@ Infix "{^}" := Fnth (at level 30, right associativity). *) (* UNEXPORTED -Section ScalarMultiplication. +Section ScalarMultiplication *) -inline "cic:/CoRN/algebra/CRings/R.var". +inline "cic:/CoRN/algebra/CRings/ScalarMultiplication/R.var" "ScalarMultiplication__". -inline "cic:/CoRN/algebra/CRings/F.var". +inline "cic:/CoRN/algebra/CRings/ScalarMultiplication/F.var" "ScalarMultiplication__". (* begin hide *) -inline "cic:/CoRN/algebra/CRings/P.con". +inline "cic:/CoRN/algebra/CRings/ScalarMultiplication/P.con" "ScalarMultiplication__". (* end hide *) -inline "cic:/CoRN/algebra/CRings/R'.var". +inline "cic:/CoRN/algebra/CRings/ScalarMultiplication/R'.var" "ScalarMultiplication__". inline "cic:/CoRN/algebra/CRings/included_FScalMult.con". inline "cic:/CoRN/algebra/CRings/included_FScalMult'.con". (* UNEXPORTED -End ScalarMultiplication. +End ScalarMultiplication *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/algebra/CSemiGroups.ma b/helm/software/matita/contribs/CoRN-Decl/algebra/CSemiGroups.ma index 85eac7de2..d1ad410c6 100644 --- a/helm/software/matita/contribs/CoRN-Decl/algebra/CSemiGroups.ma +++ b/helm/software/matita/contribs/CoRN-Decl/algebra/CSemiGroups.ma @@ -63,17 +63,17 @@ The axiomatic properties of a semi group. *) (* UNEXPORTED -Section CSemiGroup_axioms. +Section CSemiGroup_axioms *) -inline "cic:/CoRN/algebra/CSemiGroups/G.var". +inline "cic:/CoRN/algebra/CSemiGroups/CSemiGroup_axioms/G.var" "CSemiGroup_axioms__". inline "cic:/CoRN/algebra/CSemiGroups/CSemiGroup_is_CSemiGroup.con". inline "cic:/CoRN/algebra/CSemiGroups/plus_assoc.con". (* UNEXPORTED -End CSemiGroup_axioms. +End CSemiGroup_axioms *) (* Begin_SpecReals *) @@ -86,17 +86,17 @@ Let [G] be a semi-group. *) (* UNEXPORTED -Section CSemiGroup_basics. +Section CSemiGroup_basics *) -inline "cic:/CoRN/algebra/CSemiGroups/G.var". +inline "cic:/CoRN/algebra/CSemiGroups/CSemiGroup_basics/G.var" "CSemiGroup_basics__". (* End_SpecReals *) inline "cic:/CoRN/algebra/CSemiGroups/plus_assoc_unfolded.con". (* UNEXPORTED -End CSemiGroup_basics. +End CSemiGroup_basics *) (* End_SpecReals *) @@ -118,20 +118,20 @@ At this stage, we will always consider automorphisms; we %{\em %could%}% treat t *) (* UNEXPORTED -Section Part_Function_Plus. +Section Part_Function_Plus *) -inline "cic:/CoRN/algebra/CSemiGroups/G.var". +inline "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/G.var" "Part_Function_Plus__". -inline "cic:/CoRN/algebra/CSemiGroups/F.var". +inline "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/F.var" "Part_Function_Plus__". -inline "cic:/CoRN/algebra/CSemiGroups/F'.var". +inline "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/F'.var" "Part_Function_Plus__". (* begin hide *) -inline "cic:/CoRN/algebra/CSemiGroups/P.con". +inline "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/P.con" "Part_Function_Plus__". -inline "cic:/CoRN/algebra/CSemiGroups/Q.con". +inline "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/Q.con" "Part_Function_Plus__". (* end hide *) @@ -144,7 +144,7 @@ inline "cic:/CoRN/algebra/CSemiGroups/Fplus.con". %\end{convention}% *) -inline "cic:/CoRN/algebra/CSemiGroups/R.var". +inline "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/R.var" "Part_Function_Plus__". inline "cic:/CoRN/algebra/CSemiGroups/included_FPlus.con". @@ -153,7 +153,7 @@ inline "cic:/CoRN/algebra/CSemiGroups/included_FPlus'.con". inline "cic:/CoRN/algebra/CSemiGroups/included_FPlus''.con". (* UNEXPORTED -End Part_Function_Plus. +End Part_Function_Plus *) (* UNEXPORTED @@ -180,20 +180,20 @@ predicate on the semi-group which is preserved by [[+]]. *) (* UNEXPORTED -Section SubCSemiGroups. +Section SubCSemiGroups *) -inline "cic:/CoRN/algebra/CSemiGroups/csg.var". +inline "cic:/CoRN/algebra/CSemiGroups/SubCSemiGroups/csg.var" "SubCSemiGroups__". -inline "cic:/CoRN/algebra/CSemiGroups/P.var". +inline "cic:/CoRN/algebra/CSemiGroups/SubCSemiGroups/P.var" "SubCSemiGroups__". -inline "cic:/CoRN/algebra/CSemiGroups/op_pres_P.var". +inline "cic:/CoRN/algebra/CSemiGroups/SubCSemiGroups/op_pres_P.var" "SubCSemiGroups__". -inline "cic:/CoRN/algebra/CSemiGroups/subcrr.con". +inline "cic:/CoRN/algebra/CSemiGroups/SubCSemiGroups/subcrr.con" "SubCSemiGroups__". inline "cic:/CoRN/algebra/CSemiGroups/Build_SubCSemiGroup.con". (* UNEXPORTED -End SubCSemiGroups. +End SubCSemiGroups *) diff --git a/helm/software/matita/contribs/CoRN-Decl/algebra/CSetoidFun.ma b/helm/software/matita/contribs/CoRN-Decl/algebra/CSetoidFun.ma index 84c0c6c26..c72245537 100644 --- a/helm/software/matita/contribs/CoRN-Decl/algebra/CSetoidFun.ma +++ b/helm/software/matita/contribs/CoRN-Decl/algebra/CSetoidFun.ma @@ -23,7 +23,7 @@ include "CoRN.ma". include "algebra/CSetoids.ma". (* UNEXPORTED -Section unary_function_composition. +Section unary_function_composition *) (*#* ** Composition of Setoid functions @@ -32,24 +32,24 @@ 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. *) -inline "cic:/CoRN/algebra/CSetoidFun/S1.var". +inline "cic:/CoRN/algebra/CSetoidFun/unary_function_composition/S1.var" "unary_function_composition__". -inline "cic:/CoRN/algebra/CSetoidFun/S2.var". +inline "cic:/CoRN/algebra/CSetoidFun/unary_function_composition/S2.var" "unary_function_composition__". -inline "cic:/CoRN/algebra/CSetoidFun/S3.var". +inline "cic:/CoRN/algebra/CSetoidFun/unary_function_composition/S3.var" "unary_function_composition__". -inline "cic:/CoRN/algebra/CSetoidFun/f.var". +inline "cic:/CoRN/algebra/CSetoidFun/unary_function_composition/f.var" "unary_function_composition__". -inline "cic:/CoRN/algebra/CSetoidFun/g.var". +inline "cic:/CoRN/algebra/CSetoidFun/unary_function_composition/g.var" "unary_function_composition__". inline "cic:/CoRN/algebra/CSetoidFun/compose_CSetoid_fun.con". (* UNEXPORTED -End unary_function_composition. +End unary_function_composition *) (* UNEXPORTED -Section unary_and_binary_function_composition. +Section unary_and_binary_function_composition *) inline "cic:/CoRN/algebra/CSetoidFun/compose_CSetoid_bin_un_fun.con". @@ -59,14 +59,14 @@ inline "cic:/CoRN/algebra/CSetoidFun/compose_CSetoid_bin_fun.con". inline "cic:/CoRN/algebra/CSetoidFun/compose_CSetoid_un_bin_fun.con". (* UNEXPORTED -End unary_and_binary_function_composition. +End unary_and_binary_function_composition *) (*#* ***Projections *) (* UNEXPORTED -Section function_projection. +Section function_projection *) inline "cic:/CoRN/algebra/CSetoidFun/proj_bin_fun.con". @@ -74,14 +74,14 @@ inline "cic:/CoRN/algebra/CSetoidFun/proj_bin_fun.con". inline "cic:/CoRN/algebra/CSetoidFun/projected_bin_fun.con". (* UNEXPORTED -End function_projection. +End function_projection *) (* UNEXPORTED -Section BinProj. +Section BinProj *) -inline "cic:/CoRN/algebra/CSetoidFun/S.var". +inline "cic:/CoRN/algebra/CSetoidFun/BinProj/S.var" "BinProj__". inline "cic:/CoRN/algebra/CSetoidFun/binproj1.con". @@ -90,7 +90,7 @@ inline "cic:/CoRN/algebra/CSetoidFun/binproj1_strext.con". inline "cic:/CoRN/algebra/CSetoidFun/cs_binproj1.con". (* UNEXPORTED -End BinProj. +End BinProj *) (*#* **Combining operations @@ -99,14 +99,14 @@ End BinProj. *) (* UNEXPORTED -Section CombiningOperations. +Section CombiningOperations *) -inline "cic:/CoRN/algebra/CSetoidFun/S1.var". +inline "cic:/CoRN/algebra/CSetoidFun/CombiningOperations/S1.var" "CombiningOperations__". -inline "cic:/CoRN/algebra/CSetoidFun/S2.var". +inline "cic:/CoRN/algebra/CSetoidFun/CombiningOperations/S2.var" "CombiningOperations__". -inline "cic:/CoRN/algebra/CSetoidFun/S3.var". +inline "cic:/CoRN/algebra/CSetoidFun/CombiningOperations/S3.var" "CombiningOperations__". (*#* In the following definition, we assume [f] is a setoid function from @@ -115,21 +115,21 @@ Then [opOnFun] is the composition [op] after [f]. *) (* UNEXPORTED -Section CombiningUnaryOperations. +Section CombiningUnaryOperations *) -inline "cic:/CoRN/algebra/CSetoidFun/f.var". +inline "cic:/CoRN/algebra/CSetoidFun/CombiningOperations/CombiningUnaryOperations/f.var" "CombiningOperations__CombiningUnaryOperations__". -inline "cic:/CoRN/algebra/CSetoidFun/op.var". +inline "cic:/CoRN/algebra/CSetoidFun/CombiningOperations/CombiningUnaryOperations/op.var" "CombiningOperations__CombiningUnaryOperations__". inline "cic:/CoRN/algebra/CSetoidFun/opOnFun.con". (* UNEXPORTED -End CombiningUnaryOperations. +End CombiningUnaryOperations *) (* UNEXPORTED -End CombiningOperations. +End CombiningOperations *) (*#* **Partial Functions @@ -155,7 +155,7 @@ Before we state our definitions we need to do some work on domains. *) (* UNEXPORTED -Section SubSets_of_G. +Section SubSets_of_G *) (*#* ***Subsets of Setoids @@ -173,15 +173,15 @@ welldefinedness. %\end{convention}% *) -inline "cic:/CoRN/algebra/CSetoidFun/S.var". +inline "cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/S.var" "SubSets_of_G__". (* UNEXPORTED -Section Conjunction. +Section Conjunction *) -inline "cic:/CoRN/algebra/CSetoidFun/P.var". +inline "cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Conjunction/P.var" "SubSets_of_G__Conjunction__". -inline "cic:/CoRN/algebra/CSetoidFun/Q.var". +inline "cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Conjunction/Q.var" "SubSets_of_G__Conjunction__". inline "cic:/CoRN/algebra/CSetoidFun/conjP.con". @@ -192,16 +192,16 @@ inline "cic:/CoRN/algebra/CSetoidFun/prj2.con". inline "cic:/CoRN/algebra/CSetoidFun/conj_wd.con". (* UNEXPORTED -End Conjunction. +End Conjunction *) (* UNEXPORTED -Section Disjunction. +Section Disjunction *) -inline "cic:/CoRN/algebra/CSetoidFun/P.var". +inline "cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Disjunction/P.var" "SubSets_of_G__Disjunction__". -inline "cic:/CoRN/algebra/CSetoidFun/Q.var". +inline "cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Disjunction/Q.var" "SubSets_of_G__Disjunction__". (*#* Although at this stage we never use it, for completeness's sake we also treat disjunction (corresponding to union of subsets). @@ -216,20 +216,20 @@ inline "cic:/CoRN/algebra/CSetoidFun/inj2.con". inline "cic:/CoRN/algebra/CSetoidFun/disj_wd.con". (* UNEXPORTED -End Disjunction. +End Disjunction *) (* UNEXPORTED -Section Extension. +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]. *) -inline "cic:/CoRN/algebra/CSetoidFun/P.var". +inline "cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Extension/P.var" "SubSets_of_G__Extension__". -inline "cic:/CoRN/algebra/CSetoidFun/R.var". +inline "cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Extension/R.var" "SubSets_of_G__Extension__". inline "cic:/CoRN/algebra/CSetoidFun/extend.con". @@ -242,11 +242,11 @@ inline "cic:/CoRN/algebra/CSetoidFun/ext2.con". inline "cic:/CoRN/algebra/CSetoidFun/extension_wd.con". (* UNEXPORTED -End Extension. +End Extension *) (* UNEXPORTED -End SubSets_of_G. +End SubSets_of_G *) (* NOTATION @@ -365,10 +365,10 @@ Hint Resolve CI: core. *) (* UNEXPORTED -Section CSetoid_Ops. +Section CSetoid_Ops *) -inline "cic:/CoRN/algebra/CSetoidFun/S.var". +inline "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/S.var" "CSetoid_Ops__". (*#* To begin with, we want to be able to ``see'' each total function as a partial function. @@ -377,7 +377,7 @@ To begin with, we want to be able to ``see'' each total function as a partial fu inline "cic:/CoRN/algebra/CSetoidFun/total_eq_part.con". (* UNEXPORTED -Section Part_Function_Const. +Section Part_Function_Const *) (*#* @@ -387,22 +387,22 @@ In any setoid we can also define constant functions (one for each element of the %\end{convention}% *) -inline "cic:/CoRN/algebra/CSetoidFun/c.var". +inline "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Const/c.var" "CSetoid_Ops__Part_Function_Const__". inline "cic:/CoRN/algebra/CSetoidFun/Fconst.con". (* UNEXPORTED -End Part_Function_Const. +End Part_Function_Const *) (* UNEXPORTED -Section Part_Function_Id. +Section Part_Function_Id *) inline "cic:/CoRN/algebra/CSetoidFun/Fid.con". (* UNEXPORTED -End Part_Function_Id. +End Part_Function_Id *) (*#* @@ -415,22 +415,22 @@ If we have two setoid functions [F] and [G] we can always compose them. The dom *) (* UNEXPORTED -Section Part_Function_Composition. +Section Part_Function_Composition *) -inline "cic:/CoRN/algebra/CSetoidFun/G.var". +inline "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Composition/G.var" "CSetoid_Ops__Part_Function_Composition__". -inline "cic:/CoRN/algebra/CSetoidFun/F.var". +inline "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Composition/F.var" "CSetoid_Ops__Part_Function_Composition__". (* begin hide *) -inline "cic:/CoRN/algebra/CSetoidFun/P.con". +inline "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Composition/P.con" "CSetoid_Ops__Part_Function_Composition__". -inline "cic:/CoRN/algebra/CSetoidFun/Q.con". +inline "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Composition/Q.con" "CSetoid_Ops__Part_Function_Composition__". (* end hide *) -inline "cic:/CoRN/algebra/CSetoidFun/R.con". +inline "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Composition/R.con" "CSetoid_Ops__Part_Function_Composition__". inline "cic:/CoRN/algebra/CSetoidFun/part_function_comp_strext.con". @@ -439,11 +439,11 @@ inline "cic:/CoRN/algebra/CSetoidFun/part_function_comp_dom_wd.con". inline "cic:/CoRN/algebra/CSetoidFun/Fcomp.con". (* UNEXPORTED -End Part_Function_Composition. +End Part_Function_Composition *) (* UNEXPORTED -End CSetoid_Ops. +End CSetoid_Ops *) (*#* @@ -452,28 +452,28 @@ End CSetoid_Ops. *) (* UNEXPORTED -Section BinPart_Function_Composition. +Section BinPart_Function_Composition *) -inline "cic:/CoRN/algebra/CSetoidFun/S1.var". +inline "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/S1.var" "BinPart_Function_Composition__". -inline "cic:/CoRN/algebra/CSetoidFun/S2.var". +inline "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/S2.var" "BinPart_Function_Composition__". -inline "cic:/CoRN/algebra/CSetoidFun/S3.var". +inline "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/S3.var" "BinPart_Function_Composition__". -inline "cic:/CoRN/algebra/CSetoidFun/G.var". +inline "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/G.var" "BinPart_Function_Composition__". -inline "cic:/CoRN/algebra/CSetoidFun/F.var". +inline "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/F.var" "BinPart_Function_Composition__". (* begin hide *) -inline "cic:/CoRN/algebra/CSetoidFun/P.con". +inline "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/P.con" "BinPart_Function_Composition__". -inline "cic:/CoRN/algebra/CSetoidFun/Q.con". +inline "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/Q.con" "BinPart_Function_Composition__". (* end hide *) -inline "cic:/CoRN/algebra/CSetoidFun/R.con". +inline "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/R.con" "BinPart_Function_Composition__". inline "cic:/CoRN/algebra/CSetoidFun/bin_part_function_comp_strext.con". @@ -482,7 +482,7 @@ inline "cic:/CoRN/algebra/CSetoidFun/bin_part_function_comp_dom_wd.con". inline "cic:/CoRN/algebra/CSetoidFun/BinFcomp.con". (* UNEXPORTED -End BinPart_Function_Composition. +End BinPart_Function_Composition *) (* Different tokens for compatibility with coqdoc *) @@ -512,7 +512,7 @@ Hint Resolve pfwdef bpfwdef: algebra. *) (* UNEXPORTED -Section bijections. +Section bijections *) (*#* **Bijections *) @@ -574,7 +574,7 @@ Implicit Arguments Inv [A B]. inline "cic:/CoRN/algebra/CSetoidFun/Inv_bij.con". (* UNEXPORTED -End bijections. +End bijections *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/algebra/CSetoidInc.ma b/helm/software/matita/contribs/CoRN-Decl/algebra/CSetoidInc.ma index ad6490a75..578515108 100644 --- a/helm/software/matita/contribs/CoRN-Decl/algebra/CSetoidInc.ma +++ b/helm/software/matita/contribs/CoRN-Decl/algebra/CSetoidInc.ma @@ -25,26 +25,26 @@ include "CoRN.ma". include "algebra/CSetoidFun.ma". (* UNEXPORTED -Section inclusion. +Section inclusion *) (*#* ** Inclusion Let [S] be a setoid, and [P], [Q], [R] be predicates on [S]. *) -inline "cic:/CoRN/algebra/CSetoidInc/S.var". +inline "cic:/CoRN/algebra/CSetoidInc/inclusion/S.var" "inclusion__". inline "cic:/CoRN/algebra/CSetoidInc/included.con". (* UNEXPORTED -Section Basics. +Section Basics *) -inline "cic:/CoRN/algebra/CSetoidInc/P.var". +inline "cic:/CoRN/algebra/CSetoidInc/inclusion/Basics/P.var" "inclusion__Basics__". -inline "cic:/CoRN/algebra/CSetoidInc/Q.var". +inline "cic:/CoRN/algebra/CSetoidInc/inclusion/Basics/Q.var" "inclusion__Basics__". -inline "cic:/CoRN/algebra/CSetoidInc/R.var". +inline "cic:/CoRN/algebra/CSetoidInc/inclusion/Basics/R.var" "inclusion__Basics__". inline "cic:/CoRN/algebra/CSetoidInc/included_refl.con". @@ -63,7 +63,7 @@ inline "cic:/CoRN/algebra/CSetoidInc/included_conj_rht.con". inline "cic:/CoRN/algebra/CSetoidInc/included_extend.con". (* UNEXPORTED -End Basics. +End Basics *) (*#* @@ -72,26 +72,26 @@ by [P] and [Q], respectively, the domains of [F] and [G]. %\end{convention}% *) -inline "cic:/CoRN/algebra/CSetoidInc/F.var". +inline "cic:/CoRN/algebra/CSetoidInc/inclusion/F.var" "inclusion__". -inline "cic:/CoRN/algebra/CSetoidInc/G.var". +inline "cic:/CoRN/algebra/CSetoidInc/inclusion/G.var" "inclusion__". (* begin hide *) -inline "cic:/CoRN/algebra/CSetoidInc/P.con". +inline "cic:/CoRN/algebra/CSetoidInc/inclusion/P.con" "inclusion__". -inline "cic:/CoRN/algebra/CSetoidInc/Q.con". +inline "cic:/CoRN/algebra/CSetoidInc/inclusion/Q.con" "inclusion__". (* end hide *) -inline "cic:/CoRN/algebra/CSetoidInc/R.var". +inline "cic:/CoRN/algebra/CSetoidInc/inclusion/R.var" "inclusion__". inline "cic:/CoRN/algebra/CSetoidInc/included_FComp.con". inline "cic:/CoRN/algebra/CSetoidInc/included_FComp'.con". (* UNEXPORTED -End inclusion. +End inclusion *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/algebra/CSetoids.ma b/helm/software/matita/contribs/CoRN-Decl/algebra/CSetoids.ma index 2f1ed75ca..0538d085b 100644 --- a/helm/software/matita/contribs/CoRN-Decl/algebra/CSetoids.ma +++ b/helm/software/matita/contribs/CoRN-Decl/algebra/CSetoids.ma @@ -93,10 +93,10 @@ Notice that their type depends on the main logical connective. *) (* UNEXPORTED -Section Properties_of_relations. +Section Properties_of_relations *) -inline "cic:/CoRN/algebra/CSetoids/A.var". +inline "cic:/CoRN/algebra/CSetoids/Properties_of_relations/A.var" "Properties_of_relations__". inline "cic:/CoRN/algebra/CSetoids/irreflexive.con". @@ -107,7 +107,7 @@ inline "cic:/CoRN/algebra/CSetoids/tight_apart.con". inline "cic:/CoRN/algebra/CSetoids/antisymmetric.con". (* UNEXPORTED -End Properties_of_relations. +End Properties_of_relations *) (* begin hide *) @@ -177,10 +177,10 @@ Let [S] be a setoid. (* Begin_SpecReals *) (* UNEXPORTED -Section CSetoid_axioms. +Section CSetoid_axioms *) -inline "cic:/CoRN/algebra/CSetoids/S.var". +inline "cic:/CoRN/algebra/CSetoids/CSetoid_axioms/S.var" "CSetoid_axioms__". inline "cic:/CoRN/algebra/CSetoids/CSetoid_is_CSetoid.con". @@ -193,7 +193,7 @@ inline "cic:/CoRN/algebra/CSetoids/ap_cotransitive.con". inline "cic:/CoRN/algebra/CSetoids/ap_tight.con". (* UNEXPORTED -End CSetoid_axioms. +End CSetoid_axioms *) (* End_SpecReals *) @@ -206,10 +206,10 @@ End CSetoid_axioms. (* Begin_SpecReals *) (* UNEXPORTED -Section CSetoid_basics. +Section CSetoid_basics *) -inline "cic:/CoRN/algebra/CSetoids/S.var". +inline "cic:/CoRN/algebra/CSetoids/CSetoid_basics/S.var" "CSetoid_basics__". (* End_SpecReals *) @@ -285,13 +285,13 @@ inline "cic:/CoRN/algebra/CSetoids/eq_imp_not_neq.con". (* Begin_SpecReals *) (* UNEXPORTED -End CSetoid_basics. +End CSetoid_basics *) (* End_SpecReals *) (* UNEXPORTED -Section product_csetoid. +Section product_csetoid *) (*#* **The product of setoids *) @@ -305,7 +305,7 @@ inline "cic:/CoRN/algebra/CSetoids/prodcsetoid_is_CSetoid.con". inline "cic:/CoRN/algebra/CSetoids/ProdCSetoid.con". (* UNEXPORTED -End product_csetoid. +End product_csetoid *) (* UNEXPORTED @@ -345,10 +345,10 @@ on predicates and relations. *) (* UNEXPORTED -Section CSetoid_relations_and_predicates. +Section CSetoid_relations_and_predicates *) -inline "cic:/CoRN/algebra/CSetoids/S.var". +inline "cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/S.var" "CSetoid_relations_and_predicates__". (* End_SpecReals *) @@ -361,17 +361,17 @@ At this stage, we consider [CProp]- and [Prop]-valued predicates on setoids. *) (* UNEXPORTED -Section CSetoidPredicates. +Section CSetoidPredicates *) -inline "cic:/CoRN/algebra/CSetoids/P.var". +inline "cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/CSetoidPredicates/P.var" "CSetoid_relations_and_predicates__CSetoidPredicates__". inline "cic:/CoRN/algebra/CSetoids/pred_strong_ext.con". inline "cic:/CoRN/algebra/CSetoids/pred_wd.con". (* UNEXPORTED -End CSetoidPredicates. +End CSetoidPredicates *) inline "cic:/CoRN/algebra/CSetoids/CSetoid_predicate.ind". @@ -383,17 +383,17 @@ inline "cic:/CoRN/algebra/CSetoids/csp_wd.con". (*#* Similar, with [Prop] instead of [CProp]. *) (* UNEXPORTED -Section CSetoidPPredicates. +Section CSetoidPPredicates *) -inline "cic:/CoRN/algebra/CSetoids/P.var". +inline "cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/CSetoidPPredicates/P.var" "CSetoid_relations_and_predicates__CSetoidPPredicates__". inline "cic:/CoRN/algebra/CSetoids/pred_strong_ext'.con". inline "cic:/CoRN/algebra/CSetoids/pred_wd'.con". (* UNEXPORTED -End CSetoidPPredicates. +End CSetoidPPredicates *) (*#* ***Definition of a setoid predicate *) @@ -412,10 +412,10 @@ Let [R] be a relation on (the carrier of) [S]. %\end{convention}% *) (* UNEXPORTED -Section CsetoidRelations. +Section CsetoidRelations *) -inline "cic:/CoRN/algebra/CSetoids/R.var". +inline "cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/CsetoidRelations/R.var" "CSetoid_relations_and_predicates__CsetoidRelations__". inline "cic:/CoRN/algebra/CSetoids/rel_wdr.con". @@ -438,7 +438,7 @@ inline "cic:/CoRN/algebra/CSetoids/rel_strextarg_imp_strext.con". (* Begin_SpecReals *) (* UNEXPORTED -End CsetoidRelations. +End CsetoidRelations *) (*#* ***Definition of a setoid relation @@ -455,10 +455,10 @@ Let [R] be a relation on (the carrier of) [S]. *) (* UNEXPORTED -Section CCsetoidRelations. +Section CCsetoidRelations *) -inline "cic:/CoRN/algebra/CSetoids/R.var". +inline "cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/CCsetoidRelations/R.var" "CSetoid_relations_and_predicates__CCsetoidRelations__". inline "cic:/CoRN/algebra/CSetoids/Crel_wdr.con". @@ -481,7 +481,7 @@ inline "cic:/CoRN/algebra/CSetoids/Crel_strextarg_imp_strext.con". (* Begin_SpecReals *) (* UNEXPORTED -End CCsetoidRelations. +End CCsetoidRelations *) (*#* ***Definition of a [CProp] setoid relation @@ -513,7 +513,7 @@ inline "cic:/CoRN/algebra/CSetoids/predS_well_def.con". (* Begin_SpecReals *) (* UNEXPORTED -End CSetoid_relations_and_predicates. +End CSetoid_relations_and_predicates *) (* UNEXPORTED @@ -540,17 +540,17 @@ First we consider unary functions. *) (* Begin_SpecReals *) (* UNEXPORTED -Section CSetoid_functions. +Section CSetoid_functions *) -inline "cic:/CoRN/algebra/CSetoids/S1.var". +inline "cic:/CoRN/algebra/CSetoids/CSetoid_functions/S1.var" "CSetoid_functions__". -inline "cic:/CoRN/algebra/CSetoids/S2.var". +inline "cic:/CoRN/algebra/CSetoids/CSetoid_functions/S2.var" "CSetoid_functions__". -inline "cic:/CoRN/algebra/CSetoids/S3.var". +inline "cic:/CoRN/algebra/CSetoids/CSetoid_functions/S3.var" "CSetoid_functions__". (* UNEXPORTED -Section unary_functions. +Section unary_functions *) (*#* @@ -558,7 +558,7 @@ In the following two definitions, [f] is a function from (the carrier of) [S1] to (the carrier of) [S2]. *) -inline "cic:/CoRN/algebra/CSetoids/f.var". +inline "cic:/CoRN/algebra/CSetoids/CSetoid_functions/unary_functions/f.var" "CSetoid_functions__unary_functions__". inline "cic:/CoRN/algebra/CSetoids/fun_wd.con". @@ -571,7 +571,7 @@ inline "cic:/CoRN/algebra/CSetoids/fun_strext_imp_wd.con". (* Begin_SpecReals *) (* UNEXPORTED -End unary_functions. +End unary_functions *) inline "cic:/CoRN/algebra/CSetoids/CSetoid_fun.ind". @@ -587,7 +587,7 @@ inline "cic:/CoRN/algebra/CSetoids/Const_CSetoid_fun.con". (* Begin_SpecReals *) (* UNEXPORTED -Section binary_functions. +Section binary_functions *) (*#* @@ -596,7 +596,7 @@ In the following two definitions, [f] is a function from [S1] and [S2] to [S3]. *) -inline "cic:/CoRN/algebra/CSetoids/f.var". +inline "cic:/CoRN/algebra/CSetoids/CSetoid_functions/binary_functions/f.var" "CSetoid_functions__binary_functions__". inline "cic:/CoRN/algebra/CSetoids/bin_fun_wd.con". @@ -609,7 +609,7 @@ inline "cic:/CoRN/algebra/CSetoids/bin_fun_strext_imp_wd.con". (* Begin_SpecReals *) (* UNEXPORTED -End binary_functions. +End binary_functions *) inline "cic:/CoRN/algebra/CSetoids/CSetoid_bin_fun.ind". @@ -625,7 +625,7 @@ inline "cic:/CoRN/algebra/CSetoids/csf_strext_unfolded.con". inline "cic:/CoRN/algebra/CSetoids/csbf_wd_unfolded.con". (* UNEXPORTED -End CSetoid_functions. +End CSetoid_functions *) (* End_SpecReals *) @@ -658,10 +658,10 @@ Let [S] be a setoid. *) (* UNEXPORTED -Section csetoid_inner_ops. +Section csetoid_inner_ops *) -inline "cic:/CoRN/algebra/CSetoids/S.var". +inline "cic:/CoRN/algebra/CSetoids/csetoid_inner_ops/S.var" "csetoid_inner_ops__". (*#* Properties of binary operations *) @@ -750,7 +750,7 @@ inline "cic:/CoRN/algebra/CSetoids/bin_op2un_op_lft.con". (* Begin_SpecReals *) (* UNEXPORTED -End csetoid_inner_ops. +End csetoid_inner_ops *) (* End_SpecReals *) @@ -778,12 +778,12 @@ Let [S1] and [S2] be setoids. *) (* UNEXPORTED -Section csetoid_outer_ops. +Section csetoid_outer_ops *) -inline "cic:/CoRN/algebra/CSetoids/S1.var". +inline "cic:/CoRN/algebra/CSetoids/csetoid_outer_ops/S1.var" "csetoid_outer_ops__". -inline "cic:/CoRN/algebra/CSetoids/S2.var". +inline "cic:/CoRN/algebra/CSetoids/csetoid_outer_ops/S2.var" "csetoid_outer_ops__". (*#* Well-defined outer operations on a setoid. @@ -810,7 +810,7 @@ coercion cic:/matita/CoRN-Decl/algebra/CSetoids/outer_op_bin_fun.con 0 (* compou inline "cic:/CoRN/algebra/CSetoids/csoo_wd_unfolded.con". (* UNEXPORTED -End csetoid_outer_ops. +End csetoid_outer_ops *) (* UNEXPORTED @@ -826,12 +826,12 @@ Let [S] be a setoid, and [P] a predicate on the carrier of [S]. *) (* UNEXPORTED -Section SubCSetoids. +Section SubCSetoids *) -inline "cic:/CoRN/algebra/CSetoids/S.var". +inline "cic:/CoRN/algebra/CSetoids/SubCSetoids/S.var" "SubCSetoids__". -inline "cic:/CoRN/algebra/CSetoids/P.var". +inline "cic:/CoRN/algebra/CSetoids/SubCSetoids/P.var" "SubCSetoids__". inline "cic:/CoRN/algebra/CSetoids/subcsetoid_crr.ind". @@ -869,10 +869,10 @@ Let [f] be a unary setoid operation on [S]. *) (* UNEXPORTED -Section SubCSetoid_unary_operations. +Section SubCSetoid_unary_operations *) -inline "cic:/CoRN/algebra/CSetoids/f.var". +inline "cic:/CoRN/algebra/CSetoids/SubCSetoids/SubCSetoid_unary_operations/f.var" "SubCSetoids__SubCSetoid_unary_operations__". inline "cic:/CoRN/algebra/CSetoids/un_op_pres_pred.con". @@ -881,7 +881,7 @@ inline "cic:/CoRN/algebra/CSetoids/un_op_pres_pred.con". Assume [pr:un_op_pres_pred]. %\end{convention}% *) -inline "cic:/CoRN/algebra/CSetoids/pr.var". +inline "cic:/CoRN/algebra/CSetoids/SubCSetoids/SubCSetoid_unary_operations/pr.var" "SubCSetoids__SubCSetoid_unary_operations__". inline "cic:/CoRN/algebra/CSetoids/restr_un_op.con". @@ -892,7 +892,7 @@ inline "cic:/CoRN/algebra/CSetoids/restr_un_op_strext.con". inline "cic:/CoRN/algebra/CSetoids/Build_SubCSetoid_un_op.con". (* UNEXPORTED -End SubCSetoid_unary_operations. +End SubCSetoid_unary_operations *) (*#* ***Subsetoid binary operations @@ -902,10 +902,10 @@ Let [f] be a binary setoid operation on [S]. *) (* UNEXPORTED -Section SubCSetoid_binary_operations. +Section SubCSetoid_binary_operations *) -inline "cic:/CoRN/algebra/CSetoids/f.var". +inline "cic:/CoRN/algebra/CSetoids/SubCSetoids/SubCSetoid_binary_operations/f.var" "SubCSetoids__SubCSetoid_binary_operations__". inline "cic:/CoRN/algebra/CSetoids/bin_op_pres_pred.con". @@ -915,7 +915,7 @@ Assume [bin_op_pres_pred]. %\end{convention}% *) -inline "cic:/CoRN/algebra/CSetoids/pr.var". +inline "cic:/CoRN/algebra/CSetoids/SubCSetoids/SubCSetoid_binary_operations/pr.var" "SubCSetoids__SubCSetoid_binary_operations__". inline "cic:/CoRN/algebra/CSetoids/restr_bin_op.con". @@ -928,13 +928,13 @@ inline "cic:/CoRN/algebra/CSetoids/Build_SubCSetoid_bin_op.con". inline "cic:/CoRN/algebra/CSetoids/restr_f_assoc.con". (* UNEXPORTED -End SubCSetoid_binary_operations. +End SubCSetoid_binary_operations *) (* Begin_SpecReals *) (* UNEXPORTED -End SubCSetoids. +End SubCSetoids *) (* End_SpecReals *) diff --git a/helm/software/matita/contribs/CoRN-Decl/algebra/CSums.ma b/helm/software/matita/contribs/CoRN-Decl/algebra/CSums.ma index b0fc1c6a2..c90312746 100644 --- a/helm/software/matita/contribs/CoRN-Decl/algebra/CSums.ma +++ b/helm/software/matita/contribs/CoRN-Decl/algebra/CSums.ma @@ -39,10 +39,10 @@ include "algebra/CAbGroups.ma". *) (* UNEXPORTED -Section Sums. +Section Sums *) -inline "cic:/CoRN/algebra/CSums/G.var". +inline "cic:/CoRN/algebra/CSums/Sums/G.var" "Sums__". (* Sum1 and Sum use subtraction *) @@ -189,7 +189,7 @@ inline "cic:/CoRN/algebra/CSums/Sum_big_shift.con". inline "cic:/CoRN/algebra/CSums/Sumx_Sum0.con". (* UNEXPORTED -End Sums. +End Sums *) (* UNEXPORTED @@ -216,10 +216,10 @@ often referred to as ``Mengolli Sums''. *) (* UNEXPORTED -Section More_Sums. +Section More_Sums *) -inline "cic:/CoRN/algebra/CSums/G.var". +inline "cic:/CoRN/algebra/CSums/More_Sums/G.var" "More_Sums__". inline "cic:/CoRN/algebra/CSums/Mengolli_Sum.con". @@ -230,7 +230,7 @@ inline "cic:/CoRN/algebra/CSums/str_Mengolli_Sum_gen.con". inline "cic:/CoRN/algebra/CSums/Sumx_to_Sum.con". (* UNEXPORTED -End More_Sums. +End More_Sums *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/algebra/CVectorSpace.ma b/helm/software/matita/contribs/CoRN-Decl/algebra/CVectorSpace.ma index 76324bcdd..85d902536 100644 --- a/helm/software/matita/contribs/CoRN-Decl/algebra/CVectorSpace.ma +++ b/helm/software/matita/contribs/CoRN-Decl/algebra/CVectorSpace.ma @@ -77,12 +77,12 @@ Let [F] be a fiels and let [V] be a vector space over [F] *) (* UNEXPORTED -Section VS_basics. +Section VS_basics *) -inline "cic:/CoRN/algebra/CVectorSpace/F.var". +inline "cic:/CoRN/algebra/CVectorSpace/VS_basics/F.var" "VS_basics__". -inline "cic:/CoRN/algebra/CVectorSpace/V.var". +inline "cic:/CoRN/algebra/CVectorSpace/VS_basics/V.var" "VS_basics__". inline "cic:/CoRN/algebra/CVectorSpace/vs_op_zero.con". @@ -119,7 +119,7 @@ inline "cic:/CoRN/algebra/CVectorSpace/vs_op_resp_ap_zero.con". inline "cic:/CoRN/algebra/CVectorSpace/vs_op_resp_ap_lft.con". (* UNEXPORTED -End VS_basics. +End VS_basics *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/algebra/Cauchy_COF.ma b/helm/software/matita/contribs/CoRN-Decl/algebra/Cauchy_COF.ma index 7070c44d8..46cfc7647 100644 --- a/helm/software/matita/contribs/CoRN-Decl/algebra/Cauchy_COF.ma +++ b/helm/software/matita/contribs/CoRN-Decl/algebra/Cauchy_COF.ma @@ -35,10 +35,10 @@ field [F], we can define a new ordered field of Cauchy sequences over [F]. *) (* UNEXPORTED -Section Structure. +Section Structure *) -inline "cic:/CoRN/algebra/Cauchy_COF/F.var". +inline "cic:/CoRN/algebra/Cauchy_COF/Structure/F.var" "Structure__". (*#* ** Setoid Structure @@ -53,7 +53,7 @@ than the other, equality is the negation of the apartness. inline "cic:/CoRN/algebra/Cauchy_COF/R_Set.con". (* UNEXPORTED -Section CSetoid_Structure. +Section CSetoid_Structure *) inline "cic:/CoRN/algebra/Cauchy_COF/R_lt.con". @@ -77,11 +77,11 @@ inline "cic:/CoRN/algebra/Cauchy_COF/R_ap_eq_tight.con". inline "cic:/CoRN/algebra/Cauchy_COF/R_CSetoid.con". (* UNEXPORTED -End CSetoid_Structure. +End CSetoid_Structure *) (* UNEXPORTED -Section Group_Structure. +Section Group_Structure *) (*#* @@ -113,11 +113,11 @@ inline "cic:/CoRN/algebra/Cauchy_COF/Rinv.con". inline "cic:/CoRN/algebra/Cauchy_COF/R_CAbGroup.con". (* UNEXPORTED -End Group_Structure. +End Group_Structure *) (* UNEXPORTED -Section Ring_Structure. +Section Ring_Structure *) (*#* ** Ring Structure @@ -155,11 +155,11 @@ inline "cic:/CoRN/algebra/Cauchy_COF/R_one_lft_unit.con". inline "cic:/CoRN/algebra/Cauchy_COF/R_CRing.con". (* UNEXPORTED -End Ring_Structure. +End Ring_Structure *) (* UNEXPORTED -Section Field_Structure. +Section Field_Structure *) (*#* ** Field Structure @@ -181,11 +181,11 @@ inline "cic:/CoRN/algebra/Cauchy_COF/R_recip_inverse'.con". inline "cic:/CoRN/algebra/Cauchy_COF/R_CField.con". (* UNEXPORTED -End Field_Structure. +End Field_Structure *) (* UNEXPORTED -Section Order. +Section Order *) (*#* ** Order Structure @@ -208,7 +208,7 @@ inline "cic:/CoRN/algebra/Cauchy_COF/R_mult_resp_lt.con". inline "cic:/CoRN/algebra/Cauchy_COF/R_COrdField.con". (* UNEXPORTED -End Order. +End Order *) (*#* @@ -217,7 +217,7 @@ Auxiliary characterizations of the main relations on [R_Set]. *) (* UNEXPORTED -Section Auxiliary. +Section Auxiliary *) inline "cic:/CoRN/algebra/Cauchy_COF/Rlt_alt_1.con". @@ -235,10 +235,10 @@ inline "cic:/CoRN/algebra/Cauchy_COF/Eq_alt_2_1.con". inline "cic:/CoRN/algebra/Cauchy_COF/Eq_alt_2_2.con". (* UNEXPORTED -End Auxiliary. +End Auxiliary *) (* UNEXPORTED -End Structure. +End Structure *) diff --git a/helm/software/matita/contribs/CoRN-Decl/algebra/Expon.ma b/helm/software/matita/contribs/CoRN-Decl/algebra/Expon.ma index d2e834f66..e8a28b301 100644 --- a/helm/software/matita/contribs/CoRN-Decl/algebra/Expon.ma +++ b/helm/software/matita/contribs/CoRN-Decl/algebra/Expon.ma @@ -33,10 +33,10 @@ include "tactics/Transparent_algebra.ma". *) (* UNEXPORTED -Section More_Nexp. +Section More_Nexp *) -inline "cic:/CoRN/algebra/Expon/R.var". +inline "cic:/CoRN/algebra/Expon/More_Nexp/R.var" "More_Nexp__". inline "cic:/CoRN/algebra/Expon/nexp_resp_ap_zero.con". @@ -79,7 +79,7 @@ inline "cic:/CoRN/algebra/Expon/nexp_resp_le.con". inline "cic:/CoRN/algebra/Expon/bin_less_un.con". (* UNEXPORTED -End More_Nexp. +End More_Nexp *) (* UNEXPORTED @@ -96,10 +96,10 @@ Implicit Arguments nexp_resp_ap_zero [R x]. *) (* UNEXPORTED -Section Zexp_def. +Section Zexp_def *) -inline "cic:/CoRN/algebra/Expon/R.var". +inline "cic:/CoRN/algebra/Expon/Zexp_def/R.var" "Zexp_def__". (*#* It would be nicer to define [zexp] using [caseZdiff], but we already @@ -109,7 +109,7 @@ have most properties now. inline "cic:/CoRN/algebra/Expon/zexp.con". (* UNEXPORTED -End Zexp_def. +End Zexp_def *) (* UNEXPORTED @@ -126,10 +126,10 @@ Notation "( x [//] Hx ) [^^] n" := (zexp x Hx n) (at level 0). *) (* UNEXPORTED -Section Zexp_properties. +Section Zexp_properties *) -inline "cic:/CoRN/algebra/Expon/R.var". +inline "cic:/CoRN/algebra/Expon/Zexp_properties/R.var" "Zexp_properties__". inline "cic:/CoRN/algebra/Expon/zexp_zero.con". @@ -258,7 +258,7 @@ Hint Resolve zexp_funny': algebra. inline "cic:/CoRN/algebra/Expon/zexp_pos.con". (* UNEXPORTED -End Zexp_properties. +End Zexp_properties *) (* UNEXPORTED @@ -273,16 +273,16 @@ Hint Resolve zexp_wd: algebra_c. *) (* UNEXPORTED -Section Root_Unique. +Section Root_Unique *) -inline "cic:/CoRN/algebra/Expon/R.var". +inline "cic:/CoRN/algebra/Expon/Root_Unique/R.var" "Root_Unique__". inline "cic:/CoRN/algebra/Expon/root_unique.con". inline "cic:/CoRN/algebra/Expon/root_one.con". (* UNEXPORTED -End Root_Unique. +End Root_Unique *) diff --git a/helm/software/matita/contribs/CoRN-Decl/algebra/ListType.ma b/helm/software/matita/contribs/CoRN-Decl/algebra/ListType.ma index 1decb2491..45742b7c2 100644 --- a/helm/software/matita/contribs/CoRN-Decl/algebra/ListType.ma +++ b/helm/software/matita/contribs/CoRN-Decl/algebra/ListType.ma @@ -51,10 +51,10 @@ library of Coq but moved to the Type level. *) (* UNEXPORTED -Section List. +Section List *) -inline "cic:/CoRN/algebra/ListType/A.var". +inline "cic:/CoRN/algebra/ListType/List/A.var" "List__". inline "cic:/CoRN/algebra/ListType/list.ind". @@ -97,7 +97,7 @@ inline "cic:/CoRN/algebra/ListType/length.con". (*#*****************************) (* UNEXPORTED -Section length_order. +Section length_order *) inline "cic:/CoRN/algebra/ListType/lel.con". @@ -106,15 +106,15 @@ inline "cic:/CoRN/algebra/ListType/lel.con". Hint Unfold lel: list. *) -inline "cic:/CoRN/algebra/ListType/a.var". +inline "cic:/CoRN/algebra/ListType/List/length_order/a.var" "List__length_order__". -inline "cic:/CoRN/algebra/ListType/b.var". +inline "cic:/CoRN/algebra/ListType/List/length_order/b.var" "List__length_order__". -inline "cic:/CoRN/algebra/ListType/l.var". +inline "cic:/CoRN/algebra/ListType/List/length_order/l.var" "List__length_order__". -inline "cic:/CoRN/algebra/ListType/m.var". +inline "cic:/CoRN/algebra/ListType/List/length_order/m.var" "List__length_order__". -inline "cic:/CoRN/algebra/ListType/n.var". +inline "cic:/CoRN/algebra/ListType/List/length_order/n.var" "List__length_order__". inline "cic:/CoRN/algebra/ListType/lel_refl.con". @@ -129,7 +129,7 @@ inline "cic:/CoRN/algebra/ListType/lel_tail.con". inline "cic:/CoRN/algebra/ListType/lel_nil.con". (* UNEXPORTED -End length_order. +End length_order *) (* UNEXPORTED @@ -204,7 +204,7 @@ Hint Resolve incl_cons: list v62. inline "cic:/CoRN/algebra/ListType/incl_app.con". (* UNEXPORTED -End List. +End List *) (* UNEXPORTED @@ -220,19 +220,19 @@ Implicit Arguments cons [A]. *) (* UNEXPORTED -Section Map. +Section Map *) -inline "cic:/CoRN/algebra/ListType/A.var". +inline "cic:/CoRN/algebra/ListType/Map/A.var" "Map__". -inline "cic:/CoRN/algebra/ListType/B.var". +inline "cic:/CoRN/algebra/ListType/Map/B.var" "Map__". -inline "cic:/CoRN/algebra/ListType/f.var". +inline "cic:/CoRN/algebra/ListType/Map/f.var" "Map__". inline "cic:/CoRN/algebra/ListType/map.con". (* UNEXPORTED -End Map. +End Map *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/complex/AbsCC.ma b/helm/software/matita/contribs/CoRN-Decl/complex/AbsCC.ma index e2d902b9b..0182da47f 100644 --- a/helm/software/matita/contribs/CoRN-Decl/complex/AbsCC.ma +++ b/helm/software/matita/contribs/CoRN-Decl/complex/AbsCC.ma @@ -26,7 +26,7 @@ include "complex/CComplex.ma". ** Properties of [AbsCC] *) (* UNEXPORTED -Section AbsCC_properties. +Section AbsCC_properties *) inline "cic:/CoRN/complex/AbsCC/AbsCC_nonneg.con". @@ -83,7 +83,7 @@ inline "cic:/CoRN/complex/AbsCC/AbsCC_small_imp_eq.con". (* begin hide *) -inline "cic:/CoRN/complex/AbsCC/l_1_1_2.con". +inline "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_1_1_2.con" "AbsCC_properties__". (* end hide *) @@ -99,7 +99,7 @@ Hint Resolve AbsCC_square_Re_Im: algebra. (* begin hide *) -inline "cic:/CoRN/complex/AbsCC/l_1_2_3_CC.con". +inline "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_1_2_3_CC.con" "AbsCC_properties__". (* end hide *) @@ -139,16 +139,16 @@ inline "cic:/CoRN/complex/AbsCC/Cexis_AFS_CC.con". (* begin hide *) -inline "cic:/CoRN/complex/AbsCC/l_4_1_2.con". +inline "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_4_1_2.con" "AbsCC_properties__". -inline "cic:/CoRN/complex/AbsCC/l_4_2_3.con". +inline "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_4_2_3.con" "AbsCC_properties__". -inline "cic:/CoRN/complex/AbsCC/l_4_3_4.con". +inline "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_4_3_4.con" "AbsCC_properties__". (* end hide *) (* UNEXPORTED -End AbsCC_properties. +End AbsCC_properties *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/complex/CComplex.ma b/helm/software/matita/contribs/CoRN-Decl/complex/CComplex.ma index 2782cf035..de4d83dbe 100644 --- a/helm/software/matita/contribs/CoRN-Decl/complex/CComplex.ma +++ b/helm/software/matita/contribs/CoRN-Decl/complex/CComplex.ma @@ -41,7 +41,7 @@ include "reals/NRootIR.ma". *) (* UNEXPORTED -Section Complex_Numbers. +Section Complex_Numbers *) inline "cic:/CoRN/complex/CComplex/CC_set.ind". @@ -189,7 +189,7 @@ inline "cic:/CoRN/complex/CComplex/AbsCC.con". inline "cic:/CoRN/complex/CComplex/TwoCC_ap_zero.con". (* UNEXPORTED -End Complex_Numbers. +End Complex_Numbers *) (* begin hide *) @@ -209,7 +209,7 @@ Infix "[+I*]" := cc_set_CC (at level 48, no associativity). (*#* ** Properties of [II] *) (* UNEXPORTED -Section I_properties. +Section I_properties *) inline "cic:/CoRN/complex/CComplex/I_square.con". @@ -251,7 +251,7 @@ inline "cic:/CoRN/complex/CComplex/Im_resp_inv.con". inline "cic:/CoRN/complex/CComplex/cc_calculate_square.con". (* UNEXPORTED -End I_properties. +End I_properties *) (* UNEXPORTED @@ -266,7 +266,7 @@ Hint Resolve I_wd Re_wd Im_wd: algebra_c. (*#* ** Properties of conjugation *) (* UNEXPORTED -Section Conj_properties. +Section Conj_properties *) inline "cic:/CoRN/complex/CComplex/CC_conj_plus.con". @@ -292,7 +292,7 @@ Hint Resolve CC_conj_one: algebra. inline "cic:/CoRN/complex/CComplex/CC_conj_nexp.con". (* UNEXPORTED -End Conj_properties. +End Conj_properties *) (* UNEXPORTED @@ -303,7 +303,7 @@ Hint Resolve CC_conj_plus CC_conj_mult CC_conj_nexp CC_conj_conj (*#* ** Properties of the real axis *) (* UNEXPORTED -Section cc_IR_properties. +Section cc_IR_properties *) inline "cic:/CoRN/complex/CComplex/Re_cc_IR.con". @@ -353,7 +353,7 @@ inline "cic:/CoRN/complex/CComplex/cc_IR_nring.con". inline "cic:/CoRN/complex/CComplex/cc_IR_nexp.con". (* UNEXPORTED -End cc_IR_properties. +End cc_IR_properties *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/complex/NRootCC.ma b/helm/software/matita/contribs/CoRN-Decl/complex/NRootCC.ma index b8fe0878b..26a51df83 100644 --- a/helm/software/matita/contribs/CoRN-Decl/complex/NRootCC.ma +++ b/helm/software/matita/contribs/CoRN-Decl/complex/NRootCC.ma @@ -36,7 +36,7 @@ Properties of non-zero complex numbers *) (* UNEXPORTED -Section CC_ap_zero. +Section CC_ap_zero *) inline "cic:/CoRN/complex/NRootCC/cc_ap_zero.con". @@ -44,25 +44,25 @@ inline "cic:/CoRN/complex/NRootCC/cc_ap_zero.con". inline "cic:/CoRN/complex/NRootCC/C_cc_ap_zero.con". (* UNEXPORTED -End CC_ap_zero. +End CC_ap_zero *) (*#* Weird lemma. *) (* UNEXPORTED -Section Imag_to_Real. +Section Imag_to_Real *) inline "cic:/CoRN/complex/NRootCC/imag_to_real.con". (* UNEXPORTED -End Imag_to_Real. +End Imag_to_Real *) (*#* ** Roots of the imaginary unit *) (* UNEXPORTED -Section NRootI. +Section NRootI *) inline "cic:/CoRN/complex/NRootCC/sqrt_Half.con". @@ -86,20 +86,20 @@ inline "cic:/CoRN/complex/NRootCC/nroot_minus_I.con". inline "cic:/CoRN/complex/NRootCC/nroot_minus_I_nexp.con". (* UNEXPORTED -End NRootI. +End NRootI *) (*#* ** Roots of complex numbers *) (* UNEXPORTED -Section NRootCC_1. +Section NRootCC_1 *) (*#* We define the nth root of a complex number with a non zero imaginary part. *) (* UNEXPORTED -Section NRootCC_1_ap_real. +Section NRootCC_1_ap_real *) (*#* @@ -109,15 +109,15 @@ Define [c2 := a[^]2[+]b[^]2], [c := sqrt c2], [a'2 := (c[+]a) [*]Half], %\end{convention}% *) -inline "cic:/CoRN/complex/NRootCC/a.var". +inline "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/a.var" "NRootCC_1__NRootCC_1_ap_real__". -inline "cic:/CoRN/complex/NRootCC/b.var". +inline "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/b.var" "NRootCC_1__NRootCC_1_ap_real__". -inline "cic:/CoRN/complex/NRootCC/b_.var". +inline "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/b_.var" "NRootCC_1__NRootCC_1_ap_real__". (* begin hide *) -inline "cic:/CoRN/complex/NRootCC/c2.con". +inline "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/c2.con" "NRootCC_1__NRootCC_1_ap_real__". (* end hide *) @@ -125,9 +125,9 @@ inline "cic:/CoRN/complex/NRootCC/nrCC1_c2pos.con". (* begin hide *) -inline "cic:/CoRN/complex/NRootCC/c.con". +inline "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/c.con" "NRootCC_1__NRootCC_1_ap_real__". -inline "cic:/CoRN/complex/NRootCC/a'2.con". +inline "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/a'2.con" "NRootCC_1__NRootCC_1_ap_real__". (* end hide *) @@ -135,9 +135,9 @@ inline "cic:/CoRN/complex/NRootCC/nrCC1_a'2pos.con". (* begin hide *) -inline "cic:/CoRN/complex/NRootCC/a'.con". +inline "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/a'.con" "NRootCC_1__NRootCC_1_ap_real__". -inline "cic:/CoRN/complex/NRootCC/b'2.con". +inline "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/b'2.con" "NRootCC_1__NRootCC_1_ap_real__". (* end hide *) @@ -145,7 +145,7 @@ inline "cic:/CoRN/complex/NRootCC/nrCC1_b'2pos.con". (* begin hide *) -inline "cic:/CoRN/complex/NRootCC/b'.con". +inline "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/b'.con" "NRootCC_1__NRootCC_1_ap_real__". (* end hide *) @@ -182,14 +182,14 @@ inline "cic:/CoRN/complex/NRootCC/nrootCC_1_lower.con". inline "cic:/CoRN/complex/NRootCC/nrootCC_1_ap_real.con". (* UNEXPORTED -End NRootCC_1_ap_real. +End NRootCC_1_ap_real *) (*#* We now define the nth root of a complex number with a non zero real part. *) (* UNEXPORTED -Section NRootCC_1_ap_imag. +Section NRootCC_1_ap_imag *) (*#* @@ -198,19 +198,19 @@ Section NRootCC_1_ap_imag. %\end{convention}% *) -inline "cic:/CoRN/complex/NRootCC/a.var". +inline "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/a.var" "NRootCC_1__NRootCC_1_ap_imag__". -inline "cic:/CoRN/complex/NRootCC/b.var". +inline "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/b.var" "NRootCC_1__NRootCC_1_ap_imag__". -inline "cic:/CoRN/complex/NRootCC/a_.var". +inline "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/a_.var" "NRootCC_1__NRootCC_1_ap_imag__". (* begin hide *) -inline "cic:/CoRN/complex/NRootCC/c'.con". +inline "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/c'.con" "NRootCC_1__NRootCC_1_ap_imag__". -inline "cic:/CoRN/complex/NRootCC/a'.con". +inline "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/a'.con" "NRootCC_1__NRootCC_1_ap_imag__". -inline "cic:/CoRN/complex/NRootCC/b'.con". +inline "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/b'.con" "NRootCC_1__NRootCC_1_ap_imag__". (* end hide *) @@ -221,7 +221,7 @@ Hint Resolve sqrt_I_nexp: algebra. inline "cic:/CoRN/complex/NRootCC/nrootCC_1_ap_imag.con". (* UNEXPORTED -End NRootCC_1_ap_imag. +End NRootCC_1_ap_imag *) (*#* We now define the roots of arbitrary non zero complex numbers. *) @@ -229,11 +229,11 @@ End NRootCC_1_ap_imag. inline "cic:/CoRN/complex/NRootCC/nrootCC_1.con". (* UNEXPORTED -End NRootCC_1. +End NRootCC_1 *) (* UNEXPORTED -Section NRootCC_2. +Section NRootCC_2 *) (*#* @@ -241,24 +241,24 @@ Section NRootCC_2. %\end{convention}% *) -inline "cic:/CoRN/complex/NRootCC/n.var". +inline "cic:/CoRN/complex/NRootCC/NRootCC_2/n.var" "NRootCC_2__". -inline "cic:/CoRN/complex/NRootCC/c.var". +inline "cic:/CoRN/complex/NRootCC/NRootCC_2/c.var" "NRootCC_2__". -inline "cic:/CoRN/complex/NRootCC/z.var". +inline "cic:/CoRN/complex/NRootCC/NRootCC_2/z.var" "NRootCC_2__". -inline "cic:/CoRN/complex/NRootCC/c_.var". +inline "cic:/CoRN/complex/NRootCC/NRootCC_2/c_.var" "NRootCC_2__". inline "cic:/CoRN/complex/NRootCC/nrootCC_2'.con". inline "cic:/CoRN/complex/NRootCC/nrootCC_2.con". (* UNEXPORTED -End NRootCC_2. +End NRootCC_2 *) (* UNEXPORTED -Section NRootCC_3. +Section NRootCC_3 *) inline "cic:/CoRN/complex/NRootCC/Im_poly.con". @@ -272,13 +272,13 @@ inline "cic:/CoRN/complex/NRootCC/nrCC3_a2.con". %\end{convention}% *) -inline "cic:/CoRN/complex/NRootCC/a.var". +inline "cic:/CoRN/complex/NRootCC/NRootCC_3/a.var" "NRootCC_3__". -inline "cic:/CoRN/complex/NRootCC/b.var". +inline "cic:/CoRN/complex/NRootCC/NRootCC_3/b.var" "NRootCC_3__". -inline "cic:/CoRN/complex/NRootCC/b_.var". +inline "cic:/CoRN/complex/NRootCC/NRootCC_3/b_.var" "NRootCC_3__". -inline "cic:/CoRN/complex/NRootCC/n.var". +inline "cic:/CoRN/complex/NRootCC/NRootCC_3/n.var" "NRootCC_3__". inline "cic:/CoRN/complex/NRootCC/nrCC3_poly''.con". @@ -339,11 +339,11 @@ Hint Resolve nrCC3_a9: algebra. inline "cic:/CoRN/complex/NRootCC/nrootCC_3_degree.con". (* UNEXPORTED -End NRootCC_3. +End NRootCC_3 *) (* UNEXPORTED -Section NRootCC_3'. +Section NRootCC_3' *) (*#* @@ -351,11 +351,11 @@ Section NRootCC_3'. %\end{convention}% *) -inline "cic:/CoRN/complex/NRootCC/c.var". +inline "cic:/CoRN/complex/NRootCC/NRootCC_3'/c.var" "NRootCC_3'__". -inline "cic:/CoRN/complex/NRootCC/n.var". +inline "cic:/CoRN/complex/NRootCC/NRootCC_3'/n.var" "NRootCC_3'__". -inline "cic:/CoRN/complex/NRootCC/n_.var". +inline "cic:/CoRN/complex/NRootCC/NRootCC_3'/n_.var" "NRootCC_3'__". inline "cic:/CoRN/complex/NRootCC/nrootCC_3'_poly.con". @@ -364,15 +364,15 @@ inline "cic:/CoRN/complex/NRootCC/nrootCC_3'.con". inline "cic:/CoRN/complex/NRootCC/nrootCC_3'_degree.con". (* UNEXPORTED -End NRootCC_3'. +End NRootCC_3' *) (* UNEXPORTED -Section NRootCC_4. +Section NRootCC_4 *) (* UNEXPORTED -Section NRootCC_4_ap_real. +Section NRootCC_4_ap_real *) (*#* @@ -381,24 +381,24 @@ Section NRootCC_4_ap_real. %\end{convention}% *) -inline "cic:/CoRN/complex/NRootCC/a.var". +inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/a.var" "NRootCC_4__NRootCC_4_ap_real__". -inline "cic:/CoRN/complex/NRootCC/b.var". +inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/b.var" "NRootCC_4__NRootCC_4_ap_real__". -inline "cic:/CoRN/complex/NRootCC/b_.var". +inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/b_.var" "NRootCC_4__NRootCC_4_ap_real__". -inline "cic:/CoRN/complex/NRootCC/n.var". +inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/n.var" "NRootCC_4__NRootCC_4_ap_real__". -inline "cic:/CoRN/complex/NRootCC/n_.var". +inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/n_.var" "NRootCC_4__NRootCC_4_ap_real__". (* begin hide *) -inline "cic:/CoRN/complex/NRootCC/c.con". +inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/c.con" "NRootCC_4__NRootCC_4_ap_real__". (* end hide *) (* UNEXPORTED -Section NRootCC_4_solutions. +Section NRootCC_4_solutions *) (* UNEXPORTED @@ -412,11 +412,11 @@ inline "cic:/CoRN/complex/NRootCC/nrCC4_a1.con". %\end{convention}% *) -inline "cic:/CoRN/complex/NRootCC/r2'.var". +inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_solutions/r2'.var" "NRootCC_4__NRootCC_4_ap_real__NRootCC_4_solutions__". -inline "cic:/CoRN/complex/NRootCC/c2.var". +inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_solutions/c2.var" "NRootCC_4__NRootCC_4_ap_real__NRootCC_4_solutions__". -inline "cic:/CoRN/complex/NRootCC/r2'_.var". +inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_solutions/r2'_.var" "NRootCC_4__NRootCC_4_ap_real__NRootCC_4_solutions__". (* UNEXPORTED Hint Resolve nrootCC_3': algebra. @@ -425,11 +425,11 @@ Hint Resolve nrootCC_3': algebra. inline "cic:/CoRN/complex/NRootCC/nrCC4_a1'.con". (* UNEXPORTED -End NRootCC_4_solutions. +End NRootCC_4_solutions *) (* UNEXPORTED -Section NRootCC_4_equations. +Section NRootCC_4_equations *) (*#* @@ -439,13 +439,13 @@ and [(y2[*] (r[^] (2) [+]One)) [^]n [=] a[^] (2) [+]b[^] (2)]. %\end{convention}% *) -inline "cic:/CoRN/complex/NRootCC/r.var". +inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/r.var" "NRootCC_4__NRootCC_4_ap_real__NRootCC_4_equations__". -inline "cic:/CoRN/complex/NRootCC/r_property.var". +inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/r_property.var" "NRootCC_4__NRootCC_4_ap_real__NRootCC_4_equations__". -inline "cic:/CoRN/complex/NRootCC/y2.var". +inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/y2.var" "NRootCC_4__NRootCC_4_ap_real__NRootCC_4_equations__". -inline "cic:/CoRN/complex/NRootCC/y2_property.var". +inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/y2_property.var" "NRootCC_4__NRootCC_4_ap_real__NRootCC_4_equations__". inline "cic:/CoRN/complex/NRootCC/nrCC4_a2.con". @@ -455,11 +455,11 @@ inline "cic:/CoRN/complex/NRootCC/nrCC4_a4.con". inline "cic:/CoRN/complex/NRootCC/nrCC4_y.con". -inline "cic:/CoRN/complex/NRootCC/y.con". +inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/y.con" "NRootCC_4__NRootCC_4_ap_real__NRootCC_4_equations__". inline "cic:/CoRN/complex/NRootCC/nrCC4_x.con". -inline "cic:/CoRN/complex/NRootCC/x.con". +inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/x.con" "NRootCC_4__NRootCC_4_ap_real__NRootCC_4_equations__". inline "cic:/CoRN/complex/NRootCC/nrCC4_a5.con". @@ -467,7 +467,7 @@ inline "cic:/CoRN/complex/NRootCC/nrCC4_a6.con". inline "cic:/CoRN/complex/NRootCC/nrCC4_z.con". -inline "cic:/CoRN/complex/NRootCC/z.con". +inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/z.con" "NRootCC_4__NRootCC_4_ap_real__NRootCC_4_equations__". inline "cic:/CoRN/complex/NRootCC/nrCC4_a7.con". @@ -480,7 +480,7 @@ inline "cic:/CoRN/complex/NRootCC/nrCC4_a8.con". inline "cic:/CoRN/complex/NRootCC/nrCC4_a9.con". (* UNEXPORTED -End NRootCC_4_equations. +End NRootCC_4_equations *) inline "cic:/CoRN/complex/NRootCC/nrCC4_a10.con". @@ -488,11 +488,11 @@ inline "cic:/CoRN/complex/NRootCC/nrCC4_a10.con". inline "cic:/CoRN/complex/NRootCC/nrootCC_4_ap_real.con". (* UNEXPORTED -End NRootCC_4_ap_real. +End NRootCC_4_ap_real *) (* UNEXPORTED -Section NRootCC_4_ap_imag. +Section NRootCC_4_ap_imag *) (*#* @@ -501,23 +501,23 @@ and [(odd n)]; define [c' := (a[+I*]b) [*]II := a'[+I*]b']. %\end{convention}% *) -inline "cic:/CoRN/complex/NRootCC/a.var". +inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/a.var" "NRootCC_4__NRootCC_4_ap_imag__". -inline "cic:/CoRN/complex/NRootCC/b.var". +inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/b.var" "NRootCC_4__NRootCC_4_ap_imag__". -inline "cic:/CoRN/complex/NRootCC/a_.var". +inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/a_.var" "NRootCC_4__NRootCC_4_ap_imag__". -inline "cic:/CoRN/complex/NRootCC/n.var". +inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/n.var" "NRootCC_4__NRootCC_4_ap_imag__". -inline "cic:/CoRN/complex/NRootCC/n_.var". +inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/n_.var" "NRootCC_4__NRootCC_4_ap_imag__". (* begin hide *) -inline "cic:/CoRN/complex/NRootCC/c'.con". +inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/c'.con" "NRootCC_4__NRootCC_4_ap_imag__". -inline "cic:/CoRN/complex/NRootCC/a'.con". +inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/a'.con" "NRootCC_4__NRootCC_4_ap_imag__". -inline "cic:/CoRN/complex/NRootCC/b'.con". +inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/b'.con" "NRootCC_4__NRootCC_4_ap_imag__". (* end hide *) @@ -530,19 +530,19 @@ Hint Resolve nroot_minus_I_nexp: algebra. inline "cic:/CoRN/complex/NRootCC/nrootCC_4_ap_imag.con". (* UNEXPORTED -End NRootCC_4_ap_imag. +End NRootCC_4_ap_imag *) inline "cic:/CoRN/complex/NRootCC/nrootCC_4.con". (* UNEXPORTED -End NRootCC_4. +End NRootCC_4 *) (*#* Finally, the general definition of nth root. *) (* UNEXPORTED -Section NRootCC_5. +Section NRootCC_5 *) inline "cic:/CoRN/complex/NRootCC/nrCC_5a2.con". @@ -558,16 +558,16 @@ Hint Resolve nrCC_5a3: algebra. %\end{convention}% *) -inline "cic:/CoRN/complex/NRootCC/c.var". +inline "cic:/CoRN/complex/NRootCC/NRootCC_5/c.var" "NRootCC_5__". -inline "cic:/CoRN/complex/NRootCC/c_.var". +inline "cic:/CoRN/complex/NRootCC/NRootCC_5/c_.var" "NRootCC_5__". inline "cic:/CoRN/complex/NRootCC/nrCC_5a4.con". inline "cic:/CoRN/complex/NRootCC/nrootCC_5.con". (* UNEXPORTED -End NRootCC_5. +End NRootCC_5 *) (*#* Final definition *) diff --git a/helm/software/matita/contribs/CoRN-Decl/devel/loeb/IDA/Ch6.ma b/helm/software/matita/contribs/CoRN-Decl/devel/loeb/IDA/Ch6.ma index f99d50781..1b51522ab 100644 --- a/helm/software/matita/contribs/CoRN-Decl/devel/loeb/IDA/Ch6.ma +++ b/helm/software/matita/contribs/CoRN-Decl/devel/loeb/IDA/Ch6.ma @@ -48,7 +48,7 @@ inline "cic:/CoRN/devel/loeb/IDA/Ch6/plus3.con". inline "cic:/CoRN/devel/loeb/IDA/Ch6/on.con". -inline "cic:/CoRN/devel/loeb/IDA/Ch6/ex_3_ary.con". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/ex_3_ary.con" "__". (* blz 65 Example 1 *) @@ -80,23 +80,23 @@ include "model/setoids/Qsetoid.ma". (* blz 66 Examples 2 *) (* UNEXPORTED -Section p66E2. +Section p66E2 *) -inline "cic:/CoRN/devel/loeb/IDA/Ch6/X.var". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/p66E2/X.var" "p66E2__". -inline "cic:/CoRN/devel/loeb/IDA/Ch6/f.var". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/p66E2/f.var" "p66E2__". -inline "cic:/CoRN/devel/loeb/IDA/Ch6/g.var". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/p66E2/g.var" "p66E2__". -inline "cic:/CoRN/devel/loeb/IDA/Ch6/h.var". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/p66E2/h.var" "p66E2__". (* Check comp_as_bin_op.*) (* Check assoc_comp.*) (* UNEXPORTED -End p66E2. +End p66E2 *) (* blz 66 Example 2eblok 1 *) @@ -114,10 +114,10 @@ inline "cic:/CoRN/devel/loeb/IDA/Ch6/FS_is_CSemiGroup.con". (* blz 66 Example % 4 *) (* UNEXPORTED -Section p66E2b4. +Section p66E2b4 *) -inline "cic:/CoRN/devel/loeb/IDA/Ch6/A.var". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/p66E2b4/A.var" "p66E2b4__". inline "cic:/CoRN/devel/loeb/IDA/Ch6/Astar.con". @@ -154,7 +154,7 @@ inline "cic:/CoRN/devel/loeb/IDA/Ch6/Astar_is_CSemiGroup.con". inline "cic:/CoRN/devel/loeb/IDA/Ch6/Astar_as_CSemiGroup.con". (* UNEXPORTED -End p66E2b4. +End p66E2b4 *) (* Definition 5 *) @@ -170,15 +170,15 @@ inline "cic:/CoRN/devel/loeb/IDA/Ch6/is_unit_Z_0.con". (* blz 67 Remark 2 *) (* UNEXPORTED -Section p67R2. +Section p67R2 *) -inline "cic:/CoRN/devel/loeb/IDA/Ch6/X.var". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/p67R2/X.var" "p67R2__". inline "cic:/CoRN/devel/loeb/IDA/Ch6/is_unit_FS_id.con". (* UNEXPORTED -End p67R2. +End p67R2 *) (* blz 67 Remark 3 *) @@ -208,7 +208,7 @@ include "model/monoids/Zmonoid.ma". (* blz 68 Example blok1 1 *) (* UNEXPORTED -Section p68E1b1. +Section p68E1b1 *) inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1.ind". @@ -280,7 +280,7 @@ inline "cic:/CoRN/devel/loeb/IDA/Ch6/M2_as_CMonoid.con". inline "cic:/CoRN/devel/loeb/IDA/Ch6/two_element_CMonoids.con". (* UNEXPORTED -End p68E1b1. +End p68E1b1 *) (* blz 68 Example blok2 1 *) @@ -298,12 +298,12 @@ End p68E1b1. include "algebra/CMonoids.ma". (* UNEXPORTED -Section D9S. +Section D9S *) -inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1.var". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/D9S/M1.var" "D9S__". -inline "cic:/CoRN/devel/loeb/IDA/Ch6/M2.var". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/D9S/M2.var" "D9S__". inline "cic:/CoRN/devel/loeb/IDA/Ch6/dprod.con". @@ -316,16 +316,16 @@ inline "cic:/CoRN/devel/loeb/IDA/Ch6/direct_product_is_CSemiGroup.con". inline "cic:/CoRN/devel/loeb/IDA/Ch6/direct_product_as_CSemiGroup.con". (* UNEXPORTED -End D9S. +End D9S *) (* UNEXPORTED -Section D9M. +Section D9M *) -inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1.var". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/D9M/M1.var" "D9M__". -inline "cic:/CoRN/devel/loeb/IDA/Ch6/M2.var". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/D9M/M2.var" "D9M__". inline "cic:/CoRN/devel/loeb/IDA/Ch6/e1e2_is_rht_unit.con". @@ -336,42 +336,42 @@ inline "cic:/CoRN/devel/loeb/IDA/Ch6/direct_product_is_CMonoid.con". inline "cic:/CoRN/devel/loeb/IDA/Ch6/direct_product_as_CMonoid.con". (* UNEXPORTED -End D9M. +End D9M *) (* blz 69 Example *) (* UNEXPORTED -Section p69E1. +Section p69E1 *) -inline "cic:/CoRN/devel/loeb/IDA/Ch6/PM1M2.con". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/p69E1/PM1M2.con" "p69E1__". -inline "cic:/CoRN/devel/loeb/IDA/Ch6/uu.con". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/p69E1/uu.con" "p69E1__". -inline "cic:/CoRN/devel/loeb/IDA/Ch6/e1u.con". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/p69E1/e1u.con" "p69E1__". inline "cic:/CoRN/devel/loeb/IDA/Ch6/ex_69.con". (* UNEXPORTED -End p69E1. +End p69E1 *) (* Theorem 11 *) (* UNEXPORTED -Section Th11. +Section Th11 *) -inline "cic:/CoRN/devel/loeb/IDA/Ch6/M.var". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/Th11/M.var" "Th11__". -inline "cic:/CoRN/devel/loeb/IDA/Ch6/I.var". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/Th11/I.var" "Th11__". -inline "cic:/CoRN/devel/loeb/IDA/Ch6/C.var". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/Th11/C.var" "Th11__". -inline "cic:/CoRN/devel/loeb/IDA/Ch6/Cunit.var". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/Th11/Cunit.var" "Th11__". -inline "cic:/CoRN/devel/loeb/IDA/Ch6/op_pres_C.var". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/Th11/op_pres_C.var" "Th11__". inline "cic:/CoRN/devel/loeb/IDA/Ch6/K.con". @@ -380,16 +380,16 @@ inline "cic:/CoRN/devel/loeb/IDA/Ch6/op_pres_K.con". inline "cic:/CoRN/devel/loeb/IDA/Ch6/K_is_Monoid.con". (* UNEXPORTED -End Th11. +End Th11 *) (* Theorem 12 *) (* UNEXPORTED -Section Th12. +Section Th12 *) -inline "cic:/CoRN/devel/loeb/IDA/Ch6/A.var". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/Th12/A.var" "Th12__". inline "cic:/CoRN/devel/loeb/IDA/Ch6/nil_is_rht_unit.con". @@ -400,18 +400,18 @@ inline "cic:/CoRN/devel/loeb/IDA/Ch6/free_monoid_is_CMonoid.con". inline "cic:/CoRN/devel/loeb/IDA/Ch6/free_monoid_as_CMonoid.con". (* UNEXPORTED -End Th12. +End Th12 *) (* blz 70 text *) (* UNEXPORTED -Section p70text. +Section p70text *) include "devel/loeb/per/lst2fun.ma". -inline "cic:/CoRN/devel/loeb/IDA/Ch6/A.con". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/p70text/A.con" "p70text__". inline "cic:/CoRN/devel/loeb/IDA/Ch6/ZerolessOne.con". @@ -428,44 +428,44 @@ inline "cic:/CoRN/devel/loeb/IDA/Ch6/to_word_bijective.con". inline "cic:/CoRN/devel/loeb/IDA/Ch6/pres_plus_to_word.con". (* UNEXPORTED -End p70text. +End p70text *) (* Definition 13 *) (* UNEXPORTED -Section Th13. +Section Th13 *) -inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1.var". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/Th13/M1.var" "Th13__". -inline "cic:/CoRN/devel/loeb/IDA/Ch6/M2.var". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/Th13/M2.var" "Th13__". inline "cic:/CoRN/devel/loeb/IDA/Ch6/morphism.con". inline "cic:/CoRN/devel/loeb/IDA/Ch6/isomorphism.con". (* UNEXPORTED -End Th13. +End Th13 *) (* blz 71 Example 1 *) (* UNEXPORTED -Section p71E1. +Section p71E1 *) -inline "cic:/CoRN/devel/loeb/IDA/Ch6/M.var". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/p71E1/M.var" "p71E1__". -inline "cic:/CoRN/devel/loeb/IDA/Ch6/c.var". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/p71E1/c.var" "p71E1__". inline "cic:/CoRN/devel/loeb/IDA/Ch6/power_CMonoid.con". inline "cic:/CoRN/devel/loeb/IDA/Ch6/power_CMonoid_CSetoid.con". -inline "cic:/CoRN/devel/loeb/IDA/Ch6/is_generated_by.var". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/p71E1/is_generated_by.var" "p71E1__". -inline "cic:/CoRN/devel/loeb/IDA/Ch6/f.con". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/p71E1/f.con" "p71E1__". inline "cic:/CoRN/devel/loeb/IDA/Ch6/f_strext.con". @@ -474,11 +474,11 @@ inline "cic:/CoRN/devel/loeb/IDA/Ch6/f_as_CSetoid_fun.con". inline "cic:/CoRN/devel/loeb/IDA/Ch6/surjective_f.con". (* UNEXPORTED -End p71E1. +End p71E1 *) (* UNEXPORTED -Section p71E1'. +Section p71E1' *) inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_is_generated_by_u.con". @@ -486,18 +486,18 @@ inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_is_generated_by_u.con". inline "cic:/CoRN/devel/loeb/IDA/Ch6/not_injective_f.con". (* UNEXPORTED -End p71E1'. +End p71E1' *) (* Print to_word_bijective.*) (* UNEXPORTED -Section p71E2. +Section p71E2 *) -inline "cic:/CoRN/devel/loeb/IDA/Ch6/A.var". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2/A.var" "p71E2__". -inline "cic:/CoRN/devel/loeb/IDA/Ch6/L.con". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2/L.con" "p71E2__". inline "cic:/CoRN/devel/loeb/IDA/Ch6/L_strext.con". @@ -506,63 +506,63 @@ inline "cic:/CoRN/devel/loeb/IDA/Ch6/L_as_CSetoid_fun.con". inline "cic:/CoRN/devel/loeb/IDA/Ch6/L_is_morphism.con". (* UNEXPORTED -End p71E2. +End p71E2 *) (* blz 71 Remark 1 *) (* UNEXPORTED -Section p71R1. +Section p71R1 *) -inline "cic:/CoRN/devel/loeb/IDA/Ch6/S1.var". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/p71R1/S1.var" "p71R1__". -inline "cic:/CoRN/devel/loeb/IDA/Ch6/S2.var". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/p71R1/S2.var" "p71R1__". inline "cic:/CoRN/devel/loeb/IDA/Ch6/morphism_of_CSemiGroups.con". (* UNEXPORTED -End p71R1. +End p71R1 *) (* UNEXPORTED -Section p71R2. +Section p71R2 *) -inline "cic:/CoRN/devel/loeb/IDA/Ch6/M.var". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/p71R2/M.var" "p71R2__". inline "cic:/CoRN/devel/loeb/IDA/Ch6/automorphism.con". (* UNEXPORTED -End p71R2. +End p71R2 *) (* Theorem 14 *) (* UNEXPORTED -Section Th14. +Section Th14 *) -inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1.var". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/Th14/M1.var" "Th14__". -inline "cic:/CoRN/devel/loeb/IDA/Ch6/M2.var". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/Th14/M2.var" "Th14__". -inline "cic:/CoRN/devel/loeb/IDA/Ch6/f.var". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/Th14/f.var" "Th14__". -inline "cic:/CoRN/devel/loeb/IDA/Ch6/isof.var". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/Th14/isof.var" "Th14__". inline "cic:/CoRN/devel/loeb/IDA/Ch6/iso_imp_bij.con". inline "cic:/CoRN/devel/loeb/IDA/Ch6/iso_inv.con". (* UNEXPORTED -End Th14. +End Th14 *) (* blz 71 Examples 2eblok 1 *) (* UNEXPORTED -Section p71E2b1. +Section p71E2b1 *) inline "cic:/CoRN/devel/loeb/IDA/Ch6/isomorphic.con". @@ -570,18 +570,18 @@ inline "cic:/CoRN/devel/loeb/IDA/Ch6/isomorphic.con". inline "cic:/CoRN/devel/loeb/IDA/Ch6/not_isomorphic_M1_M2.con". (* UNEXPORTED -End p71E2b1. +End p71E2b1 *) (* UNEXPORTED -Section p71E2b2. +Section p71E2b2 *) -inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1.var". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2b2/M1.var" "p71E2b2__". -inline "cic:/CoRN/devel/loeb/IDA/Ch6/M2.var". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2b2/M2.var" "p71E2b2__". -inline "cic:/CoRN/devel/loeb/IDA/Ch6/f.con". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2b2/f.con" "p71E2b2__". inline "cic:/CoRN/devel/loeb/IDA/Ch6/f_strext'.con". @@ -590,18 +590,18 @@ inline "cic:/CoRN/devel/loeb/IDA/Ch6/f_as_CSetoid_fun'.con". inline "cic:/CoRN/devel/loeb/IDA/Ch6/isomorphic_PM1M2_PM2M1.con". (* UNEXPORTED -End p71E2b2. +End p71E2b2 *) (* UNEXPORTED -Section Th15. +Section Th15 *) -inline "cic:/CoRN/devel/loeb/IDA/Ch6/M.var". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/Th15/M.var" "Th15__". inline "cic:/CoRN/devel/loeb/IDA/Ch6/cm_Sum.con". -inline "cic:/CoRN/devel/loeb/IDA/Ch6/D.var". +inline "cic:/CoRN/devel/loeb/IDA/Ch6/Th15/D.var" "Th15__". inline "cic:/CoRN/devel/loeb/IDA/Ch6/member.con". @@ -622,6 +622,6 @@ inline "cic:/CoRN/devel/loeb/IDA/Ch6/op_pres_Dbrack.con". inline "cic:/CoRN/devel/loeb/IDA/Ch6/Dbrack_as_CMonoid.con". (* UNEXPORTED -End Th15. +End Th15 *) diff --git a/helm/software/matita/contribs/CoRN-Decl/fta/CC_Props.ma b/helm/software/matita/contribs/CoRN-Decl/fta/CC_Props.ma index 1203f8688..ff688c492 100644 --- a/helm/software/matita/contribs/CoRN-Decl/fta/CC_Props.ma +++ b/helm/software/matita/contribs/CoRN-Decl/fta/CC_Props.ma @@ -69,7 +69,7 @@ inline "cic:/CoRN/fta/CC_Props/CC_SeqLimit_unq.con". *) (* UNEXPORTED -Section Continuity_for_CC. +Section Continuity_for_CC *) (*#* @@ -77,7 +77,7 @@ Section Continuity_for_CC. %\end{convention}% *) -inline "cic:/CoRN/fta/CC_Props/f.var". +inline "cic:/CoRN/fta/CC_Props/Continuity_for_CC/f.var" "Continuity_for_CC__". (* (CSetoid_un_op CC). *) @@ -94,7 +94,7 @@ inline "cic:/CoRN/fta/CC_Props/f_seq.con". inline "cic:/CoRN/fta/CC_Props/poly_pres_lim.con". (* UNEXPORTED -End Continuity_for_CC. +End Continuity_for_CC *) inline "cic:/CoRN/fta/CC_Props/seq_yields_zero.con". diff --git a/helm/software/matita/contribs/CoRN-Decl/fta/CPoly_Contin1.ma b/helm/software/matita/contribs/CoRN-Decl/fta/CPoly_Contin1.ma index c331e5e37..38f8a6976 100644 --- a/helm/software/matita/contribs/CoRN-Decl/fta/CPoly_Contin1.ma +++ b/helm/software/matita/contribs/CoRN-Decl/fta/CPoly_Contin1.ma @@ -26,7 +26,7 @@ include "fta/CC_Props.ma". *) (* UNEXPORTED -Section Mult_CC_Continuous. +Section Mult_CC_Continuous *) inline "cic:/CoRN/fta/CPoly_Contin1/mult_absCC.con". @@ -36,11 +36,11 @@ inline "cic:/CoRN/fta/CPoly_Contin1/estimate_absCC.con". inline "cic:/CoRN/fta/CPoly_Contin1/mult_CC_contin.con". (* UNEXPORTED -End Mult_CC_Continuous. +End Mult_CC_Continuous *) (* UNEXPORTED -Section CPoly_CC_Continuous. +Section CPoly_CC_Continuous *) (*#* @@ -48,13 +48,13 @@ Section CPoly_CC_Continuous. %\end{convention}% *) -inline "cic:/CoRN/fta/CPoly_Contin1/g.var". +inline "cic:/CoRN/fta/CPoly_Contin1/CPoly_CC_Continuous/g.var" "CPoly_CC_Continuous__". inline "cic:/CoRN/fta/CPoly_Contin1/cpoly_CC_contin.con". inline "cic:/CoRN/fta/CPoly_Contin1/contin_polyCC.con". (* UNEXPORTED -End CPoly_CC_Continuous. +End CPoly_CC_Continuous *) diff --git a/helm/software/matita/contribs/CoRN-Decl/fta/CPoly_Rev.ma b/helm/software/matita/contribs/CoRN-Decl/fta/CPoly_Rev.ma index 32961ffe2..1f9ab8902 100644 --- a/helm/software/matita/contribs/CoRN-Decl/fta/CPoly_Rev.ma +++ b/helm/software/matita/contribs/CoRN-Decl/fta/CPoly_Rev.ma @@ -26,7 +26,7 @@ include "algebra/CPoly_Degree.ma". *) (* UNEXPORTED -Section Monomials. +Section Monomials *) (*#* @@ -35,11 +35,11 @@ polynomials over this ring. %\end{convention}% *) -inline "cic:/CoRN/fta/CPoly_Rev/R.var". +inline "cic:/CoRN/fta/CPoly_Rev/Monomials/R.var" "Monomials__". (* begin hide *) -inline "cic:/CoRN/fta/CPoly_Rev/RX.con". +inline "cic:/CoRN/fta/CPoly_Rev/Monomials/RX.con" "Monomials__". (* end hide *) @@ -78,7 +78,7 @@ inline "cic:/CoRN/fta/CPoly_Rev/monom_mult.con". inline "cic:/CoRN/fta/CPoly_Rev/monom_sum.con". (* UNEXPORTED -End Monomials. +End Monomials *) (* UNEXPORTED @@ -90,14 +90,14 @@ Implicit Arguments monom [R]. *) (* UNEXPORTED -Section Poly_Reverse. +Section Poly_Reverse *) -inline "cic:/CoRN/fta/CPoly_Rev/R.var". +inline "cic:/CoRN/fta/CPoly_Rev/Poly_Reverse/R.var" "Poly_Reverse__". (* begin hide *) -inline "cic:/CoRN/fta/CPoly_Rev/RX.con". +inline "cic:/CoRN/fta/CPoly_Rev/Poly_Reverse/RX.con" "Poly_Reverse__". (* end hide *) @@ -162,7 +162,7 @@ inline "cic:/CoRN/fta/CPoly_Rev/Rev_sum.con". inline "cic:/CoRN/fta/CPoly_Rev/Rev_mult.con". (* UNEXPORTED -End Poly_Reverse. +End Poly_Reverse *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/fta/CPoly_Shift.ma b/helm/software/matita/contribs/CoRN-Decl/fta/CPoly_Shift.ma index e0875e59f..86a438522 100644 --- a/helm/software/matita/contribs/CoRN-Decl/fta/CPoly_Shift.ma +++ b/helm/software/matita/contribs/CoRN-Decl/fta/CPoly_Shift.ma @@ -29,7 +29,7 @@ and we only need it for [CC]. *) (* UNEXPORTED -Section Poly_Shifted. +Section Poly_Shifted *) inline "cic:/CoRN/fta/CPoly_Shift/Shift.con". @@ -51,7 +51,7 @@ inline "cic:/CoRN/fta/CPoly_Shift/Shift_degree_le.con". inline "cic:/CoRN/fta/CPoly_Shift/Shift_monic.con". (* UNEXPORTED -End Poly_Shifted. +End Poly_Shifted *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/fta/FTA.ma b/helm/software/matita/contribs/CoRN-Decl/fta/FTA.ma index ba69c7ec6..b0da6ed44 100644 --- a/helm/software/matita/contribs/CoRN-Decl/fta/FTA.ma +++ b/helm/software/matita/contribs/CoRN-Decl/fta/FTA.ma @@ -31,19 +31,19 @@ degree [(S n)]. *) (* UNEXPORTED -Section FTA_reg'. +Section FTA_reg' *) -inline "cic:/CoRN/fta/FTA/f.var". +inline "cic:/CoRN/fta/FTA/FTA_reg'/f.var" "FTA_reg'__". -inline "cic:/CoRN/fta/FTA/n.var". +inline "cic:/CoRN/fta/FTA/FTA_reg'/n.var" "FTA_reg'__". -inline "cic:/CoRN/fta/FTA/f_degree.var". +inline "cic:/CoRN/fta/FTA/FTA_reg'/f_degree.var" "FTA_reg'__". inline "cic:/CoRN/fta/FTA/FTA_reg'.con". (* UNEXPORTED -End FTA_reg'. +End FTA_reg' *) (*#* @@ -54,22 +54,22 @@ less than or equal to [(S n)] and [c] be a complex number such that *) (* UNEXPORTED -Section FTA_1. +Section FTA_1 *) -inline "cic:/CoRN/fta/FTA/f.var". +inline "cic:/CoRN/fta/FTA/FTA_1/f.var" "FTA_1__". -inline "cic:/CoRN/fta/FTA/n.var". +inline "cic:/CoRN/fta/FTA/FTA_1/n.var" "FTA_1__". -inline "cic:/CoRN/fta/FTA/f_degree.var". +inline "cic:/CoRN/fta/FTA/FTA_1/f_degree.var" "FTA_1__". -inline "cic:/CoRN/fta/FTA/c.var". +inline "cic:/CoRN/fta/FTA/FTA_1/c.var" "FTA_1__". -inline "cic:/CoRN/fta/FTA/f_c.var". +inline "cic:/CoRN/fta/FTA/FTA_1/f_c.var" "FTA_1__". inline "cic:/CoRN/fta/FTA/FTA_1a.con". -inline "cic:/CoRN/fta/FTA/g.con". +inline "cic:/CoRN/fta/FTA/FTA_1/g.con" "FTA_1__". inline "cic:/CoRN/fta/FTA/FTA_1b.con". @@ -78,11 +78,11 @@ inline "cic:/CoRN/fta/FTA/FTA_1.con". inline "cic:/CoRN/fta/FTA/FTA_1'.con". (* UNEXPORTED -End FTA_1. +End FTA_1 *) (* UNEXPORTED -Section Fund_Thm_Alg. +Section Fund_Thm_Alg *) inline "cic:/CoRN/fta/FTA/FTA'.con". @@ -92,6 +92,6 @@ inline "cic:/CoRN/fta/FTA/FTA.con". inline "cic:/CoRN/fta/FTA/FTA_a_la_Henk.con". (* UNEXPORTED -End Fund_Thm_Alg. +End Fund_Thm_Alg *) diff --git a/helm/software/matita/contribs/CoRN-Decl/fta/FTAreg.ma b/helm/software/matita/contribs/CoRN-Decl/fta/FTAreg.ma index 0835edf40..7187757ad 100644 --- a/helm/software/matita/contribs/CoRN-Decl/fta/FTAreg.ma +++ b/helm/software/matita/contribs/CoRN-Decl/fta/FTAreg.ma @@ -33,12 +33,12 @@ include "fta/CPoly_Contin1.ma". *) (* UNEXPORTED -Section Seq_Exists. +Section Seq_Exists *) -inline "cic:/CoRN/fta/FTAreg/n.var". +inline "cic:/CoRN/fta/FTAreg/Seq_Exists/n.var" "Seq_Exists__". -inline "cic:/CoRN/fta/FTAreg/lt0n.var". +inline "cic:/CoRN/fta/FTAreg/Seq_Exists/lt0n.var" "Seq_Exists__". (*#* %\begin{convention}% Let [qK] be a real between 0 and 1, with @@ -52,24 +52,24 @@ Let [p] be a monic polynomial over the complex numbers with degree *) (* UNEXPORTED -Section Kneser_Sequence. +Section Kneser_Sequence *) -inline "cic:/CoRN/fta/FTAreg/qK.var". +inline "cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/qK.var" "Seq_Exists__Kneser_Sequence__". -inline "cic:/CoRN/fta/FTAreg/zltq.var". +inline "cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/zltq.var" "Seq_Exists__Kneser_Sequence__". -inline "cic:/CoRN/fta/FTAreg/qlt1.var". +inline "cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/qlt1.var" "Seq_Exists__Kneser_Sequence__". -inline "cic:/CoRN/fta/FTAreg/q_prop.var". +inline "cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/q_prop.var" "Seq_Exists__Kneser_Sequence__". -inline "cic:/CoRN/fta/FTAreg/p.var". +inline "cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/p.var" "Seq_Exists__Kneser_Sequence__". -inline "cic:/CoRN/fta/FTAreg/mp.var". +inline "cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/mp.var" "Seq_Exists__Kneser_Sequence__". -inline "cic:/CoRN/fta/FTAreg/c0.var". +inline "cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/c0.var" "Seq_Exists__Kneser_Sequence__". -inline "cic:/CoRN/fta/FTAreg/p0ltc0.var". +inline "cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/p0ltc0.var" "Seq_Exists__Kneser_Sequence__". inline "cic:/CoRN/fta/FTAreg/Knes_tup.ind". @@ -96,11 +96,11 @@ inline "cic:/CoRN/fta/FTAreg/sK_it.con". inline "cic:/CoRN/fta/FTAreg/sK_prop2.con". (* UNEXPORTED -End Kneser_Sequence. +End Kneser_Sequence *) (* UNEXPORTED -Section Seq_Exists_Main. +Section Seq_Exists_Main *) (*#* **Main results @@ -109,66 +109,66 @@ Section Seq_Exists_Main. inline "cic:/CoRN/fta/FTAreg/seq_exists.con". (* UNEXPORTED -End Seq_Exists_Main. +End Seq_Exists_Main *) (* UNEXPORTED -End Seq_Exists. +End Seq_Exists *) (* UNEXPORTED -Section N_Exists. +Section N_Exists *) -inline "cic:/CoRN/fta/FTAreg/n.var". +inline "cic:/CoRN/fta/FTAreg/N_Exists/n.var" "N_Exists__". -inline "cic:/CoRN/fta/FTAreg/lt0n.var". +inline "cic:/CoRN/fta/FTAreg/N_Exists/lt0n.var" "N_Exists__". -inline "cic:/CoRN/fta/FTAreg/q.var". +inline "cic:/CoRN/fta/FTAreg/N_Exists/q.var" "N_Exists__". -inline "cic:/CoRN/fta/FTAreg/zleq.var". +inline "cic:/CoRN/fta/FTAreg/N_Exists/zleq.var" "N_Exists__". -inline "cic:/CoRN/fta/FTAreg/qlt1.var". +inline "cic:/CoRN/fta/FTAreg/N_Exists/qlt1.var" "N_Exists__". -inline "cic:/CoRN/fta/FTAreg/c.var". +inline "cic:/CoRN/fta/FTAreg/N_Exists/c.var" "N_Exists__". -inline "cic:/CoRN/fta/FTAreg/zltc.var". +inline "cic:/CoRN/fta/FTAreg/N_Exists/zltc.var" "N_Exists__". (* begin hide *) -inline "cic:/CoRN/fta/FTAreg/q_.con". +inline "cic:/CoRN/fta/FTAreg/N_Exists/q_.con" "N_Exists__". (* end hide *) -inline "cic:/CoRN/fta/FTAreg/e.var". +inline "cic:/CoRN/fta/FTAreg/N_Exists/e.var" "N_Exists__". -inline "cic:/CoRN/fta/FTAreg/zlte.var". +inline "cic:/CoRN/fta/FTAreg/N_Exists/zlte.var" "N_Exists__". inline "cic:/CoRN/fta/FTAreg/N_exists.con". (* UNEXPORTED -End N_Exists. +End N_Exists *) (* UNEXPORTED -Section Seq_is_CC_CAuchy. +Section Seq_is_CC_CAuchy *) (*#* ** The Kneser sequence is Cauchy in [CC] *) -inline "cic:/CoRN/fta/FTAreg/n.var". +inline "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/n.var" "Seq_is_CC_CAuchy__". -inline "cic:/CoRN/fta/FTAreg/lt0n.var". +inline "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/lt0n.var" "Seq_is_CC_CAuchy__". -inline "cic:/CoRN/fta/FTAreg/q.var". +inline "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/q.var" "Seq_is_CC_CAuchy__". -inline "cic:/CoRN/fta/FTAreg/zleq.var". +inline "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/zleq.var" "Seq_is_CC_CAuchy__". -inline "cic:/CoRN/fta/FTAreg/qlt1.var". +inline "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/qlt1.var" "Seq_is_CC_CAuchy__". -inline "cic:/CoRN/fta/FTAreg/c.var". +inline "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/c.var" "Seq_is_CC_CAuchy__". -inline "cic:/CoRN/fta/FTAreg/zltc.var". +inline "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/zltc.var" "Seq_is_CC_CAuchy__". (*#* %\begin{convention}% Let: - [q_] prove [q[-]One [#] Zero] @@ -181,15 +181,15 @@ inline "cic:/CoRN/fta/FTAreg/zltc.var". (* begin hide *) -inline "cic:/CoRN/fta/FTAreg/q_.con". +inline "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/q_.con" "Seq_is_CC_CAuchy__". -inline "cic:/CoRN/fta/FTAreg/nrtq.con". +inline "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/nrtq.con" "Seq_is_CC_CAuchy__". -inline "cic:/CoRN/fta/FTAreg/nrtc.con". +inline "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/nrtc.con" "Seq_is_CC_CAuchy__". -inline "cic:/CoRN/fta/FTAreg/nrtqlt1.con". +inline "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/nrtqlt1.con" "Seq_is_CC_CAuchy__". -inline "cic:/CoRN/fta/FTAreg/nrtq_.con". +inline "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/nrtq_.con" "Seq_is_CC_CAuchy__". (* end hide *) @@ -210,7 +210,7 @@ inline "cic:/CoRN/fta/FTAreg/SublemmaIm.con". inline "cic:/CoRN/fta/FTAreg/seq_is_CC_Cauchy.con". (* UNEXPORTED -End Seq_is_CC_CAuchy. +End Seq_is_CC_CAuchy *) inline "cic:/CoRN/fta/FTAreg/FTA_monic.con". diff --git a/helm/software/matita/contribs/CoRN-Decl/fta/KeyLemma.ma b/helm/software/matita/contribs/CoRN-Decl/fta/KeyLemma.ma index caf87bea1..d2e68338e 100644 --- a/helm/software/matita/contribs/CoRN-Decl/fta/KeyLemma.ma +++ b/helm/software/matita/contribs/CoRN-Decl/fta/KeyLemma.ma @@ -31,7 +31,7 @@ include "reals/NRootIR.ma". *) (* UNEXPORTED -Section Key_Lemma. +Section Key_Lemma *) (*#* @@ -41,23 +41,23 @@ and [eps : IR] such that [(Zero [<] eps)] and [(eps [<=] a_0)]. %\end{convention}% *) -inline "cic:/CoRN/fta/KeyLemma/a.var". +inline "cic:/CoRN/fta/KeyLemma/Key_Lemma/a.var" "Key_Lemma__". -inline "cic:/CoRN/fta/KeyLemma/n.var". +inline "cic:/CoRN/fta/KeyLemma/Key_Lemma/n.var" "Key_Lemma__". -inline "cic:/CoRN/fta/KeyLemma/gt_n_0.var". +inline "cic:/CoRN/fta/KeyLemma/Key_Lemma/gt_n_0.var" "Key_Lemma__". -inline "cic:/CoRN/fta/KeyLemma/eps.var". +inline "cic:/CoRN/fta/KeyLemma/Key_Lemma/eps.var" "Key_Lemma__". -inline "cic:/CoRN/fta/KeyLemma/eps_pos.var". +inline "cic:/CoRN/fta/KeyLemma/Key_Lemma/eps_pos.var" "Key_Lemma__". -inline "cic:/CoRN/fta/KeyLemma/a_nonneg.var". +inline "cic:/CoRN/fta/KeyLemma/Key_Lemma/a_nonneg.var" "Key_Lemma__". -inline "cic:/CoRN/fta/KeyLemma/a_n_1.var". +inline "cic:/CoRN/fta/KeyLemma/Key_Lemma/a_n_1.var" "Key_Lemma__". -inline "cic:/CoRN/fta/KeyLemma/a_0.var". +inline "cic:/CoRN/fta/KeyLemma/Key_Lemma/a_0.var" "Key_Lemma__". -inline "cic:/CoRN/fta/KeyLemma/eps_le_a_0.var". +inline "cic:/CoRN/fta/KeyLemma/Key_Lemma/eps_le_a_0.var" "Key_Lemma__". inline "cic:/CoRN/fta/KeyLemma/a_0_eps_nonneg.con". @@ -158,7 +158,7 @@ inline "cic:/CoRN/fta/KeyLemma/Key.con". (* end hide *) (* UNEXPORTED -End Key_Lemma. +End Key_Lemma *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/fta/KneserLemma.ma b/helm/software/matita/contribs/CoRN-Decl/fta/KneserLemma.ma index fbbeb1c49..4644e0c90 100644 --- a/helm/software/matita/contribs/CoRN-Decl/fta/KneserLemma.ma +++ b/helm/software/matita/contribs/CoRN-Decl/fta/KneserLemma.ma @@ -33,7 +33,7 @@ include "fta/MainLemma.ma". (*#* ** Kneser Lemma *) (* UNEXPORTED -Section Kneser_Lemma. +Section Kneser_Lemma *) (*#* @@ -43,25 +43,25 @@ such that [0 < n], [b_0 := b 0], [b_n := (b n) [=] One] and %\end{convention}% *) -inline "cic:/CoRN/fta/KneserLemma/b.var". +inline "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b.var" "Kneser_Lemma__". -inline "cic:/CoRN/fta/KneserLemma/n.var". +inline "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/n.var" "Kneser_Lemma__". -inline "cic:/CoRN/fta/KneserLemma/gt_n_0.var". +inline "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/gt_n_0.var" "Kneser_Lemma__". (* begin hide *) -inline "cic:/CoRN/fta/KneserLemma/b_0.con". +inline "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b_0.con" "Kneser_Lemma__". -inline "cic:/CoRN/fta/KneserLemma/b_n.con". +inline "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b_n.con" "Kneser_Lemma__". (* end hide *) -inline "cic:/CoRN/fta/KneserLemma/b_n_1.var". +inline "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b_n_1.var" "Kneser_Lemma__". -inline "cic:/CoRN/fta/KneserLemma/c.var". +inline "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/c.var" "Kneser_Lemma__". -inline "cic:/CoRN/fta/KneserLemma/b_0_lt_c.var". +inline "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b_0_lt_c.var" "Kneser_Lemma__". (*#* %\begin{convention}% We define the following local abbreviations: @@ -77,21 +77,21 @@ inline "cic:/CoRN/fta/KneserLemma/b_0_lt_c.var". (* begin hide *) -inline "cic:/CoRN/fta/KneserLemma/two_n.con". +inline "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/two_n.con" "Kneser_Lemma__". -inline "cic:/CoRN/fta/KneserLemma/Small.con". +inline "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/Small.con" "Kneser_Lemma__". -inline "cic:/CoRN/fta/KneserLemma/Smaller.con". +inline "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/Smaller.con" "Kneser_Lemma__". -inline "cic:/CoRN/fta/KneserLemma/Smallest.con". +inline "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/Smallest.con" "Kneser_Lemma__". -inline "cic:/CoRN/fta/KneserLemma/q.con". +inline "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/q.con" "Kneser_Lemma__". (* end hide *) inline "cic:/CoRN/fta/KneserLemma/b_0'_exists.con". -inline "cic:/CoRN/fta/KneserLemma/eta_0.con". +inline "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/eta_0.con" "Kneser_Lemma__". inline "cic:/CoRN/fta/KneserLemma/eta_0_pos.con". @@ -107,7 +107,7 @@ inline "cic:/CoRN/fta/KneserLemma/eps_exists.con". (* begin hide *) -inline "cic:/CoRN/fta/KneserLemma/a.con". +inline "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/a.con" "Kneser_Lemma__". (* end hide *) @@ -138,7 +138,7 @@ inline "cic:/CoRN/fta/KneserLemma/Kneser_2.con". inline "cic:/CoRN/fta/KneserLemma/Kneser_3.con". (* UNEXPORTED -End Kneser_Lemma. +End Kneser_Lemma *) inline "cic:/CoRN/fta/KneserLemma/Kneser.con". diff --git a/helm/software/matita/contribs/CoRN-Decl/fta/MainLemma.ma b/helm/software/matita/contribs/CoRN-Decl/fta/MainLemma.ma index 350e62138..c428b591d 100644 --- a/helm/software/matita/contribs/CoRN-Decl/fta/MainLemma.ma +++ b/helm/software/matita/contribs/CoRN-Decl/fta/MainLemma.ma @@ -34,7 +34,7 @@ include "fta/KeyLemma.ma". *) (* UNEXPORTED -Section Main_Lemma. +Section Main_Lemma *) (*#* @@ -45,23 +45,23 @@ Let [a : nat->IR], [n : nat], [a_0 : IR] and [eps : IR] such that [0 < n], %\end{convention}% *) -inline "cic:/CoRN/fta/MainLemma/a.var". +inline "cic:/CoRN/fta/MainLemma/Main_Lemma/a.var" "Main_Lemma__". -inline "cic:/CoRN/fta/MainLemma/n.var". +inline "cic:/CoRN/fta/MainLemma/Main_Lemma/n.var" "Main_Lemma__". -inline "cic:/CoRN/fta/MainLemma/gt_n_0.var". +inline "cic:/CoRN/fta/MainLemma/Main_Lemma/gt_n_0.var" "Main_Lemma__". -inline "cic:/CoRN/fta/MainLemma/eps.var". +inline "cic:/CoRN/fta/MainLemma/Main_Lemma/eps.var" "Main_Lemma__". -inline "cic:/CoRN/fta/MainLemma/eps_pos.var". +inline "cic:/CoRN/fta/MainLemma/Main_Lemma/eps_pos.var" "Main_Lemma__". -inline "cic:/CoRN/fta/MainLemma/a_nonneg.var". +inline "cic:/CoRN/fta/MainLemma/Main_Lemma/a_nonneg.var" "Main_Lemma__". -inline "cic:/CoRN/fta/MainLemma/a_n_1.var". +inline "cic:/CoRN/fta/MainLemma/Main_Lemma/a_n_1.var" "Main_Lemma__". -inline "cic:/CoRN/fta/MainLemma/a_0.var". +inline "cic:/CoRN/fta/MainLemma/Main_Lemma/a_0.var" "Main_Lemma__". -inline "cic:/CoRN/fta/MainLemma/eps_le_a_0.var". +inline "cic:/CoRN/fta/MainLemma/Main_Lemma/eps_le_a_0.var" "Main_Lemma__". inline "cic:/CoRN/fta/MainLemma/a_0_pos.con". @@ -76,11 +76,11 @@ inline "cic:/CoRN/fta/MainLemma/a_0_pos.con". (* begin hide *) -inline "cic:/CoRN/fta/MainLemma/two_n.con". +inline "cic:/CoRN/fta/MainLemma/Main_Lemma/two_n.con" "Main_Lemma__". -inline "cic:/CoRN/fta/MainLemma/Small.con". +inline "cic:/CoRN/fta/MainLemma/Main_Lemma/Small.con" "Main_Lemma__". -inline "cic:/CoRN/fta/MainLemma/Smaller.con". +inline "cic:/CoRN/fta/MainLemma/Main_Lemma/Smaller.con" "Main_Lemma__". (* end hide *) @@ -123,6 +123,6 @@ inline "cic:/CoRN/fta/MainLemma/Main.con". (* end hide *) (* UNEXPORTED -End Main_Lemma. +End Main_Lemma *) diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/COrdLemmas.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/COrdLemmas.ma index bf7461582..be807b44a 100644 --- a/helm/software/matita/contribs/CoRN-Decl/ftc/COrdLemmas.ma +++ b/helm/software/matita/contribs/CoRN-Decl/ftc/COrdLemmas.ma @@ -23,7 +23,7 @@ include "CoRN.ma". include "algebra/COrdCauchy.ma". (* UNEXPORTED -Section Lemmas. +Section Lemmas *) (*#* *Lemmas for Integration @@ -39,7 +39,7 @@ the proof that any two partitions with no common point have a common refinement). *) -inline "cic:/CoRN/ftc/COrdLemmas/F.var". +inline "cic:/CoRN/ftc/COrdLemmas/Lemmas/F.var" "Lemmas__". inline "cic:/CoRN/ftc/COrdLemmas/om_fun_lt.con". @@ -65,13 +65,13 @@ inline "cic:/CoRN/ftc/COrdLemmas/om_fun_4d.con". (* begin hide *) -inline "cic:/CoRN/ftc/COrdLemmas/f.var". +inline "cic:/CoRN/ftc/COrdLemmas/Lemmas/f.var" "Lemmas__". -inline "cic:/CoRN/ftc/COrdLemmas/f0.var". +inline "cic:/CoRN/ftc/COrdLemmas/Lemmas/f0.var" "Lemmas__". -inline "cic:/CoRN/ftc/COrdLemmas/f_mon.var". +inline "cic:/CoRN/ftc/COrdLemmas/Lemmas/f_mon.var" "Lemmas__". -inline "cic:/CoRN/ftc/COrdLemmas/h.var". +inline "cic:/CoRN/ftc/COrdLemmas/Lemmas/h.var" "Lemmas__". (* end hide *) @@ -96,18 +96,18 @@ inline "cic:/CoRN/ftc/COrdLemmas/str_Sumx_Sum_Sum (* begin hide *).con". (* UNEXPORTED -End Lemmas. +End Lemmas *) (* UNEXPORTED -Section More_Lemmas. +Section More_Lemmas *) -inline "cic:/CoRN/ftc/COrdLemmas/f'.con". +inline "cic:/CoRN/ftc/COrdLemmas/More_Lemmas/f'.con" "More_Lemmas__". (* end hide *) -inline "cic:/CoRN/ftc/COrdLemmas/F.var". +inline "cic:/CoRN/ftc/COrdLemmas/More_Lemmas/F.var" "More_Lemmas__". (* begin show *) @@ -118,6 +118,6 @@ inline "cic:/CoRN/ftc/COrdLemmas/str_Sumx_Sum_Sum' (* end hide *) (* UNEXPORTED -End More_Lemmas. +End More_Lemmas *) diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/CalculusTheorems.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/CalculusTheorems.ma index 6e43129c3..375104975 100644 --- a/helm/software/matita/contribs/CoRN-Decl/ftc/CalculusTheorems.ma +++ b/helm/software/matita/contribs/CoRN-Decl/ftc/CalculusTheorems.ma @@ -29,7 +29,7 @@ Opaque Min Max. *) (* UNEXPORTED -Section Various_Theorems. +Section Various_Theorems *) (*#* *Calculus Theorems @@ -118,6 +118,6 @@ Transparent nring. inline "cic:/CoRN/ftc/CalculusTheorems/nexp_resp_leEq_odd.con". (* UNEXPORTED -End Various_Theorems. +End Various_Theorems *) diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/Composition.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/Composition.ma index 124656d5b..16cbd166d 100644 --- a/helm/software/matita/contribs/CoRN-Decl/ftc/Composition.ma +++ b/helm/software/matita/contribs/CoRN-Decl/ftc/Composition.ma @@ -23,11 +23,11 @@ include "CoRN.ma". include "ftc/MoreFunctions.ma". (* UNEXPORTED -Section Maps_into_Compacts. +Section Maps_into_Compacts *) (* UNEXPORTED -Section Part_Funct. +Section Part_Funct *) (*#* *Composition @@ -53,31 +53,31 @@ mapped into another compact interval. We define this concept for partial functions, and prove some trivial results. *) -inline "cic:/CoRN/ftc/Composition/F.var". +inline "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/F.var" "Maps_into_Compacts__Part_Funct__". -inline "cic:/CoRN/ftc/Composition/G.var". +inline "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/G.var" "Maps_into_Compacts__Part_Funct__". -inline "cic:/CoRN/ftc/Composition/a.var". +inline "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/a.var" "Maps_into_Compacts__Part_Funct__". -inline "cic:/CoRN/ftc/Composition/b.var". +inline "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/b.var" "Maps_into_Compacts__Part_Funct__". -inline "cic:/CoRN/ftc/Composition/Hab.var". +inline "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/Hab.var" "Maps_into_Compacts__Part_Funct__". -inline "cic:/CoRN/ftc/Composition/c.var". +inline "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/c.var" "Maps_into_Compacts__Part_Funct__". -inline "cic:/CoRN/ftc/Composition/d.var". +inline "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/d.var" "Maps_into_Compacts__Part_Funct__". -inline "cic:/CoRN/ftc/Composition/Hcd.var". +inline "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/Hcd.var" "Maps_into_Compacts__Part_Funct__". (* begin hide *) -inline "cic:/CoRN/ftc/Composition/I.con". +inline "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/I.con" "Maps_into_Compacts__Part_Funct__". (* end hide *) (* begin show *) -inline "cic:/CoRN/ftc/Composition/Hf.var". +inline "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/Hf.var" "Maps_into_Compacts__Part_Funct__". (* end show *) @@ -85,7 +85,7 @@ inline "cic:/CoRN/ftc/Composition/maps_into_compacts.con". (* begin show *) -inline "cic:/CoRN/ftc/Composition/maps.var". +inline "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/maps.var" "Maps_into_Compacts__Part_Funct__". (* end show *) @@ -98,15 +98,15 @@ inline "cic:/CoRN/ftc/Composition/maps_lemma_less.con". inline "cic:/CoRN/ftc/Composition/maps_lemma_inc.con". (* UNEXPORTED -End Part_Funct. +End Part_Funct *) (* UNEXPORTED -End Maps_into_Compacts. +End Maps_into_Compacts *) (* UNEXPORTED -Section Mapping. +Section Mapping *) (*#* @@ -114,40 +114,40 @@ As was the case for division of partial functions, this condition completely characterizes the domain of the composite function. *) -inline "cic:/CoRN/ftc/Composition/F.var". +inline "cic:/CoRN/ftc/Composition/Mapping/F.var" "Mapping__". -inline "cic:/CoRN/ftc/Composition/G.var". +inline "cic:/CoRN/ftc/Composition/Mapping/G.var" "Mapping__". -inline "cic:/CoRN/ftc/Composition/a.var". +inline "cic:/CoRN/ftc/Composition/Mapping/a.var" "Mapping__". -inline "cic:/CoRN/ftc/Composition/b.var". +inline "cic:/CoRN/ftc/Composition/Mapping/b.var" "Mapping__". -inline "cic:/CoRN/ftc/Composition/Hab.var". +inline "cic:/CoRN/ftc/Composition/Mapping/Hab.var" "Mapping__". -inline "cic:/CoRN/ftc/Composition/c.var". +inline "cic:/CoRN/ftc/Composition/Mapping/c.var" "Mapping__". -inline "cic:/CoRN/ftc/Composition/d.var". +inline "cic:/CoRN/ftc/Composition/Mapping/d.var" "Mapping__". -inline "cic:/CoRN/ftc/Composition/Hcd.var". +inline "cic:/CoRN/ftc/Composition/Mapping/Hcd.var" "Mapping__". (* begin show *) -inline "cic:/CoRN/ftc/Composition/Hf.var". +inline "cic:/CoRN/ftc/Composition/Mapping/Hf.var" "Mapping__". -inline "cic:/CoRN/ftc/Composition/Hg.var". +inline "cic:/CoRN/ftc/Composition/Mapping/Hg.var" "Mapping__". -inline "cic:/CoRN/ftc/Composition/maps.var". +inline "cic:/CoRN/ftc/Composition/Mapping/maps.var" "Mapping__". (* end show *) inline "cic:/CoRN/ftc/Composition/included_comp.con". (* UNEXPORTED -End Mapping. +End Mapping *) (* UNEXPORTED -Section Interval_Continuity. +Section Interval_Continuity *) (*#* **Continuity @@ -155,46 +155,46 @@ Section Interval_Continuity. We now prove that the composition of two continuous partial functions is continuous. *) -inline "cic:/CoRN/ftc/Composition/a.var". +inline "cic:/CoRN/ftc/Composition/Interval_Continuity/a.var" "Interval_Continuity__". -inline "cic:/CoRN/ftc/Composition/b.var". +inline "cic:/CoRN/ftc/Composition/Interval_Continuity/b.var" "Interval_Continuity__". -inline "cic:/CoRN/ftc/Composition/Hab.var". +inline "cic:/CoRN/ftc/Composition/Interval_Continuity/Hab.var" "Interval_Continuity__". (* begin hide *) -inline "cic:/CoRN/ftc/Composition/I.con". +inline "cic:/CoRN/ftc/Composition/Interval_Continuity/I.con" "Interval_Continuity__". (* end hide *) -inline "cic:/CoRN/ftc/Composition/c.var". +inline "cic:/CoRN/ftc/Composition/Interval_Continuity/c.var" "Interval_Continuity__". -inline "cic:/CoRN/ftc/Composition/d.var". +inline "cic:/CoRN/ftc/Composition/Interval_Continuity/d.var" "Interval_Continuity__". -inline "cic:/CoRN/ftc/Composition/Hcd.var". +inline "cic:/CoRN/ftc/Composition/Interval_Continuity/Hcd.var" "Interval_Continuity__". -inline "cic:/CoRN/ftc/Composition/F.var". +inline "cic:/CoRN/ftc/Composition/Interval_Continuity/F.var" "Interval_Continuity__". -inline "cic:/CoRN/ftc/Composition/G.var". +inline "cic:/CoRN/ftc/Composition/Interval_Continuity/G.var" "Interval_Continuity__". (* begin show *) -inline "cic:/CoRN/ftc/Composition/contF.var". +inline "cic:/CoRN/ftc/Composition/Interval_Continuity/contF.var" "Interval_Continuity__". -inline "cic:/CoRN/ftc/Composition/contG.var". +inline "cic:/CoRN/ftc/Composition/Interval_Continuity/contG.var" "Interval_Continuity__". -inline "cic:/CoRN/ftc/Composition/Hmap.var". +inline "cic:/CoRN/ftc/Composition/Interval_Continuity/Hmap.var" "Interval_Continuity__". (* end show *) inline "cic:/CoRN/ftc/Composition/Continuous_I_comp.con". (* UNEXPORTED -End Interval_Continuity. +End Interval_Continuity *) (* UNEXPORTED -Section Derivative. +Section Derivative *) (*#* **Derivative @@ -202,43 +202,43 @@ Section Derivative. We now work with the derivative relation and prove the chain rule for partial functions. *) -inline "cic:/CoRN/ftc/Composition/F.var". +inline "cic:/CoRN/ftc/Composition/Derivative/F.var" "Derivative__". -inline "cic:/CoRN/ftc/Composition/F'.var". +inline "cic:/CoRN/ftc/Composition/Derivative/F'.var" "Derivative__". -inline "cic:/CoRN/ftc/Composition/G.var". +inline "cic:/CoRN/ftc/Composition/Derivative/G.var" "Derivative__". -inline "cic:/CoRN/ftc/Composition/G'.var". +inline "cic:/CoRN/ftc/Composition/Derivative/G'.var" "Derivative__". -inline "cic:/CoRN/ftc/Composition/a.var". +inline "cic:/CoRN/ftc/Composition/Derivative/a.var" "Derivative__". -inline "cic:/CoRN/ftc/Composition/b.var". +inline "cic:/CoRN/ftc/Composition/Derivative/b.var" "Derivative__". -inline "cic:/CoRN/ftc/Composition/Hab'.var". +inline "cic:/CoRN/ftc/Composition/Derivative/Hab'.var" "Derivative__". -inline "cic:/CoRN/ftc/Composition/c.var". +inline "cic:/CoRN/ftc/Composition/Derivative/c.var" "Derivative__". -inline "cic:/CoRN/ftc/Composition/d.var". +inline "cic:/CoRN/ftc/Composition/Derivative/d.var" "Derivative__". -inline "cic:/CoRN/ftc/Composition/Hcd'.var". +inline "cic:/CoRN/ftc/Composition/Derivative/Hcd'.var" "Derivative__". (* begin hide *) -inline "cic:/CoRN/ftc/Composition/Hab.con". +inline "cic:/CoRN/ftc/Composition/Derivative/Hab.con" "Derivative__". -inline "cic:/CoRN/ftc/Composition/Hcd.con". +inline "cic:/CoRN/ftc/Composition/Derivative/Hcd.con" "Derivative__". -inline "cic:/CoRN/ftc/Composition/I.con". +inline "cic:/CoRN/ftc/Composition/Derivative/I.con" "Derivative__". (* end hide *) (* begin show *) -inline "cic:/CoRN/ftc/Composition/derF.var". +inline "cic:/CoRN/ftc/Composition/Derivative/derF.var" "Derivative__". -inline "cic:/CoRN/ftc/Composition/derG.var". +inline "cic:/CoRN/ftc/Composition/Derivative/derG.var" "Derivative__". -inline "cic:/CoRN/ftc/Composition/Hmap.var". +inline "cic:/CoRN/ftc/Composition/Derivative/Hmap.var" "Derivative__". (* end show *) @@ -255,11 +255,11 @@ The next lemma will be useful when we move on to differentiability. inline "cic:/CoRN/ftc/Composition/Diffble_I_comp_aux.con". (* UNEXPORTED -End Derivative. +End Derivative *) (* UNEXPORTED -Section Differentiability. +Section Differentiability *) (*#* **Differentiability @@ -267,50 +267,50 @@ Section Differentiability. Finally, we move on to differentiability. *) -inline "cic:/CoRN/ftc/Composition/F.var". +inline "cic:/CoRN/ftc/Composition/Differentiability/F.var" "Differentiability__". -inline "cic:/CoRN/ftc/Composition/G.var". +inline "cic:/CoRN/ftc/Composition/Differentiability/G.var" "Differentiability__". -inline "cic:/CoRN/ftc/Composition/a.var". +inline "cic:/CoRN/ftc/Composition/Differentiability/a.var" "Differentiability__". -inline "cic:/CoRN/ftc/Composition/b.var". +inline "cic:/CoRN/ftc/Composition/Differentiability/b.var" "Differentiability__". -inline "cic:/CoRN/ftc/Composition/Hab'.var". +inline "cic:/CoRN/ftc/Composition/Differentiability/Hab'.var" "Differentiability__". -inline "cic:/CoRN/ftc/Composition/c.var". +inline "cic:/CoRN/ftc/Composition/Differentiability/c.var" "Differentiability__". -inline "cic:/CoRN/ftc/Composition/d.var". +inline "cic:/CoRN/ftc/Composition/Differentiability/d.var" "Differentiability__". -inline "cic:/CoRN/ftc/Composition/Hcd'.var". +inline "cic:/CoRN/ftc/Composition/Differentiability/Hcd'.var" "Differentiability__". (* begin hide *) -inline "cic:/CoRN/ftc/Composition/Hab.con". +inline "cic:/CoRN/ftc/Composition/Differentiability/Hab.con" "Differentiability__". -inline "cic:/CoRN/ftc/Composition/Hcd.con". +inline "cic:/CoRN/ftc/Composition/Differentiability/Hcd.con" "Differentiability__". -inline "cic:/CoRN/ftc/Composition/I.con". +inline "cic:/CoRN/ftc/Composition/Differentiability/I.con" "Differentiability__". (* end hide *) (* begin show *) -inline "cic:/CoRN/ftc/Composition/diffF.var". +inline "cic:/CoRN/ftc/Composition/Differentiability/diffF.var" "Differentiability__". -inline "cic:/CoRN/ftc/Composition/diffG.var". +inline "cic:/CoRN/ftc/Composition/Differentiability/diffG.var" "Differentiability__". -inline "cic:/CoRN/ftc/Composition/Hmap.var". +inline "cic:/CoRN/ftc/Composition/Differentiability/Hmap.var" "Differentiability__". (* end show *) inline "cic:/CoRN/ftc/Composition/Diffble_I_comp.con". (* UNEXPORTED -End Differentiability. +End Differentiability *) (* UNEXPORTED -Section Generalized_Intervals. +Section Generalized_Intervals *) (*#* **Generalizations @@ -321,13 +321,13 @@ We now generalize this results to arbitrary intervals. We begin by generalizing %\end{convention}% *) -inline "cic:/CoRN/ftc/Composition/I.var". +inline "cic:/CoRN/ftc/Composition/Generalized_Intervals/I.var" "Generalized_Intervals__". -inline "cic:/CoRN/ftc/Composition/J.var". +inline "cic:/CoRN/ftc/Composition/Generalized_Intervals/J.var" "Generalized_Intervals__". -inline "cic:/CoRN/ftc/Composition/pI.var". +inline "cic:/CoRN/ftc/Composition/Generalized_Intervals/pI.var" "Generalized_Intervals__". -inline "cic:/CoRN/ftc/Composition/pJ.var". +inline "cic:/CoRN/ftc/Composition/Generalized_Intervals/pJ.var" "Generalized_Intervals__". inline "cic:/CoRN/ftc/Composition/maps_compacts_into.con". @@ -337,17 +337,17 @@ Now everything comes naturally: inline "cic:/CoRN/ftc/Composition/comp_inc_lemma.con". -inline "cic:/CoRN/ftc/Composition/F.var". +inline "cic:/CoRN/ftc/Composition/Generalized_Intervals/F.var" "Generalized_Intervals__". -inline "cic:/CoRN/ftc/Composition/F'.var". +inline "cic:/CoRN/ftc/Composition/Generalized_Intervals/F'.var" "Generalized_Intervals__". -inline "cic:/CoRN/ftc/Composition/G.var". +inline "cic:/CoRN/ftc/Composition/Generalized_Intervals/G.var" "Generalized_Intervals__". -inline "cic:/CoRN/ftc/Composition/G'.var". +inline "cic:/CoRN/ftc/Composition/Generalized_Intervals/G'.var" "Generalized_Intervals__". (* begin show *) -inline "cic:/CoRN/ftc/Composition/Hmap.var". +inline "cic:/CoRN/ftc/Composition/Generalized_Intervals/Hmap.var" "Generalized_Intervals__". (* end show *) @@ -355,18 +355,18 @@ inline "cic:/CoRN/ftc/Composition/Continuous_comp.con". (* begin show *) -inline "cic:/CoRN/ftc/Composition/Hmap'.var". +inline "cic:/CoRN/ftc/Composition/Generalized_Intervals/Hmap'.var" "Generalized_Intervals__". (* end show *) inline "cic:/CoRN/ftc/Composition/Derivative_comp.con". (* UNEXPORTED -End Generalized_Intervals. +End Generalized_Intervals *) (* UNEXPORTED -Section Corollaries. +Section Corollaries *) (*#* @@ -390,7 +390,7 @@ As a corollary, we get the generalization of differentiability property. inline "cic:/CoRN/ftc/Composition/Diffble_comp.con". (* UNEXPORTED -End Corollaries. +End Corollaries *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/Continuity.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/Continuity.ma index 113b47653..59ddd4f45 100644 --- a/helm/software/matita/contribs/CoRN-Decl/ftc/Continuity.ma +++ b/helm/software/matita/contribs/CoRN-Decl/ftc/Continuity.ma @@ -27,7 +27,7 @@ include "reals/NRootIR.ma". include "ftc/FunctSums.ma". (* UNEXPORTED -Section Definitions_and_Basic_Results. +Section Definitions_and_Basic_Results *) (*#* *Continuity @@ -54,23 +54,23 @@ respectively [P, Q] and [R]. Here we define continuity and prove some basic properties of continuous functions. *) -inline "cic:/CoRN/ftc/Continuity/a.var". +inline "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/a.var" "Definitions_and_Basic_Results__". -inline "cic:/CoRN/ftc/Continuity/b.var". +inline "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/b.var" "Definitions_and_Basic_Results__". -inline "cic:/CoRN/ftc/Continuity/Hab.var". +inline "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/Hab.var" "Definitions_and_Basic_Results__". (* begin hide *) -inline "cic:/CoRN/ftc/Continuity/I.con". +inline "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/I.con" "Definitions_and_Basic_Results__". (* end hide *) -inline "cic:/CoRN/ftc/Continuity/F.var". +inline "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/F.var" "Definitions_and_Basic_Results__". (* begin hide *) -inline "cic:/CoRN/ftc/Continuity/P.con". +inline "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/P.con" "Definitions_and_Basic_Results__". (* end hide *) @@ -88,11 +88,11 @@ inline "cic:/CoRN/ftc/Continuity/contin_prop.con". Assume [F] to be continuous in [I]. Then it has a least upper bound and a greater lower bound on [I]. *) -inline "cic:/CoRN/ftc/Continuity/contF.var". +inline "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/contF.var" "Definitions_and_Basic_Results__". (* begin hide *) -inline "cic:/CoRN/ftc/Continuity/Hinc'.con". +inline "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/Hinc'.con" "Definitions_and_Basic_Results__". (* end hide *) @@ -153,7 +153,7 @@ inline "cic:/CoRN/ftc/Continuity/leEq_Norm_Funct.con". inline "cic:/CoRN/ftc/Continuity/less_Norm_Funct.con". (* UNEXPORTED -End Definitions_and_Basic_Results. +End Definitions_and_Basic_Results *) (* UNEXPORTED @@ -165,7 +165,7 @@ Implicit Arguments Norm_Funct [a b Hab F]. *) (* UNEXPORTED -Section Local_Results. +Section Local_Results *) (*#* **Algebraic Properties @@ -173,33 +173,33 @@ 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]. *) -inline "cic:/CoRN/ftc/Continuity/a.var". +inline "cic:/CoRN/ftc/Continuity/Local_Results/a.var" "Local_Results__". -inline "cic:/CoRN/ftc/Continuity/b.var". +inline "cic:/CoRN/ftc/Continuity/Local_Results/b.var" "Local_Results__". -inline "cic:/CoRN/ftc/Continuity/Hab.var". +inline "cic:/CoRN/ftc/Continuity/Local_Results/Hab.var" "Local_Results__". (* begin hide *) -inline "cic:/CoRN/ftc/Continuity/I.con". +inline "cic:/CoRN/ftc/Continuity/Local_Results/I.con" "Local_Results__". (* end hide *) -inline "cic:/CoRN/ftc/Continuity/F.var". +inline "cic:/CoRN/ftc/Continuity/Local_Results/F.var" "Local_Results__". -inline "cic:/CoRN/ftc/Continuity/G.var". +inline "cic:/CoRN/ftc/Continuity/Local_Results/G.var" "Local_Results__". (* begin hide *) -inline "cic:/CoRN/ftc/Continuity/P.con". +inline "cic:/CoRN/ftc/Continuity/Local_Results/P.con" "Local_Results__". -inline "cic:/CoRN/ftc/Continuity/Q.con". +inline "cic:/CoRN/ftc/Continuity/Local_Results/Q.con" "Local_Results__". (* end hide *) -inline "cic:/CoRN/ftc/Continuity/incF.var". +inline "cic:/CoRN/ftc/Continuity/Local_Results/incF.var" "Local_Results__". -inline "cic:/CoRN/ftc/Continuity/incG.var". +inline "cic:/CoRN/ftc/Continuity/Local_Results/incG.var" "Local_Results__". (*#* 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. @@ -235,9 +235,9 @@ inline "cic:/CoRN/ftc/Continuity/Continuous_I_id.con". 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. *) -inline "cic:/CoRN/ftc/Continuity/contF.var". +inline "cic:/CoRN/ftc/Continuity/Local_Results/contF.var" "Local_Results__". -inline "cic:/CoRN/ftc/Continuity/contG.var". +inline "cic:/CoRN/ftc/Continuity/Local_Results/contG.var" "Local_Results__". inline "cic:/CoRN/ftc/Continuity/Continuous_I_plus.con". @@ -257,16 +257,16 @@ inline "cic:/CoRN/ftc/Continuity/Continuous_I_max.con". (* begin show *) -inline "cic:/CoRN/ftc/Continuity/Hg'.var". +inline "cic:/CoRN/ftc/Continuity/Local_Results/Hg'.var" "Local_Results__". -inline "cic:/CoRN/ftc/Continuity/Hg''.var". +inline "cic:/CoRN/ftc/Continuity/Local_Results/Hg''.var" "Local_Results__". (* end show *) inline "cic:/CoRN/ftc/Continuity/Continuous_I_recip.con". (* UNEXPORTED -End Local_Results. +End Local_Results *) (* UNEXPORTED @@ -274,36 +274,36 @@ Hint Resolve contin_imp_inc: included. *) (* UNEXPORTED -Section Corolaries. +Section Corolaries *) -inline "cic:/CoRN/ftc/Continuity/a.var". +inline "cic:/CoRN/ftc/Continuity/Corolaries/a.var" "Corolaries__". -inline "cic:/CoRN/ftc/Continuity/b.var". +inline "cic:/CoRN/ftc/Continuity/Corolaries/b.var" "Corolaries__". -inline "cic:/CoRN/ftc/Continuity/Hab.var". +inline "cic:/CoRN/ftc/Continuity/Corolaries/Hab.var" "Corolaries__". (* begin hide *) -inline "cic:/CoRN/ftc/Continuity/I.con". +inline "cic:/CoRN/ftc/Continuity/Corolaries/I.con" "Corolaries__". (* end hide *) -inline "cic:/CoRN/ftc/Continuity/F.var". +inline "cic:/CoRN/ftc/Continuity/Corolaries/F.var" "Corolaries__". -inline "cic:/CoRN/ftc/Continuity/G.var". +inline "cic:/CoRN/ftc/Continuity/Corolaries/G.var" "Corolaries__". (* begin hide *) -inline "cic:/CoRN/ftc/Continuity/P.con". +inline "cic:/CoRN/ftc/Continuity/Corolaries/P.con" "Corolaries__". -inline "cic:/CoRN/ftc/Continuity/Q.con". +inline "cic:/CoRN/ftc/Continuity/Corolaries/Q.con" "Corolaries__". (* end hide *) -inline "cic:/CoRN/ftc/Continuity/contF.var". +inline "cic:/CoRN/ftc/Continuity/Corolaries/contF.var" "Corolaries__". -inline "cic:/CoRN/ftc/Continuity/contG.var". +inline "cic:/CoRN/ftc/Continuity/Corolaries/contG.var" "Corolaries__". (*#* The corresponding properties for subtraction, division and @@ -322,39 +322,39 @@ inline "cic:/CoRN/ftc/Continuity/Continuous_I_min.con". inline "cic:/CoRN/ftc/Continuity/Continuous_I_abs.con". -inline "cic:/CoRN/ftc/Continuity/Hg'.var". +inline "cic:/CoRN/ftc/Continuity/Corolaries/Hg'.var" "Corolaries__". -inline "cic:/CoRN/ftc/Continuity/Hg''.var". +inline "cic:/CoRN/ftc/Continuity/Corolaries/Hg''.var" "Corolaries__". inline "cic:/CoRN/ftc/Continuity/Continuous_I_div.con". (* UNEXPORTED -End Corolaries. +End Corolaries *) (* UNEXPORTED -Section Other. +Section Other *) (* UNEXPORTED -Section Sums. +Section Sums *) (*#* We finally prove that the sum of an arbitrary family of continuous functions is still a continuous function. *) -inline "cic:/CoRN/ftc/Continuity/a.var". +inline "cic:/CoRN/ftc/Continuity/Other/Sums/a.var" "Other__Sums__". -inline "cic:/CoRN/ftc/Continuity/b.var". +inline "cic:/CoRN/ftc/Continuity/Other/Sums/b.var" "Other__Sums__". -inline "cic:/CoRN/ftc/Continuity/Hab.var". +inline "cic:/CoRN/ftc/Continuity/Other/Sums/Hab.var" "Other__Sums__". -inline "cic:/CoRN/ftc/Continuity/Hab'.var". +inline "cic:/CoRN/ftc/Continuity/Other/Sums/Hab'.var" "Other__Sums__". (* begin hide *) -inline "cic:/CoRN/ftc/Continuity/I.con". +inline "cic:/CoRN/ftc/Continuity/Other/Sums/I.con" "Other__Sums__". (* end hide *) @@ -365,7 +365,7 @@ inline "cic:/CoRN/ftc/Continuity/Continuous_I_Sumx.con". inline "cic:/CoRN/ftc/Continuity/Continuous_I_Sum.con". (* UNEXPORTED -End Sums. +End Sums *) (*#* @@ -395,7 +395,7 @@ The value of the norm is covariant with the length of the interval. inline "cic:/CoRN/ftc/Continuity/included_imp_norm_leEq.con". (* UNEXPORTED -End Other. +End Other *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/Derivative.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/Derivative.ma index 4551cb741..6d380017d 100644 --- a/helm/software/matita/contribs/CoRN-Decl/ftc/Derivative.ma +++ b/helm/software/matita/contribs/CoRN-Decl/ftc/Derivative.ma @@ -23,7 +23,7 @@ include "CoRN.ma". include "ftc/Continuity.ma". (* UNEXPORTED -Section Definitions. +Section Definitions *) (*#* *Derivatives @@ -53,32 +53,32 @@ will be partial functions with domains respectively [P, P', Q, Q'] and %\end{convention}% *) -inline "cic:/CoRN/ftc/Derivative/a.var". +inline "cic:/CoRN/ftc/Derivative/Definitions/a.var" "Definitions__". -inline "cic:/CoRN/ftc/Derivative/b.var". +inline "cic:/CoRN/ftc/Derivative/Definitions/b.var" "Definitions__". -inline "cic:/CoRN/ftc/Derivative/Hab'.var". +inline "cic:/CoRN/ftc/Derivative/Definitions/Hab'.var" "Definitions__". (* begin hide *) -inline "cic:/CoRN/ftc/Derivative/Hab.con". +inline "cic:/CoRN/ftc/Derivative/Definitions/Hab.con" "Definitions__". -inline "cic:/CoRN/ftc/Derivative/I.con". +inline "cic:/CoRN/ftc/Derivative/Definitions/I.con" "Definitions__". (* end hide *) -inline "cic:/CoRN/ftc/Derivative/F.var". +inline "cic:/CoRN/ftc/Derivative/Definitions/F.var" "Definitions__". (* begin hide *) -inline "cic:/CoRN/ftc/Derivative/P.con". +inline "cic:/CoRN/ftc/Derivative/Definitions/P.con" "Definitions__". (* end hide *) inline "cic:/CoRN/ftc/Derivative/Derivative_I.con". (* UNEXPORTED -End Definitions. +End Definitions *) (* UNEXPORTED @@ -86,23 +86,23 @@ Implicit Arguments Derivative_I [a b]. *) (* UNEXPORTED -Section Basic_Properties. +Section Basic_Properties *) (*#* **Basic Properties *) -inline "cic:/CoRN/ftc/Derivative/a.var". +inline "cic:/CoRN/ftc/Derivative/Basic_Properties/a.var" "Basic_Properties__". -inline "cic:/CoRN/ftc/Derivative/b.var". +inline "cic:/CoRN/ftc/Derivative/Basic_Properties/b.var" "Basic_Properties__". -inline "cic:/CoRN/ftc/Derivative/Hab'.var". +inline "cic:/CoRN/ftc/Derivative/Basic_Properties/Hab'.var" "Basic_Properties__". (* begin hide *) -inline "cic:/CoRN/ftc/Derivative/Hab.con". +inline "cic:/CoRN/ftc/Derivative/Basic_Properties/Hab.con" "Basic_Properties__". -inline "cic:/CoRN/ftc/Derivative/I.con". +inline "cic:/CoRN/ftc/Derivative/Basic_Properties/I.con" "Basic_Properties__". (* end hide *) @@ -118,19 +118,19 @@ inline "cic:/CoRN/ftc/Derivative/Derivative_I_char.con". Derivative is a well defined relation; we will make this explicit for both arguments: *) -inline "cic:/CoRN/ftc/Derivative/F.var". +inline "cic:/CoRN/ftc/Derivative/Basic_Properties/F.var" "Basic_Properties__". -inline "cic:/CoRN/ftc/Derivative/G.var". +inline "cic:/CoRN/ftc/Derivative/Basic_Properties/G.var" "Basic_Properties__". -inline "cic:/CoRN/ftc/Derivative/H.var". +inline "cic:/CoRN/ftc/Derivative/Basic_Properties/H.var" "Basic_Properties__". (* begin hide *) -inline "cic:/CoRN/ftc/Derivative/P.con". +inline "cic:/CoRN/ftc/Derivative/Basic_Properties/P.con" "Basic_Properties__". -inline "cic:/CoRN/ftc/Derivative/Q.con". +inline "cic:/CoRN/ftc/Derivative/Basic_Properties/Q.con" "Basic_Properties__". -inline "cic:/CoRN/ftc/Derivative/R.con". +inline "cic:/CoRN/ftc/Derivative/Basic_Properties/R.con" "Basic_Properties__". (* end hide *) @@ -140,7 +140,7 @@ inline "cic:/CoRN/ftc/Derivative/Derivative_I_wdr.con". (* begin hide *) -inline "cic:/CoRN/ftc/Derivative/Derivative_I_unique_lemma.con". +inline "cic:/CoRN/ftc/Derivative/Basic_Properties/Derivative_I_unique_lemma.con" "Basic_Properties__". (* end hide *) @@ -162,14 +162,14 @@ inline "cic:/CoRN/ftc/Derivative/derivative_imp_inc'.con". Any function that is or has a derivative is continuous. *) -inline "cic:/CoRN/ftc/Derivative/Hab''.var". +inline "cic:/CoRN/ftc/Derivative/Basic_Properties/Hab''.var" "Basic_Properties__". inline "cic:/CoRN/ftc/Derivative/deriv_imp_contin'_I.con". inline "cic:/CoRN/ftc/Derivative/deriv_imp_contin_I.con". (* UNEXPORTED -End Basic_Properties. +End Basic_Properties *) (*#* diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/DerivativeOps.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/DerivativeOps.ma index 25a674c26..b9b7016d3 100644 --- a/helm/software/matita/contribs/CoRN-Decl/ftc/DerivativeOps.ma +++ b/helm/software/matita/contribs/CoRN-Decl/ftc/DerivativeOps.ma @@ -23,7 +23,7 @@ include "CoRN.ma". include "ftc/Derivative.ma". (* UNEXPORTED -Section Lemmas. +Section Lemmas *) (*#* **Algebraic Operations @@ -38,36 +38,36 @@ context.%}.% We begin with some technical stuff that will be necessary for division. *) -inline "cic:/CoRN/ftc/DerivativeOps/a.var". +inline "cic:/CoRN/ftc/DerivativeOps/Lemmas/a.var" "Lemmas__". -inline "cic:/CoRN/ftc/DerivativeOps/b.var". +inline "cic:/CoRN/ftc/DerivativeOps/Lemmas/b.var" "Lemmas__". -inline "cic:/CoRN/ftc/DerivativeOps/Hab.var". +inline "cic:/CoRN/ftc/DerivativeOps/Lemmas/Hab.var" "Lemmas__". (* begin hide *) -inline "cic:/CoRN/ftc/DerivativeOps/I.con". +inline "cic:/CoRN/ftc/DerivativeOps/Lemmas/I.con" "Lemmas__". (* end hide *) -inline "cic:/CoRN/ftc/DerivativeOps/F.var". +inline "cic:/CoRN/ftc/DerivativeOps/Lemmas/F.var" "Lemmas__". (* begin hide *) -inline "cic:/CoRN/ftc/DerivativeOps/P.con". +inline "cic:/CoRN/ftc/DerivativeOps/Lemmas/P.con" "Lemmas__". (* end hide *) (* begin show *) -inline "cic:/CoRN/ftc/DerivativeOps/Fbnd.var". +inline "cic:/CoRN/ftc/DerivativeOps/Lemmas/Fbnd.var" "Lemmas__". (* end show *) inline "cic:/CoRN/ftc/DerivativeOps/bnd_away_zero_square.con". (* UNEXPORTED -End Lemmas. +End Lemmas *) (* UNEXPORTED @@ -75,7 +75,7 @@ Hint Resolve bnd_away_zero_square: included. *) (* UNEXPORTED -Section Local_Results. +Section Local_Results *) (*#* **Local Results @@ -83,17 +83,17 @@ 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. *) -inline "cic:/CoRN/ftc/DerivativeOps/a.var". +inline "cic:/CoRN/ftc/DerivativeOps/Local_Results/a.var" "Local_Results__". -inline "cic:/CoRN/ftc/DerivativeOps/b.var". +inline "cic:/CoRN/ftc/DerivativeOps/Local_Results/b.var" "Local_Results__". -inline "cic:/CoRN/ftc/DerivativeOps/Hab'.var". +inline "cic:/CoRN/ftc/DerivativeOps/Local_Results/Hab'.var" "Local_Results__". (* begin hide *) -inline "cic:/CoRN/ftc/DerivativeOps/Hab.con". +inline "cic:/CoRN/ftc/DerivativeOps/Local_Results/Hab.con" "Local_Results__". -inline "cic:/CoRN/ftc/DerivativeOps/I.con". +inline "cic:/CoRN/ftc/DerivativeOps/Local_Results/I.con" "Local_Results__". (* end hide *) @@ -101,17 +101,17 @@ inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_const.con". inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_id.con". -inline "cic:/CoRN/ftc/DerivativeOps/F.var". +inline "cic:/CoRN/ftc/DerivativeOps/Local_Results/F.var" "Local_Results__". -inline "cic:/CoRN/ftc/DerivativeOps/F'.var". +inline "cic:/CoRN/ftc/DerivativeOps/Local_Results/F'.var" "Local_Results__". -inline "cic:/CoRN/ftc/DerivativeOps/G.var". +inline "cic:/CoRN/ftc/DerivativeOps/Local_Results/G.var" "Local_Results__". -inline "cic:/CoRN/ftc/DerivativeOps/G'.var". +inline "cic:/CoRN/ftc/DerivativeOps/Local_Results/G'.var" "Local_Results__". -inline "cic:/CoRN/ftc/DerivativeOps/derF.var". +inline "cic:/CoRN/ftc/DerivativeOps/Local_Results/derF.var" "Local_Results__". -inline "cic:/CoRN/ftc/DerivativeOps/derG.var". +inline "cic:/CoRN/ftc/DerivativeOps/Local_Results/derG.var" "Local_Results__". inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_plus.con". @@ -125,14 +125,14 @@ As was the case for continuity, the rule for the reciprocal function has a side (* begin show *) -inline "cic:/CoRN/ftc/DerivativeOps/Fbnd.var". +inline "cic:/CoRN/ftc/DerivativeOps/Local_Results/Fbnd.var" "Local_Results__". (* end show *) inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_recip.con". (* UNEXPORTED -End Local_Results. +End Local_Results *) (* UNEXPORTED @@ -145,34 +145,34 @@ Hint Resolve Derivative_I_const Derivative_I_id Derivative_I_plus *) (* UNEXPORTED -Section Corolaries. +Section Corolaries *) -inline "cic:/CoRN/ftc/DerivativeOps/a.var". +inline "cic:/CoRN/ftc/DerivativeOps/Corolaries/a.var" "Corolaries__". -inline "cic:/CoRN/ftc/DerivativeOps/b.var". +inline "cic:/CoRN/ftc/DerivativeOps/Corolaries/b.var" "Corolaries__". -inline "cic:/CoRN/ftc/DerivativeOps/Hab'.var". +inline "cic:/CoRN/ftc/DerivativeOps/Corolaries/Hab'.var" "Corolaries__". (* begin hide *) -inline "cic:/CoRN/ftc/DerivativeOps/Hab.con". +inline "cic:/CoRN/ftc/DerivativeOps/Corolaries/Hab.con" "Corolaries__". -inline "cic:/CoRN/ftc/DerivativeOps/I.con". +inline "cic:/CoRN/ftc/DerivativeOps/Corolaries/I.con" "Corolaries__". (* end hide *) -inline "cic:/CoRN/ftc/DerivativeOps/F.var". +inline "cic:/CoRN/ftc/DerivativeOps/Corolaries/F.var" "Corolaries__". -inline "cic:/CoRN/ftc/DerivativeOps/F'.var". +inline "cic:/CoRN/ftc/DerivativeOps/Corolaries/F'.var" "Corolaries__". -inline "cic:/CoRN/ftc/DerivativeOps/G.var". +inline "cic:/CoRN/ftc/DerivativeOps/Corolaries/G.var" "Corolaries__". -inline "cic:/CoRN/ftc/DerivativeOps/G'.var". +inline "cic:/CoRN/ftc/DerivativeOps/Corolaries/G'.var" "Corolaries__". -inline "cic:/CoRN/ftc/DerivativeOps/derF.var". +inline "cic:/CoRN/ftc/DerivativeOps/Corolaries/derF.var" "Corolaries__". -inline "cic:/CoRN/ftc/DerivativeOps/derG.var". +inline "cic:/CoRN/ftc/DerivativeOps/Corolaries/derG.var" "Corolaries__". (*#* From this lemmas the rules for the other algebraic operations follow directly. @@ -184,12 +184,12 @@ inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_scal.con". inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_nth.con". -inline "cic:/CoRN/ftc/DerivativeOps/Gbnd.var". +inline "cic:/CoRN/ftc/DerivativeOps/Corolaries/Gbnd.var" "Corolaries__". inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_div.con". (* UNEXPORTED -End Corolaries. +End Corolaries *) (* UNEXPORTED @@ -198,24 +198,24 @@ Hint Resolve Derivative_I_minus Derivative_I_nth Derivative_I_scal *) (* UNEXPORTED -Section Derivative_Sums. +Section Derivative_Sums *) (*#* The derivation rules for families of functions are easily proved by induction using the constant and addition rules. *) -inline "cic:/CoRN/ftc/DerivativeOps/a.var". +inline "cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/a.var" "Derivative_Sums__". -inline "cic:/CoRN/ftc/DerivativeOps/b.var". +inline "cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/b.var" "Derivative_Sums__". -inline "cic:/CoRN/ftc/DerivativeOps/Hab.var". +inline "cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/Hab.var" "Derivative_Sums__". -inline "cic:/CoRN/ftc/DerivativeOps/Hab'.var". +inline "cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/Hab'.var" "Derivative_Sums__". (* begin hide *) -inline "cic:/CoRN/ftc/DerivativeOps/I.con". +inline "cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/I.con" "Derivative_Sums__". (* end hide *) @@ -226,7 +226,7 @@ inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_Sumx.con". inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_Sum.con". (* UNEXPORTED -End Derivative_Sums. +End Derivative_Sums *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/Differentiability.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/Differentiability.ma index ded63db55..aeb3bdcec 100644 --- a/helm/software/matita/contribs/CoRN-Decl/ftc/Differentiability.ma +++ b/helm/software/matita/contribs/CoRN-Decl/ftc/Differentiability.ma @@ -25,7 +25,7 @@ include "ftc/PartInterval.ma". include "ftc/DerivativeOps.ma". (* UNEXPORTED -Section Definitions. +Section Definitions *) (*#* *Differentiability @@ -61,7 +61,7 @@ problems. inline "cic:/CoRN/ftc/Differentiability/Diffble_I.con". (* UNEXPORTED -End Definitions. +End Definitions *) (* UNEXPORTED @@ -69,7 +69,7 @@ Implicit Arguments Diffble_I [a b]. *) (* UNEXPORTED -Section Local_Properties. +Section Local_Properties *) (*#* @@ -84,17 +84,17 @@ inline "cic:/CoRN/ftc/Differentiability/included_imp_diffble.con". A function differentiable in an interval is everywhere defined in that interval. *) -inline "cic:/CoRN/ftc/Differentiability/a.var". +inline "cic:/CoRN/ftc/Differentiability/Local_Properties/a.var" "Local_Properties__". -inline "cic:/CoRN/ftc/Differentiability/b.var". +inline "cic:/CoRN/ftc/Differentiability/Local_Properties/b.var" "Local_Properties__". -inline "cic:/CoRN/ftc/Differentiability/Hab'.var". +inline "cic:/CoRN/ftc/Differentiability/Local_Properties/Hab'.var" "Local_Properties__". (* begin hide *) -inline "cic:/CoRN/ftc/Differentiability/Hab.con". +inline "cic:/CoRN/ftc/Differentiability/Local_Properties/Hab.con" "Local_Properties__". -inline "cic:/CoRN/ftc/Differentiability/I.con". +inline "cic:/CoRN/ftc/Differentiability/Local_Properties/I.con" "Local_Properties__". (* end hide *) @@ -107,7 +107,7 @@ If a function has a derivative in an interval then it is differentiable in that inline "cic:/CoRN/ftc/Differentiability/deriv_imp_Diffble_I.con". (* UNEXPORTED -End Local_Properties. +End Local_Properties *) (* UNEXPORTED @@ -115,29 +115,29 @@ Hint Resolve diffble_imp_inc: included. *) (* UNEXPORTED -Section Operations. +Section Operations *) (*#* All the algebraic results carry on. *) -inline "cic:/CoRN/ftc/Differentiability/a.var". +inline "cic:/CoRN/ftc/Differentiability/Operations/a.var" "Operations__". -inline "cic:/CoRN/ftc/Differentiability/b.var". +inline "cic:/CoRN/ftc/Differentiability/Operations/b.var" "Operations__". -inline "cic:/CoRN/ftc/Differentiability/Hab'.var". +inline "cic:/CoRN/ftc/Differentiability/Operations/Hab'.var" "Operations__". (* begin hide *) -inline "cic:/CoRN/ftc/Differentiability/Hab.con". +inline "cic:/CoRN/ftc/Differentiability/Operations/Hab.con" "Operations__". -inline "cic:/CoRN/ftc/Differentiability/I.con". +inline "cic:/CoRN/ftc/Differentiability/Operations/I.con" "Operations__". (* end hide *) (* UNEXPORTED -Section Constants. +Section Constants *) inline "cic:/CoRN/ftc/Differentiability/Diffble_I_const.con". @@ -145,32 +145,32 @@ inline "cic:/CoRN/ftc/Differentiability/Diffble_I_const.con". inline "cic:/CoRN/ftc/Differentiability/Diffble_I_id.con". (* UNEXPORTED -End Constants. +End Constants *) (* UNEXPORTED -Section Well_Definedness. +Section Well_Definedness *) -inline "cic:/CoRN/ftc/Differentiability/F.var". +inline "cic:/CoRN/ftc/Differentiability/Operations/Well_Definedness/F.var" "Operations__Well_Definedness__". -inline "cic:/CoRN/ftc/Differentiability/H.var". +inline "cic:/CoRN/ftc/Differentiability/Operations/Well_Definedness/H.var" "Operations__Well_Definedness__". -inline "cic:/CoRN/ftc/Differentiability/diffF.var". +inline "cic:/CoRN/ftc/Differentiability/Operations/Well_Definedness/diffF.var" "Operations__Well_Definedness__". inline "cic:/CoRN/ftc/Differentiability/Diffble_I_wd.con". (* UNEXPORTED -End Well_Definedness. +End Well_Definedness *) -inline "cic:/CoRN/ftc/Differentiability/F.var". +inline "cic:/CoRN/ftc/Differentiability/Operations/F.var" "Operations__". -inline "cic:/CoRN/ftc/Differentiability/G.var". +inline "cic:/CoRN/ftc/Differentiability/Operations/G.var" "Operations__". -inline "cic:/CoRN/ftc/Differentiability/diffF.var". +inline "cic:/CoRN/ftc/Differentiability/Operations/diffF.var" "Operations__". -inline "cic:/CoRN/ftc/Differentiability/diffG.var". +inline "cic:/CoRN/ftc/Differentiability/Operations/diffG.var" "Operations__". inline "cic:/CoRN/ftc/Differentiability/Diffble_I_plus.con". @@ -180,41 +180,41 @@ inline "cic:/CoRN/ftc/Differentiability/Diffble_I_mult.con". (* begin show *) -inline "cic:/CoRN/ftc/Differentiability/Gbnd.var". +inline "cic:/CoRN/ftc/Differentiability/Operations/Gbnd.var" "Operations__". (* end show *) inline "cic:/CoRN/ftc/Differentiability/Diffble_I_recip.con". (* UNEXPORTED -End Operations. +End Operations *) (* UNEXPORTED -Section Corollaries. +Section Corollaries *) -inline "cic:/CoRN/ftc/Differentiability/a.var". +inline "cic:/CoRN/ftc/Differentiability/Corollaries/a.var" "Corollaries__". -inline "cic:/CoRN/ftc/Differentiability/b.var". +inline "cic:/CoRN/ftc/Differentiability/Corollaries/b.var" "Corollaries__". -inline "cic:/CoRN/ftc/Differentiability/Hab'.var". +inline "cic:/CoRN/ftc/Differentiability/Corollaries/Hab'.var" "Corollaries__". (* begin hide *) -inline "cic:/CoRN/ftc/Differentiability/Hab.con". +inline "cic:/CoRN/ftc/Differentiability/Corollaries/Hab.con" "Corollaries__". -inline "cic:/CoRN/ftc/Differentiability/I.con". +inline "cic:/CoRN/ftc/Differentiability/Corollaries/I.con" "Corollaries__". (* end hide *) -inline "cic:/CoRN/ftc/Differentiability/F.var". +inline "cic:/CoRN/ftc/Differentiability/Corollaries/F.var" "Corollaries__". -inline "cic:/CoRN/ftc/Differentiability/G.var". +inline "cic:/CoRN/ftc/Differentiability/Corollaries/G.var" "Corollaries__". -inline "cic:/CoRN/ftc/Differentiability/diffF.var". +inline "cic:/CoRN/ftc/Differentiability/Corollaries/diffF.var" "Corollaries__". -inline "cic:/CoRN/ftc/Differentiability/diffG.var". +inline "cic:/CoRN/ftc/Differentiability/Corollaries/diffG.var" "Corollaries__". inline "cic:/CoRN/ftc/Differentiability/Diffble_I_minus.con". @@ -222,16 +222,16 @@ inline "cic:/CoRN/ftc/Differentiability/Diffble_I_scal.con". inline "cic:/CoRN/ftc/Differentiability/Diffble_I_nth.con". -inline "cic:/CoRN/ftc/Differentiability/Gbnd.var". +inline "cic:/CoRN/ftc/Differentiability/Corollaries/Gbnd.var" "Corollaries__". inline "cic:/CoRN/ftc/Differentiability/Diffble_I_div.con". (* UNEXPORTED -End Corollaries. +End Corollaries *) (* UNEXPORTED -Section Other_Properties. +Section Other_Properties *) (*#* @@ -239,11 +239,11 @@ Differentiability of families of functions is proved by induction using the constant and addition rules. *) -inline "cic:/CoRN/ftc/Differentiability/a.var". +inline "cic:/CoRN/ftc/Differentiability/Other_Properties/a.var" "Other_Properties__". -inline "cic:/CoRN/ftc/Differentiability/b.var". +inline "cic:/CoRN/ftc/Differentiability/Other_Properties/b.var" "Other_Properties__". -inline "cic:/CoRN/ftc/Differentiability/Hab'.var". +inline "cic:/CoRN/ftc/Differentiability/Other_Properties/Hab'.var" "Other_Properties__". inline "cic:/CoRN/ftc/Differentiability/Diffble_I_Sum0.con". @@ -252,7 +252,7 @@ inline "cic:/CoRN/ftc/Differentiability/Diffble_I_Sumx.con". inline "cic:/CoRN/ftc/Differentiability/Diffble_I_Sum.con". (* UNEXPORTED -End Other_Properties. +End Other_Properties *) (*#* diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/FTC.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/FTC.ma index 5d764a882..6e373299c 100644 --- a/helm/software/matita/contribs/CoRN-Decl/ftc/FTC.ma +++ b/helm/software/matita/contribs/CoRN-Decl/ftc/FTC.ma @@ -31,7 +31,7 @@ Opaque Min. *) (* UNEXPORTED -Section Indefinite_Integral. +Section Indefinite_Integral *) (*#* *The Fundamental Theorem of Calculus @@ -51,15 +51,15 @@ and [a] be a point in [I]. %\end{convention}% *) -inline "cic:/CoRN/ftc/FTC/I.var". +inline "cic:/CoRN/ftc/FTC/Indefinite_Integral/I.var" "Indefinite_Integral__". -inline "cic:/CoRN/ftc/FTC/F.var". +inline "cic:/CoRN/ftc/FTC/Indefinite_Integral/F.var" "Indefinite_Integral__". -inline "cic:/CoRN/ftc/FTC/contF.var". +inline "cic:/CoRN/ftc/FTC/Indefinite_Integral/contF.var" "Indefinite_Integral__". -inline "cic:/CoRN/ftc/FTC/a.var". +inline "cic:/CoRN/ftc/FTC/Indefinite_Integral/a.var" "Indefinite_Integral__". -inline "cic:/CoRN/ftc/FTC/Ha.var". +inline "cic:/CoRN/ftc/FTC/Indefinite_Integral/Ha.var" "Indefinite_Integral__". inline "cic:/CoRN/ftc/FTC/prim_lemma.con". @@ -68,7 +68,7 @@ inline "cic:/CoRN/ftc/FTC/Fprim_strext.con". inline "cic:/CoRN/ftc/FTC/Fprim.con". (* UNEXPORTED -End Indefinite_Integral. +End Indefinite_Integral *) (* UNEXPORTED @@ -80,7 +80,7 @@ Notation "[-S-] F" := (Fprim F) (at level 20). *) (* UNEXPORTED -Section FTC. +Section FTC *) (*#* **The FTC @@ -94,19 +94,19 @@ indefinite integral of [F] from [x0]. %\end{convention}% *) -inline "cic:/CoRN/ftc/FTC/J.var". +inline "cic:/CoRN/ftc/FTC/FTC/J.var" "FTC__". -inline "cic:/CoRN/ftc/FTC/F.var". +inline "cic:/CoRN/ftc/FTC/FTC/F.var" "FTC__". -inline "cic:/CoRN/ftc/FTC/contF.var". +inline "cic:/CoRN/ftc/FTC/FTC/contF.var" "FTC__". -inline "cic:/CoRN/ftc/FTC/x0.var". +inline "cic:/CoRN/ftc/FTC/FTC/x0.var" "FTC__". -inline "cic:/CoRN/ftc/FTC/Hx0.var". +inline "cic:/CoRN/ftc/FTC/FTC/Hx0.var" "FTC__". (* begin hide *) -inline "cic:/CoRN/ftc/FTC/G.con". +inline "cic:/CoRN/ftc/FTC/FTC/G.con" "FTC__". (* end hide *) @@ -116,7 +116,7 @@ inline "cic:/CoRN/ftc/FTC/Continuous_prim.con". The derivative of [G] is simply [F]. *) -inline "cic:/CoRN/ftc/FTC/pJ.var". +inline "cic:/CoRN/ftc/FTC/FTC/pJ.var" "FTC__". inline "cic:/CoRN/ftc/FTC/FTC1.con". @@ -124,9 +124,9 @@ inline "cic:/CoRN/ftc/FTC/FTC1.con". Any other function [G0] with derivative [F] must differ from [G] by a constant. *) -inline "cic:/CoRN/ftc/FTC/G0.var". +inline "cic:/CoRN/ftc/FTC/FTC/G0.var" "FTC__". -inline "cic:/CoRN/ftc/FTC/derG0.var". +inline "cic:/CoRN/ftc/FTC/FTC/derG0.var" "FTC__". inline "cic:/CoRN/ftc/FTC/FTC2.con". @@ -136,7 +136,7 @@ The following is another statement of the Fundamental Theorem of Calculus, also (* begin hide *) -inline "cic:/CoRN/ftc/FTC/G0_inc.con". +inline "cic:/CoRN/ftc/FTC/FTC/G0_inc.con" "FTC__". (* end hide *) @@ -149,7 +149,7 @@ inline "cic:/CoRN/ftc/FTC/Barrow.con". (* end hide *) (* UNEXPORTED -End FTC. +End FTC *) (* UNEXPORTED @@ -161,7 +161,7 @@ Hint Resolve FTC1: derivate. *) (* UNEXPORTED -Section Limit_of_Integral_Seq. +Section Limit_of_Integral_Seq *) (*#* **Corollaries @@ -180,18 +180,18 @@ then the sequence of their primitives also converges, and the limit commutes with the indefinite integral. *) -inline "cic:/CoRN/ftc/FTC/J.var". +inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/J.var" "Limit_of_Integral_Seq__". -inline "cic:/CoRN/ftc/FTC/f.var". +inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/f.var" "Limit_of_Integral_Seq__". -inline "cic:/CoRN/ftc/FTC/F.var". +inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/F.var" "Limit_of_Integral_Seq__". -inline "cic:/CoRN/ftc/FTC/contf.var". +inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/contf.var" "Limit_of_Integral_Seq__". -inline "cic:/CoRN/ftc/FTC/contF.var". +inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/contF.var" "Limit_of_Integral_Seq__". (* UNEXPORTED -Section Compact. +Section Compact *) (*#* @@ -204,48 +204,48 @@ continuous in [[a,b]], $x0\in[a,b]$#x0∈[a,b]#; denote by %\end{convention}% *) -inline "cic:/CoRN/ftc/FTC/a.var". +inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/a.var" "Limit_of_Integral_Seq__Compact__". -inline "cic:/CoRN/ftc/FTC/b.var". +inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/b.var" "Limit_of_Integral_Seq__Compact__". -inline "cic:/CoRN/ftc/FTC/Hab.var". +inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/Hab.var" "Limit_of_Integral_Seq__Compact__". -inline "cic:/CoRN/ftc/FTC/contIf.var". +inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/contIf.var" "Limit_of_Integral_Seq__Compact__". -inline "cic:/CoRN/ftc/FTC/contIF.var". +inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/contIF.var" "Limit_of_Integral_Seq__Compact__". (* begin show *) -inline "cic:/CoRN/ftc/FTC/convF.var". +inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/convF.var" "Limit_of_Integral_Seq__Compact__". (* end show *) -inline "cic:/CoRN/ftc/FTC/x0.var". +inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/x0.var" "Limit_of_Integral_Seq__Compact__". -inline "cic:/CoRN/ftc/FTC/Hx0.var". +inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/Hx0.var" "Limit_of_Integral_Seq__Compact__". -inline "cic:/CoRN/ftc/FTC/Hx0'.var". +inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/Hx0'.var" "Limit_of_Integral_Seq__Compact__". (* begin hide *) -inline "cic:/CoRN/ftc/FTC/g.con". +inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/g.con" "Limit_of_Integral_Seq__Compact__". -inline "cic:/CoRN/ftc/FTC/G.con". +inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/G.con" "Limit_of_Integral_Seq__Compact__". (* end hide *) (* begin show *) -inline "cic:/CoRN/ftc/FTC/contg.var". +inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/contg.var" "Limit_of_Integral_Seq__Compact__". -inline "cic:/CoRN/ftc/FTC/contG.var". +inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/contG.var" "Limit_of_Integral_Seq__Compact__". (* end show *) inline "cic:/CoRN/ftc/FTC/fun_lim_seq_integral.con". (* UNEXPORTED -End Compact. +End Compact *) (*#* @@ -257,7 +257,7 @@ inline "cic:/CoRN/ftc/FTC/limit_of_integral.con". inline "cic:/CoRN/ftc/FTC/limit_of_Integral.con". (* UNEXPORTED -Section General. +Section General *) (*#* @@ -266,38 +266,38 @@ Finally, with [x0, g, G] as before, (* begin show *) -inline "cic:/CoRN/ftc/FTC/convF.var". +inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/convF.var" "Limit_of_Integral_Seq__General__". (* end show *) -inline "cic:/CoRN/ftc/FTC/x0.var". +inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/x0.var" "Limit_of_Integral_Seq__General__". -inline "cic:/CoRN/ftc/FTC/Hx0.var". +inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/Hx0.var" "Limit_of_Integral_Seq__General__". (* begin hide *) -inline "cic:/CoRN/ftc/FTC/g.con". +inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/g.con" "Limit_of_Integral_Seq__General__". -inline "cic:/CoRN/ftc/FTC/G.con". +inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/G.con" "Limit_of_Integral_Seq__General__". (* end hide *) -inline "cic:/CoRN/ftc/FTC/contg.var". +inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/contg.var" "Limit_of_Integral_Seq__General__". -inline "cic:/CoRN/ftc/FTC/contG.var". +inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/contG.var" "Limit_of_Integral_Seq__General__". inline "cic:/CoRN/ftc/FTC/fun_lim_seq_integral_IR.con". (* UNEXPORTED -End General. +End General *) (* UNEXPORTED -End Limit_of_Integral_Seq. +End Limit_of_Integral_Seq *) (* UNEXPORTED -Section Limit_of_Derivative_Seq. +Section Limit_of_Derivative_Seq *) (*#* @@ -307,67 +307,67 @@ Similar results hold for the sequence of derivatives of a converging sequence; t %\end{convention}% *) -inline "cic:/CoRN/ftc/FTC/J.var". +inline "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/J.var" "Limit_of_Derivative_Seq__". -inline "cic:/CoRN/ftc/FTC/pJ.var". +inline "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/pJ.var" "Limit_of_Derivative_Seq__". -inline "cic:/CoRN/ftc/FTC/f.var". +inline "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/f.var" "Limit_of_Derivative_Seq__". -inline "cic:/CoRN/ftc/FTC/g.var". +inline "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/g.var" "Limit_of_Derivative_Seq__". -inline "cic:/CoRN/ftc/FTC/F.var". +inline "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/F.var" "Limit_of_Derivative_Seq__". -inline "cic:/CoRN/ftc/FTC/G.var". +inline "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/G.var" "Limit_of_Derivative_Seq__". -inline "cic:/CoRN/ftc/FTC/contf.var". +inline "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/contf.var" "Limit_of_Derivative_Seq__". -inline "cic:/CoRN/ftc/FTC/contF.var". +inline "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/contF.var" "Limit_of_Derivative_Seq__". -inline "cic:/CoRN/ftc/FTC/convF.var". +inline "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/convF.var" "Limit_of_Derivative_Seq__". -inline "cic:/CoRN/ftc/FTC/contg.var". +inline "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/contg.var" "Limit_of_Derivative_Seq__". -inline "cic:/CoRN/ftc/FTC/contG.var". +inline "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/contG.var" "Limit_of_Derivative_Seq__". -inline "cic:/CoRN/ftc/FTC/convG.var". +inline "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/convG.var" "Limit_of_Derivative_Seq__". -inline "cic:/CoRN/ftc/FTC/derf.var". +inline "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/derf.var" "Limit_of_Derivative_Seq__". inline "cic:/CoRN/ftc/FTC/fun_lim_seq_derivative.con". (* UNEXPORTED -End Limit_of_Derivative_Seq. +End Limit_of_Derivative_Seq *) (* UNEXPORTED -Section Derivative_Series. +Section Derivative_Series *) (*#* As a very important case of this result, we get a rule for deriving series. *) -inline "cic:/CoRN/ftc/FTC/J.var". +inline "cic:/CoRN/ftc/FTC/Derivative_Series/J.var" "Derivative_Series__". -inline "cic:/CoRN/ftc/FTC/pJ.var". +inline "cic:/CoRN/ftc/FTC/Derivative_Series/pJ.var" "Derivative_Series__". -inline "cic:/CoRN/ftc/FTC/f.var". +inline "cic:/CoRN/ftc/FTC/Derivative_Series/f.var" "Derivative_Series__". -inline "cic:/CoRN/ftc/FTC/g.var". +inline "cic:/CoRN/ftc/FTC/Derivative_Series/g.var" "Derivative_Series__". (* begin show *) -inline "cic:/CoRN/ftc/FTC/convF.var". +inline "cic:/CoRN/ftc/FTC/Derivative_Series/convF.var" "Derivative_Series__". -inline "cic:/CoRN/ftc/FTC/convG.var". +inline "cic:/CoRN/ftc/FTC/Derivative_Series/convG.var" "Derivative_Series__". (* end show *) -inline "cic:/CoRN/ftc/FTC/derF.var". +inline "cic:/CoRN/ftc/FTC/Derivative_Series/derF.var" "Derivative_Series__". inline "cic:/CoRN/ftc/FTC/Derivative_FSeries.con". (* UNEXPORTED -End Derivative_Series. +End Derivative_Series *) diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/FunctSequence.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/FunctSequence.ma index 768b71285..23918bcba 100644 --- a/helm/software/matita/contribs/CoRN-Decl/ftc/FunctSequence.ma +++ b/helm/software/matita/contribs/CoRN-Decl/ftc/FunctSequence.ma @@ -25,7 +25,7 @@ include "ftc/Continuity.ma". include "ftc/PartInterval.ma". (* UNEXPORTED -Section Definitions. +Section Definitions *) (*#* *Sequences of Functions @@ -52,31 +52,31 @@ be defined. For a discussion on the different notions of convergent see Bishop 1967. *) -inline "cic:/CoRN/ftc/FunctSequence/a.var". +inline "cic:/CoRN/ftc/FunctSequence/Definitions/a.var" "Definitions__". -inline "cic:/CoRN/ftc/FunctSequence/b.var". +inline "cic:/CoRN/ftc/FunctSequence/Definitions/b.var" "Definitions__". -inline "cic:/CoRN/ftc/FunctSequence/Hab.var". +inline "cic:/CoRN/ftc/FunctSequence/Definitions/Hab.var" "Definitions__". (* begin hide *) -inline "cic:/CoRN/ftc/FunctSequence/I.con". +inline "cic:/CoRN/ftc/FunctSequence/Definitions/I.con" "Definitions__". (* end hide *) -inline "cic:/CoRN/ftc/FunctSequence/f.var". +inline "cic:/CoRN/ftc/FunctSequence/Definitions/f.var" "Definitions__". -inline "cic:/CoRN/ftc/FunctSequence/F.var". +inline "cic:/CoRN/ftc/FunctSequence/Definitions/F.var" "Definitions__". -inline "cic:/CoRN/ftc/FunctSequence/contf.var". +inline "cic:/CoRN/ftc/FunctSequence/Definitions/contf.var" "Definitions__". -inline "cic:/CoRN/ftc/FunctSequence/contF.var". +inline "cic:/CoRN/ftc/FunctSequence/Definitions/contF.var" "Definitions__". (* begin hide *) -inline "cic:/CoRN/ftc/FunctSequence/incf.con". +inline "cic:/CoRN/ftc/FunctSequence/Definitions/incf.con" "Definitions__". -inline "cic:/CoRN/ftc/FunctSequence/incF.con". +inline "cic:/CoRN/ftc/FunctSequence/Definitions/incF.con" "Definitions__". (* end hide *) @@ -125,28 +125,28 @@ A Cauchy sequence of functions is pointwise a Cauchy sequence. inline "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_real.con". (* UNEXPORTED -End Definitions. +End Definitions *) (* UNEXPORTED -Section More_Definitions. +Section More_Definitions *) -inline "cic:/CoRN/ftc/FunctSequence/a.var". +inline "cic:/CoRN/ftc/FunctSequence/More_Definitions/a.var" "More_Definitions__". -inline "cic:/CoRN/ftc/FunctSequence/b.var". +inline "cic:/CoRN/ftc/FunctSequence/More_Definitions/b.var" "More_Definitions__". -inline "cic:/CoRN/ftc/FunctSequence/Hab.var". +inline "cic:/CoRN/ftc/FunctSequence/More_Definitions/Hab.var" "More_Definitions__". (* begin hide *) -inline "cic:/CoRN/ftc/FunctSequence/I.con". +inline "cic:/CoRN/ftc/FunctSequence/More_Definitions/I.con" "More_Definitions__". (* end hide *) -inline "cic:/CoRN/ftc/FunctSequence/f.var". +inline "cic:/CoRN/ftc/FunctSequence/More_Definitions/f.var" "More_Definitions__". -inline "cic:/CoRN/ftc/FunctSequence/contf.var". +inline "cic:/CoRN/ftc/FunctSequence/More_Definitions/contf.var" "More_Definitions__". (*#* We can also say that [f] is simply convergent if it converges to some @@ -162,18 +162,18 @@ It is useful to extract the limit as a partial function: (* begin show *) -inline "cic:/CoRN/ftc/FunctSequence/H.var". +inline "cic:/CoRN/ftc/FunctSequence/More_Definitions/H.var" "More_Definitions__". (* end show *) inline "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq_Lim.con". (* UNEXPORTED -End More_Definitions. +End More_Definitions *) (* UNEXPORTED -Section Irrelevance_of_Proofs. +Section Irrelevance_of_Proofs *) (*#* **Irrelevance of Proofs @@ -181,35 +181,35 @@ 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. *) -inline "cic:/CoRN/ftc/FunctSequence/a.var". +inline "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/a.var" "Irrelevance_of_Proofs__". -inline "cic:/CoRN/ftc/FunctSequence/b.var". +inline "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/b.var" "Irrelevance_of_Proofs__". -inline "cic:/CoRN/ftc/FunctSequence/Hab.var". +inline "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/Hab.var" "Irrelevance_of_Proofs__". (* begin hide *) -inline "cic:/CoRN/ftc/FunctSequence/I.con". +inline "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/I.con" "Irrelevance_of_Proofs__". (* end hide *) -inline "cic:/CoRN/ftc/FunctSequence/f.var". +inline "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/f.var" "Irrelevance_of_Proofs__". (* begin show *) -inline "cic:/CoRN/ftc/FunctSequence/contf.var". +inline "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/contf.var" "Irrelevance_of_Proofs__". -inline "cic:/CoRN/ftc/FunctSequence/contf0.var". +inline "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/contf0.var" "Irrelevance_of_Proofs__". (* end show *) -inline "cic:/CoRN/ftc/FunctSequence/F.var". +inline "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/F.var" "Irrelevance_of_Proofs__". (* begin show *) -inline "cic:/CoRN/ftc/FunctSequence/contF.var". +inline "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/contF.var" "Irrelevance_of_Proofs__". -inline "cic:/CoRN/ftc/FunctSequence/contF0.var". +inline "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/contF0.var" "Irrelevance_of_Proofs__". (* end show *) @@ -224,21 +224,21 @@ inline "cic:/CoRN/ftc/FunctSequence/conv_norm_fun_seq_wd.con". inline "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq1_wd.con". (* UNEXPORTED -End Irrelevance_of_Proofs. +End Irrelevance_of_Proofs *) (* UNEXPORTED -Section More_Proof_Irrelevance. +Section More_Proof_Irrelevance *) inline "cic:/CoRN/ftc/FunctSequence/conv_fun_seq_wd.con". (* UNEXPORTED -End More_Proof_Irrelevance. +End More_Proof_Irrelevance *) (* UNEXPORTED -Section More_Properties. +Section More_Properties *) (*#* **Other Properties @@ -248,49 +248,49 @@ limit; the limit is a continuous function; and convergence is well defined with respect to functional equality in the interval [[a,b]]. *) -inline "cic:/CoRN/ftc/FunctSequence/a.var". +inline "cic:/CoRN/ftc/FunctSequence/More_Properties/a.var" "More_Properties__". -inline "cic:/CoRN/ftc/FunctSequence/b.var". +inline "cic:/CoRN/ftc/FunctSequence/More_Properties/b.var" "More_Properties__". -inline "cic:/CoRN/ftc/FunctSequence/Hab.var". +inline "cic:/CoRN/ftc/FunctSequence/More_Properties/Hab.var" "More_Properties__". (* begin hide *) -inline "cic:/CoRN/ftc/FunctSequence/I.con". +inline "cic:/CoRN/ftc/FunctSequence/More_Properties/I.con" "More_Properties__". (* end hide *) -inline "cic:/CoRN/ftc/FunctSequence/f.var". +inline "cic:/CoRN/ftc/FunctSequence/More_Properties/f.var" "More_Properties__". -inline "cic:/CoRN/ftc/FunctSequence/g.var". +inline "cic:/CoRN/ftc/FunctSequence/More_Properties/g.var" "More_Properties__". (* begin show *) -inline "cic:/CoRN/ftc/FunctSequence/contf.var". +inline "cic:/CoRN/ftc/FunctSequence/More_Properties/contf.var" "More_Properties__". -inline "cic:/CoRN/ftc/FunctSequence/contf0.var". +inline "cic:/CoRN/ftc/FunctSequence/More_Properties/contf0.var" "More_Properties__". -inline "cic:/CoRN/ftc/FunctSequence/contg.var". +inline "cic:/CoRN/ftc/FunctSequence/More_Properties/contg.var" "More_Properties__". -inline "cic:/CoRN/ftc/FunctSequence/contg0.var". +inline "cic:/CoRN/ftc/FunctSequence/More_Properties/contg0.var" "More_Properties__". (* end show *) inline "cic:/CoRN/ftc/FunctSequence/Cauchy_conv_fun_seq'.con". -inline "cic:/CoRN/ftc/FunctSequence/F.var". +inline "cic:/CoRN/ftc/FunctSequence/More_Properties/F.var" "More_Properties__". -inline "cic:/CoRN/ftc/FunctSequence/G.var". +inline "cic:/CoRN/ftc/FunctSequence/More_Properties/G.var" "More_Properties__". (* begin show *) -inline "cic:/CoRN/ftc/FunctSequence/contF.var". +inline "cic:/CoRN/ftc/FunctSequence/More_Properties/contF.var" "More_Properties__". -inline "cic:/CoRN/ftc/FunctSequence/contF0.var". +inline "cic:/CoRN/ftc/FunctSequence/More_Properties/contF0.var" "More_Properties__". -inline "cic:/CoRN/ftc/FunctSequence/contG.var". +inline "cic:/CoRN/ftc/FunctSequence/More_Properties/contG.var" "More_Properties__". -inline "cic:/CoRN/ftc/FunctSequence/contG0.var". +inline "cic:/CoRN/ftc/FunctSequence/More_Properties/contG0.var" "More_Properties__". (* end show *) @@ -323,7 +323,7 @@ And a sequence of real numbers converges iff the corresponding sequence of const inline "cic:/CoRN/ftc/FunctSequence/seq_conv_imp_fun_conv.con". (* UNEXPORTED -End More_Properties. +End More_Properties *) (* UNEXPORTED @@ -331,7 +331,7 @@ Hint Resolve Cauchy_cont_Lim: continuous. *) (* UNEXPORTED -Section Algebraic_Properties. +Section Algebraic_Properties *) (*#* **Algebraic Properties @@ -339,25 +339,25 @@ Section Algebraic_Properties. We now study how convergence is affected by algebraic operations, and some algebraic properties of the limit function. *) -inline "cic:/CoRN/ftc/FunctSequence/a.var". +inline "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/a.var" "Algebraic_Properties__". -inline "cic:/CoRN/ftc/FunctSequence/b.var". +inline "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/b.var" "Algebraic_Properties__". -inline "cic:/CoRN/ftc/FunctSequence/Hab.var". +inline "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/Hab.var" "Algebraic_Properties__". (* begin hide *) -inline "cic:/CoRN/ftc/FunctSequence/I.con". +inline "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/I.con" "Algebraic_Properties__". (* end hide *) -inline "cic:/CoRN/ftc/FunctSequence/f.var". +inline "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/f.var" "Algebraic_Properties__". -inline "cic:/CoRN/ftc/FunctSequence/g.var". +inline "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/g.var" "Algebraic_Properties__". -inline "cic:/CoRN/ftc/FunctSequence/contf.var". +inline "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/contf.var" "Algebraic_Properties__". -inline "cic:/CoRN/ftc/FunctSequence/contg.var". +inline "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/contg.var" "Algebraic_Properties__". (*#* First, the limit function is unique. @@ -376,31 +376,31 @@ inline "cic:/CoRN/ftc/FunctSequence/fun_Cauchy_prop_const.con". We now prove that if two sequences converge than their sum (difference, product) also converge to the sum (difference, product) of their limits. *) -inline "cic:/CoRN/ftc/FunctSequence/F.var". +inline "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/F.var" "Algebraic_Properties__". -inline "cic:/CoRN/ftc/FunctSequence/G.var". +inline "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/G.var" "Algebraic_Properties__". -inline "cic:/CoRN/ftc/FunctSequence/contF.var". +inline "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/contF.var" "Algebraic_Properties__". -inline "cic:/CoRN/ftc/FunctSequence/contG.var". +inline "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/contG.var" "Algebraic_Properties__". (* begin show *) -inline "cic:/CoRN/ftc/FunctSequence/convF.var". +inline "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/convF.var" "Algebraic_Properties__". -inline "cic:/CoRN/ftc/FunctSequence/convG.var". +inline "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/convG.var" "Algebraic_Properties__". (* end show *) (* begin hide *) -inline "cic:/CoRN/ftc/FunctSequence/incf.con". +inline "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/incf.con" "Algebraic_Properties__". -inline "cic:/CoRN/ftc/FunctSequence/incg.con". +inline "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/incg.con" "Algebraic_Properties__". -inline "cic:/CoRN/ftc/FunctSequence/incF.con". +inline "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/incF.con" "Algebraic_Properties__". -inline "cic:/CoRN/ftc/FunctSequence/incG.con". +inline "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/incG.con" "Algebraic_Properties__". (* end hide *) @@ -411,32 +411,32 @@ inline "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_minus'.con". inline "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_mult'.con". (* UNEXPORTED -End Algebraic_Properties. +End Algebraic_Properties *) (* UNEXPORTED -Section More_Algebraic_Properties. +Section More_Algebraic_Properties *) -inline "cic:/CoRN/ftc/FunctSequence/a.var". +inline "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/a.var" "More_Algebraic_Properties__". -inline "cic:/CoRN/ftc/FunctSequence/b.var". +inline "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/b.var" "More_Algebraic_Properties__". -inline "cic:/CoRN/ftc/FunctSequence/Hab.var". +inline "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/Hab.var" "More_Algebraic_Properties__". (* begin hide *) -inline "cic:/CoRN/ftc/FunctSequence/I.con". +inline "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/I.con" "More_Algebraic_Properties__". (* end hide *) -inline "cic:/CoRN/ftc/FunctSequence/f.var". +inline "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/f.var" "More_Algebraic_Properties__". -inline "cic:/CoRN/ftc/FunctSequence/g.var". +inline "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/g.var" "More_Algebraic_Properties__". -inline "cic:/CoRN/ftc/FunctSequence/contf.var". +inline "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/contf.var" "More_Algebraic_Properties__". -inline "cic:/CoRN/ftc/FunctSequence/contg.var". +inline "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/contg.var" "More_Algebraic_Properties__". (*#* The same is true if we don't make the limits explicit. @@ -444,9 +444,9 @@ The same is true if we don't make the limits explicit. (* begin hide *) -inline "cic:/CoRN/ftc/FunctSequence/Hf.var". +inline "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/Hf.var" "More_Algebraic_Properties__". -inline "cic:/CoRN/ftc/FunctSequence/Hg.var". +inline "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/Hg.var" "More_Algebraic_Properties__". (* end hide *) @@ -463,30 +463,30 @@ inline "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_mult.con". inline "cic:/CoRN/ftc/FunctSequence/fun_Cauchy_prop_mult.con". (* UNEXPORTED -End More_Algebraic_Properties. +End More_Algebraic_Properties *) (* UNEXPORTED -Section Still_More_Algebraic_Properties. +Section Still_More_Algebraic_Properties *) -inline "cic:/CoRN/ftc/FunctSequence/a.var". +inline "cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/a.var" "Still_More_Algebraic_Properties__". -inline "cic:/CoRN/ftc/FunctSequence/b.var". +inline "cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/b.var" "Still_More_Algebraic_Properties__". -inline "cic:/CoRN/ftc/FunctSequence/Hab.var". +inline "cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/Hab.var" "Still_More_Algebraic_Properties__". (* begin hide *) -inline "cic:/CoRN/ftc/FunctSequence/I.con". +inline "cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/I.con" "Still_More_Algebraic_Properties__". (* end hide *) -inline "cic:/CoRN/ftc/FunctSequence/f.var". +inline "cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/f.var" "Still_More_Algebraic_Properties__". -inline "cic:/CoRN/ftc/FunctSequence/contf.var". +inline "cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/contf.var" "Still_More_Algebraic_Properties__". -inline "cic:/CoRN/ftc/FunctSequence/Hf.var". +inline "cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/Hf.var" "Still_More_Algebraic_Properties__". (*#* As a corollary, we get the analogous property for the sequence of algebraic inverse functions. @@ -497,7 +497,7 @@ inline "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_inv.con". inline "cic:/CoRN/ftc/FunctSequence/fun_Cauchy_prop_inv.con". (* UNEXPORTED -End Still_More_Algebraic_Properties. +End Still_More_Algebraic_Properties *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/FunctSeries.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/FunctSeries.ma index 869a6a3f9..2ce9fa143 100644 --- a/helm/software/matita/contribs/CoRN-Decl/ftc/FunctSeries.ma +++ b/helm/software/matita/contribs/CoRN-Decl/ftc/FunctSeries.ma @@ -29,7 +29,7 @@ include "reals/Series.ma". (*#* printing Fun_Series_Sum %\ensuremath{\sum_0^{\infty}}% #∑0∞# *) (* UNEXPORTED -Section Definitions. +Section Definitions *) (*#* *Series of Functions @@ -53,19 +53,19 @@ defined in a compact interval. For this, partial sums are defined and convergence is simply the convergence of the sequence of partial sums. *) -inline "cic:/CoRN/ftc/FunctSeries/a.var". +inline "cic:/CoRN/ftc/FunctSeries/Definitions/a.var" "Definitions__". -inline "cic:/CoRN/ftc/FunctSeries/b.var". +inline "cic:/CoRN/ftc/FunctSeries/Definitions/b.var" "Definitions__". -inline "cic:/CoRN/ftc/FunctSeries/Hab.var". +inline "cic:/CoRN/ftc/FunctSeries/Definitions/Hab.var" "Definitions__". (* begin hide *) -inline "cic:/CoRN/ftc/FunctSeries/I.con". +inline "cic:/CoRN/ftc/FunctSeries/Definitions/I.con" "Definitions__". (* end hide *) -inline "cic:/CoRN/ftc/FunctSeries/f.var". +inline "cic:/CoRN/ftc/FunctSeries/Definitions/f.var" "Definitions__". inline "cic:/CoRN/ftc/FunctSeries/fun_seq_part_sum.con". @@ -87,15 +87,15 @@ the corresponding series. (* begin show *) -inline "cic:/CoRN/ftc/FunctSeries/H.var". +inline "cic:/CoRN/ftc/FunctSeries/Definitions/H.var" "Definitions__". (* end show *) (* begin hide *) -inline "cic:/CoRN/ftc/FunctSeries/contf.con". +inline "cic:/CoRN/ftc/FunctSeries/Definitions/contf.con" "Definitions__". -inline "cic:/CoRN/ftc/FunctSeries/incf.con". +inline "cic:/CoRN/ftc/FunctSeries/Definitions/incf.con" "Definitions__". (* end hide *) @@ -104,7 +104,7 @@ inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_strext.con". inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum.con". (* UNEXPORTED -End Definitions. +End Definitions *) (* UNEXPORTED @@ -116,27 +116,27 @@ Hint Resolve fun_seq_part_sum_cont: continuous. *) (* UNEXPORTED -Section More_Definitions. +Section More_Definitions *) -inline "cic:/CoRN/ftc/FunctSeries/a.var". +inline "cic:/CoRN/ftc/FunctSeries/More_Definitions/a.var" "More_Definitions__". -inline "cic:/CoRN/ftc/FunctSeries/b.var". +inline "cic:/CoRN/ftc/FunctSeries/More_Definitions/b.var" "More_Definitions__". -inline "cic:/CoRN/ftc/FunctSeries/Hab.var". +inline "cic:/CoRN/ftc/FunctSeries/More_Definitions/Hab.var" "More_Definitions__". -inline "cic:/CoRN/ftc/FunctSeries/f.var". +inline "cic:/CoRN/ftc/FunctSeries/More_Definitions/f.var" "More_Definitions__". (*#* A series can also be absolutely convergent. *) inline "cic:/CoRN/ftc/FunctSeries/fun_series_abs_convergent.con". (* UNEXPORTED -End More_Definitions. +End More_Definitions *) (* UNEXPORTED -Section Operations. +Section Operations *) (* **Algebraic Properties @@ -144,15 +144,15 @@ Section Operations. All of these are analogous to the properties for series of real numbers, so we won't comment much about them. *) -inline "cic:/CoRN/ftc/FunctSeries/a.var". +inline "cic:/CoRN/ftc/FunctSeries/Operations/a.var" "Operations__". -inline "cic:/CoRN/ftc/FunctSeries/b.var". +inline "cic:/CoRN/ftc/FunctSeries/Operations/b.var" "Operations__". -inline "cic:/CoRN/ftc/FunctSeries/Hab.var". +inline "cic:/CoRN/ftc/FunctSeries/Operations/Hab.var" "Operations__". (* begin hide *) -inline "cic:/CoRN/ftc/FunctSeries/I.con". +inline "cic:/CoRN/ftc/FunctSeries/Operations/I.con" "Operations__". (* end hide *) @@ -168,9 +168,9 @@ inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_zero.con". (* begin show *) -inline "cic:/CoRN/ftc/FunctSeries/f.var". +inline "cic:/CoRN/ftc/FunctSeries/Operations/f.var" "Operations__". -inline "cic:/CoRN/ftc/FunctSeries/g.var". +inline "cic:/CoRN/ftc/FunctSeries/Operations/g.var" "Operations__". (* end show *) @@ -178,9 +178,9 @@ inline "cic:/CoRN/ftc/FunctSeries/fun_series_convergent_wd.con". (* begin show *) -inline "cic:/CoRN/ftc/FunctSeries/convF.var". +inline "cic:/CoRN/ftc/FunctSeries/Operations/convF.var" "Operations__". -inline "cic:/CoRN/ftc/FunctSeries/convG.var". +inline "cic:/CoRN/ftc/FunctSeries/Operations/convG.var" "Operations__". (* end show *) @@ -199,61 +199,61 @@ inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_min.con". %\end{convention}% *) -inline "cic:/CoRN/ftc/FunctSeries/c.var". +inline "cic:/CoRN/ftc/FunctSeries/Operations/c.var" "Operations__". -inline "cic:/CoRN/ftc/FunctSeries/H.var". +inline "cic:/CoRN/ftc/FunctSeries/Operations/H.var" "Operations__". -inline "cic:/CoRN/ftc/FunctSeries/contH.var". +inline "cic:/CoRN/ftc/FunctSeries/Operations/contH.var" "Operations__". inline "cic:/CoRN/ftc/FunctSeries/conv_fun_series_scal.con". inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_scal.con". (* UNEXPORTED -End Operations. +End Operations *) (* UNEXPORTED -Section More_Operations. +Section More_Operations *) -inline "cic:/CoRN/ftc/FunctSeries/a.var". +inline "cic:/CoRN/ftc/FunctSeries/More_Operations/a.var" "More_Operations__". -inline "cic:/CoRN/ftc/FunctSeries/b.var". +inline "cic:/CoRN/ftc/FunctSeries/More_Operations/b.var" "More_Operations__". -inline "cic:/CoRN/ftc/FunctSeries/Hab.var". +inline "cic:/CoRN/ftc/FunctSeries/More_Operations/Hab.var" "More_Operations__". (* begin hide *) -inline "cic:/CoRN/ftc/FunctSeries/I.con". +inline "cic:/CoRN/ftc/FunctSeries/More_Operations/I.con" "More_Operations__". (* end hide *) -inline "cic:/CoRN/ftc/FunctSeries/f.var". +inline "cic:/CoRN/ftc/FunctSeries/More_Operations/f.var" "More_Operations__". -inline "cic:/CoRN/ftc/FunctSeries/convF.var". +inline "cic:/CoRN/ftc/FunctSeries/More_Operations/convF.var" "More_Operations__". inline "cic:/CoRN/ftc/FunctSeries/conv_fun_series_inv.con". inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_inv.con". (* UNEXPORTED -End More_Operations. +End More_Operations *) (* UNEXPORTED -Section Other_Results. +Section Other_Results *) -inline "cic:/CoRN/ftc/FunctSeries/a.var". +inline "cic:/CoRN/ftc/FunctSeries/Other_Results/a.var" "Other_Results__". -inline "cic:/CoRN/ftc/FunctSeries/b.var". +inline "cic:/CoRN/ftc/FunctSeries/Other_Results/b.var" "Other_Results__". -inline "cic:/CoRN/ftc/FunctSeries/Hab.var". +inline "cic:/CoRN/ftc/FunctSeries/Other_Results/Hab.var" "Other_Results__". -inline "cic:/CoRN/ftc/FunctSeries/f.var". +inline "cic:/CoRN/ftc/FunctSeries/Other_Results/f.var" "Other_Results__". -inline "cic:/CoRN/ftc/FunctSeries/convF.var". +inline "cic:/CoRN/ftc/FunctSeries/Other_Results/convF.var" "Other_Results__". (*#* The following relate the sum series with the limit of the sequence of @@ -272,7 +272,7 @@ inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_char.con". inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_as_Lim.con". (* UNEXPORTED -End Other_Results. +End Other_Results *) (* UNEXPORTED @@ -280,7 +280,7 @@ Hint Resolve Fun_Series_Sum_cont: continuous. *) (* UNEXPORTED -Section Convergence_Criteria. +Section Convergence_Criteria *) (*#* **Convergence Criteria @@ -288,21 +288,21 @@ 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. *) -inline "cic:/CoRN/ftc/FunctSeries/a.var". +inline "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/a.var" "Convergence_Criteria__". -inline "cic:/CoRN/ftc/FunctSeries/b.var". +inline "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/b.var" "Convergence_Criteria__". -inline "cic:/CoRN/ftc/FunctSeries/Hab.var". +inline "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/Hab.var" "Convergence_Criteria__". (* begin hide *) -inline "cic:/CoRN/ftc/FunctSeries/I.con". +inline "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/I.con" "Convergence_Criteria__". (* end hide *) -inline "cic:/CoRN/ftc/FunctSeries/f.var". +inline "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/f.var" "Convergence_Criteria__". -inline "cic:/CoRN/ftc/FunctSeries/contF.var". +inline "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/contF.var" "Convergence_Criteria__". (* UNEXPORTED Opaque Frestr. @@ -361,6 +361,6 @@ Opaque FAbs. inline "cic:/CoRN/ftc/FunctSeries/fun_ratio_test_conv.con". (* UNEXPORTED -End Convergence_Criteria. +End Convergence_Criteria *) diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/Integral.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/Integral.ma index a6bace36d..f1b87ac1e 100644 --- a/helm/software/matita/contribs/CoRN-Decl/ftc/Integral.ma +++ b/helm/software/matita/contribs/CoRN-Decl/ftc/Integral.ma @@ -29,21 +29,21 @@ include "ftc/RefLemma.ma". (* begin hide *) (* UNEXPORTED -Section Lemmas. +Section Lemmas *) -inline "cic:/CoRN/ftc/Integral/Sumx_wd_weird.con". +inline "cic:/CoRN/ftc/Integral/Lemmas/Sumx_wd_weird.con" "Lemmas__". inline "cic:/CoRN/ftc/Integral/Sumx_weird_lemma.con". (* UNEXPORTED -End Lemmas. +End Lemmas *) (* end hide *) (* UNEXPORTED -Section Integral. +Section Integral *) (*#* *Integral @@ -59,26 +59,26 @@ continuous functions in [I]. %\end{convention}% *) -inline "cic:/CoRN/ftc/Integral/a.var". +inline "cic:/CoRN/ftc/Integral/Integral/a.var" "Integral__". -inline "cic:/CoRN/ftc/Integral/b.var". +inline "cic:/CoRN/ftc/Integral/Integral/b.var" "Integral__". -inline "cic:/CoRN/ftc/Integral/Hab.var". +inline "cic:/CoRN/ftc/Integral/Integral/Hab.var" "Integral__". (* begin hide *) -inline "cic:/CoRN/ftc/Integral/I.con". +inline "cic:/CoRN/ftc/Integral/Integral/I.con" "Integral__". -inline "cic:/CoRN/ftc/Integral/F.var". +inline "cic:/CoRN/ftc/Integral/Integral/F.var" "Integral__". -inline "cic:/CoRN/ftc/Integral/contF.var". +inline "cic:/CoRN/ftc/Integral/Integral/contF.var" "Integral__". -inline "cic:/CoRN/ftc/Integral/contF'.con". +inline "cic:/CoRN/ftc/Integral/Integral/contF'.con" "Integral__". (* end hide *) (* UNEXPORTED -Section Darboux_Sum. +Section Darboux_Sum *) inline "cic:/CoRN/ftc/Integral/integral_seq.con". @@ -88,11 +88,11 @@ inline "cic:/CoRN/ftc/Integral/Cauchy_Darboux_Seq.con". inline "cic:/CoRN/ftc/Integral/integral.con". (* UNEXPORTED -End Darboux_Sum. +End Darboux_Sum *) (* UNEXPORTED -Section Integral_Thm. +Section Integral_Thm *) (*#* @@ -106,57 +106,57 @@ respecting [P]. %\end{convention}% *) -inline "cic:/CoRN/ftc/Integral/n.var". +inline "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/n.var" "Integral__Integral_Thm__". -inline "cic:/CoRN/ftc/Integral/P.var". +inline "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/P.var" "Integral__Integral_Thm__". -inline "cic:/CoRN/ftc/Integral/e.var". +inline "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/e.var" "Integral__Integral_Thm__". -inline "cic:/CoRN/ftc/Integral/He.var". +inline "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/He.var" "Integral__Integral_Thm__". (* begin hide *) -inline "cic:/CoRN/ftc/Integral/d.con". +inline "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/d.con" "Integral__Integral_Thm__". (* end hide *) -inline "cic:/CoRN/ftc/Integral/HmeshP.var". +inline "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/HmeshP.var" "Integral__Integral_Thm__". -inline "cic:/CoRN/ftc/Integral/fP.var". +inline "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/fP.var" "Integral__Integral_Thm__". -inline "cic:/CoRN/ftc/Integral/HfP.var". +inline "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/HfP.var" "Integral__Integral_Thm__". -inline "cic:/CoRN/ftc/Integral/HfP'.var". +inline "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/HfP'.var" "Integral__Integral_Thm__". -inline "cic:/CoRN/ftc/Integral/incF.var". +inline "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/incF.var" "Integral__Integral_Thm__". inline "cic:/CoRN/ftc/Integral/partition_Sum_conv_integral.con". (* UNEXPORTED -End Integral_Thm. +End Integral_Thm *) (* UNEXPORTED -End Integral. +End Integral *) (* UNEXPORTED -Section Basic_Properties. +Section Basic_Properties *) (*#* The usual extensionality and strong extensionality results hold. *) -inline "cic:/CoRN/ftc/Integral/a.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/a.var" "Basic_Properties__". -inline "cic:/CoRN/ftc/Integral/b.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/b.var" "Basic_Properties__". -inline "cic:/CoRN/ftc/Integral/Hab.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Hab.var" "Basic_Properties__". (* begin hide *) -inline "cic:/CoRN/ftc/Integral/I.con". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/I.con" "Basic_Properties__". (* end hide *) @@ -165,16 +165,16 @@ Notation Integral := (integral _ _ Hab). *) (* UNEXPORTED -Section Well_Definedness. +Section Well_Definedness *) -inline "cic:/CoRN/ftc/Integral/F.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Well_Definedness/F.var" "Basic_Properties__Well_Definedness__". -inline "cic:/CoRN/ftc/Integral/G.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Well_Definedness/G.var" "Basic_Properties__Well_Definedness__". -inline "cic:/CoRN/ftc/Integral/contF.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Well_Definedness/contF.var" "Basic_Properties__Well_Definedness__". -inline "cic:/CoRN/ftc/Integral/contG.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Well_Definedness/contG.var" "Basic_Properties__Well_Definedness__". inline "cic:/CoRN/ftc/Integral/integral_strext.con". @@ -185,11 +185,11 @@ inline "cic:/CoRN/ftc/Integral/integral_wd.con". inline "cic:/CoRN/ftc/Integral/integral_wd'.con". (* UNEXPORTED -End Well_Definedness. +End Well_Definedness *) (* UNEXPORTED -Section Linearity_and_Monotonicity. +Section Linearity_and_Monotonicity *) (* UNEXPORTED @@ -202,13 +202,13 @@ The integral is a linear and monotonous function; in order to prove these facts inline "cic:/CoRN/ftc/Integral/integral_one.con". -inline "cic:/CoRN/ftc/Integral/F.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity/F.var" "Basic_Properties__Linearity_and_Monotonicity__". -inline "cic:/CoRN/ftc/Integral/G.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity/G.var" "Basic_Properties__Linearity_and_Monotonicity__". -inline "cic:/CoRN/ftc/Integral/contF.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity/contF.var" "Basic_Properties__Linearity_and_Monotonicity__". -inline "cic:/CoRN/ftc/Integral/contG.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity/contG.var" "Basic_Properties__Linearity_and_Monotonicity__". inline "cic:/CoRN/ftc/Integral/integral_comm_scal.con". @@ -221,20 +221,20 @@ Transparent Even_Partition. inline "cic:/CoRN/ftc/Integral/integral_empty.con". (* UNEXPORTED -End Linearity_and_Monotonicity. +End Linearity_and_Monotonicity *) (* UNEXPORTED -Section Linearity_and_Monotonicity'. +Section Linearity_and_Monotonicity' *) -inline "cic:/CoRN/ftc/Integral/F.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/F.var" "Basic_Properties__Linearity_and_Monotonicity'__". -inline "cic:/CoRN/ftc/Integral/G.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/G.var" "Basic_Properties__Linearity_and_Monotonicity'__". -inline "cic:/CoRN/ftc/Integral/contF.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/contF.var" "Basic_Properties__Linearity_and_Monotonicity'__". -inline "cic:/CoRN/ftc/Integral/contG.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/contG.var" "Basic_Properties__Linearity_and_Monotonicity'__". (*#* %\begin{convention}% Let [alpha, beta : IR] and assume that @@ -242,17 +242,17 @@ inline "cic:/CoRN/ftc/Integral/contG.var". %\end{convention}% *) -inline "cic:/CoRN/ftc/Integral/alpha.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/alpha.var" "Basic_Properties__Linearity_and_Monotonicity'__". -inline "cic:/CoRN/ftc/Integral/beta.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/beta.var" "Basic_Properties__Linearity_and_Monotonicity'__". (* begin hide *) -inline "cic:/CoRN/ftc/Integral/h.con". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/h.con" "Basic_Properties__Linearity_and_Monotonicity'__". (* end hide *) -inline "cic:/CoRN/ftc/Integral/contH.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/contH.var" "Basic_Properties__Linearity_and_Monotonicity'__". inline "cic:/CoRN/ftc/Integral/linear_integral.con". @@ -267,20 +267,20 @@ Transparent nring. *) (* UNEXPORTED -End Linearity_and_Monotonicity'. +End Linearity_and_Monotonicity' *) (* UNEXPORTED -Section Corollaries. +Section Corollaries *) -inline "cic:/CoRN/ftc/Integral/F.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Corollaries/F.var" "Basic_Properties__Corollaries__". -inline "cic:/CoRN/ftc/Integral/G.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Corollaries/G.var" "Basic_Properties__Corollaries__". -inline "cic:/CoRN/ftc/Integral/contF.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Corollaries/contF.var" "Basic_Properties__Corollaries__". -inline "cic:/CoRN/ftc/Integral/contG.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Corollaries/contG.var" "Basic_Properties__Corollaries__". (*#* As corollaries we can calculate integrals of group operations applied to functions. @@ -303,11 +303,11 @@ inline "cic:/CoRN/ftc/Integral/ub_integral.con". inline "cic:/CoRN/ftc/Integral/integral_leEq_norm.con". (* UNEXPORTED -End Corollaries. +End Corollaries *) (* UNEXPORTED -Section Integral_Sum. +Section Integral_Sum *) (*#* @@ -319,22 +319,22 @@ $c\in[a,b]$#c∈[a,b]#. %\end{convention}% *) -inline "cic:/CoRN/ftc/Integral/F.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/F.var" "Basic_Properties__Integral_Sum__". -inline "cic:/CoRN/ftc/Integral/c.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/c.var" "Basic_Properties__Integral_Sum__". -inline "cic:/CoRN/ftc/Integral/Hac.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Hac.var" "Basic_Properties__Integral_Sum__". -inline "cic:/CoRN/ftc/Integral/Hcb.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Hcb.var" "Basic_Properties__Integral_Sum__". -inline "cic:/CoRN/ftc/Integral/Hab'.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Hab'.var" "Basic_Properties__Integral_Sum__". -inline "cic:/CoRN/ftc/Integral/Hac'.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Hac'.var" "Basic_Properties__Integral_Sum__". -inline "cic:/CoRN/ftc/Integral/Hcb'.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Hcb'.var" "Basic_Properties__Integral_Sum__". (* UNEXPORTED -Section Partition_Join. +Section Partition_Join *) (*#* @@ -349,13 +349,13 @@ inequality). %\end{convention}% *) -inline "cic:/CoRN/ftc/Integral/n.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/n.var" "Basic_Properties__Integral_Sum__Partition_Join__". -inline "cic:/CoRN/ftc/Integral/m.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/m.var" "Basic_Properties__Integral_Sum__Partition_Join__". -inline "cic:/CoRN/ftc/Integral/P.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/P.var" "Basic_Properties__Integral_Sum__Partition_Join__". -inline "cic:/CoRN/ftc/Integral/Q.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/Q.var" "Basic_Properties__Integral_Sum__Partition_Join__". (* begin hide *) @@ -392,17 +392,17 @@ inline "cic:/CoRN/ftc/Integral/partition_join.con". %\end{convention}% *) -inline "cic:/CoRN/ftc/Integral/fP.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/fP.var" "Basic_Properties__Integral_Sum__Partition_Join__". -inline "cic:/CoRN/ftc/Integral/HfP.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/HfP.var" "Basic_Properties__Integral_Sum__Partition_Join__". -inline "cic:/CoRN/ftc/Integral/HfP'.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/HfP'.var" "Basic_Properties__Integral_Sum__Partition_Join__". -inline "cic:/CoRN/ftc/Integral/fQ.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/fQ.var" "Basic_Properties__Integral_Sum__Partition_Join__". -inline "cic:/CoRN/ftc/Integral/HfQ.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/HfQ.var" "Basic_Properties__Integral_Sum__Partition_Join__". -inline "cic:/CoRN/ftc/Integral/HfQ'.var". +inline "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/HfQ'.var" "Basic_Properties__Integral_Sum__Partition_Join__". (* begin hide *) @@ -455,7 +455,7 @@ inline "cic:/CoRN/ftc/Integral/partition_join_Sum_lemma.con". inline "cic:/CoRN/ftc/Integral/partition_join_mesh.con". (* UNEXPORTED -End Partition_Join. +End Partition_Join *) (*#* @@ -469,7 +469,7 @@ Opaque Even_Partition. inline "cic:/CoRN/ftc/Integral/integral_plus_integral.con". (* UNEXPORTED -End Integral_Sum. +End Integral_Sum *) (* UNEXPORTED @@ -477,7 +477,7 @@ Transparent Even_Partition. *) (* UNEXPORTED -End Basic_Properties. +End Basic_Properties *) (*#* diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/IntervalFunct.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/IntervalFunct.ma index bf128f9a0..3587525bc 100644 --- a/helm/software/matita/contribs/CoRN-Decl/ftc/IntervalFunct.ma +++ b/helm/software/matita/contribs/CoRN-Decl/ftc/IntervalFunct.ma @@ -23,7 +23,7 @@ include "CoRN.ma". include "ftc/PartFunEquality.ma". (* UNEXPORTED -Section Operations. +Section Operations *) (*#* * Functions with compact domain @@ -47,24 +47,24 @@ type [I -> IR]. %\end{convention}% *) -inline "cic:/CoRN/ftc/IntervalFunct/a.var". +inline "cic:/CoRN/ftc/IntervalFunct/Operations/a.var" "Operations__". -inline "cic:/CoRN/ftc/IntervalFunct/b.var". +inline "cic:/CoRN/ftc/IntervalFunct/Operations/b.var" "Operations__". -inline "cic:/CoRN/ftc/IntervalFunct/Hab.var". +inline "cic:/CoRN/ftc/IntervalFunct/Operations/Hab.var" "Operations__". (* begin hide *) -inline "cic:/CoRN/ftc/IntervalFunct/I.con". +inline "cic:/CoRN/ftc/IntervalFunct/Operations/I.con" "Operations__". (* end hide *) -inline "cic:/CoRN/ftc/IntervalFunct/f.var". +inline "cic:/CoRN/ftc/IntervalFunct/Operations/f.var" "Operations__". -inline "cic:/CoRN/ftc/IntervalFunct/g.var". +inline "cic:/CoRN/ftc/IntervalFunct/Operations/g.var" "Operations__". (* UNEXPORTED -Section Const. +Section Const *) (*#* @@ -74,14 +74,14 @@ Constant and identity functions are defined. %\end{convention}% *) -inline "cic:/CoRN/ftc/IntervalFunct/c.var". +inline "cic:/CoRN/ftc/IntervalFunct/Operations/Const/c.var" "Operations__Const__". inline "cic:/CoRN/ftc/IntervalFunct/IConst_strext.con". inline "cic:/CoRN/ftc/IntervalFunct/IConst.con". (* UNEXPORTED -End Const. +End Const *) inline "cic:/CoRN/ftc/IntervalFunct/IId_strext.con". @@ -109,21 +109,21 @@ inline "cic:/CoRN/ftc/IntervalFunct/IMult_strext.con". inline "cic:/CoRN/ftc/IntervalFunct/IMult.con". (* UNEXPORTED -Section Nth_Power. +Section Nth_Power *) (*#* Exponentiation to a natural power [n] is also useful. *) -inline "cic:/CoRN/ftc/IntervalFunct/n.var". +inline "cic:/CoRN/ftc/IntervalFunct/Operations/Nth_Power/n.var" "Operations__Nth_Power__". inline "cic:/CoRN/ftc/IntervalFunct/INth_strext.con". inline "cic:/CoRN/ftc/IntervalFunct/INth.con". (* UNEXPORTED -End Nth_Power. +End Nth_Power *) (*#* @@ -131,12 +131,12 @@ If a function is non-zero in all the interval then we can define its multiplicat *) (* UNEXPORTED -Section Recip_Div. +Section Recip_Div *) (* begin show *) -inline "cic:/CoRN/ftc/IntervalFunct/Hg.var". +inline "cic:/CoRN/ftc/IntervalFunct/Operations/Recip_Div/Hg.var" "Operations__Recip_Div__". (* end show *) @@ -149,7 +149,7 @@ inline "cic:/CoRN/ftc/IntervalFunct/IDiv_strext.con". inline "cic:/CoRN/ftc/IntervalFunct/IDiv.con". (* UNEXPORTED -End Recip_Div. +End Recip_Div *) (*#* @@ -161,7 +161,7 @@ inline "cic:/CoRN/ftc/IntervalFunct/IAbs_strext.con". inline "cic:/CoRN/ftc/IntervalFunct/IAbs.con". (* UNEXPORTED -End Operations. +End Operations *) (*#* @@ -183,45 +183,45 @@ compact interval [[a',b']], and let [g] be a setoid function of type *) (* UNEXPORTED -Section Composition. +Section Composition *) -inline "cic:/CoRN/ftc/IntervalFunct/a.var". +inline "cic:/CoRN/ftc/IntervalFunct/Composition/a.var" "Composition__". -inline "cic:/CoRN/ftc/IntervalFunct/b.var". +inline "cic:/CoRN/ftc/IntervalFunct/Composition/b.var" "Composition__". -inline "cic:/CoRN/ftc/IntervalFunct/Hab.var". +inline "cic:/CoRN/ftc/IntervalFunct/Composition/Hab.var" "Composition__". (* begin hide *) -inline "cic:/CoRN/ftc/IntervalFunct/I.con". +inline "cic:/CoRN/ftc/IntervalFunct/Composition/I.con" "Composition__". (* end hide *) -inline "cic:/CoRN/ftc/IntervalFunct/a'.var". +inline "cic:/CoRN/ftc/IntervalFunct/Composition/a'.var" "Composition__". -inline "cic:/CoRN/ftc/IntervalFunct/b'.var". +inline "cic:/CoRN/ftc/IntervalFunct/Composition/b'.var" "Composition__". -inline "cic:/CoRN/ftc/IntervalFunct/Hab'.var". +inline "cic:/CoRN/ftc/IntervalFunct/Composition/Hab'.var" "Composition__". (* begin hide *) -inline "cic:/CoRN/ftc/IntervalFunct/I'.con". +inline "cic:/CoRN/ftc/IntervalFunct/Composition/I'.con" "Composition__". (* end hide *) -inline "cic:/CoRN/ftc/IntervalFunct/f.var". +inline "cic:/CoRN/ftc/IntervalFunct/Composition/f.var" "Composition__". -inline "cic:/CoRN/ftc/IntervalFunct/g.var". +inline "cic:/CoRN/ftc/IntervalFunct/Composition/g.var" "Composition__". -inline "cic:/CoRN/ftc/IntervalFunct/Hfg.var". +inline "cic:/CoRN/ftc/IntervalFunct/Composition/Hfg.var" "Composition__". inline "cic:/CoRN/ftc/IntervalFunct/IComp_strext.con". inline "cic:/CoRN/ftc/IntervalFunct/IComp.con". (* UNEXPORTED -End Composition. +End Composition *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/MoreFunSeries.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/MoreFunSeries.ma index 20eaa0dcd..8ca95c449 100644 --- a/helm/software/matita/contribs/CoRN-Decl/ftc/MoreFunSeries.ma +++ b/helm/software/matita/contribs/CoRN-Decl/ftc/MoreFunSeries.ma @@ -27,7 +27,7 @@ include "ftc/MoreFunctions.ma". (*#* printing FSeries_Sum %\ensuremath{\sum_{\infty}}% #∑'∞# *) (* UNEXPORTED -Section Definitions. +Section Definitions *) (*#* *More on Sequences and Series @@ -52,15 +52,15 @@ 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. *) -inline "cic:/CoRN/ftc/MoreFunSeries/J.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Definitions/J.var" "Definitions__". -inline "cic:/CoRN/ftc/MoreFunSeries/f.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Definitions/f.var" "Definitions__". -inline "cic:/CoRN/ftc/MoreFunSeries/F.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Definitions/F.var" "Definitions__". -inline "cic:/CoRN/ftc/MoreFunSeries/contf.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Definitions/contf.var" "Definitions__". -inline "cic:/CoRN/ftc/MoreFunSeries/contF.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Definitions/contF.var" "Definitions__". inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_IR.con". @@ -83,26 +83,26 @@ inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq2_seq_IR.con". inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_real_IR.con". (* UNEXPORTED -End Definitions. +End Definitions *) (* UNEXPORTED -Section More_Definitions. +Section More_Definitions *) (*#* Limit is defined and works in the same way as before. *) -inline "cic:/CoRN/ftc/MoreFunSeries/J.var". +inline "cic:/CoRN/ftc/MoreFunSeries/More_Definitions/J.var" "More_Definitions__". -inline "cic:/CoRN/ftc/MoreFunSeries/f.var". +inline "cic:/CoRN/ftc/MoreFunSeries/More_Definitions/f.var" "More_Definitions__". -inline "cic:/CoRN/ftc/MoreFunSeries/contf.var". +inline "cic:/CoRN/ftc/MoreFunSeries/More_Definitions/contf.var" "More_Definitions__". (* begin show *) -inline "cic:/CoRN/ftc/MoreFunSeries/conv.var". +inline "cic:/CoRN/ftc/MoreFunSeries/More_Definitions/conv.var" "More_Definitions__". (* end show *) @@ -111,11 +111,11 @@ inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_Lim_IR.con". inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_Lim_char.con". (* UNEXPORTED -End More_Definitions. +End More_Definitions *) (* UNEXPORTED -Section Irrelevance_of_Proofs. +Section Irrelevance_of_Proofs *) (*#* ***Basic Properties @@ -123,25 +123,25 @@ Section Irrelevance_of_Proofs. Proofs are irrelevant as before---they just have to be present. *) -inline "cic:/CoRN/ftc/MoreFunSeries/J.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/J.var" "Irrelevance_of_Proofs__". -inline "cic:/CoRN/ftc/MoreFunSeries/f.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/f.var" "Irrelevance_of_Proofs__". (* begin show *) -inline "cic:/CoRN/ftc/MoreFunSeries/contf.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/contf.var" "Irrelevance_of_Proofs__". -inline "cic:/CoRN/ftc/MoreFunSeries/contf0.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/contf0.var" "Irrelevance_of_Proofs__". (* end show *) -inline "cic:/CoRN/ftc/MoreFunSeries/F.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/F.var" "Irrelevance_of_Proofs__". (* begin show *) -inline "cic:/CoRN/ftc/MoreFunSeries/contF.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/contF.var" "Irrelevance_of_Proofs__". -inline "cic:/CoRN/ftc/MoreFunSeries/contF0.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/contF0.var" "Irrelevance_of_Proofs__". (* end show *) @@ -152,7 +152,7 @@ inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq2_wd_IR.con". inline "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq_wd_IR.con". (* UNEXPORTED -End Irrelevance_of_Proofs. +End Irrelevance_of_Proofs *) (* UNEXPORTED @@ -160,42 +160,42 @@ Opaque Cauchy_fun_seq_Lim_IR. *) (* UNEXPORTED -Section More_Properties. +Section More_Properties *) -inline "cic:/CoRN/ftc/MoreFunSeries/J.var". +inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/J.var" "More_Properties__". -inline "cic:/CoRN/ftc/MoreFunSeries/f.var". +inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/f.var" "More_Properties__". -inline "cic:/CoRN/ftc/MoreFunSeries/g.var". +inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/g.var" "More_Properties__". (* begin show *) -inline "cic:/CoRN/ftc/MoreFunSeries/contf.var". +inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contf.var" "More_Properties__". -inline "cic:/CoRN/ftc/MoreFunSeries/contf0.var". +inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contf0.var" "More_Properties__". -inline "cic:/CoRN/ftc/MoreFunSeries/contg.var". +inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contg.var" "More_Properties__". -inline "cic:/CoRN/ftc/MoreFunSeries/contg0.var". +inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contg0.var" "More_Properties__". (* end show *) inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_conv_fun_seq'_IR.con". -inline "cic:/CoRN/ftc/MoreFunSeries/F.var". +inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/F.var" "More_Properties__". -inline "cic:/CoRN/ftc/MoreFunSeries/G.var". +inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/G.var" "More_Properties__". (* begin show *) -inline "cic:/CoRN/ftc/MoreFunSeries/contF.var". +inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contF.var" "More_Properties__". -inline "cic:/CoRN/ftc/MoreFunSeries/contF0.var". +inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contF0.var" "More_Properties__". -inline "cic:/CoRN/ftc/MoreFunSeries/contG.var". +inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contG.var" "More_Properties__". -inline "cic:/CoRN/ftc/MoreFunSeries/contG0.var". +inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contG0.var" "More_Properties__". (* end show *) @@ -214,7 +214,7 @@ inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_conv_fun_seq_IR.con". inline "cic:/CoRN/ftc/MoreFunSeries/conv_Cauchy_fun_seq_IR.con". (* UNEXPORTED -End More_Properties. +End More_Properties *) (* UNEXPORTED @@ -222,7 +222,7 @@ Hint Resolve Cauchy_cont_Lim_IR: continuous. *) (* UNEXPORTED -Section Algebraic_Properties. +Section Algebraic_Properties *) (*#* ***Algebraic Properties @@ -230,15 +230,15 @@ Section Algebraic_Properties. Algebraic operations still work well. *) -inline "cic:/CoRN/ftc/MoreFunSeries/J.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/J.var" "Algebraic_Properties__". -inline "cic:/CoRN/ftc/MoreFunSeries/f.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/f.var" "Algebraic_Properties__". -inline "cic:/CoRN/ftc/MoreFunSeries/g.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/g.var" "Algebraic_Properties__". -inline "cic:/CoRN/ftc/MoreFunSeries/contf.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/contf.var" "Algebraic_Properties__". -inline "cic:/CoRN/ftc/MoreFunSeries/contg.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/contg.var" "Algebraic_Properties__". inline "cic:/CoRN/ftc/MoreFunSeries/FLim_unique_IR.con". @@ -248,19 +248,19 @@ inline "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_const_IR.con". inline "cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_const_IR.con". -inline "cic:/CoRN/ftc/MoreFunSeries/F.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/F.var" "Algebraic_Properties__". -inline "cic:/CoRN/ftc/MoreFunSeries/G.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/G.var" "Algebraic_Properties__". -inline "cic:/CoRN/ftc/MoreFunSeries/contF.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/contF.var" "Algebraic_Properties__". -inline "cic:/CoRN/ftc/MoreFunSeries/contG.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/contG.var" "Algebraic_Properties__". (* begin show *) -inline "cic:/CoRN/ftc/MoreFunSeries/convF.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/convF.var" "Algebraic_Properties__". -inline "cic:/CoRN/ftc/MoreFunSeries/convG.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/convG.var" "Algebraic_Properties__". (* end show *) @@ -271,32 +271,32 @@ inline "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_minus'_IR.con". inline "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_mult'_IR.con". (* UNEXPORTED -End Algebraic_Properties. +End Algebraic_Properties *) (* UNEXPORTED -Section More_Algebraic_Properties. +Section More_Algebraic_Properties *) (*#* If we work with the limit function things fit in just as well. *) -inline "cic:/CoRN/ftc/MoreFunSeries/J.var". +inline "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/J.var" "More_Algebraic_Properties__". -inline "cic:/CoRN/ftc/MoreFunSeries/f.var". +inline "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/f.var" "More_Algebraic_Properties__". -inline "cic:/CoRN/ftc/MoreFunSeries/g.var". +inline "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/g.var" "More_Algebraic_Properties__". -inline "cic:/CoRN/ftc/MoreFunSeries/contf.var". +inline "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/contf.var" "More_Algebraic_Properties__". -inline "cic:/CoRN/ftc/MoreFunSeries/contg.var". +inline "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/contg.var" "More_Algebraic_Properties__". (* begin show *) -inline "cic:/CoRN/ftc/MoreFunSeries/Hf.var". +inline "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/Hf.var" "More_Algebraic_Properties__". -inline "cic:/CoRN/ftc/MoreFunSeries/Hg.var". +inline "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/Hg.var" "More_Algebraic_Properties__". (* end show *) @@ -317,11 +317,11 @@ inline "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_mult_IR.con". inline "cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_mult.con". (* UNEXPORTED -End More_Algebraic_Properties. +End More_Algebraic_Properties *) (* UNEXPORTED -Section Other. +Section Other *) (*#* ***Miscellaneous @@ -340,11 +340,11 @@ Another interesting fact: if a sequence of constant functions converges then it inline "cic:/CoRN/ftc/MoreFunSeries/fun_const_Lim.con". (* UNEXPORTED -End Other. +End Other *) (* UNEXPORTED -Section Series_Definitions. +Section Series_Definitions *) (*#* **Series @@ -354,9 +354,9 @@ We now consider series of functions defined in arbitrary intervals. Convergence is defined as expected---through convergence in every compact interval. *) -inline "cic:/CoRN/ftc/MoreFunSeries/J.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Series_Definitions/J.var" "Series_Definitions__". -inline "cic:/CoRN/ftc/MoreFunSeries/f.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Series_Definitions/f.var" "Series_Definitions__". inline "cic:/CoRN/ftc/MoreFunSeries/fun_series_convergent_IR.con". @@ -364,7 +364,7 @@ inline "cic:/CoRN/ftc/MoreFunSeries/fun_series_conv_imp_conv_IR.con". (* begin show *) -inline "cic:/CoRN/ftc/MoreFunSeries/H.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Series_Definitions/H.var" "Series_Definitions__". (* end show *) @@ -374,7 +374,7 @@ inline "cic:/CoRN/ftc/MoreFunSeries/fun_series_inc_IR.con". (* begin hide *) -inline "cic:/CoRN/ftc/MoreFunSeries/h.con". +inline "cic:/CoRN/ftc/MoreFunSeries/Series_Definitions/h.con" "Series_Definitions__". (* end hide *) @@ -385,7 +385,7 @@ inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum.con". inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_char.con". (* UNEXPORTED -End Series_Definitions. +End Series_Definitions *) (* UNEXPORTED @@ -393,12 +393,12 @@ Implicit Arguments FSeries_Sum [J f]. *) (* UNEXPORTED -Section More_Series_Definitions. +Section More_Series_Definitions *) -inline "cic:/CoRN/ftc/MoreFunSeries/J.var". +inline "cic:/CoRN/ftc/MoreFunSeries/More_Series_Definitions/J.var" "More_Series_Definitions__". -inline "cic:/CoRN/ftc/MoreFunSeries/f.var". +inline "cic:/CoRN/ftc/MoreFunSeries/More_Series_Definitions/f.var" "More_Series_Definitions__". (*#* Absolute convergence still exists. @@ -407,20 +407,20 @@ Absolute convergence still exists. inline "cic:/CoRN/ftc/MoreFunSeries/fun_series_abs_convergent_IR.con". (* UNEXPORTED -End More_Series_Definitions. +End More_Series_Definitions *) (* UNEXPORTED -Section Convergence_Results. +Section Convergence_Results *) (*#* As before, any series converges to its sum. *) -inline "cic:/CoRN/ftc/MoreFunSeries/J.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Convergence_Results/J.var" "Convergence_Results__". -inline "cic:/CoRN/ftc/MoreFunSeries/f.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Convergence_Results/f.var" "Convergence_Results__". inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_conv.con". @@ -431,7 +431,7 @@ inline "cic:/CoRN/ftc/MoreFunSeries/convergent_imp_Continuous.con". inline "cic:/CoRN/ftc/MoreFunSeries/Continuous_FSeries_Sum.con". (* UNEXPORTED -End Convergence_Results. +End Convergence_Results *) (* UNEXPORTED @@ -443,7 +443,7 @@ Hint Resolve convergent_imp_Continuous Continuous_FSeries_Sum: continuous. *) (* UNEXPORTED -Section Operations. +Section Operations *) (*#* **Algebraic Operations @@ -451,7 +451,7 @@ Section Operations. Convergence is well defined and preserved by operations. *) -inline "cic:/CoRN/ftc/MoreFunSeries/J.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Operations/J.var" "Operations__". inline "cic:/CoRN/ftc/MoreFunSeries/conv_fun_const_series_IR.con". @@ -461,17 +461,17 @@ inline "cic:/CoRN/ftc/MoreFunSeries/conv_zero_fun_series_IR.con". inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_zero_IR.con". -inline "cic:/CoRN/ftc/MoreFunSeries/f.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Operations/f.var" "Operations__". -inline "cic:/CoRN/ftc/MoreFunSeries/g.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Operations/g.var" "Operations__". inline "cic:/CoRN/ftc/MoreFunSeries/fun_series_convergent_wd_IR.con". (* begin show *) -inline "cic:/CoRN/ftc/MoreFunSeries/convF.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Operations/convF.var" "Operations__". -inline "cic:/CoRN/ftc/MoreFunSeries/convG.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Operations/convG.var" "Operations__". (* end show *) @@ -494,22 +494,22 @@ inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_minus.con". %\end{convention}% *) -inline "cic:/CoRN/ftc/MoreFunSeries/c.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Operations/c.var" "Operations__". -inline "cic:/CoRN/ftc/MoreFunSeries/H.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Operations/H.var" "Operations__". -inline "cic:/CoRN/ftc/MoreFunSeries/contH.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Operations/contH.var" "Operations__". inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_scal_conv.con". inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_scal.con". (* UNEXPORTED -End Operations. +End Operations *) (* UNEXPORTED -Section Convergence_Criteria. +Section Convergence_Criteria *) (*#* ***Convergence Criteria @@ -518,11 +518,11 @@ The most important tests for convergence of series still apply: the comparison test (in both versions) and the ratio test. *) -inline "cic:/CoRN/ftc/MoreFunSeries/J.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Convergence_Criteria/J.var" "Convergence_Criteria__". -inline "cic:/CoRN/ftc/MoreFunSeries/f.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Convergence_Criteria/f.var" "Convergence_Criteria__". -inline "cic:/CoRN/ftc/MoreFunSeries/contF.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Convergence_Criteria/contF.var" "Convergence_Criteria__". inline "cic:/CoRN/ftc/MoreFunSeries/fun_str_comparison_IR.con". @@ -533,11 +533,11 @@ inline "cic:/CoRN/ftc/MoreFunSeries/abs_imp_conv_IR.con". inline "cic:/CoRN/ftc/MoreFunSeries/fun_ratio_test_conv_IR.con". (* UNEXPORTED -End Convergence_Criteria. +End Convergence_Criteria *) (* UNEXPORTED -Section Insert_Series. +Section Insert_Series *) (*#* ***Translation @@ -549,11 +549,11 @@ $f_i$#fi# and inserting the null function in the first position. This does not affect convergence or the sum of the series. *) -inline "cic:/CoRN/ftc/MoreFunSeries/J.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Insert_Series/J.var" "Insert_Series__". -inline "cic:/CoRN/ftc/MoreFunSeries/f.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Insert_Series/f.var" "Insert_Series__". -inline "cic:/CoRN/ftc/MoreFunSeries/convF.var". +inline "cic:/CoRN/ftc/MoreFunSeries/Insert_Series/convF.var" "Insert_Series__". inline "cic:/CoRN/ftc/MoreFunSeries/insert_series.con". @@ -566,6 +566,6 @@ inline "cic:/CoRN/ftc/MoreFunSeries/insert_series_conv.con". inline "cic:/CoRN/ftc/MoreFunSeries/insert_series_sum.con". (* UNEXPORTED -End Insert_Series. +End Insert_Series *) diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/MoreFunctions.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/MoreFunctions.ma index 71333c0bd..1849daa9d 100644 --- a/helm/software/matita/contribs/CoRN-Decl/ftc/MoreFunctions.ma +++ b/helm/software/matita/contribs/CoRN-Decl/ftc/MoreFunctions.ma @@ -29,7 +29,7 @@ Opaque Min Max. *) (* UNEXPORTED -Section Basic_Results. +Section Basic_Results *) (*#* *More about Functions @@ -44,7 +44,7 @@ arbitrary intervals. **Continuity *) -inline "cic:/CoRN/ftc/MoreFunctions/I.var". +inline "cic:/CoRN/ftc/MoreFunctions/Basic_Results/I.var" "Basic_Results__". (*#* Trivial stuff. @@ -57,17 +57,17 @@ inline "cic:/CoRN/ftc/MoreFunctions/Continuous_imp_inc.con". %\end{convention}% *) -inline "cic:/CoRN/ftc/MoreFunctions/cI.var". +inline "cic:/CoRN/ftc/MoreFunctions/Basic_Results/cI.var" "Basic_Results__". -inline "cic:/CoRN/ftc/MoreFunctions/F.var". +inline "cic:/CoRN/ftc/MoreFunctions/Basic_Results/F.var" "Basic_Results__". -inline "cic:/CoRN/ftc/MoreFunctions/contF.var". +inline "cic:/CoRN/ftc/MoreFunctions/Basic_Results/contF.var" "Basic_Results__". inline "cic:/CoRN/ftc/MoreFunctions/continuous_compact.con". (* begin show *) -inline "cic:/CoRN/ftc/MoreFunctions/Hinc.var". +inline "cic:/CoRN/ftc/MoreFunctions/Basic_Results/Hinc.var" "Basic_Results__". (* end show *) @@ -78,7 +78,7 @@ inline "cic:/CoRN/ftc/MoreFunctions/FNorm.con". inline "cic:/CoRN/ftc/MoreFunctions/FNorm_bnd_AbsIR.con". (* UNEXPORTED -End Basic_Results. +End Basic_Results *) (* UNEXPORTED @@ -86,26 +86,26 @@ Hint Resolve Continuous_imp_inc: included. *) (* UNEXPORTED -Section Other_Results. +Section Other_Results *) (*#* The usual stuff. *) -inline "cic:/CoRN/ftc/MoreFunctions/I.var". +inline "cic:/CoRN/ftc/MoreFunctions/Other_Results/I.var" "Other_Results__". -inline "cic:/CoRN/ftc/MoreFunctions/F.var". +inline "cic:/CoRN/ftc/MoreFunctions/Other_Results/F.var" "Other_Results__". -inline "cic:/CoRN/ftc/MoreFunctions/G.var". +inline "cic:/CoRN/ftc/MoreFunctions/Other_Results/G.var" "Other_Results__". inline "cic:/CoRN/ftc/MoreFunctions/Continuous_wd.con". (* begin show *) -inline "cic:/CoRN/ftc/MoreFunctions/contF.var". +inline "cic:/CoRN/ftc/MoreFunctions/Other_Results/contF.var" "Other_Results__". -inline "cic:/CoRN/ftc/MoreFunctions/contG.var". +inline "cic:/CoRN/ftc/MoreFunctions/Other_Results/contG.var" "Other_Results__". (* end show *) @@ -134,7 +134,7 @@ inline "cic:/CoRN/ftc/MoreFunctions/Continuous_abs.con". inline "cic:/CoRN/ftc/MoreFunctions/Continuous_recip.con". (* UNEXPORTED -End Other_Results. +End Other_Results *) (* UNEXPORTED @@ -148,27 +148,27 @@ Hint Immediate included_imp_Continuous Included_imp_Continuous: continuous. *) (* UNEXPORTED -Section Corollaries. +Section Corollaries *) -inline "cic:/CoRN/ftc/MoreFunctions/I.var". +inline "cic:/CoRN/ftc/MoreFunctions/Corollaries/I.var" "Corollaries__". -inline "cic:/CoRN/ftc/MoreFunctions/cI.var". +inline "cic:/CoRN/ftc/MoreFunctions/Corollaries/cI.var" "Corollaries__". -inline "cic:/CoRN/ftc/MoreFunctions/F.var". +inline "cic:/CoRN/ftc/MoreFunctions/Corollaries/F.var" "Corollaries__". -inline "cic:/CoRN/ftc/MoreFunctions/G.var". +inline "cic:/CoRN/ftc/MoreFunctions/Corollaries/G.var" "Corollaries__". -inline "cic:/CoRN/ftc/MoreFunctions/contF.var". +inline "cic:/CoRN/ftc/MoreFunctions/Corollaries/contF.var" "Corollaries__". -inline "cic:/CoRN/ftc/MoreFunctions/contG.var". +inline "cic:/CoRN/ftc/MoreFunctions/Corollaries/contG.var" "Corollaries__". inline "cic:/CoRN/ftc/MoreFunctions/Continuous_div.con". inline "cic:/CoRN/ftc/MoreFunctions/FNorm_wd.con". (* UNEXPORTED -End Corollaries. +End Corollaries *) (* UNEXPORTED @@ -176,10 +176,10 @@ Hint Resolve Continuous_div: continuous. *) (* UNEXPORTED -Section Sums. +Section Sums *) -inline "cic:/CoRN/ftc/MoreFunctions/I.var". +inline "cic:/CoRN/ftc/MoreFunctions/Sums/I.var" "Sums__". inline "cic:/CoRN/ftc/MoreFunctions/Continuous_Sumx.con". @@ -188,16 +188,16 @@ inline "cic:/CoRN/ftc/MoreFunctions/Continuous_Sumx.con". %\end{convention}% *) -inline "cic:/CoRN/ftc/MoreFunctions/f.var". +inline "cic:/CoRN/ftc/MoreFunctions/Sums/f.var" "Sums__". -inline "cic:/CoRN/ftc/MoreFunctions/contF.var". +inline "cic:/CoRN/ftc/MoreFunctions/Sums/contF.var" "Sums__". inline "cic:/CoRN/ftc/MoreFunctions/Continuous_Sum0.con". inline "cic:/CoRN/ftc/MoreFunctions/Continuous_Sum.con". (* UNEXPORTED -End Sums. +End Sums *) (* UNEXPORTED @@ -205,7 +205,7 @@ Hint Resolve Continuous_Sum0 Continuous_Sumx Continuous_Sum: continuous. *) (* UNEXPORTED -Section Basic_Properties. +Section Basic_Properties *) (*#* **Derivative @@ -216,15 +216,15 @@ Derivative is not that much different. %\end{convention}% *) -inline "cic:/CoRN/ftc/MoreFunctions/I.var". +inline "cic:/CoRN/ftc/MoreFunctions/Basic_Properties/I.var" "Basic_Properties__". -inline "cic:/CoRN/ftc/MoreFunctions/pI.var". +inline "cic:/CoRN/ftc/MoreFunctions/Basic_Properties/pI.var" "Basic_Properties__". -inline "cic:/CoRN/ftc/MoreFunctions/F.var". +inline "cic:/CoRN/ftc/MoreFunctions/Basic_Properties/F.var" "Basic_Properties__". -inline "cic:/CoRN/ftc/MoreFunctions/G.var". +inline "cic:/CoRN/ftc/MoreFunctions/Basic_Properties/G.var" "Basic_Properties__". -inline "cic:/CoRN/ftc/MoreFunctions/H.var". +inline "cic:/CoRN/ftc/MoreFunctions/Basic_Properties/H.var" "Basic_Properties__". inline "cic:/CoRN/ftc/MoreFunctions/Derivative_wdl.con". @@ -241,7 +241,7 @@ inline "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_Continuous.con". inline "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_Continuous'.con". (* UNEXPORTED -End Basic_Properties. +End Basic_Properties *) (* UNEXPORTED @@ -254,29 +254,29 @@ Hint Immediate Derivative_imp_Continuous Derivative_imp_Continuous': *) (* UNEXPORTED -Section More_Results. +Section More_Results *) -inline "cic:/CoRN/ftc/MoreFunctions/I.var". +inline "cic:/CoRN/ftc/MoreFunctions/More_Results/I.var" "More_Results__". -inline "cic:/CoRN/ftc/MoreFunctions/pI.var". +inline "cic:/CoRN/ftc/MoreFunctions/More_Results/pI.var" "More_Results__". (*#* %\begin{convention}% Assume that [F'] and [G'] are derivatives of [F] and [G], respectively, in [I]. %\end{convention}% *) -inline "cic:/CoRN/ftc/MoreFunctions/F.var". +inline "cic:/CoRN/ftc/MoreFunctions/More_Results/F.var" "More_Results__". -inline "cic:/CoRN/ftc/MoreFunctions/F'.var". +inline "cic:/CoRN/ftc/MoreFunctions/More_Results/F'.var" "More_Results__". -inline "cic:/CoRN/ftc/MoreFunctions/G.var". +inline "cic:/CoRN/ftc/MoreFunctions/More_Results/G.var" "More_Results__". -inline "cic:/CoRN/ftc/MoreFunctions/G'.var". +inline "cic:/CoRN/ftc/MoreFunctions/More_Results/G'.var" "More_Results__". -inline "cic:/CoRN/ftc/MoreFunctions/derF.var". +inline "cic:/CoRN/ftc/MoreFunctions/More_Results/derF.var" "More_Results__". -inline "cic:/CoRN/ftc/MoreFunctions/derG.var". +inline "cic:/CoRN/ftc/MoreFunctions/More_Results/derG.var" "More_Results__". inline "cic:/CoRN/ftc/MoreFunctions/included_imp_Derivative.con". @@ -301,58 +301,58 @@ inline "cic:/CoRN/ftc/MoreFunctions/Derivative_nth.con". inline "cic:/CoRN/ftc/MoreFunctions/Derivative_recip.con". (* UNEXPORTED -End More_Results. +End More_Results *) (* UNEXPORTED -Section More_Corollaries. +Section More_Corollaries *) -inline "cic:/CoRN/ftc/MoreFunctions/I.var". +inline "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/I.var" "More_Corollaries__". -inline "cic:/CoRN/ftc/MoreFunctions/pI.var". +inline "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/pI.var" "More_Corollaries__". -inline "cic:/CoRN/ftc/MoreFunctions/F.var". +inline "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/F.var" "More_Corollaries__". -inline "cic:/CoRN/ftc/MoreFunctions/F'.var". +inline "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/F'.var" "More_Corollaries__". -inline "cic:/CoRN/ftc/MoreFunctions/G.var". +inline "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/G.var" "More_Corollaries__". -inline "cic:/CoRN/ftc/MoreFunctions/G'.var". +inline "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/G'.var" "More_Corollaries__". -inline "cic:/CoRN/ftc/MoreFunctions/derF.var". +inline "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/derF.var" "More_Corollaries__". -inline "cic:/CoRN/ftc/MoreFunctions/derG.var". +inline "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/derG.var" "More_Corollaries__". (* begin show *) -inline "cic:/CoRN/ftc/MoreFunctions/Gbnd.var". +inline "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/Gbnd.var" "More_Corollaries__". (* end show *) inline "cic:/CoRN/ftc/MoreFunctions/Derivative_div.con". (* UNEXPORTED -End More_Corollaries. +End More_Corollaries *) (* UNEXPORTED -Section More_Sums. +Section More_Sums *) -inline "cic:/CoRN/ftc/MoreFunctions/I.var". +inline "cic:/CoRN/ftc/MoreFunctions/More_Sums/I.var" "More_Sums__". -inline "cic:/CoRN/ftc/MoreFunctions/pI.var". +inline "cic:/CoRN/ftc/MoreFunctions/More_Sums/pI.var" "More_Sums__". inline "cic:/CoRN/ftc/MoreFunctions/Derivative_Sumx.con". (* begin show *) -inline "cic:/CoRN/ftc/MoreFunctions/f.var". +inline "cic:/CoRN/ftc/MoreFunctions/More_Sums/f.var" "More_Sums__". -inline "cic:/CoRN/ftc/MoreFunctions/f'.var". +inline "cic:/CoRN/ftc/MoreFunctions/More_Sums/f'.var" "More_Sums__". -inline "cic:/CoRN/ftc/MoreFunctions/derF.var". +inline "cic:/CoRN/ftc/MoreFunctions/More_Sums/derF.var" "More_Sums__". (* end show *) @@ -361,11 +361,11 @@ inline "cic:/CoRN/ftc/MoreFunctions/Derivative_Sum0.con". inline "cic:/CoRN/ftc/MoreFunctions/Derivative_Sum.con". (* UNEXPORTED -End More_Sums. +End More_Sums *) (* UNEXPORTED -Section Diffble_Basic_Properties. +Section Diffble_Basic_Properties *) (*#* **Differentiability @@ -373,9 +373,9 @@ Section Diffble_Basic_Properties. Mutatis mutandis for differentiability. *) -inline "cic:/CoRN/ftc/MoreFunctions/I.var". +inline "cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/I.var" "Diffble_Basic_Properties__". -inline "cic:/CoRN/ftc/MoreFunctions/pI.var". +inline "cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/pI.var" "Diffble_Basic_Properties__". inline "cic:/CoRN/ftc/MoreFunctions/Diffble_imp_inc.con". @@ -383,13 +383,13 @@ inline "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_Diffble.con". inline "cic:/CoRN/ftc/MoreFunctions/Diffble_wd.con". -inline "cic:/CoRN/ftc/MoreFunctions/F.var". +inline "cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/F.var" "Diffble_Basic_Properties__". -inline "cic:/CoRN/ftc/MoreFunctions/G.var". +inline "cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/G.var" "Diffble_Basic_Properties__". -inline "cic:/CoRN/ftc/MoreFunctions/diffF.var". +inline "cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/diffF.var" "Diffble_Basic_Properties__". -inline "cic:/CoRN/ftc/MoreFunctions/diffG.var". +inline "cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/diffG.var" "Diffble_Basic_Properties__". (*#* %\begin{convention}% Assume [F] and [G] are differentiable in [I]. @@ -419,7 +419,7 @@ inline "cic:/CoRN/ftc/MoreFunctions/Diffble_scal.con". inline "cic:/CoRN/ftc/MoreFunctions/Diffble_recip.con". (* UNEXPORTED -End Diffble_Basic_Properties. +End Diffble_Basic_Properties *) (* UNEXPORTED @@ -427,20 +427,20 @@ Hint Immediate Diffble_imp_inc: included. *) (* UNEXPORTED -Section Diffble_Corollaries. +Section Diffble_Corollaries *) -inline "cic:/CoRN/ftc/MoreFunctions/I.var". +inline "cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/I.var" "Diffble_Corollaries__". -inline "cic:/CoRN/ftc/MoreFunctions/pI.var". +inline "cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/pI.var" "Diffble_Corollaries__". -inline "cic:/CoRN/ftc/MoreFunctions/F.var". +inline "cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/F.var" "Diffble_Corollaries__". -inline "cic:/CoRN/ftc/MoreFunctions/G.var". +inline "cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/G.var" "Diffble_Corollaries__". -inline "cic:/CoRN/ftc/MoreFunctions/diffF.var". +inline "cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/diffF.var" "Diffble_Corollaries__". -inline "cic:/CoRN/ftc/MoreFunctions/diffG.var". +inline "cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/diffG.var" "Diffble_Corollaries__". inline "cic:/CoRN/ftc/MoreFunctions/Diffble_div.con". @@ -451,11 +451,11 @@ inline "cic:/CoRN/ftc/MoreFunctions/Diffble_Sumx.con". inline "cic:/CoRN/ftc/MoreFunctions/Diffble_Sum.con". (* UNEXPORTED -End Diffble_Corollaries. +End Diffble_Corollaries *) (* UNEXPORTED -Section Nth_Derivative. +Section Nth_Derivative *) (*#* **Nth Derivative @@ -463,12 +463,12 @@ 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. *) -inline "cic:/CoRN/ftc/MoreFunctions/I.var". +inline "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/I.var" "Nth_Derivative__". -inline "cic:/CoRN/ftc/MoreFunctions/pI.var". +inline "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/pI.var" "Nth_Derivative__". (* UNEXPORTED -Section Definitions. +Section Definitions *) (*#* @@ -476,11 +476,11 @@ Section Definitions. %\end{convention}% *) -inline "cic:/CoRN/ftc/MoreFunctions/n.var". +inline "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Definitions/n.var" "Nth_Derivative__Definitions__". -inline "cic:/CoRN/ftc/MoreFunctions/F.var". +inline "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Definitions/F.var" "Nth_Derivative__Definitions__". -inline "cic:/CoRN/ftc/MoreFunctions/diffF.var". +inline "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Definitions/diffF.var" "Nth_Derivative__Definitions__". inline "cic:/CoRN/ftc/MoreFunctions/N_Deriv_fun.con". @@ -496,11 +496,11 @@ inline "cic:/CoRN/ftc/MoreFunctions/N_Deriv_wd.con". inline "cic:/CoRN/ftc/MoreFunctions/N_Deriv.con". (* UNEXPORTED -End Definitions. +End Definitions *) (* UNEXPORTED -Section Basic_Results. +Section Basic_Results *) (*#* @@ -542,11 +542,11 @@ inline "cic:/CoRN/ftc/MoreFunctions/Included_imp_Diffble_n.con". inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_plus.con". (* UNEXPORTED -End Basic_Results. +End Basic_Results *) (* UNEXPORTED -Section More_Results. +Section More_Results *) (*#* @@ -570,22 +570,22 @@ inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_O.con". inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_Sn.con". (* UNEXPORTED -End More_Results. +End More_Results *) (* UNEXPORTED -Section Derivating_Diffble. +Section Derivating_Diffble *) (*#* As a special case we get a differentiation operator%\ldots%#...# *) -inline "cic:/CoRN/ftc/MoreFunctions/F.var". +inline "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Derivating_Diffble/F.var" "Nth_Derivative__Derivating_Diffble__". (* begin show *) -inline "cic:/CoRN/ftc/MoreFunctions/diffF.var". +inline "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Derivating_Diffble/diffF.var" "Nth_Derivative__Derivating_Diffble__". (* end show *) @@ -594,11 +594,11 @@ inline "cic:/CoRN/ftc/MoreFunctions/Diffble_imp_Diffble_n.con". inline "cic:/CoRN/ftc/MoreFunctions/Deriv.con". (* UNEXPORTED -End Derivating_Diffble. +End Derivating_Diffble *) (* UNEXPORTED -Section Corollaries. +Section Corollaries *) (*#* @@ -620,11 +620,11 @@ inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Continuous.con". inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Continuous'.con". (* UNEXPORTED -End Corollaries. +End Corollaries *) (* UNEXPORTED -End Nth_Derivative. +End Nth_Derivative *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/MoreIntegrals.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/MoreIntegrals.ma index 50a087bf7..080394841 100644 --- a/helm/software/matita/contribs/CoRN-Decl/ftc/MoreIntegrals.ma +++ b/helm/software/matita/contribs/CoRN-Decl/ftc/MoreIntegrals.ma @@ -25,7 +25,7 @@ include "ftc/Integral.ma". include "ftc/MoreFunctions.ma". (* UNEXPORTED -Section Lemmas. +Section Lemmas *) (*#* printing Integral %\ensuremath{\int}% #∫# *) @@ -48,22 +48,22 @@ partial functions continuous in [[Min(a,b),Max(a,b)]]. Before we define the new integral we need to some trivial interval inclusions. *) -inline "cic:/CoRN/ftc/MoreIntegrals/a.var". +inline "cic:/CoRN/ftc/MoreIntegrals/Lemmas/a.var" "Lemmas__". -inline "cic:/CoRN/ftc/MoreIntegrals/b.var". +inline "cic:/CoRN/ftc/MoreIntegrals/Lemmas/b.var" "Lemmas__". -inline "cic:/CoRN/ftc/MoreIntegrals/Hab.var". +inline "cic:/CoRN/ftc/MoreIntegrals/Lemmas/Hab.var" "Lemmas__". inline "cic:/CoRN/ftc/MoreIntegrals/compact_inc_Min_lft.con". inline "cic:/CoRN/ftc/MoreIntegrals/compact_inc_Min_rht.con". (* UNEXPORTED -End Lemmas. +End Lemmas *) (* UNEXPORTED -Section Definitions. +Section Definitions *) (*#* @@ -74,15 +74,15 @@ classical definition, and it collapses to the old one in the case [a [<=] b]. *) -inline "cic:/CoRN/ftc/MoreIntegrals/a.var". +inline "cic:/CoRN/ftc/MoreIntegrals/Definitions/a.var" "Definitions__". -inline "cic:/CoRN/ftc/MoreIntegrals/b.var". +inline "cic:/CoRN/ftc/MoreIntegrals/Definitions/b.var" "Definitions__". -inline "cic:/CoRN/ftc/MoreIntegrals/Hab.var". +inline "cic:/CoRN/ftc/MoreIntegrals/Definitions/Hab.var" "Definitions__". -inline "cic:/CoRN/ftc/MoreIntegrals/F.var". +inline "cic:/CoRN/ftc/MoreIntegrals/Definitions/F.var" "Definitions__". -inline "cic:/CoRN/ftc/MoreIntegrals/HF.var". +inline "cic:/CoRN/ftc/MoreIntegrals/Definitions/HF.var" "Definitions__". inline "cic:/CoRN/ftc/MoreIntegrals/Integral_inc1.con". @@ -93,7 +93,7 @@ inline "cic:/CoRN/ftc/MoreIntegrals/Integral.con". inline "cic:/CoRN/ftc/MoreIntegrals/Integral_integral.con". (* UNEXPORTED -End Definitions. +End Definitions *) (* UNEXPORTED @@ -101,7 +101,7 @@ Implicit Arguments Integral [a b Hab F]. *) (* UNEXPORTED -Section Properties_of_Integral. +Section Properties_of_Integral *) (*#* **Properties of the Integral @@ -110,19 +110,19 @@ All our old properties carry over to this new definition---and some new ones, too. We begin with (strong) extensionality. *) -inline "cic:/CoRN/ftc/MoreIntegrals/a.var". +inline "cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/a.var" "Properties_of_Integral__". -inline "cic:/CoRN/ftc/MoreIntegrals/b.var". +inline "cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/b.var" "Properties_of_Integral__". -inline "cic:/CoRN/ftc/MoreIntegrals/Hab.var". +inline "cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/Hab.var" "Properties_of_Integral__". -inline "cic:/CoRN/ftc/MoreIntegrals/F.var". +inline "cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/F.var" "Properties_of_Integral__". -inline "cic:/CoRN/ftc/MoreIntegrals/G.var". +inline "cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/G.var" "Properties_of_Integral__". -inline "cic:/CoRN/ftc/MoreIntegrals/contF.var". +inline "cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/contF.var" "Properties_of_Integral__". -inline "cic:/CoRN/ftc/MoreIntegrals/contG.var". +inline "cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/contG.var" "Properties_of_Integral__". inline "cic:/CoRN/ftc/MoreIntegrals/Integral_strext.con". @@ -161,11 +161,11 @@ And the norm provides an upper bound for the absolute value of the integral. inline "cic:/CoRN/ftc/MoreIntegrals/Integral_leEq_norm.con". (* UNEXPORTED -End Properties_of_Integral. +End Properties_of_Integral *) (* UNEXPORTED -Section More_Properties. +Section More_Properties *) (*#* @@ -183,77 +183,77 @@ And now we can prove the addition law for domains with our general operator. %\end{convention}% *) -inline "cic:/CoRN/ftc/MoreIntegrals/a.var". +inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/a.var" "More_Properties__". -inline "cic:/CoRN/ftc/MoreIntegrals/b.var". +inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/b.var" "More_Properties__". -inline "cic:/CoRN/ftc/MoreIntegrals/c.var". +inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/c.var" "More_Properties__". (* begin show *) -inline "cic:/CoRN/ftc/MoreIntegrals/Hab'.var". +inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Hab'.var" "More_Properties__". -inline "cic:/CoRN/ftc/MoreIntegrals/Hac'.var". +inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Hac'.var" "More_Properties__". -inline "cic:/CoRN/ftc/MoreIntegrals/Hcb'.var". +inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Hcb'.var" "More_Properties__". -inline "cic:/CoRN/ftc/MoreIntegrals/Habc'.var". +inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc'.var" "More_Properties__". (* end show *) -inline "cic:/CoRN/ftc/MoreIntegrals/F.var". +inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/F.var" "More_Properties__". (* begin show *) -inline "cic:/CoRN/ftc/MoreIntegrals/Hab.var". +inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Hab.var" "More_Properties__". -inline "cic:/CoRN/ftc/MoreIntegrals/Hac.var". +inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Hac.var" "More_Properties__". -inline "cic:/CoRN/ftc/MoreIntegrals/Hcb.var". +inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Hcb.var" "More_Properties__". -inline "cic:/CoRN/ftc/MoreIntegrals/Habc.var". +inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc.var" "More_Properties__". (* end show *) (* begin hide *) -inline "cic:/CoRN/ftc/MoreIntegrals/le_abc_ab.con". +inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_abc_ab.con" "More_Properties__". -inline "cic:/CoRN/ftc/MoreIntegrals/le_abc_ac.con". +inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_abc_ac.con" "More_Properties__". -inline "cic:/CoRN/ftc/MoreIntegrals/le_abc_cb.con". +inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_abc_cb.con" "More_Properties__". -inline "cic:/CoRN/ftc/MoreIntegrals/le_abc_a.con". +inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_abc_a.con" "More_Properties__". -inline "cic:/CoRN/ftc/MoreIntegrals/le_abc_b.con". +inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_abc_b.con" "More_Properties__". -inline "cic:/CoRN/ftc/MoreIntegrals/le_abc_c.con". +inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_abc_c.con" "More_Properties__". -inline "cic:/CoRN/ftc/MoreIntegrals/le_ab_a.con". +inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_ab_a.con" "More_Properties__". -inline "cic:/CoRN/ftc/MoreIntegrals/le_cb_c.con". +inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_cb_c.con" "More_Properties__". -inline "cic:/CoRN/ftc/MoreIntegrals/le_ac_a.con". +inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_ac_a.con" "More_Properties__". -inline "cic:/CoRN/ftc/MoreIntegrals/le_ab_b.con". +inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_ab_b.con" "More_Properties__". -inline "cic:/CoRN/ftc/MoreIntegrals/le_cb_b.con". +inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_cb_b.con" "More_Properties__". -inline "cic:/CoRN/ftc/MoreIntegrals/le_ac_c.con". +inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_ac_c.con" "More_Properties__". -inline "cic:/CoRN/ftc/MoreIntegrals/Habc_abc.con". +inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_abc.con" "More_Properties__". -inline "cic:/CoRN/ftc/MoreIntegrals/Habc_ab.con". +inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_ab.con" "More_Properties__". -inline "cic:/CoRN/ftc/MoreIntegrals/Habc_ac.con". +inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_ac.con" "More_Properties__". -inline "cic:/CoRN/ftc/MoreIntegrals/Habc_cb.con". +inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_cb.con" "More_Properties__". -inline "cic:/CoRN/ftc/MoreIntegrals/Habc_a.con". +inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_a.con" "More_Properties__". -inline "cic:/CoRN/ftc/MoreIntegrals/Habc_b.con". +inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_b.con" "More_Properties__". -inline "cic:/CoRN/ftc/MoreIntegrals/Habc_c.con". +inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_c.con" "More_Properties__". (* end hide *) @@ -265,22 +265,22 @@ continuity of [F] in the interval [[Min(a,b,c),Max(a,b,c)]]) must be assumed. *) (* UNEXPORTED -End More_Properties. +End More_Properties *) (* UNEXPORTED -Section Corollaries. +Section Corollaries *) -inline "cic:/CoRN/ftc/MoreIntegrals/a.var". +inline "cic:/CoRN/ftc/MoreIntegrals/Corollaries/a.var" "Corollaries__". -inline "cic:/CoRN/ftc/MoreIntegrals/b.var". +inline "cic:/CoRN/ftc/MoreIntegrals/Corollaries/b.var" "Corollaries__". -inline "cic:/CoRN/ftc/MoreIntegrals/Hab.var". +inline "cic:/CoRN/ftc/MoreIntegrals/Corollaries/Hab.var" "Corollaries__". -inline "cic:/CoRN/ftc/MoreIntegrals/F.var". +inline "cic:/CoRN/ftc/MoreIntegrals/Corollaries/F.var" "Corollaries__". -inline "cic:/CoRN/ftc/MoreIntegrals/contF.var". +inline "cic:/CoRN/ftc/MoreIntegrals/Corollaries/contF.var" "Corollaries__". (*#* As a corollary, we get the following rule: *) @@ -293,7 +293,7 @@ inline "cic:/CoRN/ftc/MoreIntegrals/Integral_less_norm.con". inline "cic:/CoRN/ftc/MoreIntegrals/ub_Integral.con". (* UNEXPORTED -End Corollaries. +End Corollaries *) inline "cic:/CoRN/ftc/MoreIntegrals/Integral_ap_zero.con". diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/MoreIntervals.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/MoreIntervals.ma index 40719fd59..bf25f0f7f 100644 --- a/helm/software/matita/contribs/CoRN-Decl/ftc/MoreIntervals.ma +++ b/helm/software/matita/contribs/CoRN-Decl/ftc/MoreIntervals.ma @@ -27,7 +27,7 @@ Opaque Min Max. *) (* UNEXPORTED -Section Intervals. +Section Intervals *) (*#* printing realline %\ensuremath{\RR}% #(-∞,+∞)# *) @@ -186,7 +186,7 @@ Finally, all intervals are characterized by well defined predicates. inline "cic:/CoRN/ftc/MoreIntervals/iprop_wd.con". (* UNEXPORTED -End Intervals. +End Intervals *) (* UNEXPORTED @@ -198,11 +198,11 @@ Implicit Arguments Rend [I]. *) (* UNEXPORTED -Section Compact_Constructions. +Section Compact_Constructions *) (* UNEXPORTED -Section Single_Compact_Interval. +Section Single_Compact_Interval *) (*#* **Constructions with Compact Intervals @@ -216,13 +216,13 @@ such that [P(x)] holds. %\end{convention}% *) -inline "cic:/CoRN/ftc/MoreIntervals/P.var". +inline "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Single_Compact_Interval/P.var" "Compact_Constructions__Single_Compact_Interval__". -inline "cic:/CoRN/ftc/MoreIntervals/wdP.var". +inline "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Single_Compact_Interval/wdP.var" "Compact_Constructions__Single_Compact_Interval__". -inline "cic:/CoRN/ftc/MoreIntervals/x.var". +inline "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Single_Compact_Interval/x.var" "Compact_Constructions__Single_Compact_Interval__". -inline "cic:/CoRN/ftc/MoreIntervals/Hx.var". +inline "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Single_Compact_Interval/Hx.var" "Compact_Constructions__Single_Compact_Interval__". inline "cic:/CoRN/ftc/MoreIntervals/compact_single.con". @@ -237,7 +237,7 @@ inline "cic:/CoRN/ftc/MoreIntervals/compact_single_pt.con". inline "cic:/CoRN/ftc/MoreIntervals/compact_single_inc.con". (* UNEXPORTED -End Single_Compact_Interval. +End Single_Compact_Interval *) (*#* @@ -255,34 +255,34 @@ I$#x∈[a,b]⊆I#. *) (* UNEXPORTED -Section Proper_Compact_with_One_or_Two_Points. +Section Proper_Compact_with_One_or_Two_Points *) (* begin hide *) -inline "cic:/CoRN/ftc/MoreIntervals/cip1'.con". +inline "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip1'.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__". -inline "cic:/CoRN/ftc/MoreIntervals/cip1''.con". +inline "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip1''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__". -inline "cic:/CoRN/ftc/MoreIntervals/cip1'''.con". +inline "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip1'''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__". -inline "cic:/CoRN/ftc/MoreIntervals/cip1''''.con". +inline "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip1''''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__". -inline "cic:/CoRN/ftc/MoreIntervals/cip2.con". +inline "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip2.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__". -inline "cic:/CoRN/ftc/MoreIntervals/cip2'.con". +inline "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip2'.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__". -inline "cic:/CoRN/ftc/MoreIntervals/cip2''.con". +inline "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip2''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__". -inline "cic:/CoRN/ftc/MoreIntervals/cip2'''.con". +inline "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip2'''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__". -inline "cic:/CoRN/ftc/MoreIntervals/cip3.con". +inline "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip3.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__". -inline "cic:/CoRN/ftc/MoreIntervals/cip3'.con". +inline "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip3'.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__". -inline "cic:/CoRN/ftc/MoreIntervals/cip3''.con". +inline "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip3''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__". -inline "cic:/CoRN/ftc/MoreIntervals/cip3'''.con". +inline "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip3'''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__". (* end hide *) @@ -350,7 +350,7 @@ inline "cic:/CoRN/ftc/MoreIntervals/compact_in_interval_x_rht.con". inline "cic:/CoRN/ftc/MoreIntervals/compact_in_interval_y_rht.con". (* UNEXPORTED -End Proper_Compact_with_One_or_Two_Points. +End Proper_Compact_with_One_or_Two_Points *) (*#* @@ -370,11 +370,11 @@ $[a,b]\subseteq[a',b']\subseteq J$#[a,b]⊆[a',b']⊆J#. inline "cic:/CoRN/ftc/MoreIntervals/compact_proper_in_interval.con". (* UNEXPORTED -End Compact_Constructions. +End Compact_Constructions *) (* UNEXPORTED -Section Functions. +Section Functions *) (*#* **Properties of Functions in Intervals @@ -389,9 +389,9 @@ previously defined concepts. %\end{convention}% *) -inline "cic:/CoRN/ftc/MoreIntervals/n.var". +inline "cic:/CoRN/ftc/MoreIntervals/Functions/n.var" "Functions__". -inline "cic:/CoRN/ftc/MoreIntervals/I.var". +inline "cic:/CoRN/ftc/MoreIntervals/Functions/I.var" "Functions__". inline "cic:/CoRN/ftc/MoreIntervals/Continuous.con". @@ -404,11 +404,11 @@ inline "cic:/CoRN/ftc/MoreIntervals/Derivative_n.con". inline "cic:/CoRN/ftc/MoreIntervals/Diffble_n.con". (* UNEXPORTED -End Functions. +End Functions *) (* UNEXPORTED -Section Reflexivity_Properties. +Section Reflexivity_Properties *) (*#* @@ -428,11 +428,11 @@ inline "cic:/CoRN/ftc/MoreIntervals/Diffble_Int.con". inline "cic:/CoRN/ftc/MoreIntervals/Int_Diffble.con". (* UNEXPORTED -End Reflexivity_Properties. +End Reflexivity_Properties *) (* UNEXPORTED -Section Lemmas. +Section Lemmas *) (*#* @@ -446,7 +446,7 @@ inline "cic:/CoRN/ftc/MoreIntervals/included_Feq''.con". inline "cic:/CoRN/ftc/MoreIntervals/included_Feq'.con". (* UNEXPORTED -End Lemmas. +End Lemmas *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/NthDerivative.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/NthDerivative.ma index 0900e8703..dbcbf20ac 100644 --- a/helm/software/matita/contribs/CoRN-Decl/ftc/NthDerivative.ma +++ b/helm/software/matita/contribs/CoRN-Decl/ftc/NthDerivative.ma @@ -23,7 +23,7 @@ include "CoRN.ma". include "ftc/Differentiability.ma". (* UNEXPORTED -Section Nth_Derivative. +Section Nth_Derivative *) (*#* *Nth Derivative @@ -42,17 +42,17 @@ We now study higher order differentiability. We first define what we mean by the derivative of order [n] of a function. *) -inline "cic:/CoRN/ftc/NthDerivative/a.var". +inline "cic:/CoRN/ftc/NthDerivative/Nth_Derivative/a.var" "Nth_Derivative__". -inline "cic:/CoRN/ftc/NthDerivative/b.var". +inline "cic:/CoRN/ftc/NthDerivative/Nth_Derivative/b.var" "Nth_Derivative__". -inline "cic:/CoRN/ftc/NthDerivative/Hab'.var". +inline "cic:/CoRN/ftc/NthDerivative/Nth_Derivative/Hab'.var" "Nth_Derivative__". (* begin hide *) -inline "cic:/CoRN/ftc/NthDerivative/Hab.con". +inline "cic:/CoRN/ftc/NthDerivative/Nth_Derivative/Hab.con" "Nth_Derivative__". -inline "cic:/CoRN/ftc/NthDerivative/I.con". +inline "cic:/CoRN/ftc/NthDerivative/Nth_Derivative/I.con" "Nth_Derivative__". (* end hide *) @@ -68,7 +68,7 @@ to be [n] times differentiable instead of quantifying over the inline "cic:/CoRN/ftc/NthDerivative/Diffble_I_n.con". (* UNEXPORTED -End Nth_Derivative. +End Nth_Derivative *) (* UNEXPORTED @@ -80,7 +80,7 @@ Implicit Arguments Diffble_I_n [a b]. *) (* UNEXPORTED -Section Trivia. +Section Trivia *) (*#* **Trivia @@ -88,17 +88,17 @@ Section Trivia. These are the expected extensionality and uniqueness results. *) -inline "cic:/CoRN/ftc/NthDerivative/a.var". +inline "cic:/CoRN/ftc/NthDerivative/Trivia/a.var" "Trivia__". -inline "cic:/CoRN/ftc/NthDerivative/b.var". +inline "cic:/CoRN/ftc/NthDerivative/Trivia/b.var" "Trivia__". -inline "cic:/CoRN/ftc/NthDerivative/Hab'.var". +inline "cic:/CoRN/ftc/NthDerivative/Trivia/Hab'.var" "Trivia__". (* begin hide *) -inline "cic:/CoRN/ftc/NthDerivative/Hab.con". +inline "cic:/CoRN/ftc/NthDerivative/Trivia/Hab.con" "Trivia__". -inline "cic:/CoRN/ftc/NthDerivative/I.con". +inline "cic:/CoRN/ftc/NthDerivative/Trivia/I.con" "Trivia__". (* end hide *) @@ -111,11 +111,11 @@ inline "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_wdl.con". inline "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_unique.con". (* UNEXPORTED -End Trivia. +End Trivia *) (* UNEXPORTED -Section Basic_Results. +Section Basic_Results *) (*#* **Basic Results @@ -126,17 +126,17 @@ the relation of [n] times derivative, but focus rather on the definition of [Diffble_I_n]. *) -inline "cic:/CoRN/ftc/NthDerivative/a.var". +inline "cic:/CoRN/ftc/NthDerivative/Basic_Results/a.var" "Basic_Results__". -inline "cic:/CoRN/ftc/NthDerivative/b.var". +inline "cic:/CoRN/ftc/NthDerivative/Basic_Results/b.var" "Basic_Results__". -inline "cic:/CoRN/ftc/NthDerivative/Hab'.var". +inline "cic:/CoRN/ftc/NthDerivative/Basic_Results/Hab'.var" "Basic_Results__". (* begin hide *) -inline "cic:/CoRN/ftc/NthDerivative/Hab.con". +inline "cic:/CoRN/ftc/NthDerivative/Basic_Results/Hab.con" "Basic_Results__". -inline "cic:/CoRN/ftc/NthDerivative/I.con". +inline "cic:/CoRN/ftc/NthDerivative/Basic_Results/I.con" "Basic_Results__". (* end hide *) @@ -187,7 +187,7 @@ inline "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_imp_inc.con". inline "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_imp_inc'.con". (* UNEXPORTED -Section aux. +Section aux *) (*#* @@ -196,11 +196,11 @@ First order differentiability is just a special case. (* begin show *) -inline "cic:/CoRN/ftc/NthDerivative/F.var". +inline "cic:/CoRN/ftc/NthDerivative/Basic_Results/aux/F.var" "Basic_Results__aux__". -inline "cic:/CoRN/ftc/NthDerivative/diffF.var". +inline "cic:/CoRN/ftc/NthDerivative/Basic_Results/aux/diffF.var" "Basic_Results__aux__". -inline "cic:/CoRN/ftc/NthDerivative/diffFn.var". +inline "cic:/CoRN/ftc/NthDerivative/Basic_Results/aux/diffFn.var" "Basic_Results__aux__". (* end show *) @@ -209,7 +209,7 @@ inline "cic:/CoRN/ftc/NthDerivative/deriv_1_deriv.con". inline "cic:/CoRN/ftc/NthDerivative/deriv_1_deriv'.con". (* UNEXPORTED -End aux. +End aux *) (*#* @@ -227,24 +227,24 @@ And finally we have an addition rule for the order of the derivative. inline "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_plus.con". (* UNEXPORTED -End Basic_Results. +End Basic_Results *) (* UNEXPORTED -Section More_Results. +Section More_Results *) -inline "cic:/CoRN/ftc/NthDerivative/a.var". +inline "cic:/CoRN/ftc/NthDerivative/More_Results/a.var" "More_Results__". -inline "cic:/CoRN/ftc/NthDerivative/b.var". +inline "cic:/CoRN/ftc/NthDerivative/More_Results/b.var" "More_Results__". -inline "cic:/CoRN/ftc/NthDerivative/Hab'.var". +inline "cic:/CoRN/ftc/NthDerivative/More_Results/Hab'.var" "More_Results__". (* begin hide *) -inline "cic:/CoRN/ftc/NthDerivative/Hab.con". +inline "cic:/CoRN/ftc/NthDerivative/More_Results/Hab.con" "More_Results__". -inline "cic:/CoRN/ftc/NthDerivative/I.con". +inline "cic:/CoRN/ftc/NthDerivative/More_Results/I.con" "More_Results__". (* end hide *) @@ -279,11 +279,11 @@ inline "cic:/CoRN/ftc/NthDerivative/n_Sn_deriv.con". inline "cic:/CoRN/ftc/NthDerivative/n_deriv_plus.con". (* UNEXPORTED -End More_Results. +End More_Results *) (* UNEXPORTED -Section More_on_n_deriv. +Section More_on_n_deriv *) (*#* @@ -297,6 +297,6 @@ inline "cic:/CoRN/ftc/NthDerivative/n_deriv_I_wd''.con". inline "cic:/CoRN/ftc/NthDerivative/n_deriv_I_strext'.con". (* UNEXPORTED -End More_on_n_deriv. +End More_on_n_deriv *) diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/PartFunEquality.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/PartFunEquality.ma index c3b8f1c56..833fe2bc9 100644 --- a/helm/software/matita/contribs/CoRN-Decl/ftc/PartFunEquality.ma +++ b/helm/software/matita/contribs/CoRN-Decl/ftc/PartFunEquality.ma @@ -27,7 +27,7 @@ include "reals/Intervals.ma". include "tactics/DiffTactics1.ma". (* UNEXPORTED -Section Definitions. +Section Definitions *) (*#* *Equality of Partial Functions @@ -71,11 +71,11 @@ than in an existentially quantified one. *) (* UNEXPORTED -End Definitions. +End Definitions *) (* UNEXPORTED -Section Equality_Results. +Section Equality_Results *) (*#* **Properties of Inclusion @@ -87,21 +87,21 @@ by [P] and [Q], respectively, the domains of [F] and [G]. %\end{convention}% *) -inline "cic:/CoRN/ftc/PartFunEquality/I.var". +inline "cic:/CoRN/ftc/PartFunEquality/Equality_Results/I.var" "Equality_Results__". -inline "cic:/CoRN/ftc/PartFunEquality/F.var". +inline "cic:/CoRN/ftc/PartFunEquality/Equality_Results/F.var" "Equality_Results__". -inline "cic:/CoRN/ftc/PartFunEquality/G.var". +inline "cic:/CoRN/ftc/PartFunEquality/Equality_Results/G.var" "Equality_Results__". (* begin hide *) -inline "cic:/CoRN/ftc/PartFunEquality/P.con". +inline "cic:/CoRN/ftc/PartFunEquality/Equality_Results/P.con" "Equality_Results__". -inline "cic:/CoRN/ftc/PartFunEquality/Q.con". +inline "cic:/CoRN/ftc/PartFunEquality/Equality_Results/Q.con" "Equality_Results__". (* end hide *) -inline "cic:/CoRN/ftc/PartFunEquality/R.var". +inline "cic:/CoRN/ftc/PartFunEquality/Equality_Results/R.var" "Equality_Results__". (*#* We start with two lemmas which make it much easier to prove and use @@ -115,7 +115,7 @@ inline "cic:/CoRN/ftc/PartFunEquality/Feq_imp_eq.con". inline "cic:/CoRN/ftc/PartFunEquality/included_IR.con". (* UNEXPORTED -End Equality_Results. +End Equality_Results *) (* UNEXPORTED @@ -123,7 +123,7 @@ Hint Resolve included_IR : included. *) (* UNEXPORTED -Section Some_More. +Section Some_More *) (*#* @@ -133,15 +133,15 @@ If two function coincide on a given subset then they coincide in any smaller sub inline "cic:/CoRN/ftc/PartFunEquality/included_Feq.con". (* UNEXPORTED -End Some_More. +End Some_More *) (* UNEXPORTED -Section Away_from_Zero. +Section Away_from_Zero *) (* UNEXPORTED -Section Definitions. +Section Definitions *) (*#* **Away from Zero @@ -156,13 +156,13 @@ the domain of [F]. %\end{convention}% *) -inline "cic:/CoRN/ftc/PartFunEquality/I.var". +inline "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Definitions/I.var" "Away_from_Zero__Definitions__". -inline "cic:/CoRN/ftc/PartFunEquality/F.var". +inline "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Definitions/F.var" "Away_from_Zero__Definitions__". (* begin hide *) -inline "cic:/CoRN/ftc/PartFunEquality/P.con". +inline "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Definitions/P.con" "Away_from_Zero__Definitions__". (* end hide *) @@ -174,7 +174,7 @@ If [F] is bounded away from zero in [I] then [F] is necessarily apart from zero (* begin show *) -inline "cic:/CoRN/ftc/PartFunEquality/Hf.var". +inline "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Definitions/Hf.var" "Away_from_Zero__Definitions__". (* end show *) @@ -185,7 +185,7 @@ inline "cic:/CoRN/ftc/PartFunEquality/bnd_imp_inc_recip.con". inline "cic:/CoRN/ftc/PartFunEquality/bnd_imp_inc_div.con". (* UNEXPORTED -End Definitions. +End Definitions *) (*#* @@ -195,11 +195,11 @@ Boundedness away from zero is preserved through restriction of the set. %\end{convention}% *) -inline "cic:/CoRN/ftc/PartFunEquality/F.var". +inline "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/F.var" "Away_from_Zero__". -inline "cic:/CoRN/ftc/PartFunEquality/P.var". +inline "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/P.var" "Away_from_Zero__". -inline "cic:/CoRN/ftc/PartFunEquality/Q.var". +inline "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Q.var" "Away_from_Zero__". inline "cic:/CoRN/ftc/PartFunEquality/included_imp_bnd.con". @@ -222,7 +222,7 @@ inline "cic:/CoRN/ftc/PartFunEquality/bnd_in_P_imp_ap_zero.con". inline "cic:/CoRN/ftc/PartFunEquality/FRestr_bnd'.con". (* UNEXPORTED -End Away_from_Zero. +End Away_from_Zero *) (* UNEXPORTED @@ -249,7 +249,7 @@ Ltac FEQ := apply eq_imp_Feq; (* end hide *) (* UNEXPORTED -Section More_on_Equality. +Section More_on_Equality *) (*#* **Properties of Equality @@ -261,17 +261,17 @@ partial functions. %\end{convention}% *) -inline "cic:/CoRN/ftc/PartFunEquality/I.var". +inline "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/I.var" "More_on_Equality__". (* UNEXPORTED -Section Feq_Equivalence. +Section Feq_Equivalence *) -inline "cic:/CoRN/ftc/PartFunEquality/F.var". +inline "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Feq_Equivalence/F.var" "More_on_Equality__Feq_Equivalence__". -inline "cic:/CoRN/ftc/PartFunEquality/G.var". +inline "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Feq_Equivalence/G.var" "More_on_Equality__Feq_Equivalence__". -inline "cic:/CoRN/ftc/PartFunEquality/H.var". +inline "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Feq_Equivalence/H.var" "More_on_Equality__Feq_Equivalence__". inline "cic:/CoRN/ftc/PartFunEquality/Feq_reflexive.con". @@ -280,24 +280,24 @@ inline "cic:/CoRN/ftc/PartFunEquality/Feq_symmetric.con". inline "cic:/CoRN/ftc/PartFunEquality/Feq_transitive.con". (* UNEXPORTED -End Feq_Equivalence. +End Feq_Equivalence *) (* UNEXPORTED -Section Operations. +Section Operations *) (*#* Also it is preserved through application of functional constructors and restriction. *) -inline "cic:/CoRN/ftc/PartFunEquality/F.var". +inline "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Operations/F.var" "More_on_Equality__Operations__". -inline "cic:/CoRN/ftc/PartFunEquality/F'.var". +inline "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Operations/F'.var" "More_on_Equality__Operations__". -inline "cic:/CoRN/ftc/PartFunEquality/G.var". +inline "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Operations/G.var" "More_on_Equality__Operations__". -inline "cic:/CoRN/ftc/PartFunEquality/G'.var". +inline "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Operations/G'.var" "More_on_Equality__Operations__". inline "cic:/CoRN/ftc/PartFunEquality/Feq_plus.con". @@ -332,15 +332,15 @@ The image of a set is extensional. inline "cic:/CoRN/ftc/PartFunEquality/fun_image_wd.con". (* UNEXPORTED -End Operations. +End Operations *) (* UNEXPORTED -End More_on_Equality. +End More_on_Equality *) (* UNEXPORTED -Section Nth_Power. +Section Nth_Power *) (*#* **Nth Power @@ -355,34 +355,34 @@ equality relation. %\end{convention}% *) -inline "cic:/CoRN/ftc/PartFunEquality/F.var". +inline "cic:/CoRN/ftc/PartFunEquality/Nth_Power/F.var" "Nth_Power__". (* begin hide *) -inline "cic:/CoRN/ftc/PartFunEquality/P.con". +inline "cic:/CoRN/ftc/PartFunEquality/Nth_Power/P.con" "Nth_Power__". (* end hide *) -inline "cic:/CoRN/ftc/PartFunEquality/Q.var". +inline "cic:/CoRN/ftc/PartFunEquality/Nth_Power/Q.var" "Nth_Power__". -inline "cic:/CoRN/ftc/PartFunEquality/H.var". +inline "cic:/CoRN/ftc/PartFunEquality/Nth_Power/H.var" "Nth_Power__". -inline "cic:/CoRN/ftc/PartFunEquality/Hf.var". +inline "cic:/CoRN/ftc/PartFunEquality/Nth_Power/Hf.var" "Nth_Power__". inline "cic:/CoRN/ftc/PartFunEquality/FNth_zero.con". -inline "cic:/CoRN/ftc/PartFunEquality/n.var". +inline "cic:/CoRN/ftc/PartFunEquality/Nth_Power/n.var" "Nth_Power__". -inline "cic:/CoRN/ftc/PartFunEquality/H'.var". +inline "cic:/CoRN/ftc/PartFunEquality/Nth_Power/H'.var" "Nth_Power__". inline "cic:/CoRN/ftc/PartFunEquality/FNth_mult.con". (* UNEXPORTED -End Nth_Power. +End Nth_Power *) (* UNEXPORTED -Section Strong_Nth_Power. +Section Strong_Nth_Power *) (*#* @@ -391,27 +391,27 @@ is included in the domain of [F]. %\end{convention}% *) -inline "cic:/CoRN/ftc/PartFunEquality/a.var". +inline "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/a.var" "Strong_Nth_Power__". -inline "cic:/CoRN/ftc/PartFunEquality/b.var". +inline "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/b.var" "Strong_Nth_Power__". -inline "cic:/CoRN/ftc/PartFunEquality/Hab.var". +inline "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/Hab.var" "Strong_Nth_Power__". (* begin hide *) -inline "cic:/CoRN/ftc/PartFunEquality/I.con". +inline "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/I.con" "Strong_Nth_Power__". (* end hide *) -inline "cic:/CoRN/ftc/PartFunEquality/F.var". +inline "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/F.var" "Strong_Nth_Power__". -inline "cic:/CoRN/ftc/PartFunEquality/incF.var". +inline "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/incF.var" "Strong_Nth_Power__". inline "cic:/CoRN/ftc/PartFunEquality/FNth_zero'.con". inline "cic:/CoRN/ftc/PartFunEquality/FNth_mult'.con". (* UNEXPORTED -End Strong_Nth_Power. +End Strong_Nth_Power *) diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/PartInterval.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/PartInterval.ma index 47e164663..129048447 100644 --- a/helm/software/matita/contribs/CoRN-Decl/ftc/PartInterval.ma +++ b/helm/software/matita/contribs/CoRN-Decl/ftc/PartInterval.ma @@ -23,7 +23,7 @@ include "CoRN.ma". include "ftc/IntervalFunct.ma". (* UNEXPORTED -Section Conversion. +Section Conversion *) (*#* *Correspondence @@ -45,28 +45,28 @@ that [I [=] [a,b]] is included in the domain of [F]. %\end{convention}% *) -inline "cic:/CoRN/ftc/PartInterval/F.var". +inline "cic:/CoRN/ftc/PartInterval/Conversion/F.var" "Conversion__". -inline "cic:/CoRN/ftc/PartInterval/a.var". +inline "cic:/CoRN/ftc/PartInterval/Conversion/a.var" "Conversion__". -inline "cic:/CoRN/ftc/PartInterval/b.var". +inline "cic:/CoRN/ftc/PartInterval/Conversion/b.var" "Conversion__". -inline "cic:/CoRN/ftc/PartInterval/Hab.var". +inline "cic:/CoRN/ftc/PartInterval/Conversion/Hab.var" "Conversion__". (* begin hide *) -inline "cic:/CoRN/ftc/PartInterval/I.con". +inline "cic:/CoRN/ftc/PartInterval/Conversion/I.con" "Conversion__". (* end hide *) -inline "cic:/CoRN/ftc/PartInterval/Hf.var". +inline "cic:/CoRN/ftc/PartInterval/Conversion/Hf.var" "Conversion__". inline "cic:/CoRN/ftc/PartInterval/IntPartIR_strext.con". inline "cic:/CoRN/ftc/PartInterval/IntPartIR.con". (* UNEXPORTED -End Conversion. +End Conversion *) (* UNEXPORTED @@ -74,7 +74,7 @@ Implicit Arguments IntPartIR [F a b Hab]. *) (* UNEXPORTED -Section AntiConversion. +Section AntiConversion *) (*#* @@ -82,26 +82,26 @@ To go the other way around, we simply take a setoid function [f] with domain [[a,b]] and build the corresponding partial function. *) -inline "cic:/CoRN/ftc/PartInterval/a.var". +inline "cic:/CoRN/ftc/PartInterval/AntiConversion/a.var" "AntiConversion__". -inline "cic:/CoRN/ftc/PartInterval/b.var". +inline "cic:/CoRN/ftc/PartInterval/AntiConversion/b.var" "AntiConversion__". -inline "cic:/CoRN/ftc/PartInterval/Hab.var". +inline "cic:/CoRN/ftc/PartInterval/AntiConversion/Hab.var" "AntiConversion__". (* begin hide *) -inline "cic:/CoRN/ftc/PartInterval/I.con". +inline "cic:/CoRN/ftc/PartInterval/AntiConversion/I.con" "AntiConversion__". (* end hide *) -inline "cic:/CoRN/ftc/PartInterval/f.var". +inline "cic:/CoRN/ftc/PartInterval/AntiConversion/f.var" "AntiConversion__". inline "cic:/CoRN/ftc/PartInterval/PartInt_strext.con". inline "cic:/CoRN/ftc/PartInterval/PartInt.con". (* UNEXPORTED -End AntiConversion. +End AntiConversion *) (* UNEXPORTED @@ -109,7 +109,7 @@ Implicit Arguments PartInt [a b Hab]. *) (* UNEXPORTED -Section Inverses. +Section Inverses *) (*#* @@ -119,11 +119,11 @@ In one direction these operators are inverses. inline "cic:/CoRN/ftc/PartInterval/int_part_int.con". (* UNEXPORTED -End Inverses. +End Inverses *) (* UNEXPORTED -Section Equivalences. +Section Equivalences *) (*#* **Mappings Preserve Operations @@ -137,31 +137,31 @@ type [I->IR] equal respectively to [F] and [G] in [I]. %\end{convention}% *) -inline "cic:/CoRN/ftc/PartInterval/F.var". +inline "cic:/CoRN/ftc/PartInterval/Equivalences/F.var" "Equivalences__". -inline "cic:/CoRN/ftc/PartInterval/G.var". +inline "cic:/CoRN/ftc/PartInterval/Equivalences/G.var" "Equivalences__". -inline "cic:/CoRN/ftc/PartInterval/a.var". +inline "cic:/CoRN/ftc/PartInterval/Equivalences/a.var" "Equivalences__". -inline "cic:/CoRN/ftc/PartInterval/b.var". +inline "cic:/CoRN/ftc/PartInterval/Equivalences/b.var" "Equivalences__". -inline "cic:/CoRN/ftc/PartInterval/c.var". +inline "cic:/CoRN/ftc/PartInterval/Equivalences/c.var" "Equivalences__". -inline "cic:/CoRN/ftc/PartInterval/Hab.var". +inline "cic:/CoRN/ftc/PartInterval/Equivalences/Hab.var" "Equivalences__". (* begin hide *) -inline "cic:/CoRN/ftc/PartInterval/I.con". +inline "cic:/CoRN/ftc/PartInterval/Equivalences/I.con" "Equivalences__". (* end hide *) -inline "cic:/CoRN/ftc/PartInterval/f.var". +inline "cic:/CoRN/ftc/PartInterval/Equivalences/f.var" "Equivalences__". -inline "cic:/CoRN/ftc/PartInterval/g.var". +inline "cic:/CoRN/ftc/PartInterval/Equivalences/g.var" "Equivalences__". -inline "cic:/CoRN/ftc/PartInterval/Ff.var". +inline "cic:/CoRN/ftc/PartInterval/Equivalences/Ff.var" "Equivalences__". -inline "cic:/CoRN/ftc/PartInterval/Gg.var". +inline "cic:/CoRN/ftc/PartInterval/Equivalences/Gg.var" "Equivalences__". inline "cic:/CoRN/ftc/PartInterval/part_int_const.con". @@ -179,9 +179,9 @@ inline "cic:/CoRN/ftc/PartInterval/part_int_nth.con". (* begin show *) -inline "cic:/CoRN/ftc/PartInterval/HG.var". +inline "cic:/CoRN/ftc/PartInterval/Equivalences/HG.var" "Equivalences__". -inline "cic:/CoRN/ftc/PartInterval/Hg.var". +inline "cic:/CoRN/ftc/PartInterval/Equivalences/Hg.var" "Equivalences__". (* end show *) @@ -190,6 +190,6 @@ inline "cic:/CoRN/ftc/PartInterval/part_int_recip.con". inline "cic:/CoRN/ftc/PartInterval/part_int_div.con". (* UNEXPORTED -End Equivalences. +End Equivalences *) diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/Partitions.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/Partitions.ma index 58a7651fc..f99410089 100644 --- a/helm/software/matita/contribs/CoRN-Decl/ftc/Partitions.ma +++ b/helm/software/matita/contribs/CoRN-Decl/ftc/Partitions.ma @@ -25,7 +25,7 @@ include "ftc/Continuity.ma". (*#* printing Partition_Sum %\ensuremath{\sum_P}% #∑P# *) (* UNEXPORTED -Section Definitions. +Section Definitions *) (*#* *Partitions @@ -104,22 +104,22 @@ inline "cic:/CoRN/ftc/Partitions/even_part_2.con". inline "cic:/CoRN/ftc/Partitions/Even_Partition.con". (* UNEXPORTED -Section Refinements. +Section Refinements *) -inline "cic:/CoRN/ftc/Partitions/a.var". +inline "cic:/CoRN/ftc/Partitions/Definitions/Refinements/a.var" "Definitions__Refinements__". -inline "cic:/CoRN/ftc/Partitions/b.var". +inline "cic:/CoRN/ftc/Partitions/Definitions/Refinements/b.var" "Definitions__Refinements__". -inline "cic:/CoRN/ftc/Partitions/Hab.var". +inline "cic:/CoRN/ftc/Partitions/Definitions/Refinements/Hab.var" "Definitions__Refinements__". -inline "cic:/CoRN/ftc/Partitions/m.var". +inline "cic:/CoRN/ftc/Partitions/Definitions/Refinements/m.var" "Definitions__Refinements__". -inline "cic:/CoRN/ftc/Partitions/n.var". +inline "cic:/CoRN/ftc/Partitions/Definitions/Refinements/n.var" "Definitions__Refinements__". -inline "cic:/CoRN/ftc/Partitions/P.var". +inline "cic:/CoRN/ftc/Partitions/Definitions/Refinements/P.var" "Definitions__Refinements__". -inline "cic:/CoRN/ftc/Partitions/Q.var". +inline "cic:/CoRN/ftc/Partitions/Definitions/Refinements/Q.var" "Definitions__Refinements__". (*#* We now define what it means for a partition [Q] to be a refinement of @@ -146,7 +146,7 @@ inline "cic:/CoRN/ftc/Partitions/Pts_part_lemma.con". inline "cic:/CoRN/ftc/Partitions/Partition_Sum.con". (* UNEXPORTED -End Refinements. +End Refinements *) (* UNEXPORTED @@ -165,20 +165,20 @@ We now formalize some trivial and helpful constructions. %\end{convention}% *) -inline "cic:/CoRN/ftc/Partitions/a.var". +inline "cic:/CoRN/ftc/Partitions/Definitions/a.var" "Definitions__". -inline "cic:/CoRN/ftc/Partitions/b.var". +inline "cic:/CoRN/ftc/Partitions/Definitions/b.var" "Definitions__". -inline "cic:/CoRN/ftc/Partitions/Hab.var". +inline "cic:/CoRN/ftc/Partitions/Definitions/Hab.var" "Definitions__". (* begin hide *) -inline "cic:/CoRN/ftc/Partitions/I.con". +inline "cic:/CoRN/ftc/Partitions/Definitions/I.con" "Definitions__". (* end hide *) (* UNEXPORTED -Section Getting_Points. +Section Getting_Points *) (*#* @@ -190,9 +190,9 @@ partition. %\end{convention}% *) -inline "cic:/CoRN/ftc/Partitions/m.var". +inline "cic:/CoRN/ftc/Partitions/Definitions/Getting_Points/m.var" "Definitions__Getting_Points__". -inline "cic:/CoRN/ftc/Partitions/Q.var". +inline "cic:/CoRN/ftc/Partitions/Definitions/Getting_Points/Q.var" "Definitions__Getting_Points__". inline "cic:/CoRN/ftc/Partitions/Partition_imp_points.con". @@ -201,21 +201,21 @@ inline "cic:/CoRN/ftc/Partitions/Partition_imp_points_1.con". inline "cic:/CoRN/ftc/Partitions/Partition_imp_points_2.con". (* UNEXPORTED -End Getting_Points. +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]]. *) -inline "cic:/CoRN/ftc/Partitions/F.var". +inline "cic:/CoRN/ftc/Partitions/Definitions/F.var" "Definitions__". -inline "cic:/CoRN/ftc/Partitions/contF.var". +inline "cic:/CoRN/ftc/Partitions/Definitions/contF.var" "Definitions__". inline "cic:/CoRN/ftc/Partitions/Even_Partition_Sum.con". (* UNEXPORTED -End Definitions. +End Definitions *) (* UNEXPORTED @@ -267,7 +267,7 @@ Hint Resolve start finish: algebra. *) (* UNEXPORTED -Section Lemmas. +Section Lemmas *) (*#* ** Properties of the mesh @@ -300,21 +300,21 @@ with [n] points. %\end{convention}% *) -inline "cic:/CoRN/ftc/Partitions/a.var". +inline "cic:/CoRN/ftc/Partitions/Lemmas/a.var" "Lemmas__". -inline "cic:/CoRN/ftc/Partitions/b.var". +inline "cic:/CoRN/ftc/Partitions/Lemmas/b.var" "Lemmas__". (* begin hide *) -inline "cic:/CoRN/ftc/Partitions/I.con". +inline "cic:/CoRN/ftc/Partitions/Lemmas/I.con" "Lemmas__". (* end hide *) -inline "cic:/CoRN/ftc/Partitions/Hab.var". +inline "cic:/CoRN/ftc/Partitions/Lemmas/Hab.var" "Lemmas__". -inline "cic:/CoRN/ftc/Partitions/n.var". +inline "cic:/CoRN/ftc/Partitions/Lemmas/n.var" "Lemmas__". -inline "cic:/CoRN/ftc/Partitions/P.var". +inline "cic:/CoRN/ftc/Partitions/Lemmas/P.var" "Lemmas__". inline "cic:/CoRN/ftc/Partitions/Mesh_lemma.con". @@ -323,11 +323,11 @@ inline "cic:/CoRN/ftc/Partitions/AntiMesh_lemma.con". inline "cic:/CoRN/ftc/Partitions/Mesh_leEq.con". (* UNEXPORTED -End Lemmas. +End Lemmas *) (* UNEXPORTED -Section Even_Partitions. +Section Even_Partitions *) (*#* More technical stuff. Two equal partitions have the same mesh. @@ -348,17 +348,17 @@ inline "cic:/CoRN/ftc/Partitions/even_partition_Mesh.con". %\end{convention}% *) -inline "cic:/CoRN/ftc/Partitions/a.var". +inline "cic:/CoRN/ftc/Partitions/Even_Partitions/a.var" "Even_Partitions__". -inline "cic:/CoRN/ftc/Partitions/b.var". +inline "cic:/CoRN/ftc/Partitions/Even_Partitions/b.var" "Even_Partitions__". (* begin hide *) -inline "cic:/CoRN/ftc/Partitions/I.con". +inline "cic:/CoRN/ftc/Partitions/Even_Partitions/I.con" "Even_Partitions__". (* end hide *) -inline "cic:/CoRN/ftc/Partitions/Hab.var". +inline "cic:/CoRN/ftc/Partitions/Even_Partitions/Hab.var" "Even_Partitions__". (*#* An interesting property: in a partition, if [ai [<] aj] then [i < j]. @@ -377,30 +377,30 @@ denote by [P] and [Q] the even partitions with, respectively, [m] and Even partitions always have a common refinement. *) -inline "cic:/CoRN/ftc/Partitions/m.var". +inline "cic:/CoRN/ftc/Partitions/Even_Partitions/m.var" "Even_Partitions__". -inline "cic:/CoRN/ftc/Partitions/n.var". +inline "cic:/CoRN/ftc/Partitions/Even_Partitions/n.var" "Even_Partitions__". -inline "cic:/CoRN/ftc/Partitions/Hm.var". +inline "cic:/CoRN/ftc/Partitions/Even_Partitions/Hm.var" "Even_Partitions__". -inline "cic:/CoRN/ftc/Partitions/Hn.var". +inline "cic:/CoRN/ftc/Partitions/Even_Partitions/Hn.var" "Even_Partitions__". (* begin hide *) -inline "cic:/CoRN/ftc/Partitions/P.con". +inline "cic:/CoRN/ftc/Partitions/Even_Partitions/P.con" "Even_Partitions__". -inline "cic:/CoRN/ftc/Partitions/Q.con". +inline "cic:/CoRN/ftc/Partitions/Even_Partitions/Q.con" "Even_Partitions__". (* end hide *) inline "cic:/CoRN/ftc/Partitions/even_partition_refinement.con". (* UNEXPORTED -End Even_Partitions. +End Even_Partitions *) (* UNEXPORTED -Section More_Definitions. +Section More_Definitions *) (*#* ** Separation @@ -408,11 +408,11 @@ Section More_Definitions. Some auxiliary definitions. A partition is said to be separated if all its points are distinct. *) -inline "cic:/CoRN/ftc/Partitions/a.var". +inline "cic:/CoRN/ftc/Partitions/More_Definitions/a.var" "More_Definitions__". -inline "cic:/CoRN/ftc/Partitions/b.var". +inline "cic:/CoRN/ftc/Partitions/More_Definitions/b.var" "More_Definitions__". -inline "cic:/CoRN/ftc/Partitions/Hab.var". +inline "cic:/CoRN/ftc/Partitions/More_Definitions/Hab.var" "More_Definitions__". inline "cic:/CoRN/ftc/Partitions/_Separated.con". @@ -426,18 +426,18 @@ respectively, [n] and [m] points. %\end{convention}% *) -inline "cic:/CoRN/ftc/Partitions/n.var". +inline "cic:/CoRN/ftc/Partitions/More_Definitions/n.var" "More_Definitions__". -inline "cic:/CoRN/ftc/Partitions/m.var". +inline "cic:/CoRN/ftc/Partitions/More_Definitions/m.var" "More_Definitions__". -inline "cic:/CoRN/ftc/Partitions/P.var". +inline "cic:/CoRN/ftc/Partitions/More_Definitions/P.var" "More_Definitions__". -inline "cic:/CoRN/ftc/Partitions/Q.var". +inline "cic:/CoRN/ftc/Partitions/More_Definitions/Q.var" "More_Definitions__". inline "cic:/CoRN/ftc/Partitions/Separated.con". (* UNEXPORTED -End More_Definitions. +End More_Definitions *) (* UNEXPORTED @@ -449,20 +449,20 @@ Implicit Arguments Separated [a b Hab n m]. *) (* UNEXPORTED -Section Sep_Partitions. +Section Sep_Partitions *) -inline "cic:/CoRN/ftc/Partitions/a.var". +inline "cic:/CoRN/ftc/Partitions/Sep_Partitions/a.var" "Sep_Partitions__". -inline "cic:/CoRN/ftc/Partitions/b.var". +inline "cic:/CoRN/ftc/Partitions/Sep_Partitions/b.var" "Sep_Partitions__". (* begin hide *) -inline "cic:/CoRN/ftc/Partitions/I.con". +inline "cic:/CoRN/ftc/Partitions/Sep_Partitions/I.con" "Sep_Partitions__". (* end hide *) -inline "cic:/CoRN/ftc/Partitions/Hab.var". +inline "cic:/CoRN/ftc/Partitions/Sep_Partitions/Hab.var" "Sep_Partitions__". (*#* The antimesh of a separated partition is always positive. @@ -483,6 +483,6 @@ inline "cic:/CoRN/ftc/Partitions/_Separated_imp_length_zero.con". inline "cic:/CoRN/ftc/Partitions/partition_less_imp_gt_zero.con". (* UNEXPORTED -End Sep_Partitions. +End Sep_Partitions *) diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/RefLemma.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/RefLemma.ma index 9503e78c1..d739213c0 100644 --- a/helm/software/matita/contribs/CoRN-Decl/ftc/RefLemma.ma +++ b/helm/software/matita/contribs/CoRN-Decl/ftc/RefLemma.ma @@ -27,7 +27,7 @@ include "ftc/RefSeparated.ma". include "ftc/RefSepRef.ma". (* UNEXPORTED -Section Refinement_Lemma. +Section Refinement_Lemma *) (*#* *The Refinement Lemmas @@ -81,32 +81,32 @@ Using the results from these files, we prove our main lemma in several steps %\end{convention}% *) -inline "cic:/CoRN/ftc/RefLemma/a.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/a.var" "Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/b.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/b.var" "Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/Hab.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Hab.var" "Refinement_Lemma__". (* begin hide *) -inline "cic:/CoRN/ftc/RefLemma/I.con". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/I.con" "Refinement_Lemma__". (* end hide *) -inline "cic:/CoRN/ftc/RefLemma/F.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/F.var" "Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/contF.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/contF.var" "Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/incF.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/incF.var" "Refinement_Lemma__". (* begin hide *) -inline "cic:/CoRN/ftc/RefLemma/contF'.con". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/contF'.con" "Refinement_Lemma__". (* end hide *) (* UNEXPORTED -Section First_Refinement_Lemma. +Section First_Refinement_Lemma *) (*#* @@ -124,43 +124,43 @@ respectively. %\end{convention}% *) -inline "cic:/CoRN/ftc/RefLemma/e.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/e.var" "Refinement_Lemma__First_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/He.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/He.var" "Refinement_Lemma__First_Refinement_Lemma__". (* begin hide *) -inline "cic:/CoRN/ftc/RefLemma/d.con". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/d.con" "Refinement_Lemma__First_Refinement_Lemma__". (* end hide *) -inline "cic:/CoRN/ftc/RefLemma/m.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/m.var" "Refinement_Lemma__First_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/n.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/n.var" "Refinement_Lemma__First_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/P.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/P.var" "Refinement_Lemma__First_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/HMesh.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/HMesh.var" "Refinement_Lemma__First_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/Q.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/Q.var" "Refinement_Lemma__First_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/Href.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/Href.var" "Refinement_Lemma__First_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/fP.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/fP.var" "Refinement_Lemma__First_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/HfP.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/HfP.var" "Refinement_Lemma__First_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/HfP'.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/HfP'.var" "Refinement_Lemma__First_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/fQ.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/fQ.var" "Refinement_Lemma__First_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/HfQ.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/HfQ.var" "Refinement_Lemma__First_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/HfQ'.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/HfQ'.var" "Refinement_Lemma__First_Refinement_Lemma__". (* begin hide *) -inline "cic:/CoRN/ftc/RefLemma/sub.con". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/sub.con" "Refinement_Lemma__First_Refinement_Lemma__". inline "cic:/CoRN/ftc/RefLemma/RL_sub_0.con". @@ -174,11 +174,11 @@ inline "cic:/CoRN/ftc/RefLemma/RL_sub_hyp.con". inline "cic:/CoRN/ftc/RefLemma/RL_sub_S.con". -inline "cic:/CoRN/ftc/RefLemma/H.con". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/H.con" "Refinement_Lemma__First_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/H'.con". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/H'.con" "Refinement_Lemma__First_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/H0.con". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/H0.con" "Refinement_Lemma__First_Refinement_Lemma__". inline "cic:/CoRN/ftc/RefLemma/RL_sub_SS.con". @@ -223,11 +223,11 @@ inline "cic:/CoRN/ftc/RefLemma/ref_calc8.con". inline "cic:/CoRN/ftc/RefLemma/first_refinement_lemma.con". (* UNEXPORTED -End First_Refinement_Lemma. +End First_Refinement_Lemma *) (* UNEXPORTED -Section Second_Refinement_Lemma. +Section Second_Refinement_Lemma *) (*#* @@ -246,62 +246,62 @@ and [R], respectively. %\end{convention}% *) -inline "cic:/CoRN/ftc/RefLemma/n.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/n.var" "Refinement_Lemma__Second_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/j.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/j.var" "Refinement_Lemma__Second_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/k.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/k.var" "Refinement_Lemma__Second_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/P.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/P.var" "Refinement_Lemma__Second_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/Q.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/Q.var" "Refinement_Lemma__Second_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/R.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/R.var" "Refinement_Lemma__Second_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/HrefP.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HrefP.var" "Refinement_Lemma__Second_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/HrefR.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HrefR.var" "Refinement_Lemma__Second_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/e.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/e.var" "Refinement_Lemma__Second_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/e'.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/e'.var" "Refinement_Lemma__Second_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/He.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/He.var" "Refinement_Lemma__Second_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/He'.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/He'.var" "Refinement_Lemma__Second_Refinement_Lemma__". (* begin hide *) -inline "cic:/CoRN/ftc/RefLemma/d.con". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/d.con" "Refinement_Lemma__Second_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/d'.con". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/d'.con" "Refinement_Lemma__Second_Refinement_Lemma__". (* end hide *) -inline "cic:/CoRN/ftc/RefLemma/HMeshP.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HMeshP.var" "Refinement_Lemma__Second_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/HMeshR.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HMeshR.var" "Refinement_Lemma__Second_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/fP.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/fP.var" "Refinement_Lemma__Second_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/HfP.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HfP.var" "Refinement_Lemma__Second_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/HfP'.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HfP'.var" "Refinement_Lemma__Second_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/fR.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/fR.var" "Refinement_Lemma__Second_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/HfR.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HfR.var" "Refinement_Lemma__Second_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/HfR'.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HfR'.var" "Refinement_Lemma__Second_Refinement_Lemma__". inline "cic:/CoRN/ftc/RefLemma/second_refinement_lemma.con". (* UNEXPORTED -End Second_Refinement_Lemma. +End Second_Refinement_Lemma *) (* UNEXPORTED -Section Third_Refinement_Lemma. +Section Third_Refinement_Lemma *) (*#* @@ -320,109 +320,109 @@ respectively; %\end{convention}% *) -inline "cic:/CoRN/ftc/RefLemma/n.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/n.var" "Refinement_Lemma__Third_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/m.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/m.var" "Refinement_Lemma__Third_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/P.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/P.var" "Refinement_Lemma__Third_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/R.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/R.var" "Refinement_Lemma__Third_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/e.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/e.var" "Refinement_Lemma__Third_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/e'.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/e'.var" "Refinement_Lemma__Third_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/He.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/He.var" "Refinement_Lemma__Third_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/He'.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/He'.var" "Refinement_Lemma__Third_Refinement_Lemma__". (* begin hide *) -inline "cic:/CoRN/ftc/RefLemma/d.con". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/d.con" "Refinement_Lemma__Third_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/d'.con". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/d'.con" "Refinement_Lemma__Third_Refinement_Lemma__". (* end hide *) -inline "cic:/CoRN/ftc/RefLemma/HMeshP.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/HMeshP.var" "Refinement_Lemma__Third_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/HMeshR.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/HMeshR.var" "Refinement_Lemma__Third_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/fP.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/fP.var" "Refinement_Lemma__Third_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/HfP.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/HfP.var" "Refinement_Lemma__Third_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/HfP'.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/HfP'.var" "Refinement_Lemma__Third_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/fR.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/fR.var" "Refinement_Lemma__Third_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/HfR.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/HfR.var" "Refinement_Lemma__Third_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/HfR'.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/HfR'.var" "Refinement_Lemma__Third_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/Hab'.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/Hab'.var" "Refinement_Lemma__Third_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/beta.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/beta.var" "Refinement_Lemma__Third_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/Hbeta.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/Hbeta.var" "Refinement_Lemma__Third_Refinement_Lemma__". (* begin hide *) -inline "cic:/CoRN/ftc/RefLemma/alpha.con". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/alpha.con" "Refinement_Lemma__Third_Refinement_Lemma__". inline "cic:/CoRN/ftc/RefLemma/RL_alpha.con". -inline "cic:/CoRN/ftc/RefLemma/csi1.con". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/csi1.con" "Refinement_Lemma__Third_Refinement_Lemma__". inline "cic:/CoRN/ftc/RefLemma/RL_csi1.con". -inline "cic:/CoRN/ftc/RefLemma/delta1.con". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/delta1.con" "Refinement_Lemma__Third_Refinement_Lemma__". inline "cic:/CoRN/ftc/RefLemma/RL_delta1.con". -inline "cic:/CoRN/ftc/RefLemma/P'.con". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/P'.con" "Refinement_Lemma__Third_Refinement_Lemma__". inline "cic:/CoRN/ftc/RefLemma/RL_P'_sep.con". inline "cic:/CoRN/ftc/RefLemma/RL_P'_Mesh.con". -inline "cic:/CoRN/ftc/RefLemma/fP'.con". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/fP'.con" "Refinement_Lemma__Third_Refinement_Lemma__". inline "cic:/CoRN/ftc/RefLemma/RL_fP'_in_P'.con". inline "cic:/CoRN/ftc/RefLemma/RL_P'_P_sum.con". -inline "cic:/CoRN/ftc/RefLemma/csi2.con". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/csi2.con" "Refinement_Lemma__Third_Refinement_Lemma__". inline "cic:/CoRN/ftc/RefLemma/RL_csi2.con". -inline "cic:/CoRN/ftc/RefLemma/delta2.con". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/delta2.con" "Refinement_Lemma__Third_Refinement_Lemma__". inline "cic:/CoRN/ftc/RefLemma/RL_delta2.con". -inline "cic:/CoRN/ftc/RefLemma/R'.con". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/R'.con" "Refinement_Lemma__Third_Refinement_Lemma__". inline "cic:/CoRN/ftc/RefLemma/RL_R'_sep.con". inline "cic:/CoRN/ftc/RefLemma/RL_R'_Mesh.con". -inline "cic:/CoRN/ftc/RefLemma/fR'.con". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/fR'.con" "Refinement_Lemma__Third_Refinement_Lemma__". inline "cic:/CoRN/ftc/RefLemma/RL_fR'_in_R'.con". inline "cic:/CoRN/ftc/RefLemma/RL_R'_R_sum.con". -inline "cic:/CoRN/ftc/RefLemma/csi3.con". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/csi3.con" "Refinement_Lemma__Third_Refinement_Lemma__". inline "cic:/CoRN/ftc/RefLemma/RL_csi3.con". -inline "cic:/CoRN/ftc/RefLemma/Q.con". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/Q.con" "Refinement_Lemma__Third_Refinement_Lemma__". inline "cic:/CoRN/ftc/RefLemma/RL_Q_Mesh.con". inline "cic:/CoRN/ftc/RefLemma/RL_Q_sep.con". -inline "cic:/CoRN/ftc/RefLemma/fQ.con". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/fQ.con" "Refinement_Lemma__Third_Refinement_Lemma__". inline "cic:/CoRN/ftc/RefLemma/RL_fQ_in_Q.con". @@ -433,16 +433,16 @@ inline "cic:/CoRN/ftc/RefLemma/RL_Q_P'_sum.con". inline "cic:/CoRN/ftc/RefLemma/third_refinement_lemma.con". (* UNEXPORTED -End Third_Refinement_Lemma. +End Third_Refinement_Lemma *) (* UNEXPORTED -Section Fourth_Refinement_Lemma. +Section Fourth_Refinement_Lemma *) (* begin hide *) -inline "cic:/CoRN/ftc/RefLemma/Fa.con". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/Fa.con" "Refinement_Lemma__Fourth_Refinement_Lemma__". (* NOTATION Notation just := (fun z => incF _ (Pts_part_lemma _ _ _ _ _ _ z _ _)). @@ -457,111 +457,111 @@ Finally, this is inequality (2.6.7) exactly as stated (same conventions as above) *) -inline "cic:/CoRN/ftc/RefLemma/n.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/n.var" "Refinement_Lemma__Fourth_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/m.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/m.var" "Refinement_Lemma__Fourth_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/P.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/P.var" "Refinement_Lemma__Fourth_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/R.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/R.var" "Refinement_Lemma__Fourth_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/e.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/e.var" "Refinement_Lemma__Fourth_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/e'.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/e'.var" "Refinement_Lemma__Fourth_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/He.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/He.var" "Refinement_Lemma__Fourth_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/He'.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/He'.var" "Refinement_Lemma__Fourth_Refinement_Lemma__". (* begin hide *) -inline "cic:/CoRN/ftc/RefLemma/d.con". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/d.con" "Refinement_Lemma__Fourth_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/d'.con". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/d'.con" "Refinement_Lemma__Fourth_Refinement_Lemma__". (* end hide *) -inline "cic:/CoRN/ftc/RefLemma/HMeshP.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/HMeshP.var" "Refinement_Lemma__Fourth_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/HMeshR.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/HMeshR.var" "Refinement_Lemma__Fourth_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/fP.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/fP.var" "Refinement_Lemma__Fourth_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/HfP.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/HfP.var" "Refinement_Lemma__Fourth_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/HfP'.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/HfP'.var" "Refinement_Lemma__Fourth_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/fR.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/fR.var" "Refinement_Lemma__Fourth_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/HfR.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/HfR.var" "Refinement_Lemma__Fourth_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/HfR'.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/HfR'.var" "Refinement_Lemma__Fourth_Refinement_Lemma__". (* begin show *) -inline "cic:/CoRN/ftc/RefLemma/Hab'.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/Hab'.var" "Refinement_Lemma__Fourth_Refinement_Lemma__". (* end show *) inline "cic:/CoRN/ftc/RefLemma/fourth_refinement_lemma.con". (* UNEXPORTED -End Fourth_Refinement_Lemma. +End Fourth_Refinement_Lemma *) (* UNEXPORTED -Section Main_Refinement_Lemma. +Section Main_Refinement_Lemma *) (*#* We finish by presenting Theorem 9. *) -inline "cic:/CoRN/ftc/RefLemma/n.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/n.var" "Refinement_Lemma__Main_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/m.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/m.var" "Refinement_Lemma__Main_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/P.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/P.var" "Refinement_Lemma__Main_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/R.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/R.var" "Refinement_Lemma__Main_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/e.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/e.var" "Refinement_Lemma__Main_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/e'.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/e'.var" "Refinement_Lemma__Main_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/He.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/He.var" "Refinement_Lemma__Main_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/He'.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/He'.var" "Refinement_Lemma__Main_Refinement_Lemma__". (* begin hide *) -inline "cic:/CoRN/ftc/RefLemma/d.con". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/d.con" "Refinement_Lemma__Main_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/d'.con". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/d'.con" "Refinement_Lemma__Main_Refinement_Lemma__". (* end hide *) -inline "cic:/CoRN/ftc/RefLemma/HMeshP.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HMeshP.var" "Refinement_Lemma__Main_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/HMeshR.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HMeshR.var" "Refinement_Lemma__Main_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/fP.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/fP.var" "Refinement_Lemma__Main_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/HfP.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HfP.var" "Refinement_Lemma__Main_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/HfP'.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HfP'.var" "Refinement_Lemma__Main_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/fR.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/fR.var" "Refinement_Lemma__Main_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/HfR.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HfR.var" "Refinement_Lemma__Main_Refinement_Lemma__". -inline "cic:/CoRN/ftc/RefLemma/HfR'.var". +inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HfR'.var" "Refinement_Lemma__Main_Refinement_Lemma__". inline "cic:/CoRN/ftc/RefLemma/refinement_lemma.con". (* UNEXPORTED -End Main_Refinement_Lemma. +End Main_Refinement_Lemma *) (* UNEXPORTED -End Refinement_Lemma. +End Refinement_Lemma *) diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/RefSepRef.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/RefSepRef.ma index ab403b372..e44cc3d50 100644 --- a/helm/software/matita/contribs/CoRN-Decl/ftc/RefSepRef.ma +++ b/helm/software/matita/contribs/CoRN-Decl/ftc/RefSepRef.ma @@ -27,32 +27,32 @@ include "ftc/COrdLemmas.ma". include "ftc/Partitions.ma". (* UNEXPORTED -Section Refining_Separated. +Section Refining_Separated *) -inline "cic:/CoRN/ftc/RefSepRef/a.var". +inline "cic:/CoRN/ftc/RefSepRef/Refining_Separated/a.var" "Refining_Separated__". -inline "cic:/CoRN/ftc/RefSepRef/b.var". +inline "cic:/CoRN/ftc/RefSepRef/Refining_Separated/b.var" "Refining_Separated__". -inline "cic:/CoRN/ftc/RefSepRef/Hab.var". +inline "cic:/CoRN/ftc/RefSepRef/Refining_Separated/Hab.var" "Refining_Separated__". -inline "cic:/CoRN/ftc/RefSepRef/I.con". +inline "cic:/CoRN/ftc/RefSepRef/Refining_Separated/I.con" "Refining_Separated__". -inline "cic:/CoRN/ftc/RefSepRef/F.var". +inline "cic:/CoRN/ftc/RefSepRef/Refining_Separated/F.var" "Refining_Separated__". -inline "cic:/CoRN/ftc/RefSepRef/contF.var". +inline "cic:/CoRN/ftc/RefSepRef/Refining_Separated/contF.var" "Refining_Separated__". -inline "cic:/CoRN/ftc/RefSepRef/incF.var". +inline "cic:/CoRN/ftc/RefSepRef/Refining_Separated/incF.var" "Refining_Separated__". -inline "cic:/CoRN/ftc/RefSepRef/m.var". +inline "cic:/CoRN/ftc/RefSepRef/Refining_Separated/m.var" "Refining_Separated__". -inline "cic:/CoRN/ftc/RefSepRef/n.var". +inline "cic:/CoRN/ftc/RefSepRef/Refining_Separated/n.var" "Refining_Separated__". -inline "cic:/CoRN/ftc/RefSepRef/P.var". +inline "cic:/CoRN/ftc/RefSepRef/Refining_Separated/P.var" "Refining_Separated__". -inline "cic:/CoRN/ftc/RefSepRef/R.var". +inline "cic:/CoRN/ftc/RefSepRef/Refining_Separated/R.var" "Refining_Separated__". -inline "cic:/CoRN/ftc/RefSepRef/HPR.var". +inline "cic:/CoRN/ftc/RefSepRef/Refining_Separated/HPR.var" "Refining_Separated__". inline "cic:/CoRN/ftc/RefSepRef/RSR_HP.con". @@ -68,9 +68,9 @@ inline "cic:/CoRN/ftc/RefSepRef/RSR_nm0.con". inline "cic:/CoRN/ftc/RefSepRef/RSR_H'.con". -inline "cic:/CoRN/ftc/RefSepRef/f'.con". +inline "cic:/CoRN/ftc/RefSepRef/Refining_Separated/f'.con" "Refining_Separated__". -inline "cic:/CoRN/ftc/RefSepRef/g'.con". +inline "cic:/CoRN/ftc/RefSepRef/Refining_Separated/g'.con" "Refining_Separated__". inline "cic:/CoRN/ftc/RefSepRef/RSR_f'_nlnf.con". @@ -82,7 +82,7 @@ inline "cic:/CoRN/ftc/RefSepRef/RSR_g'_mon.con". inline "cic:/CoRN/ftc/RefSepRef/RSR_f'_ap_g'.con". -inline "cic:/CoRN/ftc/RefSepRef/h.con". +inline "cic:/CoRN/ftc/RefSepRef/Refining_Separated/h.con" "Refining_Separated__". inline "cic:/CoRN/ftc/RefSepRef/RSR_h_nlnf.con". @@ -141,7 +141,7 @@ inline "cic:/CoRN/ftc/RefSepRef/RSR_auxR_lemma2.con". inline "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_rht.con". (* UNEXPORTED -End Refining_Separated. +End Refining_Separated *) (* end hide *) diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/RefSeparated.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/RefSeparated.ma index 440ec7a98..f69063ad8 100644 --- a/helm/software/matita/contribs/CoRN-Decl/ftc/RefSeparated.ma +++ b/helm/software/matita/contribs/CoRN-Decl/ftc/RefSeparated.ma @@ -27,68 +27,68 @@ include "ftc/COrdLemmas.ma". include "ftc/Partitions.ma". (* UNEXPORTED -Section Separating__Separated. +Section Separating__Separated *) -inline "cic:/CoRN/ftc/RefSeparated/a.var". +inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/a.var" "Separating__Separated__". -inline "cic:/CoRN/ftc/RefSeparated/b.var". +inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/b.var" "Separating__Separated__". -inline "cic:/CoRN/ftc/RefSeparated/Hab.var". +inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Hab.var" "Separating__Separated__". -inline "cic:/CoRN/ftc/RefSeparated/I.con". +inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/I.con" "Separating__Separated__". -inline "cic:/CoRN/ftc/RefSeparated/F.var". +inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/F.var" "Separating__Separated__". -inline "cic:/CoRN/ftc/RefSeparated/contF.var". +inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/contF.var" "Separating__Separated__". -inline "cic:/CoRN/ftc/RefSeparated/incF.var". +inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/incF.var" "Separating__Separated__". -inline "cic:/CoRN/ftc/RefSeparated/Hab'.var". +inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Hab'.var" "Separating__Separated__". -inline "cic:/CoRN/ftc/RefSeparated/m.var". +inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/m.var" "Separating__Separated__". -inline "cic:/CoRN/ftc/RefSeparated/n.var". +inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/n.var" "Separating__Separated__". -inline "cic:/CoRN/ftc/RefSeparated/P.var". +inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/P.var" "Separating__Separated__". -inline "cic:/CoRN/ftc/RefSeparated/R.var". +inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/R.var" "Separating__Separated__". -inline "cic:/CoRN/ftc/RefSeparated/HP.var". +inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/HP.var" "Separating__Separated__". -inline "cic:/CoRN/ftc/RefSeparated/HR.var". +inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/HR.var" "Separating__Separated__". inline "cic:/CoRN/ftc/RefSeparated/RS_pos_n.con". inline "cic:/CoRN/ftc/RefSeparated/RS_pos_m.con". -inline "cic:/CoRN/ftc/RefSeparated/alpha.var". +inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/alpha.var" "Separating__Separated__". -inline "cic:/CoRN/ftc/RefSeparated/Halpha.var". +inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Halpha.var" "Separating__Separated__". -inline "cic:/CoRN/ftc/RefSeparated/e.con". +inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/e.con" "Separating__Separated__". inline "cic:/CoRN/ftc/RefSeparated/RS_He.con". -inline "cic:/CoRN/ftc/RefSeparated/contF'.con". +inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/contF'.con" "Separating__Separated__". -inline "cic:/CoRN/ftc/RefSeparated/d.con". +inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/d.con" "Separating__Separated__". inline "cic:/CoRN/ftc/RefSeparated/RS_Hd.con". inline "cic:/CoRN/ftc/RefSeparated/RS_Hd'.con". -inline "cic:/CoRN/ftc/RefSeparated/csi.var". +inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/csi.var" "Separating__Separated__". -inline "cic:/CoRN/ftc/RefSeparated/Hcsi.var". +inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Hcsi.var" "Separating__Separated__". -inline "cic:/CoRN/ftc/RefSeparated/M.con". +inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/M.con" "Separating__Separated__". -inline "cic:/CoRN/ftc/RefSeparated/deltaP.con". +inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/deltaP.con" "Separating__Separated__". -inline "cic:/CoRN/ftc/RefSeparated/deltaR.con". +inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/deltaR.con" "Separating__Separated__". -inline "cic:/CoRN/ftc/RefSeparated/delta.con". +inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/delta.con" "Separating__Separated__". inline "cic:/CoRN/ftc/RefSeparated/RS_delta_deltaP.con". @@ -101,24 +101,24 @@ inline "cic:/CoRN/ftc/RefSeparated/RS_delta_d.con". inline "cic:/CoRN/ftc/RefSeparated/RS_delta_pos.con". (* UNEXPORTED -Section Defining_ai'. +Section Defining_ai' *) -inline "cic:/CoRN/ftc/RefSeparated/i.var". +inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/i.var" "Separating__Separated__Defining_ai'__". -inline "cic:/CoRN/ftc/RefSeparated/Hi.var". +inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/Hi.var" "Separating__Separated__Defining_ai'__". inline "cic:/CoRN/ftc/RefSeparated/separation_conseq.con". -inline "cic:/CoRN/ftc/RefSeparated/pred1.con". +inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/pred1.con" "Separating__Separated__Defining_ai'__". -inline "cic:/CoRN/ftc/RefSeparated/pred2.con". +inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/pred2.con" "Separating__Separated__Defining_ai'__". inline "cic:/CoRN/ftc/RefSeparated/sep__sep_aux_lemma.con". -inline "cic:/CoRN/ftc/RefSeparated/Hi0.var". +inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/Hi0.var" "Separating__Separated__Defining_ai'__". -inline "cic:/CoRN/ftc/RefSeparated/Hin.var". +inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/Hin.var" "Separating__Separated__Defining_ai'__". inline "cic:/CoRN/ftc/RefSeparated/sep__sep_fun_i.con". @@ -129,7 +129,7 @@ inline "cic:/CoRN/ftc/RefSeparated/sep__sep_less.con". inline "cic:/CoRN/ftc/RefSeparated/sep__sep_ap.con". (* UNEXPORTED -End Defining_ai'. +End Defining_ai' *) inline "cic:/CoRN/ftc/RefSeparated/sep__sep_fun.con". @@ -150,9 +150,9 @@ inline "cic:/CoRN/ftc/RefSeparated/sep__sep_part.con". inline "cic:/CoRN/ftc/RefSeparated/sep__sep_lemma.con". -inline "cic:/CoRN/ftc/RefSeparated/g.var". +inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/g.var" "Separating__Separated__". -inline "cic:/CoRN/ftc/RefSeparated/gP.var". +inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/gP.var" "Separating__Separated__". inline "cic:/CoRN/ftc/RefSeparated/sep__sep_points.con". @@ -174,7 +174,7 @@ inline "cic:/CoRN/ftc/RefSeparated/sep__sep_Sum.con". inline "cic:/CoRN/ftc/RefSeparated/sep__sep_Mesh.con". (* UNEXPORTED -End Separating__Separated. +End Separating__Separated *) (* end hide *) diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/RefSeparating.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/RefSeparating.ma index 4a30dc549..1fc9f41f8 100644 --- a/helm/software/matita/contribs/CoRN-Decl/ftc/RefSeparating.ma +++ b/helm/software/matita/contribs/CoRN-Decl/ftc/RefSeparating.ma @@ -27,50 +27,50 @@ include "ftc/COrdLemmas.ma". include "ftc/Partitions.ma". (* UNEXPORTED -Section Separating_Partition. +Section Separating_Partition *) -inline "cic:/CoRN/ftc/RefSeparating/a.var". +inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/a.var" "Separating_Partition__". -inline "cic:/CoRN/ftc/RefSeparating/b.var". +inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/b.var" "Separating_Partition__". -inline "cic:/CoRN/ftc/RefSeparating/Hab.var". +inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/Hab.var" "Separating_Partition__". -inline "cic:/CoRN/ftc/RefSeparating/I.con". +inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/I.con" "Separating_Partition__". -inline "cic:/CoRN/ftc/RefSeparating/F.var". +inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/F.var" "Separating_Partition__". -inline "cic:/CoRN/ftc/RefSeparating/contF.var". +inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/contF.var" "Separating_Partition__". -inline "cic:/CoRN/ftc/RefSeparating/incF.var". +inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/incF.var" "Separating_Partition__". -inline "cic:/CoRN/ftc/RefSeparating/Hab'.var". +inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/Hab'.var" "Separating_Partition__". -inline "cic:/CoRN/ftc/RefSeparating/n.var". +inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/n.var" "Separating_Partition__". -inline "cic:/CoRN/ftc/RefSeparating/P.var". +inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/P.var" "Separating_Partition__". -inline "cic:/CoRN/ftc/RefSeparating/alpha.var". +inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/alpha.var" "Separating_Partition__". -inline "cic:/CoRN/ftc/RefSeparating/Halpha.var". +inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/Halpha.var" "Separating_Partition__". -inline "cic:/CoRN/ftc/RefSeparating/csi.var". +inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/csi.var" "Separating_Partition__". -inline "cic:/CoRN/ftc/RefSeparating/Hcsi.var". +inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/Hcsi.var" "Separating_Partition__". -inline "cic:/CoRN/ftc/RefSeparating/M.con". +inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/M.con" "Separating_Partition__". inline "cic:/CoRN/ftc/RefSeparating/RS'_pos_n.con". inline "cic:/CoRN/ftc/RefSeparating/SPap_n.con". -inline "cic:/CoRN/ftc/RefSeparating/delta.con". +inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/delta.con" "Separating_Partition__". inline "cic:/CoRN/ftc/RefSeparating/RS'_delta_pos.con". inline "cic:/CoRN/ftc/RefSeparating/RS'_delta_csi.con". -inline "cic:/CoRN/ftc/RefSeparating/Hab''.var". +inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/Hab''.var" "Separating_Partition__". inline "cic:/CoRN/ftc/RefSeparating/sep__part_lemma.con". @@ -134,11 +134,11 @@ inline "cic:/CoRN/ftc/RefSeparating/sep__part_mon.con". inline "cic:/CoRN/ftc/RefSeparating/sep__part_mon_Mesh.con". -inline "cic:/CoRN/ftc/RefSeparating/g.var". +inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/g.var" "Separating_Partition__". -inline "cic:/CoRN/ftc/RefSeparating/gP.var". +inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/gP.var" "Separating_Partition__". -inline "cic:/CoRN/ftc/RefSeparating/gP'.var". +inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/gP'.var" "Separating_Partition__". inline "cic:/CoRN/ftc/RefSeparating/sep__part_pts.con". @@ -178,7 +178,7 @@ inline "cic:/CoRN/ftc/RefSeparating/sep__part_aux.con". inline "cic:/CoRN/ftc/RefSeparating/sep__part_Sum.con". (* UNEXPORTED -End Separating_Partition. +End Separating_Partition *) (* end hide *) diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/Rolle.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/Rolle.ma index 7eda2c5ae..47e13105b 100644 --- a/helm/software/matita/contribs/CoRN-Decl/ftc/Rolle.ma +++ b/helm/software/matita/contribs/CoRN-Decl/ftc/Rolle.ma @@ -25,7 +25,7 @@ include "tactics/DiffTactics2.ma". include "ftc/MoreFunctions.ma". (* UNEXPORTED -Section Rolle. +Section Rolle *) (*#* *Rolle's Theorem @@ -42,189 +42,189 @@ We now begin to work with partial functions. We begin by stating and proving Ro (* begin hide *) -inline "cic:/CoRN/ftc/Rolle/a.var". +inline "cic:/CoRN/ftc/Rolle/Rolle/a.var" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/b.var". +inline "cic:/CoRN/ftc/Rolle/Rolle/b.var" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/Hab'.var". +inline "cic:/CoRN/ftc/Rolle/Rolle/Hab'.var" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/Hab.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/Hab.con" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/I.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/I.con" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/F.var". +inline "cic:/CoRN/ftc/Rolle/Rolle/F.var" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/F'.var". +inline "cic:/CoRN/ftc/Rolle/Rolle/F'.var" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/derF.var". +inline "cic:/CoRN/ftc/Rolle/Rolle/derF.var" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/Ha.var". +inline "cic:/CoRN/ftc/Rolle/Rolle/Ha.var" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/Hb.var". +inline "cic:/CoRN/ftc/Rolle/Rolle/Hb.var" "Rolle__". (* end hide *) (* begin show *) -inline "cic:/CoRN/ftc/Rolle/Fab.var". +inline "cic:/CoRN/ftc/Rolle/Rolle/Fab.var" "Rolle__". (* end show *) (* begin hide *) -inline "cic:/CoRN/ftc/Rolle/e.var". +inline "cic:/CoRN/ftc/Rolle/Rolle/e.var" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/He.var". +inline "cic:/CoRN/ftc/Rolle/Rolle/He.var" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/contF'.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/contF'.con" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/derivF.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/derivF.con" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/Rolle_lemma2.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma2.con" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/df.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/df.con" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/Hdf.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/Hdf.con" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/Hf.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/Hf.con" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/Rolle_lemma3.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma3.con" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/df'.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/df'.con" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/Hdf'.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/Hdf'.con" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/Hf'.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/Hf'.con" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/d.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/d.con" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/Hd.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/Hd.con" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/incF.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/incF.con" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/n.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/n.con" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/fcp.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/fcp.con" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/Rolle_lemma1.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma1.con" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/incF'.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/incF'.con" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/fcp'.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/fcp'.con" "Rolle__". (* NOTATION Notation cp := (compact_part a b Hab' d Hd). *) -inline "cic:/CoRN/ftc/Rolle/Rolle_lemma4.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma4.con" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/Rolle_lemma5.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma5.con" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/Rolle_lemma6.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma6.con" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/Rolle_lemma7.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma7.con" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/j.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/j.con" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/Hj.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/Hj.con" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/Hj'.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/Hj'.con" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/k.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/k.con" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/Hk.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/Hk.con" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/Hk'.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/Hk'.con" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/Rolle_lemma8.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma8.con" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/Rolle_lemma9.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma9.con" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/Rolle_lemma10.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma10.con" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/Rolle_lemma11.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma11.con" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/Rolle_lemma12.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma12.con" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/Rolle_lemma13.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma13.con" "Rolle__". -inline "cic:/CoRN/ftc/Rolle/Rolle_lemma15.con". +inline "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma15.con" "Rolle__". (* end hide *) inline "cic:/CoRN/ftc/Rolle/Rolle.con". (* UNEXPORTED -End Rolle. +End Rolle *) (* UNEXPORTED -Section Law_of_the_Mean. +Section Law_of_the_Mean *) (*#* The following is a simple corollary: *) -inline "cic:/CoRN/ftc/Rolle/a.var". +inline "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/a.var" "Law_of_the_Mean__". -inline "cic:/CoRN/ftc/Rolle/b.var". +inline "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/b.var" "Law_of_the_Mean__". -inline "cic:/CoRN/ftc/Rolle/Hab'.var". +inline "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/Hab'.var" "Law_of_the_Mean__". (* begin hide *) -inline "cic:/CoRN/ftc/Rolle/Hab.con". +inline "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/Hab.con" "Law_of_the_Mean__". -inline "cic:/CoRN/ftc/Rolle/I.con". +inline "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/I.con" "Law_of_the_Mean__". (* end hide *) -inline "cic:/CoRN/ftc/Rolle/F.var". +inline "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/F.var" "Law_of_the_Mean__". -inline "cic:/CoRN/ftc/Rolle/F'.var". +inline "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/F'.var" "Law_of_the_Mean__". -inline "cic:/CoRN/ftc/Rolle/HF.var". +inline "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/HF.var" "Law_of_the_Mean__". (* begin show *) -inline "cic:/CoRN/ftc/Rolle/HA.var". +inline "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/HA.var" "Law_of_the_Mean__". -inline "cic:/CoRN/ftc/Rolle/HB.var". +inline "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/HB.var" "Law_of_the_Mean__". (* end show *) inline "cic:/CoRN/ftc/Rolle/Law_of_the_Mean_I.con". (* UNEXPORTED -End Law_of_the_Mean. +End Law_of_the_Mean *) (* UNEXPORTED -Section Corollaries. +Section Corollaries *) (*#* We can also state these theorems without expliciting the derivative of [F]. *) -inline "cic:/CoRN/ftc/Rolle/a.var". +inline "cic:/CoRN/ftc/Rolle/Corollaries/a.var" "Corollaries__". -inline "cic:/CoRN/ftc/Rolle/b.var". +inline "cic:/CoRN/ftc/Rolle/Corollaries/b.var" "Corollaries__". -inline "cic:/CoRN/ftc/Rolle/Hab'.var". +inline "cic:/CoRN/ftc/Rolle/Corollaries/Hab'.var" "Corollaries__". (* begin hide *) -inline "cic:/CoRN/ftc/Rolle/Hab.con". +inline "cic:/CoRN/ftc/Rolle/Corollaries/Hab.con" "Corollaries__". (* end hide *) -inline "cic:/CoRN/ftc/Rolle/F.var". +inline "cic:/CoRN/ftc/Rolle/Corollaries/F.var" "Corollaries__". (* begin show *) -inline "cic:/CoRN/ftc/Rolle/HF.var". +inline "cic:/CoRN/ftc/Rolle/Corollaries/HF.var" "Corollaries__". (* end show *) @@ -233,11 +233,11 @@ inline "cic:/CoRN/ftc/Rolle/Rolle'.con". inline "cic:/CoRN/ftc/Rolle/Law_of_the_Mean'_I.con". (* UNEXPORTED -End Corollaries. +End Corollaries *) (* UNEXPORTED -Section Generalizations. +Section Generalizations *) (*#* @@ -250,25 +250,25 @@ state it also in this form. %\end{convention}% *) -inline "cic:/CoRN/ftc/Rolle/I.var". +inline "cic:/CoRN/ftc/Rolle/Generalizations/I.var" "Generalizations__". -inline "cic:/CoRN/ftc/Rolle/pI.var". +inline "cic:/CoRN/ftc/Rolle/Generalizations/pI.var" "Generalizations__". -inline "cic:/CoRN/ftc/Rolle/F.var". +inline "cic:/CoRN/ftc/Rolle/Generalizations/F.var" "Generalizations__". -inline "cic:/CoRN/ftc/Rolle/F'.var". +inline "cic:/CoRN/ftc/Rolle/Generalizations/F'.var" "Generalizations__". (* begin show *) -inline "cic:/CoRN/ftc/Rolle/derF.var". +inline "cic:/CoRN/ftc/Rolle/Generalizations/derF.var" "Generalizations__". (* end show *) (* begin hide *) -inline "cic:/CoRN/ftc/Rolle/incF.con". +inline "cic:/CoRN/ftc/Rolle/Generalizations/incF.con" "Generalizations__". -inline "cic:/CoRN/ftc/Rolle/incF'.con". +inline "cic:/CoRN/ftc/Rolle/Generalizations/incF'.con" "Generalizations__". (* end hide *) @@ -281,6 +281,6 @@ We further generalize the mean law by writing as an explicit bound. inline "cic:/CoRN/ftc/Rolle/Law_of_the_Mean_ineq.con". (* UNEXPORTED -End Generalizations. +End Generalizations *) diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/StrongIVT.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/StrongIVT.ma index fe8820e0a..b0f800d00 100644 --- a/helm/software/matita/contribs/CoRN-Decl/ftc/StrongIVT.ma +++ b/helm/software/matita/contribs/CoRN-Decl/ftc/StrongIVT.ma @@ -25,7 +25,7 @@ include "ftc/WeakIVT.ma". include "ftc/CalculusTheorems.ma". (* UNEXPORTED -Section IVT'. +Section IVT' *) (*#* ** Strong IVT for partial functions @@ -36,55 +36,55 @@ part, we will simply do that, repeating the previous construction. The same notations and conventions apply as before. *) -inline "cic:/CoRN/ftc/StrongIVT/a.var". +inline "cic:/CoRN/ftc/StrongIVT/IVT'/a.var" "IVT'__". -inline "cic:/CoRN/ftc/StrongIVT/b.var". +inline "cic:/CoRN/ftc/StrongIVT/IVT'/b.var" "IVT'__". -inline "cic:/CoRN/ftc/StrongIVT/Hab'.var". +inline "cic:/CoRN/ftc/StrongIVT/IVT'/Hab'.var" "IVT'__". -inline "cic:/CoRN/ftc/StrongIVT/Hab.var". +inline "cic:/CoRN/ftc/StrongIVT/IVT'/Hab.var" "IVT'__". (* begin hide *) -inline "cic:/CoRN/ftc/StrongIVT/I.con". +inline "cic:/CoRN/ftc/StrongIVT/IVT'/I.con" "IVT'__". -inline "cic:/CoRN/ftc/StrongIVT/I'.con". +inline "cic:/CoRN/ftc/StrongIVT/IVT'/I'.con" "IVT'__". (* end hide *) -inline "cic:/CoRN/ftc/StrongIVT/F.var". +inline "cic:/CoRN/ftc/StrongIVT/IVT'/F.var" "IVT'__". -inline "cic:/CoRN/ftc/StrongIVT/contF.var". +inline "cic:/CoRN/ftc/StrongIVT/IVT'/contF.var" "IVT'__". (* begin hide *) -inline "cic:/CoRN/ftc/StrongIVT/incF.con". +inline "cic:/CoRN/ftc/StrongIVT/IVT'/incF.con" "IVT'__". (* end hide *) (* begin show *) -inline "cic:/CoRN/ftc/StrongIVT/incrF.var". +inline "cic:/CoRN/ftc/StrongIVT/IVT'/incrF.var" "IVT'__". (* end show *) (* begin hide *) -inline "cic:/CoRN/ftc/StrongIVT/Ha.con". +inline "cic:/CoRN/ftc/StrongIVT/IVT'/Ha.con" "IVT'__". -inline "cic:/CoRN/ftc/StrongIVT/Hb.con". +inline "cic:/CoRN/ftc/StrongIVT/IVT'/Hb.con" "IVT'__". -inline "cic:/CoRN/ftc/StrongIVT/HFab'.con". +inline "cic:/CoRN/ftc/StrongIVT/IVT'/HFab'.con" "IVT'__". (* end hide *) (* begin show *) -inline "cic:/CoRN/ftc/StrongIVT/z.var". +inline "cic:/CoRN/ftc/StrongIVT/IVT'/z.var" "IVT'__". -inline "cic:/CoRN/ftc/StrongIVT/Haz.var". +inline "cic:/CoRN/ftc/StrongIVT/IVT'/Haz.var" "IVT'__". -inline "cic:/CoRN/ftc/StrongIVT/Hzb.var". +inline "cic:/CoRN/ftc/StrongIVT/IVT'/Hzb.var" "IVT'__". (* end show *) @@ -124,9 +124,9 @@ inline "cic:/CoRN/ftc/StrongIVT/a'_seq_Cauchy.con". inline "cic:/CoRN/ftc/StrongIVT/b'_seq_Cauchy.con". -inline "cic:/CoRN/ftc/StrongIVT/xa.con". +inline "cic:/CoRN/ftc/StrongIVT/IVT'/xa.con" "IVT'__". -inline "cic:/CoRN/ftc/StrongIVT/xb.con". +inline "cic:/CoRN/ftc/StrongIVT/IVT'/xb.con" "IVT'__". inline "cic:/CoRN/ftc/StrongIVT/a'_seq_b'_seq_lim.con". @@ -135,7 +135,7 @@ inline "cic:/CoRN/ftc/StrongIVT/xa'_in_interval.con". inline "cic:/CoRN/ftc/StrongIVT/IVT'_I.con". (* UNEXPORTED -End IVT'. +End IVT' *) (*#* **Other formulations diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/Taylor.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/Taylor.ma index 9a9437ade..2bd2f07aa 100644 --- a/helm/software/matita/contribs/CoRN-Decl/ftc/Taylor.ma +++ b/helm/software/matita/contribs/CoRN-Decl/ftc/Taylor.ma @@ -27,7 +27,7 @@ Opaque Min Max N_Deriv. *) (* UNEXPORTED -Section More_Taylor_Defs. +Section More_Taylor_Defs *) (*#* **General case @@ -39,31 +39,31 @@ The generalization to arbitrary intervals just needs a few more definitions. %\end{convention}% *) -inline "cic:/CoRN/ftc/Taylor/I.var". +inline "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/I.var" "More_Taylor_Defs__". -inline "cic:/CoRN/ftc/Taylor/pI.var". +inline "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/pI.var" "More_Taylor_Defs__". -inline "cic:/CoRN/ftc/Taylor/F.var". +inline "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/F.var" "More_Taylor_Defs__". (* begin show *) -inline "cic:/CoRN/ftc/Taylor/deriv_Sn.con". +inline "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/deriv_Sn.con" "More_Taylor_Defs__". (* end show *) -inline "cic:/CoRN/ftc/Taylor/a.var". +inline "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/a.var" "More_Taylor_Defs__". -inline "cic:/CoRN/ftc/Taylor/b.var". +inline "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/b.var" "More_Taylor_Defs__". -inline "cic:/CoRN/ftc/Taylor/Ha.var". +inline "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/Ha.var" "More_Taylor_Defs__". -inline "cic:/CoRN/ftc/Taylor/Hb.var". +inline "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/Hb.var" "More_Taylor_Defs__". (* begin show *) -inline "cic:/CoRN/ftc/Taylor/fi.con". +inline "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/fi.con" "More_Taylor_Defs__". -inline "cic:/CoRN/ftc/Taylor/funct_i.con". +inline "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/funct_i.con" "More_Taylor_Defs__". (* end show *) @@ -88,11 +88,11 @@ inline "cic:/CoRN/ftc/Taylor/Taylor_lemma_ap.con". inline "cic:/CoRN/ftc/Taylor/Taylor'.con". (* UNEXPORTED -End More_Taylor_Defs. +End More_Taylor_Defs *) (* UNEXPORTED -Section Taylor_Theorem. +Section Taylor_Theorem *) (*#* @@ -104,41 +104,41 @@ order up to [n] and [F'] be the nth-derivative of [F]. %\end{convention}% *) -inline "cic:/CoRN/ftc/Taylor/I.var". +inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/I.var" "Taylor_Theorem__". -inline "cic:/CoRN/ftc/Taylor/pI.var". +inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/pI.var" "Taylor_Theorem__". -inline "cic:/CoRN/ftc/Taylor/F.var". +inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/F.var" "Taylor_Theorem__". -inline "cic:/CoRN/ftc/Taylor/n.var". +inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/n.var" "Taylor_Theorem__". -inline "cic:/CoRN/ftc/Taylor/f.var". +inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/f.var" "Taylor_Theorem__". -inline "cic:/CoRN/ftc/Taylor/goodF.var". +inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/goodF.var" "Taylor_Theorem__". -inline "cic:/CoRN/ftc/Taylor/goodF'.var". +inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/goodF'.var" "Taylor_Theorem__". -inline "cic:/CoRN/ftc/Taylor/derF.var". +inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/derF.var" "Taylor_Theorem__". -inline "cic:/CoRN/ftc/Taylor/F'.var". +inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/F'.var" "Taylor_Theorem__". -inline "cic:/CoRN/ftc/Taylor/derF'.var". +inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/derF'.var" "Taylor_Theorem__". -inline "cic:/CoRN/ftc/Taylor/a.var". +inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/a.var" "Taylor_Theorem__". -inline "cic:/CoRN/ftc/Taylor/b.var". +inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/b.var" "Taylor_Theorem__". -inline "cic:/CoRN/ftc/Taylor/Ha.var". +inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/Ha.var" "Taylor_Theorem__". -inline "cic:/CoRN/ftc/Taylor/Hb.var". +inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/Hb.var" "Taylor_Theorem__". (* begin show *) -inline "cic:/CoRN/ftc/Taylor/funct_i.con". +inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/funct_i.con" "Taylor_Theorem__". inline "cic:/CoRN/ftc/Taylor/Taylor_Seq.con". -inline "cic:/CoRN/ftc/Taylor/deriv_Sn.con". +inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/deriv_Sn.con" "Taylor_Theorem__". (* end show *) @@ -151,6 +151,6 @@ Transparent N_Deriv. inline "cic:/CoRN/ftc/Taylor/Taylor.con". (* UNEXPORTED -End Taylor_Theorem. +End Taylor_Theorem *) diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/TaylorLemma.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/TaylorLemma.ma index 7f704092e..29affb739 100644 --- a/helm/software/matita/contribs/CoRN-Decl/ftc/TaylorLemma.ma +++ b/helm/software/matita/contribs/CoRN-Decl/ftc/TaylorLemma.ma @@ -27,7 +27,7 @@ Opaque Min. *) (* UNEXPORTED -Section Taylor_Defs. +Section Taylor_Defs *) (*#* *Taylor's Theorem @@ -44,31 +44,31 @@ define the nth order derivative of [F] in the interval [[Min(a,b),Max(a,b)]]. *) -inline "cic:/CoRN/ftc/TaylorLemma/a.var". +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/a.var" "Taylor_Defs__". -inline "cic:/CoRN/ftc/TaylorLemma/b.var". +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/b.var" "Taylor_Defs__". -inline "cic:/CoRN/ftc/TaylorLemma/Hap.var". +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Hap.var" "Taylor_Defs__". (* begin hide *) -inline "cic:/CoRN/ftc/TaylorLemma/Hab'.con". +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Hab'.con" "Taylor_Defs__". -inline "cic:/CoRN/ftc/TaylorLemma/Hab.con". +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Hab.con" "Taylor_Defs__". -inline "cic:/CoRN/ftc/TaylorLemma/I.con". +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/I.con" "Taylor_Defs__". (* end hide *) -inline "cic:/CoRN/ftc/TaylorLemma/F.var". +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/F.var" "Taylor_Defs__". -inline "cic:/CoRN/ftc/TaylorLemma/Ha.var". +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Ha.var" "Taylor_Defs__". -inline "cic:/CoRN/ftc/TaylorLemma/Hb.var". +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Hb.var" "Taylor_Defs__". (* begin show *) -inline "cic:/CoRN/ftc/TaylorLemma/fi.con". +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/fi.con" "Taylor_Defs__". (* end show *) @@ -94,9 +94,9 @@ corresponding to [a] and [b]. (* begin hide *) -inline "cic:/CoRN/ftc/TaylorLemma/TL_compact_a.con". +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/TL_compact_a.con" "Taylor_Defs__". -inline "cic:/CoRN/ftc/TaylorLemma/TL_compact_b.con". +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/TL_compact_b.con" "Taylor_Defs__". (* NOTATION Notation A := (Build_subcsetoid_crr IR _ _ TL_compact_a). @@ -110,13 +110,13 @@ Notation B := (Build_subcsetoid_crr IR _ _ TL_compact_b). (* begin show *) -inline "cic:/CoRN/ftc/TaylorLemma/funct_i.con". +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/funct_i.con" "Taylor_Defs__". (* end show *) (* begin hide *) -inline "cic:/CoRN/ftc/TaylorLemma/funct_i'.con". +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/funct_i'.con" "Taylor_Defs__". inline "cic:/CoRN/ftc/TaylorLemma/TL_a_i.con". @@ -149,7 +149,7 @@ inline "cic:/CoRN/ftc/TaylorLemma/Taylor_seq'.con". (* begin hide *) -inline "cic:/CoRN/ftc/TaylorLemma/Taylor_seq'_aux.con". +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Taylor_seq'_aux.con" "Taylor_Defs__". inline "cic:/CoRN/ftc/TaylorLemma/TL_lemma_a.con". @@ -173,7 +173,7 @@ inline "cic:/CoRN/ftc/TaylorLemma/Taylor_rem.con". (* begin hide *) -inline "cic:/CoRN/ftc/TaylorLemma/g.con". +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/g.con" "Taylor_Defs__". (* UNEXPORTED Opaque Taylor_seq'_aux Taylor_rem. @@ -227,7 +227,7 @@ inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma5.con". Transparent funct_i' FSumx. *) -inline "cic:/CoRN/ftc/TaylorLemma/funct_aux.con". +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/funct_aux.con" "Taylor_Defs__". inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma6.con". @@ -267,7 +267,7 @@ Transparent funct_aux. inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma9.con". -inline "cic:/CoRN/ftc/TaylorLemma/g'.con". +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/g'.con" "Taylor_Defs__". (* UNEXPORTED Opaque Taylor_rem funct_aux. @@ -288,9 +288,9 @@ Now Taylor's theorem. %\end{convention}% *) -inline "cic:/CoRN/ftc/TaylorLemma/e.var". +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/e.var" "Taylor_Defs__". -inline "cic:/CoRN/ftc/TaylorLemma/He.var". +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/He.var" "Taylor_Defs__". (* begin hide *) @@ -300,7 +300,7 @@ inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma11.con". (* begin show *) -inline "cic:/CoRN/ftc/TaylorLemma/deriv_Sn'.con". +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/deriv_Sn'.con" "Taylor_Defs__". (* end show *) @@ -325,6 +325,6 @@ Transparent Taylor_rem funct_aux. inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma.con". (* UNEXPORTED -End Taylor_Defs. +End Taylor_Defs *) diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/WeakIVT.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/WeakIVT.ma index 8001b5376..e59f23e88 100644 --- a/helm/software/matita/contribs/CoRN-Decl/ftc/WeakIVT.ma +++ b/helm/software/matita/contribs/CoRN-Decl/ftc/WeakIVT.ma @@ -44,24 +44,24 @@ will prove them here. *) (* UNEXPORTED -Section Lemma1. +Section Lemma1 *) -inline "cic:/CoRN/ftc/WeakIVT/a.var". +inline "cic:/CoRN/ftc/WeakIVT/Lemma1/a.var" "Lemma1__". -inline "cic:/CoRN/ftc/WeakIVT/b.var". +inline "cic:/CoRN/ftc/WeakIVT/Lemma1/b.var" "Lemma1__". -inline "cic:/CoRN/ftc/WeakIVT/Hab.var". +inline "cic:/CoRN/ftc/WeakIVT/Lemma1/Hab.var" "Lemma1__". (* begin hide *) -inline "cic:/CoRN/ftc/WeakIVT/I.con". +inline "cic:/CoRN/ftc/WeakIVT/Lemma1/I.con" "Lemma1__". (* end hide *) -inline "cic:/CoRN/ftc/WeakIVT/F.var". +inline "cic:/CoRN/ftc/WeakIVT/Lemma1/F.var" "Lemma1__". -inline "cic:/CoRN/ftc/WeakIVT/contF.var". +inline "cic:/CoRN/ftc/WeakIVT/Lemma1/contF.var" "Lemma1__". (*#* **First Lemmas @@ -77,28 +77,28 @@ enough to [z]. inline "cic:/CoRN/ftc/WeakIVT/Weak_IVT_ap_lft.con". (* UNEXPORTED -End Lemma1. +End Lemma1 *) (* UNEXPORTED -Section Lemma2. +Section Lemma2 *) -inline "cic:/CoRN/ftc/WeakIVT/a.var". +inline "cic:/CoRN/ftc/WeakIVT/Lemma2/a.var" "Lemma2__". -inline "cic:/CoRN/ftc/WeakIVT/b.var". +inline "cic:/CoRN/ftc/WeakIVT/Lemma2/b.var" "Lemma2__". -inline "cic:/CoRN/ftc/WeakIVT/Hab.var". +inline "cic:/CoRN/ftc/WeakIVT/Lemma2/Hab.var" "Lemma2__". (* begin hide *) -inline "cic:/CoRN/ftc/WeakIVT/I.con". +inline "cic:/CoRN/ftc/WeakIVT/Lemma2/I.con" "Lemma2__". (* end hide *) -inline "cic:/CoRN/ftc/WeakIVT/F.var". +inline "cic:/CoRN/ftc/WeakIVT/Lemma2/F.var" "Lemma2__". -inline "cic:/CoRN/ftc/WeakIVT/contF.var". +inline "cic:/CoRN/ftc/WeakIVT/Lemma2/contF.var" "Lemma2__". (*#* If [f(b) [<] f(a)], a similar result holds: @@ -107,11 +107,11 @@ If [f(b) [<] f(a)], a similar result holds: inline "cic:/CoRN/ftc/WeakIVT/Weak_IVT_ap_rht.con". (* UNEXPORTED -End Lemma2. +End Lemma2 *) (* UNEXPORTED -Section IVT. +Section IVT *) (*#* **The IVT @@ -122,53 +122,53 @@ these assumptions, we can build two sequences of values which converge to [x0] such that [f(x0) [=] z]. *) -inline "cic:/CoRN/ftc/WeakIVT/a.var". +inline "cic:/CoRN/ftc/WeakIVT/IVT/a.var" "IVT__". -inline "cic:/CoRN/ftc/WeakIVT/b.var". +inline "cic:/CoRN/ftc/WeakIVT/IVT/b.var" "IVT__". -inline "cic:/CoRN/ftc/WeakIVT/Hab'.var". +inline "cic:/CoRN/ftc/WeakIVT/IVT/Hab'.var" "IVT__". -inline "cic:/CoRN/ftc/WeakIVT/Hab.var". +inline "cic:/CoRN/ftc/WeakIVT/IVT/Hab.var" "IVT__". (* begin hide *) -inline "cic:/CoRN/ftc/WeakIVT/I.con". +inline "cic:/CoRN/ftc/WeakIVT/IVT/I.con" "IVT__". (* end hide *) -inline "cic:/CoRN/ftc/WeakIVT/F.var". +inline "cic:/CoRN/ftc/WeakIVT/IVT/F.var" "IVT__". -inline "cic:/CoRN/ftc/WeakIVT/contF.var". +inline "cic:/CoRN/ftc/WeakIVT/IVT/contF.var" "IVT__". (* begin hide *) -inline "cic:/CoRN/ftc/WeakIVT/incF.con". +inline "cic:/CoRN/ftc/WeakIVT/IVT/incF.con" "IVT__". (* end hide *) (* begin show *) -inline "cic:/CoRN/ftc/WeakIVT/incrF.var". +inline "cic:/CoRN/ftc/WeakIVT/IVT/incrF.var" "IVT__". (* end show *) (* begin hide *) -inline "cic:/CoRN/ftc/WeakIVT/Ha.con". +inline "cic:/CoRN/ftc/WeakIVT/IVT/Ha.con" "IVT__". -inline "cic:/CoRN/ftc/WeakIVT/Hb.con". +inline "cic:/CoRN/ftc/WeakIVT/IVT/Hb.con" "IVT__". -inline "cic:/CoRN/ftc/WeakIVT/HFab'.con". +inline "cic:/CoRN/ftc/WeakIVT/IVT/HFab'.con" "IVT__". (* end hide *) (* begin show *) -inline "cic:/CoRN/ftc/WeakIVT/z.var". +inline "cic:/CoRN/ftc/WeakIVT/IVT/z.var" "IVT__". -inline "cic:/CoRN/ftc/WeakIVT/Haz.var". +inline "cic:/CoRN/ftc/WeakIVT/IVT/Haz.var" "IVT__". -inline "cic:/CoRN/ftc/WeakIVT/Hzb.var". +inline "cic:/CoRN/ftc/WeakIVT/IVT/Hzb.var" "IVT__". (* end show *) @@ -221,9 +221,9 @@ inline "cic:/CoRN/ftc/WeakIVT/a_seq_Cauchy.con". inline "cic:/CoRN/ftc/WeakIVT/b_seq_Cauchy.con". -inline "cic:/CoRN/ftc/WeakIVT/xa.con". +inline "cic:/CoRN/ftc/WeakIVT/IVT/xa.con" "IVT__". -inline "cic:/CoRN/ftc/WeakIVT/xb.con". +inline "cic:/CoRN/ftc/WeakIVT/IVT/xb.con" "IVT__". inline "cic:/CoRN/ftc/WeakIVT/a_seq_b_seq_lim.con". @@ -232,6 +232,6 @@ inline "cic:/CoRN/ftc/WeakIVT/xa_in_interval.con". inline "cic:/CoRN/ftc/WeakIVT/IVT_I.con". (* UNEXPORTED -End IVT. +End IVT *) diff --git a/helm/software/matita/contribs/CoRN-Decl/metrics/CMetricSpaces.ma b/helm/software/matita/contribs/CoRN-Decl/metrics/CMetricSpaces.ma index c50761c19..45f6ff0c6 100644 --- a/helm/software/matita/contribs/CoRN-Decl/metrics/CMetricSpaces.ma +++ b/helm/software/matita/contribs/CoRN-Decl/metrics/CMetricSpaces.ma @@ -25,7 +25,7 @@ include "metrics/Prod_Sub.ma". include "metrics/Equiv.ma". (* UNEXPORTED -Section Definition_MS. +Section Definition_MS *) (*#* **Definition of Metric Space @@ -36,11 +36,11 @@ inline "cic:/CoRN/metrics/CMetricSpaces/CMetricSpace.ind". coercion cic:/matita/CoRN-Decl/metrics/CMetricSpaces/scms_crr.con 0 (* compounds *). (* UNEXPORTED -End Definition_MS. +End Definition_MS *) (* UNEXPORTED -Section MS_basics. +Section MS_basics *) (*#* **Metric Space basics @@ -53,11 +53,11 @@ inline "cic:/CoRN/metrics/CMetricSpaces/d_zero_imp_eq.con". inline "cic:/CoRN/metrics/CMetricSpaces/is_CMetricSpace_diag_zero.con". (* UNEXPORTED -End MS_basics. +End MS_basics *) (* UNEXPORTED -Section prodandsub. +Section prodandsub *) (*#* **Product-Metric-Spaces and Sub-Metric-Spaces @@ -88,11 +88,11 @@ Implicit Arguments SubMetricSpace [X]. *) (* UNEXPORTED -End prodandsub. +End prodandsub *) (* UNEXPORTED -Section Zeroff. +Section Zeroff *) (*#* **Pseudo Metric Spaces vs Metric Spaces @@ -167,11 +167,11 @@ inline "cic:/CoRN/metrics/CMetricSpaces/Emb.con". inline "cic:/CoRN/metrics/CMetricSpaces/Quotient_pres_CMetricSpace.con". (* UNEXPORTED -End Zeroff. +End Zeroff *) (* UNEXPORTED -Section Limitt. +Section Limitt *) (*#* **Limit @@ -200,6 +200,6 @@ inline "cic:/CoRN/metrics/CMetricSpaces/d_wd.con". inline "cic:/CoRN/metrics/CMetricSpaces/unique_MSseqLim.con". (* UNEXPORTED -End Limitt. +End Limitt *) diff --git a/helm/software/matita/contribs/CoRN-Decl/metrics/CPMSTheory.ma b/helm/software/matita/contribs/CoRN-Decl/metrics/CPMSTheory.ma index aef56d5a9..50786005f 100644 --- a/helm/software/matita/contribs/CoRN-Decl/metrics/CPMSTheory.ma +++ b/helm/software/matita/contribs/CoRN-Decl/metrics/CPMSTheory.ma @@ -23,7 +23,7 @@ include "CoRN.ma". include "metrics/Prod_Sub.ma". (* UNEXPORTED -Section lists. +Section lists *) (*#* **Lists @@ -67,11 +67,11 @@ of the list of images of elements of $l$ #l#. inline "cic:/CoRN/metrics/CPMSTheory/map_member.con". (* UNEXPORTED -End lists. +End lists *) (* UNEXPORTED -Section loc_and_bound. +Section loc_and_bound *) (*#* **Pseudo Metric Space theory @@ -223,6 +223,6 @@ all points that are in some sense close to $P$#P#. inline "cic:/CoRN/metrics/CPMSTheory/well_contained.con". (* UNEXPORTED -End loc_and_bound. +End loc_and_bound *) diff --git a/helm/software/matita/contribs/CoRN-Decl/metrics/CPseudoMSpaces.ma b/helm/software/matita/contribs/CoRN-Decl/metrics/CPseudoMSpaces.ma index a22750116..93a5a663f 100644 --- a/helm/software/matita/contribs/CoRN-Decl/metrics/CPseudoMSpaces.ma +++ b/helm/software/matita/contribs/CoRN-Decl/metrics/CPseudoMSpaces.ma @@ -26,7 +26,7 @@ include "reals/Intervals.ma". *) (* UNEXPORTED -Section Relations. +Section Relations *) (*#* **Relations necessary for Pseudo Metric Spaces and Metric Spaces @@ -35,9 +35,9 @@ Let [A : CSetoid], [d : (CSetoid_bin_fun A A IR)]. %\end{convention}% *) -inline "cic:/CoRN/metrics/CPseudoMSpaces/A.var". +inline "cic:/CoRN/metrics/CPseudoMSpaces/Relations/A.var" "Relations__". -inline "cic:/CoRN/metrics/CPseudoMSpaces/d.var". +inline "cic:/CoRN/metrics/CPseudoMSpaces/Relations/d.var" "Relations__". (* UNEXPORTED Set Implicit Arguments. @@ -68,11 +68,11 @@ inline "cic:/CoRN/metrics/CPseudoMSpaces/diag_zero.con". inline "cic:/CoRN/metrics/CPseudoMSpaces/apdiag_imp_grzero.con". (* UNEXPORTED -End Relations. +End Relations *) (* UNEXPORTED -Section Definition_PsMS0. +Section Definition_PsMS0 *) (*#* **Definition of Pseudo Metric Space @@ -90,7 +90,7 @@ inline "cic:/CoRN/metrics/CPseudoMSpaces/CPsMetricSpace.ind". coercion cic:/matita/CoRN-Decl/metrics/CPseudoMSpaces/cms_crr.con 0 (* compounds *). (* UNEXPORTED -End Definition_PsMS0. +End Definition_PsMS0 *) (* UNEXPORTED @@ -102,7 +102,7 @@ Infix "[-d]" := cms_d (at level 68, left associativity). *) (* UNEXPORTED -Section PsMS_axioms. +Section PsMS_axioms *) (*#* **Pseudo Metric Space axioms @@ -111,7 +111,7 @@ Let [A] be a pseudo metric space. %\end{convention}% *) -inline "cic:/CoRN/metrics/CPseudoMSpaces/A.var". +inline "cic:/CoRN/metrics/CPseudoMSpaces/PsMS_axioms/A.var" "PsMS_axioms__". inline "cic:/CoRN/metrics/CPseudoMSpaces/CPsMetricSpace_is_CPsMetricSpace.con". @@ -124,11 +124,11 @@ inline "cic:/CoRN/metrics/CPseudoMSpaces/d_pos_imp_ap.con". inline "cic:/CoRN/metrics/CPseudoMSpaces/d_tri_ineq.con". (* UNEXPORTED -End PsMS_axioms. +End PsMS_axioms *) (* UNEXPORTED -Section PsMS_basics. +Section PsMS_basics *) (*#* **Pseudo Metric Space basics @@ -137,7 +137,7 @@ Let [Y] be a pseudo metric space. %\end{convention}% *) -inline "cic:/CoRN/metrics/CPseudoMSpaces/Y.var". +inline "cic:/CoRN/metrics/CPseudoMSpaces/PsMS_basics/Y.var" "PsMS_basics__". inline "cic:/CoRN/metrics/CPseudoMSpaces/rev_tri_ineq.con". @@ -153,11 +153,11 @@ inline "cic:/CoRN/metrics/CPseudoMSpaces/pos_imp_ap_imp_diag_zero.con". inline "cic:/CoRN/metrics/CPseudoMSpaces/is_CPsMetricSpace_diag_zero.con". (* UNEXPORTED -End PsMS_basics. +End PsMS_basics *) (* UNEXPORTED -Section Zerof. +Section Zerof *) (*#* **Zero function @@ -187,6 +187,6 @@ inline "cic:/CoRN/metrics/CPseudoMSpaces/zf_is_CPsMetricSpace.con". inline "cic:/CoRN/metrics/CPseudoMSpaces/zf_as_CPsMetricSpace.con". (* UNEXPORTED -End Zerof. +End Zerof *) diff --git a/helm/software/matita/contribs/CoRN-Decl/metrics/ContFunctions.ma b/helm/software/matita/contribs/CoRN-Decl/metrics/ContFunctions.ma index 0f93560af..3fe1765ef 100644 --- a/helm/software/matita/contribs/CoRN-Decl/metrics/ContFunctions.ma +++ b/helm/software/matita/contribs/CoRN-Decl/metrics/ContFunctions.ma @@ -23,7 +23,7 @@ include "CoRN.ma". include "metrics/CPseudoMSpaces.ma". (* UNEXPORTED -Section Continuous_functions. +Section Continuous_functions *) (*#* **Continuous functions, uniformly continuous functions and Lipschitz functions @@ -32,9 +32,9 @@ Let [A] and [B] be pseudo metric spaces. %\end{convention}% *) -inline "cic:/CoRN/metrics/ContFunctions/A.var". +inline "cic:/CoRN/metrics/ContFunctions/Continuous_functions/A.var" "Continuous_functions__". -inline "cic:/CoRN/metrics/ContFunctions/B.var". +inline "cic:/CoRN/metrics/ContFunctions/Continuous_functions/B.var" "Continuous_functions__". (*#* We will look at some notions of continuous functions. @@ -55,7 +55,7 @@ inline "cic:/CoRN/metrics/ContFunctions/lipschitz.con". inline "cic:/CoRN/metrics/ContFunctions/lipschitz'.con". (* UNEXPORTED -End Continuous_functions. +End Continuous_functions *) (* UNEXPORTED @@ -87,7 +87,7 @@ Implicit Arguments lipschitz' [A B]. *) (* UNEXPORTED -Section Lemmas. +Section Lemmas *) (* begin hide *) @@ -120,11 +120,11 @@ inline "cic:/CoRN/metrics/ContFunctions/uni_continuous_imp_continuous.con". inline "cic:/CoRN/metrics/ContFunctions/lipschitz_imp_uni_continuous.con". (* UNEXPORTED -End Lemmas. +End Lemmas *) (* UNEXPORTED -Section Identity. +Section Identity *) (*#* **Identity @@ -142,11 +142,11 @@ inline "cic:/CoRN/metrics/ContFunctions/id_is_uni_continuous.con". inline "cic:/CoRN/metrics/ContFunctions/id_is_continuous.con". (* UNEXPORTED -End Identity. +End Identity *) (* UNEXPORTED -Section Constant. +Section Constant *) (*#* **Constant functions @@ -160,9 +160,9 @@ Any constant function is Lipschitz. Hence it is uniformly continuous and continuous. *) -inline "cic:/CoRN/metrics/ContFunctions/B.var". +inline "cic:/CoRN/metrics/ContFunctions/Constant/B.var" "Constant__". -inline "cic:/CoRN/metrics/ContFunctions/X.var". +inline "cic:/CoRN/metrics/ContFunctions/Constant/X.var" "Constant__". inline "cic:/CoRN/metrics/ContFunctions/const_fun_is_lipschitz.con". @@ -171,11 +171,11 @@ inline "cic:/CoRN/metrics/ContFunctions/const_fun_is_uni_continuous.con". inline "cic:/CoRN/metrics/ContFunctions/const_fun_is_continuous.con". (* UNEXPORTED -End Constant. +End Constant *) (* UNEXPORTED -Section Composition. +Section Composition *) (*#* **Composition @@ -191,15 +191,15 @@ The composition of two Lipschitz/uniformly continous/continuous functions is again Lipschitz/uniformly continuous/continuous. *) -inline "cic:/CoRN/metrics/ContFunctions/X.var". +inline "cic:/CoRN/metrics/ContFunctions/Composition/X.var" "Composition__". -inline "cic:/CoRN/metrics/ContFunctions/B.var". +inline "cic:/CoRN/metrics/ContFunctions/Composition/B.var" "Composition__". -inline "cic:/CoRN/metrics/ContFunctions/f.var". +inline "cic:/CoRN/metrics/ContFunctions/Composition/f.var" "Composition__". -inline "cic:/CoRN/metrics/ContFunctions/C.var". +inline "cic:/CoRN/metrics/ContFunctions/Composition/C.var" "Composition__". -inline "cic:/CoRN/metrics/ContFunctions/g.var". +inline "cic:/CoRN/metrics/ContFunctions/Composition/g.var" "Composition__". inline "cic:/CoRN/metrics/ContFunctions/comp_resp_lipschitz.con". @@ -208,11 +208,11 @@ inline "cic:/CoRN/metrics/ContFunctions/comp_resp_uni_continuous.con". inline "cic:/CoRN/metrics/ContFunctions/comp_resp_continuous.con". (* UNEXPORTED -End Composition. +End Composition *) (* UNEXPORTED -Section Limit. +Section Limit *) (*#* **Limit @@ -243,6 +243,6 @@ Implicit Arguments seqcontinuous' [A B]. inline "cic:/CoRN/metrics/ContFunctions/continuous'_imp_seqcontinuous'.con". (* UNEXPORTED -End Limit. +End Limit *) diff --git a/helm/software/matita/contribs/CoRN-Decl/metrics/Equiv.ma b/helm/software/matita/contribs/CoRN-Decl/metrics/Equiv.ma index 037029733..22f6da216 100644 --- a/helm/software/matita/contribs/CoRN-Decl/metrics/Equiv.ma +++ b/helm/software/matita/contribs/CoRN-Decl/metrics/Equiv.ma @@ -23,7 +23,7 @@ include "CoRN.ma". include "metrics/IR_CPMSpace.ma". (* UNEXPORTED -Section equivalent. +Section equivalent *) (*#* **Equivalent Pseudo Metric Spaces @@ -61,6 +61,6 @@ Not all pseudo metric spaces are equivalent: inline "cic:/CoRN/metrics/Equiv/MSequivalent_discr.con". (* UNEXPORTED -End equivalent. +End equivalent *) diff --git a/helm/software/matita/contribs/CoRN-Decl/metrics/IR_CPMSpace.ma b/helm/software/matita/contribs/CoRN-Decl/metrics/IR_CPMSpace.ma index 1bd2da730..796d75108 100644 --- a/helm/software/matita/contribs/CoRN-Decl/metrics/IR_CPMSpace.ma +++ b/helm/software/matita/contribs/CoRN-Decl/metrics/IR_CPMSpace.ma @@ -23,7 +23,7 @@ include "CoRN.ma". include "metrics/ContFunctions.ma". (* UNEXPORTED -Section Reals. +Section Reals *) (*#* **Real numbers @@ -63,7 +63,7 @@ inline "cic:/CoRN/metrics/IR_CPMSpace/IR_dIR_is_CPsMetricSpace.con". inline "cic:/CoRN/metrics/IR_CPMSpace/IR_as_CPsMetricSpace.con". -inline "cic:/CoRN/metrics/IR_CPMSpace/X.var". +inline "cic:/CoRN/metrics/IR_CPMSpace/Reals/X.var" "Reals__". inline "cic:/CoRN/metrics/IR_CPMSpace/rev_tri_ineq'.con". @@ -78,11 +78,11 @@ inline "cic:/CoRN/metrics/IR_CPMSpace/d_is_uni_continuous.con". inline "cic:/CoRN/metrics/IR_CPMSpace/d_is_continuous.con". (* UNEXPORTED -End Reals. +End Reals *) (* UNEXPORTED -Section Addition. +Section Addition *) (*#* **Addition of continuous functions @@ -100,6 +100,6 @@ inline "cic:/CoRN/metrics/IR_CPMSpace/plus_resp_uni_continuous.con". inline "cic:/CoRN/metrics/IR_CPMSpace/plus_resp_continuous.con". (* UNEXPORTED -End Addition. +End Addition *) diff --git a/helm/software/matita/contribs/CoRN-Decl/metrics/Prod_Sub.ma b/helm/software/matita/contribs/CoRN-Decl/metrics/Prod_Sub.ma index f30b3c65d..46746e6f4 100644 --- a/helm/software/matita/contribs/CoRN-Decl/metrics/Prod_Sub.ma +++ b/helm/software/matita/contribs/CoRN-Decl/metrics/Prod_Sub.ma @@ -23,7 +23,7 @@ include "CoRN.ma". include "metrics/IR_CPMSpace.ma". (* UNEXPORTED -Section prodpsmetrics. +Section prodpsmetrics *) (*#* **Product-Pseudo-Metric-Spaces @@ -48,11 +48,11 @@ inline "cic:/CoRN/metrics/Prod_Sub/prod0cpsmetricspace_is_CPsMetricSpace.con". inline "cic:/CoRN/metrics/Prod_Sub/Prod0CPsMetricSpace.con". (* UNEXPORTED -End prodpsmetrics. +End prodpsmetrics *) (* UNEXPORTED -Section subpsmetrics. +Section subpsmetrics *) (*#* **Sub-Pseudo-Metric-Spaces @@ -126,6 +126,6 @@ Implicit Arguments dsub'_as_cs_fun [X]. inline "cic:/CoRN/metrics/Prod_Sub/dsub'_uni_continuous''.con". (* UNEXPORTED -End subpsmetrics. +End subpsmetrics *) diff --git a/helm/software/matita/contribs/CoRN-Decl/model/structures/Qsec.ma b/helm/software/matita/contribs/CoRN-Decl/model/structures/Qsec.ma index 595c037a0..42d6e5671 100644 --- a/helm/software/matita/contribs/CoRN-Decl/model/structures/Qsec.ma +++ b/helm/software/matita/contribs/CoRN-Decl/model/structures/Qsec.ma @@ -47,7 +47,7 @@ also define apartness, order, addition, multiplication, opposite, inverse an de constants 0 and 1. *) (* UNEXPORTED -Section Q. +Section Q *) inline "cic:/CoRN/model/structures/Qsec/Q.ind". @@ -71,7 +71,7 @@ inline "cic:/CoRN/model/structures/Qsec/QONE.con". inline "cic:/CoRN/model/structures/Qsec/Qinv.con". (* UNEXPORTED -End Q. +End Q *) (* NOTATION diff --git a/helm/software/matita/contribs/CoRN-Decl/reals/Bridges_LUB.ma b/helm/software/matita/contribs/CoRN-Decl/reals/Bridges_LUB.ma index e5f71e1e1..9ebc96842 100644 --- a/helm/software/matita/contribs/CoRN-Decl/reals/Bridges_LUB.ma +++ b/helm/software/matita/contribs/CoRN-Decl/reals/Bridges_LUB.ma @@ -39,20 +39,20 @@ include "reals/iso_CReals.ma". include "algebra/Expon.ma". (* UNEXPORTED -Section LUBP. +Section LUBP *) -inline "cic:/CoRN/reals/Bridges_LUB/R1.var". +inline "cic:/CoRN/reals/Bridges_LUB/LUBP/R1.var" "LUBP__". (* SUBSECTION ON GENRAL DEFINITIONS *) (* UNEXPORTED -Section lub_definitions. +Section lub_definitions *) -inline "cic:/CoRN/reals/Bridges_LUB/OF.var". +inline "cic:/CoRN/reals/Bridges_LUB/LUBP/lub_definitions/OF.var" "LUBP__lub_definitions__". -inline "cic:/CoRN/reals/Bridges_LUB/SS.var". +inline "cic:/CoRN/reals/Bridges_LUB/LUBP/lub_definitions/SS.var" "LUBP__lub_definitions__". inline "cic:/CoRN/reals/Bridges_LUB/member.con". @@ -79,38 +79,38 @@ inline "cic:/CoRN/reals/Bridges_LUB/infimum.con". inline "cic:/CoRN/reals/Bridges_LUB/Pinfimum.con". (* UNEXPORTED -End lub_definitions. +End lub_definitions *) (* MAIN SECTION *) (* UNEXPORTED -Section upper_bound_sequence. +Section upper_bound_sequence *) -inline "cic:/CoRN/reals/Bridges_LUB/A.var". +inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/A.var" "LUBP__upper_bound_sequence__". -inline "cic:/CoRN/reals/Bridges_LUB/is_inhabitted.var". +inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/is_inhabitted.var" "LUBP__upper_bound_sequence__". -inline "cic:/CoRN/reals/Bridges_LUB/bounded_above.var". +inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/bounded_above.var" "LUBP__upper_bound_sequence__". -inline "cic:/CoRN/reals/Bridges_LUB/located.var". +inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/located.var" "LUBP__upper_bound_sequence__". -inline "cic:/CoRN/reals/Bridges_LUB/s.con". +inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/s.con" "LUBP__upper_bound_sequence__". -inline "cic:/CoRN/reals/Bridges_LUB/Ps.con". +inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/Ps.con" "LUBP__upper_bound_sequence__". -inline "cic:/CoRN/reals/Bridges_LUB/b0.con". +inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/b0.con" "LUBP__upper_bound_sequence__". -inline "cic:/CoRN/reals/Bridges_LUB/Pb0.con". +inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/Pb0.con" "LUBP__upper_bound_sequence__". inline "cic:/CoRN/reals/Bridges_LUB/b0_is_upper_bound.con". inline "cic:/CoRN/reals/Bridges_LUB/s_inhabits_A.con". -inline "cic:/CoRN/reals/Bridges_LUB/dstart_l.con". +inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/dstart_l.con" "LUBP__upper_bound_sequence__". -inline "cic:/CoRN/reals/Bridges_LUB/dstart_r.con". +inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/dstart_r.con" "LUBP__upper_bound_sequence__". inline "cic:/CoRN/reals/Bridges_LUB/dl_less_dr.con". @@ -136,11 +136,11 @@ inline "cic:/CoRN/reals/Bridges_LUB/dif_cotrans_strong.con". inline "cic:/CoRN/reals/Bridges_LUB/dIntrvl.con". -inline "cic:/CoRN/reals/Bridges_LUB/U.con". +inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/U.con" "LUBP__upper_bound_sequence__". -inline "cic:/CoRN/reals/Bridges_LUB/V.con". +inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/V.con" "LUBP__upper_bound_sequence__". -inline "cic:/CoRN/reals/Bridges_LUB/W.con". +inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/W.con" "LUBP__upper_bound_sequence__". inline "cic:/CoRN/reals/Bridges_LUB/delta_dIntrvl.con". @@ -170,7 +170,7 @@ inline "cic:/CoRN/reals/Bridges_LUB/CS_seq_U.con". inline "cic:/CoRN/reals/Bridges_LUB/U_as_CauchySeq.con". -inline "cic:/CoRN/reals/Bridges_LUB/B.con". +inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/B.con" "LUBP__upper_bound_sequence__". inline "cic:/CoRN/reals/Bridges_LUB/U_minus_V.con". @@ -209,11 +209,11 @@ inline "cic:/CoRN/reals/Bridges_LUB/A_bounds_V_n.con". inline "cic:/CoRN/reals/Bridges_LUB/cauchy_gives_lub.con". (* UNEXPORTED -End upper_bound_sequence. +End upper_bound_sequence *) (* UNEXPORTED -End LUBP. +End LUBP *) (* end hide *) diff --git a/helm/software/matita/contribs/CoRN-Decl/reals/Bridges_iso.ma b/helm/software/matita/contribs/CoRN-Decl/reals/Bridges_iso.ma index e2a8ca76c..6c3b241e3 100644 --- a/helm/software/matita/contribs/CoRN-Decl/reals/Bridges_iso.ma +++ b/helm/software/matita/contribs/CoRN-Decl/reals/Bridges_iso.ma @@ -41,19 +41,19 @@ include "reals/Bridges_LUB.ma". inline "cic:/CoRN/reals/Bridges_iso/le_witness_informative.con". (* UNEXPORTED -Section bridges_axioms_imply_ours. +Section bridges_axioms_imply_ours *) -inline "cic:/CoRN/reals/Bridges_iso/OF.var". +inline "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/OF.var" "bridges_axioms_imply_ours__". -inline "cic:/CoRN/reals/Bridges_iso/lubp.var". +inline "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/lubp.var" "bridges_axioms_imply_ours__". -inline "cic:/CoRN/reals/Bridges_iso/is_Archimedes.var". +inline "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/is_Archimedes.var" "bridges_axioms_imply_ours__". inline "cic:/CoRN/reals/Bridges_iso/is_Archimedes'.con". (* UNEXPORTED -Section proofs_in_TCS. +Section proofs_in_TCS *) inline "cic:/CoRN/reals/Bridges_iso/leEq_geEq.con". @@ -61,10 +61,10 @@ inline "cic:/CoRN/reals/Bridges_iso/leEq_geEq.con". inline "cic:/CoRN/reals/Bridges_iso/glbp.con". (* UNEXPORTED -Section supremum. +Section supremum *) -inline "cic:/CoRN/reals/Bridges_iso/P.var". +inline "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/supremum/P.var" "bridges_axioms_imply_ours__proofs_in_TCS__supremum__". inline "cic:/CoRN/reals/Bridges_iso/inequality1.con". @@ -96,7 +96,7 @@ inline "cic:/CoRN/reals/Bridges_iso/kaf.con". inline "cic:/CoRN/reals/Bridges_iso/Pkaf.con". -inline "cic:/CoRN/reals/Bridges_iso/is_finite_P.var". +inline "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/supremum/is_finite_P.var" "bridges_axioms_imply_ours__proofs_in_TCS__supremum__". inline "cic:/CoRN/reals/Bridges_iso/card.con". @@ -112,7 +112,7 @@ inline "cic:/CoRN/reals/Bridges_iso/indeks.con". inline "cic:/CoRN/reals/Bridges_iso/Pindeks.con". -inline "cic:/CoRN/reals/Bridges_iso/is_onto_seq_P.var". +inline "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/supremum/is_onto_seq_P.var" "bridges_axioms_imply_ours__proofs_in_TCS__supremum__". inline "cic:/CoRN/reals/Bridges_iso/P_is_inhabited.con". @@ -189,12 +189,12 @@ inline "cic:/CoRN/reals/Bridges_iso/bounded_quantifier_informative.con". inline "cic:/CoRN/reals/Bridges_iso/bridges_lemma1a.con". -inline "cic:/CoRN/reals/Bridges_iso/P_is_strongly_extensional.var". +inline "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/supremum/P_is_strongly_extensional.var" "bridges_axioms_imply_ours__proofs_in_TCS__supremum__". inline "cic:/CoRN/reals/Bridges_iso/bridges_lemma1b.con". (* UNEXPORTED -End supremum. +End supremum *) (*#**********************************) @@ -206,18 +206,18 @@ End supremum. (*#**********************************) (* UNEXPORTED -Section Every_Cauchy_Sequence_is_bounded. +Section Every_Cauchy_Sequence_is_bounded *) inline "cic:/CoRN/reals/Bridges_iso/seq2set.con". -inline "cic:/CoRN/reals/Bridges_iso/g.var". +inline "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/Every_Cauchy_Sequence_is_bounded/g.var" "bridges_axioms_imply_ours__proofs_in_TCS__Every_Cauchy_Sequence_is_bounded__". -inline "cic:/CoRN/reals/Bridges_iso/g_.con". +inline "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/Every_Cauchy_Sequence_is_bounded/g_.con" "bridges_axioms_imply_ours__proofs_in_TCS__Every_Cauchy_Sequence_is_bounded__". -inline "cic:/CoRN/reals/Bridges_iso/pg.con". +inline "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/Every_Cauchy_Sequence_is_bounded/pg.con" "bridges_axioms_imply_ours__proofs_in_TCS__Every_Cauchy_Sequence_is_bounded__". -inline "cic:/CoRN/reals/Bridges_iso/P.con". +inline "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/Every_Cauchy_Sequence_is_bounded/P.con" "bridges_axioms_imply_ours__proofs_in_TCS__Every_Cauchy_Sequence_is_bounded__". inline "cic:/CoRN/reals/Bridges_iso/fin_is_fin.con". @@ -260,16 +260,16 @@ inline "cic:/CoRN/reals/Bridges_iso/tail_is_Cauchy.con". inline "cic:/CoRN/reals/Bridges_iso/tail_seq.con". (* UNEXPORTED -End Every_Cauchy_Sequence_is_bounded. +End Every_Cauchy_Sequence_is_bounded *) -inline "cic:/CoRN/reals/Bridges_iso/g.var". +inline "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/g.var" "bridges_axioms_imply_ours__proofs_in_TCS__". -inline "cic:/CoRN/reals/Bridges_iso/g_.con". +inline "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/g_.con" "bridges_axioms_imply_ours__proofs_in_TCS__". -inline "cic:/CoRN/reals/Bridges_iso/pg.con". +inline "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/pg.con" "bridges_axioms_imply_ours__proofs_in_TCS__". -inline "cic:/CoRN/reals/Bridges_iso/sup_tail.con". +inline "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/sup_tail.con" "bridges_axioms_imply_ours__proofs_in_TCS__". inline "cic:/CoRN/reals/Bridges_iso/sup_tail_leEq.con". @@ -277,7 +277,7 @@ inline "cic:/CoRN/reals/Bridges_iso/sup_tail_is_Cauchy.con". inline "cic:/CoRN/reals/Bridges_iso/sup_tail_as_Cauchy.con". -inline "cic:/CoRN/reals/Bridges_iso/L.con". +inline "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/L.con" "bridges_axioms_imply_ours__proofs_in_TCS__". inline "cic:/CoRN/reals/Bridges_iso/sup_tail_decrease.con". @@ -294,7 +294,7 @@ inline "cic:/CoRN/reals/Bridges_iso/convergent_subseq.con". inline "cic:/CoRN/reals/Bridges_iso/lubp_gives_Cauchy.con". (* UNEXPORTED -End proofs_in_TCS. +End proofs_in_TCS *) inline "cic:/CoRN/reals/Bridges_iso/Bridges_R_is_CReals.con". @@ -302,7 +302,7 @@ inline "cic:/CoRN/reals/Bridges_iso/Bridges_R_is_CReals.con". inline "cic:/CoRN/reals/Bridges_iso/Bridges_R_as_CReals.con". (* UNEXPORTED -End bridges_axioms_imply_ours. +End bridges_axioms_imply_ours *) (* end hide *) diff --git a/helm/software/matita/contribs/CoRN-Decl/reals/CMetricFields.ma b/helm/software/matita/contribs/CoRN-Decl/reals/CMetricFields.ma index 14fe73bda..70924e79d 100644 --- a/helm/software/matita/contribs/CoRN-Decl/reals/CMetricFields.ma +++ b/helm/software/matita/contribs/CoRN-Decl/reals/CMetricFields.ma @@ -23,7 +23,7 @@ include "CoRN.ma". include "reals/CReals1.ma". (* UNEXPORTED -Section CMetric_Fields. +Section CMetric_Fields *) (*#* *Metric Fields *) @@ -35,7 +35,7 @@ inline "cic:/CoRN/reals/CMetricFields/CMetricField.ind". coercion cic:/matita/CoRN-Decl/reals/CMetricFields/cmf_crr.con 0 (* compounds *). (* UNEXPORTED -End CMetric_Fields. +End CMetric_Fields *) (* NOTATION @@ -43,7 +43,7 @@ Notation MAbs := (cmf_abs _). *) (* UNEXPORTED -Section basics. +Section basics *) inline "cic:/CoRN/reals/CMetricFields/MAbs_one.con". @@ -55,14 +55,14 @@ inline "cic:/CoRN/reals/CMetricFields/MAbs_one_recip_one.con". (* end hide *) (* UNEXPORTED -End basics. +End basics *) (* UNEXPORTED -Section CMetric_Field_Cauchy. +Section CMetric_Field_Cauchy *) -inline "cic:/CoRN/reals/CMetricFields/F.var". +inline "cic:/CoRN/reals/CMetricFields/CMetric_Field_Cauchy/F.var" "CMetric_Field_Cauchy__". (*#* %\begin{convention}% Let [F:CMetricField]. @@ -80,7 +80,7 @@ inline "cic:/CoRN/reals/CMetricFields/MseqLimit.con". inline "cic:/CoRN/reals/CMetricFields/is_MCauchyCompl.con". (* UNEXPORTED -End CMetric_Field_Cauchy. +End CMetric_Field_Cauchy *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/reals/CReals1.ma b/helm/software/matita/contribs/CoRN-Decl/reals/CReals1.ma index 21dc9e6e4..b690ee0a0 100644 --- a/helm/software/matita/contribs/CoRN-Decl/reals/CReals1.ma +++ b/helm/software/matita/contribs/CoRN-Decl/reals/CReals1.ma @@ -27,7 +27,7 @@ include "algebra/Expon.ma". include "algebra/CPoly_ApZero.ma". (* UNEXPORTED -Section More_Cauchy_Props. +Section More_Cauchy_Props *) (*#* **Miscellaneous @@ -54,11 +54,11 @@ inline "cic:/CoRN/reals/CReals1/Cauchy_abs.con". inline "cic:/CoRN/reals/CReals1/Lim_abs.con". (* UNEXPORTED -End More_Cauchy_Props. +End More_Cauchy_Props *) (* UNEXPORTED -Section Subsequences. +Section Subsequences *) (*#* *** Subsequences @@ -77,25 +77,25 @@ Finally, for some of our results it is important to assume that [seq2] is monotonous. *) -inline "cic:/CoRN/reals/CReals1/seq1.var". +inline "cic:/CoRN/reals/CReals1/Subsequences/seq1.var" "Subsequences__". -inline "cic:/CoRN/reals/CReals1/seq2.var". +inline "cic:/CoRN/reals/CReals1/Subsequences/seq2.var" "Subsequences__". -inline "cic:/CoRN/reals/CReals1/f.var". +inline "cic:/CoRN/reals/CReals1/Subsequences/f.var" "Subsequences__". -inline "cic:/CoRN/reals/CReals1/monF.var". +inline "cic:/CoRN/reals/CReals1/Subsequences/monF.var" "Subsequences__". -inline "cic:/CoRN/reals/CReals1/crescF.var". +inline "cic:/CoRN/reals/CReals1/Subsequences/crescF.var" "Subsequences__". -inline "cic:/CoRN/reals/CReals1/subseq.var". +inline "cic:/CoRN/reals/CReals1/Subsequences/subseq.var" "Subsequences__". -inline "cic:/CoRN/reals/CReals1/mon_seq2.var". +inline "cic:/CoRN/reals/CReals1/Subsequences/mon_seq2.var" "Subsequences__". inline "cic:/CoRN/reals/CReals1/unbnd_f.con". (* begin hide *) -inline "cic:/CoRN/reals/CReals1/mon_F'.con". +inline "cic:/CoRN/reals/CReals1/Subsequences/mon_F'.con" "Subsequences__". (* end hide *) @@ -108,37 +108,37 @@ inline "cic:/CoRN/reals/CReals1/conv_seq_imp_conv_subseq.con". inline "cic:/CoRN/reals/CReals1/Cprop2_subseq_imp_Cprop2_seq.con". (* UNEXPORTED -End Subsequences. +End Subsequences *) (* UNEXPORTED -Section Cauchy_Subsequences. +Section Cauchy_Subsequences *) -inline "cic:/CoRN/reals/CReals1/seq1.var". +inline "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/seq1.var" "Cauchy_Subsequences__". -inline "cic:/CoRN/reals/CReals1/seq2.var". +inline "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/seq2.var" "Cauchy_Subsequences__". -inline "cic:/CoRN/reals/CReals1/f.var". +inline "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/f.var" "Cauchy_Subsequences__". -inline "cic:/CoRN/reals/CReals1/monF.var". +inline "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/monF.var" "Cauchy_Subsequences__". -inline "cic:/CoRN/reals/CReals1/crescF.var". +inline "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/crescF.var" "Cauchy_Subsequences__". -inline "cic:/CoRN/reals/CReals1/subseq.var". +inline "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/subseq.var" "Cauchy_Subsequences__". -inline "cic:/CoRN/reals/CReals1/mon_seq2.var". +inline "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/mon_seq2.var" "Cauchy_Subsequences__". inline "cic:/CoRN/reals/CReals1/Lim_seq_eq_Lim_subseq.con". inline "cic:/CoRN/reals/CReals1/Lim_subseq_eq_Lim_seq.con". (* UNEXPORTED -End Cauchy_Subsequences. +End Cauchy_Subsequences *) (* UNEXPORTED -Section Properties_of_Exponentiation. +Section Properties_of_Exponentiation *) (*#* *** More properties of Exponentiation @@ -155,7 +155,7 @@ inline "cic:/CoRN/reals/CReals1/qi_yields_zero.con". inline "cic:/CoRN/reals/CReals1/qi_lim_zero.con". (* UNEXPORTED -End Properties_of_Exponentiation. +End Properties_of_Exponentiation *) (*#* *** [IR] has characteristic zero *) diff --git a/helm/software/matita/contribs/CoRN-Decl/reals/CSumsReals.ma b/helm/software/matita/contribs/CoRN-Decl/reals/CSumsReals.ma index 5799a997a..6e691c38f 100644 --- a/helm/software/matita/contribs/CoRN-Decl/reals/CSumsReals.ma +++ b/helm/software/matita/contribs/CoRN-Decl/reals/CSumsReals.ma @@ -33,10 +33,10 @@ $\Sigma_{m\leq i \leq n}~c^k = \frac{c^{n+1}-c^m}{c-1}.$ *) (* UNEXPORTED -Section Sums_over_Reals. +Section Sums_over_Reals *) -inline "cic:/CoRN/reals/CSumsReals/c.var". +inline "cic:/CoRN/reals/CSumsReals/Sums_over_Reals/c.var" "Sums_over_Reals__". inline "cic:/CoRN/reals/CSumsReals/Sum0_c_exp.con". @@ -59,7 +59,7 @@ Hint Resolve Sum_c_exp'. *) (* UNEXPORTED -End Sums_over_Reals. +End Sums_over_Reals *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/reals/CauchySeq.ma b/helm/software/matita/contribs/CoRN-Decl/reals/CauchySeq.ma index 18e25f5e1..36ca57d6d 100644 --- a/helm/software/matita/contribs/CoRN-Decl/reals/CauchySeq.ma +++ b/helm/software/matita/contribs/CoRN-Decl/reals/CauchySeq.ma @@ -72,7 +72,7 @@ Notation OneR := (One:IR). (* end hide *) (* UNEXPORTED -Section CReals_axioms. +Section CReals_axioms *) (*#* ** [CReals] axioms *) @@ -94,11 +94,11 @@ inline "cic:/CoRN/reals/CauchySeq/str_Archimedes.con". inline "cic:/CoRN/reals/CauchySeq/CauchySeqR.con". (* UNEXPORTED -End CReals_axioms. +End CReals_axioms *) (* UNEXPORTED -Section Cauchy_Defs. +Section Cauchy_Defs *) (*#* ** Cauchy sequences @@ -169,11 +169,11 @@ inline "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop4.con". inline "cic:/CoRN/reals/CauchySeq/Cauchy_prop4.con". (* UNEXPORTED -End Cauchy_Defs. +End Cauchy_Defs *) (* UNEXPORTED -Section Inequalities. +Section Inequalities *) (*#* *** Inequalities of Limits @@ -215,11 +215,11 @@ inline "cic:/CoRN/reals/CauchySeq/Lim_ap_imp_seq_ap.con". inline "cic:/CoRN/reals/CauchySeq/Lim_ap_imp_seq_ap'.con". (* UNEXPORTED -End Inequalities. +End Inequalities *) (* UNEXPORTED -Section Equiv_Cauchy. +Section Equiv_Cauchy *) (*#* *** Equivalence of formulations of Cauchy *) @@ -267,11 +267,11 @@ inline "cic:/CoRN/reals/CauchySeq/Lim_wd'.con". inline "cic:/CoRN/reals/CauchySeq/Lim_unique.con". (* UNEXPORTED -End Equiv_Cauchy. +End Equiv_Cauchy *) (* UNEXPORTED -Section Cauchy_props. +Section Cauchy_props *) (*#* *** Properties of Cauchy sequences @@ -310,6 +310,6 @@ inline "cic:/CoRN/reals/CauchySeq/Cauchy_mult.con". inline "cic:/CoRN/reals/CauchySeq/Lim_mult.con". (* UNEXPORTED -End Cauchy_props. +End Cauchy_props *) diff --git a/helm/software/matita/contribs/CoRN-Decl/reals/Cauchy_CReals.ma b/helm/software/matita/contribs/CoRN-Decl/reals/Cauchy_CReals.ma index ed2df485d..8cbd634d0 100644 --- a/helm/software/matita/contribs/CoRN-Decl/reals/Cauchy_CReals.ma +++ b/helm/software/matita/contribs/CoRN-Decl/reals/Cauchy_CReals.ma @@ -25,7 +25,7 @@ include "algebra/Cauchy_COF.ma". include "reals/CReals.ma". (* UNEXPORTED -Section R_CReals. +Section R_CReals *) (*#* * The Real Number Structure @@ -40,7 +40,7 @@ We start by showing how to inject the rational numbers in the field of Cauchy se %\end{convention}% *) -inline "cic:/CoRN/reals/Cauchy_CReals/F.var". +inline "cic:/CoRN/reals/Cauchy_CReals/R_CReals/F.var" "R_CReals__". (* NOTATION Notation "'R_COrdField''" := (R_COrdField F). @@ -92,19 +92,19 @@ inline "cic:/CoRN/reals/Cauchy_CReals/expand_Q_R.con". inline "cic:/CoRN/reals/Cauchy_CReals/conv_modulus.con". -inline "cic:/CoRN/reals/Cauchy_CReals/T.con". +inline "cic:/CoRN/reals/Cauchy_CReals/R_CReals/T.con" "R_CReals__". (*#* We now assume our original field is archimedean and prove that the resulting one is, too. *) -inline "cic:/CoRN/reals/Cauchy_CReals/F_is_archemaedian.var". +inline "cic:/CoRN/reals/Cauchy_CReals/R_CReals/F_is_archemaedian.var" "R_CReals__". inline "cic:/CoRN/reals/Cauchy_CReals/R_is_archemaedian.con". (* begin hide *) -inline "cic:/CoRN/reals/Cauchy_CReals/PT.con". +inline "cic:/CoRN/reals/Cauchy_CReals/R_CReals/PT.con" "R_CReals__". (* end hide *) @@ -131,6 +131,6 @@ inline "cic:/CoRN/reals/Cauchy_CReals/R_is_CReals.con". inline "cic:/CoRN/reals/Cauchy_CReals/R_as_CReals.con". (* UNEXPORTED -End R_CReals. +End R_CReals *) diff --git a/helm/software/matita/contribs/CoRN-Decl/reals/IVT.ma b/helm/software/matita/contribs/CoRN-Decl/reals/IVT.ma index 7da887f6a..d0a71f3ec 100644 --- a/helm/software/matita/contribs/CoRN-Decl/reals/IVT.ma +++ b/helm/software/matita/contribs/CoRN-Decl/reals/IVT.ma @@ -23,7 +23,7 @@ include "CoRN.ma". include "reals/CPoly_Contin.ma". (* UNEXPORTED -Section Nested_Intervals. +Section Nested_Intervals *) (*#* * Intermediate Value Theorem @@ -39,17 +39,17 @@ Section Nested_Intervals. %\end{convention}% *) -inline "cic:/CoRN/reals/IVT/a.var". +inline "cic:/CoRN/reals/IVT/Nested_Intervals/a.var" "Nested_Intervals__". -inline "cic:/CoRN/reals/IVT/b.var". +inline "cic:/CoRN/reals/IVT/Nested_Intervals/b.var" "Nested_Intervals__". -inline "cic:/CoRN/reals/IVT/a_mon.var". +inline "cic:/CoRN/reals/IVT/Nested_Intervals/a_mon.var" "Nested_Intervals__". -inline "cic:/CoRN/reals/IVT/b_mon.var". +inline "cic:/CoRN/reals/IVT/Nested_Intervals/b_mon.var" "Nested_Intervals__". -inline "cic:/CoRN/reals/IVT/a_b.var". +inline "cic:/CoRN/reals/IVT/Nested_Intervals/a_b.var" "Nested_Intervals__". -inline "cic:/CoRN/reals/IVT/b_a.var". +inline "cic:/CoRN/reals/IVT/Nested_Intervals/b_a.var" "Nested_Intervals__". inline "cic:/CoRN/reals/IVT/a_mon'.con". @@ -61,7 +61,7 @@ inline "cic:/CoRN/reals/IVT/intervals_cauchy.con". (* begin hide *) -inline "cic:/CoRN/reals/IVT/a'.con". +inline "cic:/CoRN/reals/IVT/Nested_Intervals/a'.con" "Nested_Intervals__". (* end hide *) @@ -71,9 +71,9 @@ inline "cic:/CoRN/reals/IVT/Cnested_intervals_limit.con". %\end{convention}% *) -inline "cic:/CoRN/reals/IVT/f.var". +inline "cic:/CoRN/reals/IVT/Nested_Intervals/f.var" "Nested_Intervals__". -inline "cic:/CoRN/reals/IVT/f_contin.var". +inline "cic:/CoRN/reals/IVT/Nested_Intervals/f_contin.var" "Nested_Intervals__". inline "cic:/CoRN/reals/IVT/f_contin_pos.con". @@ -81,35 +81,35 @@ inline "cic:/CoRN/reals/IVT/f_contin_neg.con". (*#* Assume also that [forall i, f (a i) [<=] Zero [<=] f (b i)]. *) -inline "cic:/CoRN/reals/IVT/f_a.var". +inline "cic:/CoRN/reals/IVT/Nested_Intervals/f_a.var" "Nested_Intervals__". -inline "cic:/CoRN/reals/IVT/f_b.var". +inline "cic:/CoRN/reals/IVT/Nested_Intervals/f_b.var" "Nested_Intervals__". inline "cic:/CoRN/reals/IVT/Cnested_intervals_zero.con". (* UNEXPORTED -End Nested_Intervals. +End Nested_Intervals *) (* UNEXPORTED -Section Bisection. +Section Bisection *) (*#* ** Bissections *) -inline "cic:/CoRN/reals/IVT/f.var". +inline "cic:/CoRN/reals/IVT/Bisection/f.var" "Bisection__". -inline "cic:/CoRN/reals/IVT/f_apzero_interval.var". +inline "cic:/CoRN/reals/IVT/Bisection/f_apzero_interval.var" "Bisection__". -inline "cic:/CoRN/reals/IVT/a.var". +inline "cic:/CoRN/reals/IVT/Bisection/a.var" "Bisection__". -inline "cic:/CoRN/reals/IVT/b.var". +inline "cic:/CoRN/reals/IVT/Bisection/b.var" "Bisection__". -inline "cic:/CoRN/reals/IVT/a_b.var". +inline "cic:/CoRN/reals/IVT/Bisection/a_b.var" "Bisection__". -inline "cic:/CoRN/reals/IVT/f_a.var". +inline "cic:/CoRN/reals/IVT/Bisection/f_a.var" "Bisection__". -inline "cic:/CoRN/reals/IVT/f_b.var". +inline "cic:/CoRN/reals/IVT/Bisection/f_b.var" "Bisection__". (*#* %\begin{convention}% Let [Small] denote [Two[/]ThreeNZ], [lft] be [(Two[*]a[+]b) [/]ThreeNZ] and [rht] be [(a[+]Two[*]b) [/]ThreeNZ]. @@ -118,11 +118,11 @@ inline "cic:/CoRN/reals/IVT/f_b.var". (* begin hide *) -inline "cic:/CoRN/reals/IVT/Small.con". +inline "cic:/CoRN/reals/IVT/Bisection/Small.con" "Bisection__". -inline "cic:/CoRN/reals/IVT/lft.con". +inline "cic:/CoRN/reals/IVT/Bisection/lft.con" "Bisection__". -inline "cic:/CoRN/reals/IVT/rht.con". +inline "cic:/CoRN/reals/IVT/Bisection/rht.con" "Bisection__". (* end hide *) @@ -143,20 +143,20 @@ Hint Resolve smaller_lft smaller_rht: algebra. inline "cic:/CoRN/reals/IVT/Cbisect'.con". (* UNEXPORTED -End Bisection. +End Bisection *) (* UNEXPORTED -Section Bisect_Interval. +Section Bisect_Interval *) -inline "cic:/CoRN/reals/IVT/f.var". +inline "cic:/CoRN/reals/IVT/Bisect_Interval/f.var" "Bisect_Interval__". -inline "cic:/CoRN/reals/IVT/C_f_apzero_interval.var". +inline "cic:/CoRN/reals/IVT/Bisect_Interval/C_f_apzero_interval.var" "Bisect_Interval__". (* begin hide *) -inline "cic:/CoRN/reals/IVT/Small.con". +inline "cic:/CoRN/reals/IVT/Bisect_Interval/Small.con" "Bisect_Interval__". (* end hide *) @@ -169,44 +169,44 @@ inline "cic:/CoRN/reals/IVT/bisect.con". inline "cic:/CoRN/reals/IVT/bisect_prop.con". (* UNEXPORTED -End Bisect_Interval. +End Bisect_Interval *) (* UNEXPORTED -Section IVT_Op. +Section IVT_Op *) (*#* ** IVT for operations Same conventions as before. *) -inline "cic:/CoRN/reals/IVT/f.var". +inline "cic:/CoRN/reals/IVT/IVT_Op/f.var" "IVT_Op__". -inline "cic:/CoRN/reals/IVT/f_contin.var". +inline "cic:/CoRN/reals/IVT/IVT_Op/f_contin.var" "IVT_Op__". -inline "cic:/CoRN/reals/IVT/f_apzero_interval.var". +inline "cic:/CoRN/reals/IVT/IVT_Op/f_apzero_interval.var" "IVT_Op__". -inline "cic:/CoRN/reals/IVT/a.var". +inline "cic:/CoRN/reals/IVT/IVT_Op/a.var" "IVT_Op__". -inline "cic:/CoRN/reals/IVT/b.var". +inline "cic:/CoRN/reals/IVT/IVT_Op/b.var" "IVT_Op__". -inline "cic:/CoRN/reals/IVT/a_b.var". +inline "cic:/CoRN/reals/IVT/IVT_Op/a_b.var" "IVT_Op__". -inline "cic:/CoRN/reals/IVT/f_a.var". +inline "cic:/CoRN/reals/IVT/IVT_Op/f_a.var" "IVT_Op__". -inline "cic:/CoRN/reals/IVT/f_b.var". +inline "cic:/CoRN/reals/IVT/IVT_Op/f_b.var" "IVT_Op__". (* begin hide *) -inline "cic:/CoRN/reals/IVT/Small.con". +inline "cic:/CoRN/reals/IVT/IVT_Op/Small.con" "IVT_Op__". (* end hide *) inline "cic:/CoRN/reals/IVT/interval_sequence.con". -inline "cic:/CoRN/reals/IVT/a_.con". +inline "cic:/CoRN/reals/IVT/IVT_Op/a_.con" "IVT_Op__". -inline "cic:/CoRN/reals/IVT/b_.con". +inline "cic:/CoRN/reals/IVT/IVT_Op/b_.con" "IVT_Op__". inline "cic:/CoRN/reals/IVT/intervals_smaller.con". @@ -219,11 +219,11 @@ inline "cic:/CoRN/reals/IVT/intervals_small.con". inline "cic:/CoRN/reals/IVT/Civt_op.con". (* UNEXPORTED -End IVT_Op. +End IVT_Op *) (* UNEXPORTED -Section IVT_Poly. +Section IVT_Poly *) (*#* ** IVT for polynomials *) @@ -231,6 +231,6 @@ Section IVT_Poly. inline "cic:/CoRN/reals/IVT/Civt_poly.con". (* UNEXPORTED -End IVT_Poly. +End IVT_Poly *) diff --git a/helm/software/matita/contribs/CoRN-Decl/reals/Intervals.ma b/helm/software/matita/contribs/CoRN-Decl/reals/Intervals.ma index 914586e0d..630801a2a 100644 --- a/helm/software/matita/contribs/CoRN-Decl/reals/Intervals.ma +++ b/helm/software/matita/contribs/CoRN-Decl/reals/Intervals.ma @@ -25,7 +25,7 @@ include "algebra/CSetoidInc.ma". include "reals/RealLists.ma". (* UNEXPORTED -Section Intervals. +Section Intervals *) (*#* * Intervals @@ -49,11 +49,11 @@ As expected, both [a] and [b] are members of [[a,b]]. Also they are members of the interval [[Min(a,b),Max(a,b)]]. *) -inline "cic:/CoRN/reals/Intervals/a.var". +inline "cic:/CoRN/reals/Intervals/Intervals/a.var" "Intervals__". -inline "cic:/CoRN/reals/Intervals/b.var". +inline "cic:/CoRN/reals/Intervals/Intervals/b.var" "Intervals__". -inline "cic:/CoRN/reals/Intervals/Hab.var". +inline "cic:/CoRN/reals/Intervals/Intervals/Hab.var" "Intervals__". inline "cic:/CoRN/reals/Intervals/compact_inc_lft.con". @@ -89,7 +89,7 @@ returns the restriction $F|_P$# of F to P#. inline "cic:/CoRN/reals/Intervals/Frestr.con". (* UNEXPORTED -End Intervals. +End Intervals *) (* NOTATION @@ -105,7 +105,7 @@ Notation FRestr := (Frestr (compact_wd _ _ _)). *) (* UNEXPORTED -Section More_Intervals. +Section More_Intervals *) inline "cic:/CoRN/reals/Intervals/included_refl'.con". @@ -119,7 +119,7 @@ inline "cic:/CoRN/reals/Intervals/compact_map2.con". inline "cic:/CoRN/reals/Intervals/compact_map3.con". (* UNEXPORTED -End More_Intervals. +End More_Intervals *) (* UNEXPORTED @@ -127,7 +127,7 @@ Hint Resolve included_refl' compact_map1 compact_map2 compact_map3 : included. *) (* UNEXPORTED -Section Totally_Bounded. +Section Totally_Bounded *) (*#* ** Totally Bounded @@ -172,9 +172,9 @@ inline "cic:/CoRN/reals/Intervals/fun_lub_IR.con". (* begin hide *) -inline "cic:/CoRN/reals/Intervals/aux_seq_lub.con". +inline "cic:/CoRN/reals/Intervals/Totally_Bounded/aux_seq_lub.con" "Totally_Bounded__". -inline "cic:/CoRN/reals/Intervals/aux_seq_lub_prop.con". +inline "cic:/CoRN/reals/Intervals/Totally_Bounded/aux_seq_lub_prop.con" "Totally_Bounded__". (* end hide *) @@ -186,20 +186,20 @@ inline "cic:/CoRN/reals/Intervals/totally_bounded_has_lub.con". (* begin hide *) -inline "cic:/CoRN/reals/Intervals/aux_seq_glb.con". +inline "cic:/CoRN/reals/Intervals/Totally_Bounded/aux_seq_glb.con" "Totally_Bounded__". -inline "cic:/CoRN/reals/Intervals/aux_seq_glb_prop.con". +inline "cic:/CoRN/reals/Intervals/Totally_Bounded/aux_seq_glb_prop.con" "Totally_Bounded__". (* end hide *) inline "cic:/CoRN/reals/Intervals/totally_bounded_has_glb.con". (* UNEXPORTED -End Totally_Bounded. +End Totally_Bounded *) (* UNEXPORTED -Section Compact. +Section Compact *) (*#* ** Compact sets @@ -227,23 +227,23 @@ a positive real number. %\end{convention}% *) -inline "cic:/CoRN/reals/Intervals/a.var". +inline "cic:/CoRN/reals/Intervals/Compact/a.var" "Compact__". -inline "cic:/CoRN/reals/Intervals/b.var". +inline "cic:/CoRN/reals/Intervals/Compact/b.var" "Compact__". -inline "cic:/CoRN/reals/Intervals/Hab.var". +inline "cic:/CoRN/reals/Intervals/Compact/Hab.var" "Compact__". (* begin hide *) -inline "cic:/CoRN/reals/Intervals/I.con". +inline "cic:/CoRN/reals/Intervals/Compact/I.con" "Compact__". (* end hide *) -inline "cic:/CoRN/reals/Intervals/Hab'.var". +inline "cic:/CoRN/reals/Intervals/Compact/Hab'.var" "Compact__". -inline "cic:/CoRN/reals/Intervals/e.var". +inline "cic:/CoRN/reals/Intervals/Compact/e.var" "Compact__". -inline "cic:/CoRN/reals/Intervals/He.var". +inline "cic:/CoRN/reals/Intervals/Compact/He.var" "Compact__". (*#* We start by finding a natural number [n] such that [(b[-]a) [/] n [<] e]. @@ -304,7 +304,7 @@ inline "cic:/CoRN/reals/Intervals/included2_compact.con". inline "cic:/CoRN/reals/Intervals/included3_compact.con". (* UNEXPORTED -End Compact. +End Compact *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/reals/Max_AbsIR.ma b/helm/software/matita/contribs/CoRN-Decl/reals/Max_AbsIR.ma index 91cb3e481..6c3b89c8d 100644 --- a/helm/software/matita/contribs/CoRN-Decl/reals/Max_AbsIR.ma +++ b/helm/software/matita/contribs/CoRN-Decl/reals/Max_AbsIR.ma @@ -27,11 +27,11 @@ include "CoRN.ma". include "reals/CauchySeq.ma". (* UNEXPORTED -Section Maximum. +Section Maximum *) (* UNEXPORTED -Section Max_function. +Section Max_function *) (*#* ** Maximum, Minimum and Absolute Value @@ -42,9 +42,9 @@ Let [x] and [y] be reals %\end{convention}% *) -inline "cic:/CoRN/reals/Max_AbsIR/x.var". +inline "cic:/CoRN/reals/Max_AbsIR/Maximum/Max_function/x.var" "Maximum__Max_function__". -inline "cic:/CoRN/reals/Max_AbsIR/y.var". +inline "cic:/CoRN/reals/Max_AbsIR/Maximum/Max_function/y.var" "Maximum__Max_function__". inline "cic:/CoRN/reals/Max_AbsIR/Max_seq.con". @@ -77,7 +77,7 @@ inline "cic:/CoRN/reals/Max_AbsIR/rht_leEq_MAX.con". inline "cic:/CoRN/reals/Max_AbsIR/less_MAX_imp.con". (* UNEXPORTED -End Max_function. +End Max_function *) inline "cic:/CoRN/reals/Max_AbsIR/MAX_strext.con". @@ -85,7 +85,7 @@ inline "cic:/CoRN/reals/Max_AbsIR/MAX_strext.con". inline "cic:/CoRN/reals/Max_AbsIR/MAX_wd.con". (* UNEXPORTED -Section properties_of_Max. +Section properties_of_Max *) (*#* *** Maximum *) @@ -123,11 +123,11 @@ inline "cic:/CoRN/reals/Max_AbsIR/pos_max_one.con". inline "cic:/CoRN/reals/Max_AbsIR/x_div_Max_leEq_x.con". (* UNEXPORTED -End properties_of_Max. +End properties_of_Max *) (* UNEXPORTED -End Maximum. +End Maximum *) (* UNEXPORTED @@ -135,7 +135,7 @@ Hint Resolve Max_id: algebra. *) (* UNEXPORTED -Section Minimum. +Section Minimum *) (*#* *** Mininum @@ -178,9 +178,9 @@ inline "cic:/CoRN/reals/Max_AbsIR/Min_is_lft_imp_leEq.con". inline "cic:/CoRN/reals/Max_AbsIR/leEq_Min_plus_eps.con". -inline "cic:/CoRN/reals/Max_AbsIR/a.var". +inline "cic:/CoRN/reals/Max_AbsIR/Minimum/a.var" "Minimum__". -inline "cic:/CoRN/reals/Max_AbsIR/b.var". +inline "cic:/CoRN/reals/Max_AbsIR/Minimum/b.var" "Minimum__". inline "cic:/CoRN/reals/Max_AbsIR/Min_leEq_Max.con". @@ -195,13 +195,13 @@ inline "cic:/CoRN/reals/Max_AbsIR/ap_imp_Min_less_Max.con". inline "cic:/CoRN/reals/Max_AbsIR/Min_less_Max_imp_ap.con". (* UNEXPORTED -End Minimum. +End Minimum *) (*#**********************************) (* UNEXPORTED -Section Absolute. +Section Absolute *) (*#**********************************) @@ -271,7 +271,7 @@ inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_str_bnd.con". inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_bnd.con". (* UNEXPORTED -End Absolute. +End Absolute *) (* UNEXPORTED @@ -279,7 +279,7 @@ Hint Resolve AbsIRz_isz: algebra. *) (* UNEXPORTED -Section Part_Function_Max. +Section Part_Function_Max *) (*#* *** Functional Operators @@ -291,15 +291,15 @@ Let [F,G:PartIR] and denote by [P] and [Q] their respective domains. %\end{convention}% *) -inline "cic:/CoRN/reals/Max_AbsIR/F.var". +inline "cic:/CoRN/reals/Max_AbsIR/Part_Function_Max/F.var" "Part_Function_Max__". -inline "cic:/CoRN/reals/Max_AbsIR/G.var". +inline "cic:/CoRN/reals/Max_AbsIR/Part_Function_Max/G.var" "Part_Function_Max__". (* begin hide *) -inline "cic:/CoRN/reals/Max_AbsIR/P.con". +inline "cic:/CoRN/reals/Max_AbsIR/Part_Function_Max/P.con" "Part_Function_Max__". -inline "cic:/CoRN/reals/Max_AbsIR/Q.con". +inline "cic:/CoRN/reals/Max_AbsIR/Part_Function_Max/Q.con" "Part_Function_Max__". (* end hide *) @@ -308,22 +308,22 @@ inline "cic:/CoRN/reals/Max_AbsIR/part_function_Max_strext.con". inline "cic:/CoRN/reals/Max_AbsIR/FMax.con". (* UNEXPORTED -End Part_Function_Max. +End Part_Function_Max *) (* UNEXPORTED -Section Part_Function_Abs. +Section Part_Function_Abs *) -inline "cic:/CoRN/reals/Max_AbsIR/F.var". +inline "cic:/CoRN/reals/Max_AbsIR/Part_Function_Abs/F.var" "Part_Function_Abs__". -inline "cic:/CoRN/reals/Max_AbsIR/G.var". +inline "cic:/CoRN/reals/Max_AbsIR/Part_Function_Abs/G.var" "Part_Function_Abs__". (* begin hide *) -inline "cic:/CoRN/reals/Max_AbsIR/P.con". +inline "cic:/CoRN/reals/Max_AbsIR/Part_Function_Abs/P.con" "Part_Function_Abs__". -inline "cic:/CoRN/reals/Max_AbsIR/Q.con". +inline "cic:/CoRN/reals/Max_AbsIR/Part_Function_Abs/Q.con" "Part_Function_Abs__". (* end hide *) @@ -344,7 +344,7 @@ Transparent Max. inline "cic:/CoRN/reals/Max_AbsIR/FAbs_char.con". (* UNEXPORTED -End Part_Function_Abs. +End Part_Function_Abs *) (* UNEXPORTED @@ -360,18 +360,18 @@ Hint Resolve FAbs_char': algebra. *) (* UNEXPORTED -Section Inclusion. +Section Inclusion *) -inline "cic:/CoRN/reals/Max_AbsIR/F.var". +inline "cic:/CoRN/reals/Max_AbsIR/Inclusion/F.var" "Inclusion__". -inline "cic:/CoRN/reals/Max_AbsIR/G.var". +inline "cic:/CoRN/reals/Max_AbsIR/Inclusion/G.var" "Inclusion__". (* begin hide *) -inline "cic:/CoRN/reals/Max_AbsIR/P.con". +inline "cic:/CoRN/reals/Max_AbsIR/Inclusion/P.con" "Inclusion__". -inline "cic:/CoRN/reals/Max_AbsIR/Q.con". +inline "cic:/CoRN/reals/Max_AbsIR/Inclusion/Q.con" "Inclusion__". (* end hide *) @@ -380,7 +380,7 @@ inline "cic:/CoRN/reals/Max_AbsIR/Q.con". %\end{convention}% *) -inline "cic:/CoRN/reals/Max_AbsIR/R.var". +inline "cic:/CoRN/reals/Max_AbsIR/Inclusion/R.var" "Inclusion__". inline "cic:/CoRN/reals/Max_AbsIR/included_FMax.con". @@ -399,7 +399,7 @@ inline "cic:/CoRN/reals/Max_AbsIR/included_FAbs.con". inline "cic:/CoRN/reals/Max_AbsIR/included_FAbs'.con". (* UNEXPORTED -End Inclusion. +End Inclusion *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/reals/NRootIR.ma b/helm/software/matita/contribs/CoRN-Decl/reals/NRootIR.ma index c82c1cde3..c27fc2556 100644 --- a/helm/software/matita/contribs/CoRN-Decl/reals/NRootIR.ma +++ b/helm/software/matita/contribs/CoRN-Decl/reals/NRootIR.ma @@ -29,7 +29,7 @@ include "reals/OddPolyRootIR.ma". (*#* * Roots of Real Numbers *) (* UNEXPORTED -Section NRoot. +Section NRoot *) (*#* ** Existence of roots @@ -39,24 +39,24 @@ Section NRoot. %\end{convention}% *) -inline "cic:/CoRN/reals/NRootIR/n.var". +inline "cic:/CoRN/reals/NRootIR/NRoot/n.var" "NRoot__". -inline "cic:/CoRN/reals/NRootIR/n_pos.var". +inline "cic:/CoRN/reals/NRootIR/NRoot/n_pos.var" "NRoot__". -inline "cic:/CoRN/reals/NRootIR/c.var". +inline "cic:/CoRN/reals/NRootIR/NRoot/c.var" "NRoot__". -inline "cic:/CoRN/reals/NRootIR/c_nonneg.var". +inline "cic:/CoRN/reals/NRootIR/NRoot/c_nonneg.var" "NRoot__". (* begin hide *) -inline "cic:/CoRN/reals/NRootIR/p.con". +inline "cic:/CoRN/reals/NRootIR/NRoot/p.con" "NRoot__". (* end hide *) inline "cic:/CoRN/reals/NRootIR/CnrootIR.con". (* UNEXPORTED -End NRoot. +End NRoot *) (*#* We define the root of order [n] for any nonnegative real number and @@ -72,7 +72,7 @@ prove its main properties: *) (* UNEXPORTED -Section Nth_Root. +Section Nth_Root *) inline "cic:/CoRN/reals/NRootIR/nroot.con". @@ -100,20 +100,20 @@ inline "cic:/CoRN/reals/NRootIR/NRoot_cancel.con". (*#* %\begin{convention}% Let [x,y] be nonnegative real numbers. %\end{convention}% *) -inline "cic:/CoRN/reals/NRootIR/x.var". +inline "cic:/CoRN/reals/NRootIR/Nth_Root/x.var" "Nth_Root__". -inline "cic:/CoRN/reals/NRootIR/y.var". +inline "cic:/CoRN/reals/NRootIR/Nth_Root/y.var" "Nth_Root__". -inline "cic:/CoRN/reals/NRootIR/Hx.var". +inline "cic:/CoRN/reals/NRootIR/Nth_Root/Hx.var" "Nth_Root__". -inline "cic:/CoRN/reals/NRootIR/Hy.var". +inline "cic:/CoRN/reals/NRootIR/Nth_Root/Hy.var" "Nth_Root__". inline "cic:/CoRN/reals/NRootIR/NRoot_wd.con". inline "cic:/CoRN/reals/NRootIR/NRoot_unique.con". (* UNEXPORTED -End Nth_Root. +End Nth_Root *) (* UNEXPORTED @@ -129,7 +129,7 @@ inline "cic:/CoRN/reals/NRootIR/NRoot_resp_leEq.con". (*#**********************************) (* UNEXPORTED -Section Square_root. +Section Square_root *) (*#**********************************) @@ -173,7 +173,7 @@ inline "cic:/CoRN/reals/NRootIR/sqrt_resp_leEq.con". inline "cic:/CoRN/reals/NRootIR/sqrt_resp_less.con". (* UNEXPORTED -End Square_root. +End Square_root *) (* UNEXPORTED @@ -185,7 +185,7 @@ Hint Resolve sqrt_sqr sqrt_mult: algebra. *) (* UNEXPORTED -Section Absolute_Props. +Section Absolute_Props *) (*#* ** More on absolute value @@ -243,11 +243,11 @@ inline "cic:/CoRN/reals/NRootIR/AbsIR_str_bnd_AbsIR.con". inline "cic:/CoRN/reals/NRootIR/AbsIR_bnd_AbsIR.con". (* UNEXPORTED -End Absolute_Props. +End Absolute_Props *) (* UNEXPORTED -Section Consequences. +Section Consequences *) (*#* **Cauchy sequences @@ -264,6 +264,6 @@ inline "cic:/CoRN/reals/NRootIR/Cauchy_recip.con". inline "cic:/CoRN/reals/NRootIR/Lim_recip.con". (* UNEXPORTED -End Consequences. +End Consequences *) diff --git a/helm/software/matita/contribs/CoRN-Decl/reals/OddPolyRootIR.ma b/helm/software/matita/contribs/CoRN-Decl/reals/OddPolyRootIR.ma index ae1943b24..5631b9ac4 100644 --- a/helm/software/matita/contribs/CoRN-Decl/reals/OddPolyRootIR.ma +++ b/helm/software/matita/contribs/CoRN-Decl/reals/OddPolyRootIR.ma @@ -25,7 +25,7 @@ include "reals/IVT.ma". (*#* * Roots of polynomials of odd degree *) (* UNEXPORTED -Section CPoly_Big. +Section CPoly_Big *) (*#* ** Monic polynomials are positive near infinity @@ -33,11 +33,11 @@ Section CPoly_Big. %\end{convention}% *) -inline "cic:/CoRN/reals/OddPolyRootIR/R.var". +inline "cic:/CoRN/reals/OddPolyRootIR/CPoly_Big/R.var" "CPoly_Big__". (* begin hide *) -inline "cic:/CoRN/reals/OddPolyRootIR/RX.con". +inline "cic:/CoRN/reals/OddPolyRootIR/CPoly_Big/RX.con" "CPoly_Big__". (* end hide *) @@ -50,11 +50,11 @@ inline "cic:/CoRN/reals/OddPolyRootIR/cpoly_pos.con". inline "cic:/CoRN/reals/OddPolyRootIR/Ccpoly_pos'.con". (* UNEXPORTED -End CPoly_Big. +End CPoly_Big *) (* UNEXPORTED -Section Flip_Poly. +Section Flip_Poly *) (*#* **Flipping a polynomial @@ -62,11 +62,11 @@ Section Flip_Poly. %\end{convention}% *) -inline "cic:/CoRN/reals/OddPolyRootIR/R.var". +inline "cic:/CoRN/reals/OddPolyRootIR/Flip_Poly/R.var" "Flip_Poly__". (* begin hide *) -inline "cic:/CoRN/reals/OddPolyRootIR/RX.con". +inline "cic:/CoRN/reals/OddPolyRootIR/Flip_Poly/RX.con" "Flip_Poly__". (* end hide *) @@ -83,7 +83,7 @@ Hint Resolve flip_coefficient: algebra. inline "cic:/CoRN/reals/OddPolyRootIR/flip_odd.con". (* UNEXPORTED -End Flip_Poly. +End Flip_Poly *) (* UNEXPORTED @@ -91,7 +91,7 @@ Hint Resolve flip_poly: algebra. *) (* UNEXPORTED -Section OddPoly_Signs. +Section OddPoly_Signs *) (*#* ** Sign of a polynomial of odd degree @@ -99,11 +99,11 @@ Section OddPoly_Signs. %\end{convention}% *) -inline "cic:/CoRN/reals/OddPolyRootIR/R.var". +inline "cic:/CoRN/reals/OddPolyRootIR/OddPoly_Signs/R.var" "OddPoly_Signs__". (* begin hide *) -inline "cic:/CoRN/reals/OddPolyRootIR/RX.con". +inline "cic:/CoRN/reals/OddPolyRootIR/OddPoly_Signs/RX.con" "OddPoly_Signs__". (* end hide *) @@ -114,11 +114,11 @@ inline "cic:/CoRN/reals/OddPolyRootIR/oddpoly_pos'.con". inline "cic:/CoRN/reals/OddPolyRootIR/oddpoly_neg.con". (* UNEXPORTED -End OddPoly_Signs. +End OddPoly_Signs *) (* UNEXPORTED -Section Poly_Norm. +Section Poly_Norm *) (*#* ** The norm of a polynomial @@ -127,11 +127,11 @@ this field. %\end{convention}% *) -inline "cic:/CoRN/reals/OddPolyRootIR/R.var". +inline "cic:/CoRN/reals/OddPolyRootIR/Poly_Norm/R.var" "Poly_Norm__". (* begin hide *) -inline "cic:/CoRN/reals/OddPolyRootIR/RX.con". +inline "cic:/CoRN/reals/OddPolyRootIR/Poly_Norm/RX.con" "Poly_Norm__". (* end hide *) @@ -144,11 +144,11 @@ inline "cic:/CoRN/reals/OddPolyRootIR/poly_norm_monic.con". inline "cic:/CoRN/reals/OddPolyRootIR/poly_norm_apply.con". (* UNEXPORTED -End Poly_Norm. +End Poly_Norm *) (* UNEXPORTED -Section OddPoly_Root. +Section OddPoly_Root *) (*#* ** Roots of polynomials of odd degree @@ -161,6 +161,6 @@ inline "cic:/CoRN/reals/OddPolyRootIR/oddpoly_root.con". inline "cic:/CoRN/reals/OddPolyRootIR/realpolyn_oddhaszero.con". (* UNEXPORTED -End OddPoly_Root. +End OddPoly_Root *) diff --git a/helm/software/matita/contribs/CoRN-Decl/reals/Q_dense.ma b/helm/software/matita/contribs/CoRN-Decl/reals/Q_dense.ma index ef7bf1d79..a5ce0fcda 100644 --- a/helm/software/matita/contribs/CoRN-Decl/reals/Q_dense.ma +++ b/helm/software/matita/contribs/CoRN-Decl/reals/Q_dense.ma @@ -27,10 +27,10 @@ include "reals/Q_in_CReals.ma". inline "cic:/CoRN/reals/Q_dense/or_not_and.con". (* UNEXPORTED -Section Interval_definition. +Section Interval_definition *) -inline "cic:/CoRN/reals/Q_dense/OF.var". +inline "cic:/CoRN/reals/Q_dense/Interval_definition/OF.var" "Interval_definition__". inline "cic:/CoRN/reals/Q_dense/Interval.ind". @@ -39,7 +39,7 @@ coercion cic:/matita/CoRN-Decl/reals/Q_dense/pair_crr.con 0 (* compounds *). inline "cic:/CoRN/reals/Q_dense/Length.con". (* UNEXPORTED -End Interval_definition. +End Interval_definition *) inline "cic:/CoRN/reals/Q_dense/Rat_Interval.con". @@ -60,10 +60,10 @@ Qed. *) (* UNEXPORTED -Section COrdField_extra. +Section COrdField_extra *) -inline "cic:/CoRN/reals/Q_dense/OF.var". +inline "cic:/CoRN/reals/Q_dense/COrdField_extra/OF.var" "COrdField_extra__". inline "cic:/CoRN/reals/Q_dense/AbsSmall_pos_reflexive.con". @@ -72,18 +72,18 @@ inline "cic:/CoRN/reals/Q_dense/AbsSmall_neg_reflexive.con". inline "cic:/CoRN/reals/Q_dense/AbsSmall_subinterval.con". (* UNEXPORTED -End COrdField_extra. +End COrdField_extra *) (* UNEXPORTED -Section Rational_sequence. +Section Rational_sequence *) include "tactics/Opaque_algebra.ma". (*#*** WARNING: A file is being loaded *****) -inline "cic:/CoRN/reals/Q_dense/R1.var". +inline "cic:/CoRN/reals/Q_dense/Rational_sequence/R1.var" "Rational_sequence__". inline "cic:/CoRN/reals/Q_dense/start_l.con". @@ -162,7 +162,7 @@ inline "cic:/CoRN/reals/Q_dense/G_conversion_rate_resp_x.con". inline "cic:/CoRN/reals/Q_dense/x_is_SeqLimit_G.con". (* UNEXPORTED -End Rational_sequence. +End Rational_sequence *) (* end hide *) diff --git a/helm/software/matita/contribs/CoRN-Decl/reals/Q_in_CReals.ma b/helm/software/matita/contribs/CoRN-Decl/reals/Q_in_CReals.ma index 8bcdda3dd..f9fca0040 100644 --- a/helm/software/matita/contribs/CoRN-Decl/reals/Q_in_CReals.ma +++ b/helm/software/matita/contribs/CoRN-Decl/reals/Q_in_CReals.ma @@ -35,7 +35,7 @@ include "model/monoids/Nmonoid.ma". include "model/rings/Zring.ma". (* UNEXPORTED -Section Rational_sequence_prelogue. +Section Rational_sequence_prelogue *) (*#* @@ -43,7 +43,7 @@ Section Rational_sequence_prelogue. %\end{convention}% *) -inline "cic:/CoRN/reals/Q_in_CReals/R1.var". +inline "cic:/CoRN/reals/Q_in_CReals/Rational_sequence_prelogue/R1.var" "Rational_sequence_prelogue__". (* We clone these proofs from CReals1.v just because there IR is an axiom *) @@ -165,6 +165,6 @@ is a rational number between any two real numbers. *) inline "cic:/CoRN/reals/Q_in_CReals/Q_dense_in_CReals.con". (* UNEXPORTED -End Rational_sequence_prelogue. +End Rational_sequence_prelogue *) diff --git a/helm/software/matita/contribs/CoRN-Decl/reals/R_morphism.ma b/helm/software/matita/contribs/CoRN-Decl/reals/R_morphism.ma index a72a7f423..d11235f39 100644 --- a/helm/software/matita/contribs/CoRN-Decl/reals/R_morphism.ma +++ b/helm/software/matita/contribs/CoRN-Decl/reals/R_morphism.ma @@ -31,30 +31,30 @@ include "reals/CReals.ma". inline "cic:/CoRN/reals/R_morphism/Cauchy_Lim_prop2.con". (* UNEXPORTED -Section morphism. +Section morphism *) -inline "cic:/CoRN/reals/R_morphism/R1.var". +inline "cic:/CoRN/reals/R_morphism/morphism/R1.var" "morphism__". -inline "cic:/CoRN/reals/R_morphism/R2.var". +inline "cic:/CoRN/reals/R_morphism/morphism/R2.var" "morphism__". (* UNEXPORTED -Section morphism_details. +Section morphism_details *) -inline "cic:/CoRN/reals/R_morphism/phi.var". +inline "cic:/CoRN/reals/R_morphism/morphism/morphism_details/phi.var" "morphism__morphism_details__". -inline "cic:/CoRN/reals/R_morphism/p1.var". +inline "cic:/CoRN/reals/R_morphism/morphism/morphism_details/p1.var" "morphism__morphism_details__". -inline "cic:/CoRN/reals/R_morphism/p2.var". +inline "cic:/CoRN/reals/R_morphism/morphism/morphism_details/p2.var" "morphism__morphism_details__". -inline "cic:/CoRN/reals/R_morphism/f1.var". +inline "cic:/CoRN/reals/R_morphism/morphism/morphism_details/f1.var" "morphism__morphism_details__". -inline "cic:/CoRN/reals/R_morphism/f2.var". +inline "cic:/CoRN/reals/R_morphism/morphism/morphism_details/f2.var" "morphism__morphism_details__". -inline "cic:/CoRN/reals/R_morphism/g1.var". +inline "cic:/CoRN/reals/R_morphism/morphism/morphism_details/g1.var" "morphism__morphism_details__". -inline "cic:/CoRN/reals/R_morphism/g2.var". +inline "cic:/CoRN/reals/R_morphism/morphism/morphism_details/g2.var" "morphism__morphism_details__". inline "cic:/CoRN/reals/R_morphism/fun_pres_relation.con". @@ -70,7 +70,7 @@ Definition fun_pres_partial_fun:=(x:R1;H1:x[#]Zero;H2:(phi x)[#]Zero) inline "cic:/CoRN/reals/R_morphism/fun_pres_Lim.con". (* UNEXPORTED -End morphism_details. +End morphism_details *) inline "cic:/CoRN/reals/R_morphism/Homomorphism.ind". @@ -121,22 +121,22 @@ inline "cic:/CoRN/reals/R_morphism/map_pres_one_unfolded.con". inline "cic:/CoRN/reals/R_morphism/map_pres_inv_unfolded.con". (* UNEXPORTED -End morphism. +End morphism *) (* UNEXPORTED -Section composition. +Section composition *) -inline "cic:/CoRN/reals/R_morphism/R1.var". +inline "cic:/CoRN/reals/R_morphism/composition/R1.var" "composition__". -inline "cic:/CoRN/reals/R_morphism/R2.var". +inline "cic:/CoRN/reals/R_morphism/composition/R2.var" "composition__". -inline "cic:/CoRN/reals/R_morphism/R3.var". +inline "cic:/CoRN/reals/R_morphism/composition/R3.var" "composition__". -inline "cic:/CoRN/reals/R_morphism/f.var". +inline "cic:/CoRN/reals/R_morphism/composition/f.var" "composition__". -inline "cic:/CoRN/reals/R_morphism/g.var". +inline "cic:/CoRN/reals/R_morphism/composition/g.var" "composition__". inline "cic:/CoRN/reals/R_morphism/compose.con". @@ -153,72 +153,72 @@ inline "cic:/CoRN/reals/R_morphism/compose_pres_Lim.con". inline "cic:/CoRN/reals/R_morphism/Compose.con". (* UNEXPORTED -End composition. +End composition *) (* UNEXPORTED -Section isomorphism. +Section isomorphism *) -inline "cic:/CoRN/reals/R_morphism/R1.var". +inline "cic:/CoRN/reals/R_morphism/isomorphism/R1.var" "isomorphism__". -inline "cic:/CoRN/reals/R_morphism/R2.var". +inline "cic:/CoRN/reals/R_morphism/isomorphism/R2.var" "isomorphism__". (* UNEXPORTED -Section identity_map. +Section identity_map *) -inline "cic:/CoRN/reals/R_morphism/R3.var". +inline "cic:/CoRN/reals/R_morphism/isomorphism/identity_map/R3.var" "isomorphism__identity_map__". -inline "cic:/CoRN/reals/R_morphism/f.var". +inline "cic:/CoRN/reals/R_morphism/isomorphism/identity_map/f.var" "isomorphism__identity_map__". inline "cic:/CoRN/reals/R_morphism/map_is_id.con". (* UNEXPORTED -End identity_map. +End identity_map *) inline "cic:/CoRN/reals/R_morphism/Isomorphism.ind". (* UNEXPORTED -End isomorphism. +End isomorphism *) (* UNEXPORTED -Section surjective_map. +Section surjective_map *) -inline "cic:/CoRN/reals/R_morphism/R1.var". +inline "cic:/CoRN/reals/R_morphism/surjective_map/R1.var" "surjective_map__". -inline "cic:/CoRN/reals/R_morphism/R2.var". +inline "cic:/CoRN/reals/R_morphism/surjective_map/R2.var" "surjective_map__". -inline "cic:/CoRN/reals/R_morphism/f.var". +inline "cic:/CoRN/reals/R_morphism/surjective_map/f.var" "surjective_map__". inline "cic:/CoRN/reals/R_morphism/map_is_surjective.con". (* UNEXPORTED -End surjective_map. +End surjective_map *) (* UNEXPORTED -Section simplification. +Section simplification *) -inline "cic:/CoRN/reals/R_morphism/R1.var". +inline "cic:/CoRN/reals/R_morphism/simplification/R1.var" "simplification__". -inline "cic:/CoRN/reals/R_morphism/R2.var". +inline "cic:/CoRN/reals/R_morphism/simplification/R2.var" "simplification__". -inline "cic:/CoRN/reals/R_morphism/f.var". +inline "cic:/CoRN/reals/R_morphism/simplification/f.var" "simplification__". -inline "cic:/CoRN/reals/R_morphism/H1.var". +inline "cic:/CoRN/reals/R_morphism/simplification/H1.var" "simplification__". inline "cic:/CoRN/reals/R_morphism/f_well_def.con". (* UNEXPORTED -Section with_less. +Section with_less *) -inline "cic:/CoRN/reals/R_morphism/H2.var". +inline "cic:/CoRN/reals/R_morphism/simplification/with_less/H2.var" "simplification__with_less__". inline "cic:/CoRN/reals/R_morphism/less_pres_f.con". @@ -229,14 +229,14 @@ inline "cic:/CoRN/reals/R_morphism/f_pres_leEq.con". inline "cic:/CoRN/reals/R_morphism/f_pres_apartness.con". (* UNEXPORTED -End with_less. +End with_less *) (* UNEXPORTED -Section with_plus. +Section with_plus *) -inline "cic:/CoRN/reals/R_morphism/H3.var". +inline "cic:/CoRN/reals/R_morphism/simplification/with_plus/H3.var" "simplification__with_plus__". inline "cic:/CoRN/reals/R_morphism/f_pres_Zero.con". @@ -245,36 +245,36 @@ inline "cic:/CoRN/reals/R_morphism/f_pres_minus.con". inline "cic:/CoRN/reals/R_morphism/f_pres_min.con". (* UNEXPORTED -End with_plus. +End with_plus *) (* UNEXPORTED -Section with_plus_less. +Section with_plus_less *) -inline "cic:/CoRN/reals/R_morphism/H2.var". +inline "cic:/CoRN/reals/R_morphism/simplification/with_plus_less/H2.var" "simplification__with_plus_less__". -inline "cic:/CoRN/reals/R_morphism/H3.var". +inline "cic:/CoRN/reals/R_morphism/simplification/with_plus_less/H3.var" "simplification__with_plus_less__". inline "cic:/CoRN/reals/R_morphism/f_pres_ap_zero.con". (* UNEXPORTED -Section surjectivity_helps. +Section surjectivity_helps *) -inline "cic:/CoRN/reals/R_morphism/f_surj.var". +inline "cic:/CoRN/reals/R_morphism/simplification/with_plus_less/surjectivity_helps/f_surj.var" "simplification__with_plus_less__surjectivity_helps__". inline "cic:/CoRN/reals/R_morphism/f_pres_Lim.con". (* UNEXPORTED -End surjectivity_helps. +End surjectivity_helps *) (* UNEXPORTED -Section with_mult_plus_less. +Section with_mult_plus_less *) -inline "cic:/CoRN/reals/R_morphism/H4.var". +inline "cic:/CoRN/reals/R_morphism/simplification/with_plus_less/with_mult_plus_less/H4.var" "simplification__with_plus_less__with_mult_plus_less__". inline "cic:/CoRN/reals/R_morphism/f_pres_one.con". @@ -283,15 +283,15 @@ inline "cic:/CoRN/reals/R_morphism/f_pres_inv.con". inline "cic:/CoRN/reals/R_morphism/simplified_Homomorphism.con". (* UNEXPORTED -End with_mult_plus_less. +End with_mult_plus_less *) (* UNEXPORTED -End with_plus_less. +End with_plus_less *) (* UNEXPORTED -End simplification. +End simplification *) (* end hide *) diff --git a/helm/software/matita/contribs/CoRN-Decl/reals/RealFuncts.ma b/helm/software/matita/contribs/CoRN-Decl/reals/RealFuncts.ma index ad7b03872..e2414af0c 100644 --- a/helm/software/matita/contribs/CoRN-Decl/reals/RealFuncts.ma +++ b/helm/software/matita/contribs/CoRN-Decl/reals/RealFuncts.ma @@ -38,12 +38,12 @@ Unset Strict Implicit. (* end hide *) (* UNEXPORTED -Section Continuity. +Section Continuity *) -inline "cic:/CoRN/reals/RealFuncts/f.var". +inline "cic:/CoRN/reals/RealFuncts/Continuity/f.var" "Continuity__". -inline "cic:/CoRN/reals/RealFuncts/f2.var". +inline "cic:/CoRN/reals/RealFuncts/Continuity/f2.var" "Continuity__". (*#* Let [f] be a unary setoid operation on [IR] and @@ -247,7 +247,7 @@ End Monotonic_functions. *) (* UNEXPORTED -End Continuity. +End Continuity *) (* begin hide *) diff --git a/helm/software/matita/contribs/CoRN-Decl/reals/RealLists.ma b/helm/software/matita/contribs/CoRN-Decl/reals/RealLists.ma index c3aba7338..322b20456 100644 --- a/helm/software/matita/contribs/CoRN-Decl/reals/RealLists.ma +++ b/helm/software/matita/contribs/CoRN-Decl/reals/RealLists.ma @@ -23,7 +23,7 @@ include "CoRN.ma". include "reals/CReals1.ma". (* UNEXPORTED -Section Lists. +Section Lists *) (*#* * Lists of Real Numbers @@ -76,7 +76,7 @@ inline "cic:/CoRN/reals/RealLists/maxlist_greater.con". (* begin hide *) -inline "cic:/CoRN/reals/RealLists/maxlist_aux.con". +inline "cic:/CoRN/reals/RealLists/Lists/maxlist_aux.con" "Lists__". (* end hide *) @@ -90,7 +90,7 @@ inline "cic:/CoRN/reals/RealLists/minlist_smaller.con". (* begin hide *) -inline "cic:/CoRN/reals/RealLists/minlist_aux.con". +inline "cic:/CoRN/reals/RealLists/Lists/minlist_aux.con" "Lists__". (* end hide *) @@ -101,6 +101,6 @@ inline "cic:/CoRN/reals/RealLists/less_minlist.con". inline "cic:/CoRN/reals/RealLists/leEq_minlist.con". (* UNEXPORTED -End Lists. +End Lists *) diff --git a/helm/software/matita/contribs/CoRN-Decl/reals/Series.ma b/helm/software/matita/contribs/CoRN-Decl/reals/Series.ma index 50dd1005f..3a90759c0 100644 --- a/helm/software/matita/contribs/CoRN-Decl/reals/Series.ma +++ b/helm/software/matita/contribs/CoRN-Decl/reals/Series.ma @@ -31,7 +31,7 @@ include "reals/CSumsReals.ma". include "reals/NRootIR.ma". (* UNEXPORTED -Section Definitions. +Section Definitions *) (*#* *Series of Real Numbers @@ -45,7 +45,7 @@ To each such sequence we can assign a sequence of partial sums. %\end{convention}% *) -inline "cic:/CoRN/reals/Series/x.var". +inline "cic:/CoRN/reals/Series/Definitions/x.var" "Definitions__". inline "cic:/CoRN/reals/Series/seq_part_sum.con". @@ -92,25 +92,25 @@ inline "cic:/CoRN/reals/Series/series_seq_Lim.con". inline "cic:/CoRN/reals/Series/series_seq_Lim'.con". (* UNEXPORTED -End Definitions. +End Definitions *) (* UNEXPORTED -Section More_Definitions. +Section More_Definitions *) -inline "cic:/CoRN/reals/Series/x.var". +inline "cic:/CoRN/reals/Series/More_Definitions/x.var" "More_Definitions__". (*#* We also define absolute convergence. *) inline "cic:/CoRN/reals/Series/abs_convergent.con". (* UNEXPORTED -End More_Definitions. +End More_Definitions *) (* UNEXPORTED -Section Power_Series. +Section Power_Series *) (*#* **Power Series @@ -129,11 +129,11 @@ we can also compute its sum. %\end{convention}% *) -inline "cic:/CoRN/reals/Series/c.var". +inline "cic:/CoRN/reals/Series/Power_Series/c.var" "Power_Series__". -inline "cic:/CoRN/reals/Series/H0c.var". +inline "cic:/CoRN/reals/Series/Power_Series/H0c.var" "Power_Series__". -inline "cic:/CoRN/reals/Series/Hc1.var". +inline "cic:/CoRN/reals/Series/Power_Series/Hc1.var" "Power_Series__". inline "cic:/CoRN/reals/Series/c_exp_Lim.con". @@ -144,11 +144,11 @@ inline "cic:/CoRN/reals/Series/power_series_conv.con". inline "cic:/CoRN/reals/Series/power_series_sum.con". (* UNEXPORTED -End Power_Series. +End Power_Series *) (* UNEXPORTED -Section Operations. +Section Operations *) (*#* **Operations @@ -168,13 +168,13 @@ of two convergent series. %\end{convention}% *) -inline "cic:/CoRN/reals/Series/x.var". +inline "cic:/CoRN/reals/Series/Operations/x.var" "Operations__". -inline "cic:/CoRN/reals/Series/y.var". +inline "cic:/CoRN/reals/Series/Operations/y.var" "Operations__". -inline "cic:/CoRN/reals/Series/convX.var". +inline "cic:/CoRN/reals/Series/Operations/convX.var" "Operations__". -inline "cic:/CoRN/reals/Series/convY.var". +inline "cic:/CoRN/reals/Series/Operations/convY.var" "Operations__". inline "cic:/CoRN/reals/Series/convergent_wd.con". @@ -190,23 +190,23 @@ inline "cic:/CoRN/reals/Series/series_sum_minus.con". (*#* Multiplication by a scalar [c] is also permitted. *) -inline "cic:/CoRN/reals/Series/c.var". +inline "cic:/CoRN/reals/Series/Operations/c.var" "Operations__". inline "cic:/CoRN/reals/Series/conv_series_mult_scal.con". inline "cic:/CoRN/reals/Series/series_sum_mult_scal.con". (* UNEXPORTED -End Operations. +End Operations *) (* UNEXPORTED -Section More_Operations. +Section More_Operations *) -inline "cic:/CoRN/reals/Series/x.var". +inline "cic:/CoRN/reals/Series/More_Operations/x.var" "More_Operations__". -inline "cic:/CoRN/reals/Series/convX.var". +inline "cic:/CoRN/reals/Series/More_Operations/convX.var" "More_Operations__". (*#* As a corollary, we get the series of the inverses. *) @@ -215,11 +215,11 @@ inline "cic:/CoRN/reals/Series/conv_series_inv.con". inline "cic:/CoRN/reals/Series/series_sum_inv.con". (* UNEXPORTED -End More_Operations. +End More_Operations *) (* UNEXPORTED -Section Almost_Everywhere. +Section Almost_Everywhere *) (*#* ** Almost Everywhere @@ -230,13 +230,13 @@ and derive an important corollary for series. Let [x,y : nat->IR] be equal after some natural number. *) -inline "cic:/CoRN/reals/Series/x.var". +inline "cic:/CoRN/reals/Series/Almost_Everywhere/x.var" "Almost_Everywhere__". -inline "cic:/CoRN/reals/Series/y.var". +inline "cic:/CoRN/reals/Series/Almost_Everywhere/y.var" "Almost_Everywhere__". inline "cic:/CoRN/reals/Series/aew_eq.con". -inline "cic:/CoRN/reals/Series/aew_equal.var". +inline "cic:/CoRN/reals/Series/Almost_Everywhere/aew_equal.var" "Almost_Everywhere__". inline "cic:/CoRN/reals/Series/aew_Cauchy.con". @@ -245,29 +245,29 @@ inline "cic:/CoRN/reals/Series/aew_Cauchy2.con". inline "cic:/CoRN/reals/Series/aew_series_conv.con". (* UNEXPORTED -End Almost_Everywhere. +End Almost_Everywhere *) (* UNEXPORTED -Section Cauchy_Almost_Everywhere. +Section Cauchy_Almost_Everywhere *) (*#* Suppose furthermore that [x,y] are Cauchy sequences. *) -inline "cic:/CoRN/reals/Series/x.var". +inline "cic:/CoRN/reals/Series/Cauchy_Almost_Everywhere/x.var" "Cauchy_Almost_Everywhere__". -inline "cic:/CoRN/reals/Series/y.var". +inline "cic:/CoRN/reals/Series/Cauchy_Almost_Everywhere/y.var" "Cauchy_Almost_Everywhere__". -inline "cic:/CoRN/reals/Series/aew_equal.var". +inline "cic:/CoRN/reals/Series/Cauchy_Almost_Everywhere/aew_equal.var" "Cauchy_Almost_Everywhere__". inline "cic:/CoRN/reals/Series/aew_Lim.con". (* UNEXPORTED -End Cauchy_Almost_Everywhere. +End Cauchy_Almost_Everywhere *) (* UNEXPORTED -Section Convergence_Criteria. +Section Convergence_Criteria *) (*#* **Convergence Criteria @@ -276,7 +276,7 @@ Section Convergence_Criteria. %\end{convention}% *) -inline "cic:/CoRN/reals/Series/x.var". +inline "cic:/CoRN/reals/Series/Convergence_Criteria/x.var" "Convergence_Criteria__". (*#* We include the comparison test for series, both in a strong and in a less general (but simpler) form. @@ -299,25 +299,25 @@ inline "cic:/CoRN/reals/Series/tail_series.con". inline "cic:/CoRN/reals/Series/join_series.con". (* UNEXPORTED -End Convergence_Criteria. +End Convergence_Criteria *) (* UNEXPORTED -Section More_CC. +Section More_CC *) -inline "cic:/CoRN/reals/Series/x.var". +inline "cic:/CoRN/reals/Series/More_CC/x.var" "More_CC__". inline "cic:/CoRN/reals/Series/ratio_test_conv.con". inline "cic:/CoRN/reals/Series/ratio_test_div.con". (* UNEXPORTED -End More_CC. +End More_CC *) (* UNEXPORTED -Section Alternate_Series. +Section Alternate_Series *) (*#* **Alternate Series @@ -326,36 +326,36 @@ Alternate series are a special case. Suppose that [x] is nonnegative and decreasing convergent to 0. *) -inline "cic:/CoRN/reals/Series/x.var". +inline "cic:/CoRN/reals/Series/Alternate_Series/x.var" "Alternate_Series__". -inline "cic:/CoRN/reals/Series/pos_x.var". +inline "cic:/CoRN/reals/Series/Alternate_Series/pos_x.var" "Alternate_Series__". -inline "cic:/CoRN/reals/Series/Lim_x.var". +inline "cic:/CoRN/reals/Series/Alternate_Series/Lim_x.var" "Alternate_Series__". -inline "cic:/CoRN/reals/Series/mon_x.var". +inline "cic:/CoRN/reals/Series/Alternate_Series/mon_x.var" "Alternate_Series__". (* begin hide *) -inline "cic:/CoRN/reals/Series/y.con". +inline "cic:/CoRN/reals/Series/Alternate_Series/y.con" "Alternate_Series__". -inline "cic:/CoRN/reals/Series/alternate_lemma1.con". +inline "cic:/CoRN/reals/Series/Alternate_Series/alternate_lemma1.con" "Alternate_Series__". -inline "cic:/CoRN/reals/Series/alternate_lemma2.con". +inline "cic:/CoRN/reals/Series/Alternate_Series/alternate_lemma2.con" "Alternate_Series__". -inline "cic:/CoRN/reals/Series/alternate_lemma3.con". +inline "cic:/CoRN/reals/Series/Alternate_Series/alternate_lemma3.con" "Alternate_Series__". -inline "cic:/CoRN/reals/Series/alternate_lemma4.con". +inline "cic:/CoRN/reals/Series/Alternate_Series/alternate_lemma4.con" "Alternate_Series__". (* end hide *) inline "cic:/CoRN/reals/Series/alternate_series_conv.con". (* UNEXPORTED -End Alternate_Series. +End Alternate_Series *) (* UNEXPORTED -Section Important_Numbers. +Section Important_Numbers *) (*#* **Important Numbers @@ -377,6 +377,6 @@ inline "cic:/CoRN/reals/Series/pi_series_conv.con". inline "cic:/CoRN/reals/Series/pi.con". (* UNEXPORTED -End Important_Numbers. +End Important_Numbers *) diff --git a/helm/software/matita/contribs/CoRN-Decl/reals/iso_CReals.ma b/helm/software/matita/contribs/CoRN-Decl/reals/iso_CReals.ma index 414856a30..c7e115dd9 100644 --- a/helm/software/matita/contribs/CoRN-Decl/reals/iso_CReals.ma +++ b/helm/software/matita/contribs/CoRN-Decl/reals/iso_CReals.ma @@ -58,12 +58,12 @@ inline "cic:/CoRN/reals/iso_CReals/Lim_pres_mult.con". inline "cic:/CoRN/reals/iso_CReals/G_pres_mult.con". (* UNEXPORTED -Section Concrete_iso_between_Creals. +Section Concrete_iso_between_Creals *) -inline "cic:/CoRN/reals/iso_CReals/R1.var". +inline "cic:/CoRN/reals/iso_CReals/Concrete_iso_between_Creals/R1.var" "Concrete_iso_between_Creals__". -inline "cic:/CoRN/reals/iso_CReals/R2.var". +inline "cic:/CoRN/reals/iso_CReals/Concrete_iso_between_Creals/R2.var" "Concrete_iso_between_Creals__". inline "cic:/CoRN/reals/iso_CReals/image_Cauchy12.con". @@ -118,7 +118,7 @@ inline "cic:/CoRN/reals/iso_CReals/g21_inverse_rht.con". inline "cic:/CoRN/reals/iso_CReals/Canonic_Isomorphism_between_CReals.con". (* UNEXPORTED -End Concrete_iso_between_Creals. +End Concrete_iso_between_Creals *) (* end hide *) diff --git a/helm/software/matita/contribs/CoRN-Decl/tactics/AlgReflection.ma b/helm/software/matita/contribs/CoRN-Decl/tactics/AlgReflection.ma index fa4524743..51ba402fa 100644 --- a/helm/software/matita/contribs/CoRN-Decl/tactics/AlgReflection.ma +++ b/helm/software/matita/contribs/CoRN-Decl/tactics/AlgReflection.ma @@ -25,7 +25,7 @@ include "CoRN.ma". include "algebra/CLogic.ma". (* UNEXPORTED -Section Syntactic_Expressions. +Section Syntactic_Expressions *) inline "cic:/CoRN/tactics/AlgReflection/varindex.con". @@ -51,11 +51,11 @@ inline "cic:/CoRN/tactics/AlgReflection/expr_minus.con". inline "cic:/CoRN/tactics/AlgReflection/expr_power.con". (* UNEXPORTED -End Syntactic_Expressions. +End Syntactic_Expressions *) (* UNEXPORTED -Section Normalization_Function. +Section Normalization_Function *) inline "cic:/CoRN/tactics/AlgReflection/eq_nat.con". @@ -111,11 +111,11 @@ inline "cic:/CoRN/tactics/AlgReflection/NormF.con". inline "cic:/CoRN/tactics/AlgReflection/expr_is_zero.con". (* UNEXPORTED -End Normalization_Function. +End Normalization_Function *) (* UNEXPORTED -Section Correctness_Results. +Section Correctness_Results *) inline "cic:/CoRN/tactics/AlgReflection/eq_nat_corr.con". @@ -125,7 +125,7 @@ inline "cic:/CoRN/tactics/AlgReflection/eq_int_corr.con". inline "cic:/CoRN/tactics/AlgReflection/eq_expr_corr.con". (* UNEXPORTED -End Correctness_Results. +End Correctness_Results *) (* end hide *) diff --git a/helm/software/matita/contribs/CoRN-Decl/tactics/DiffTactics2.ma b/helm/software/matita/contribs/CoRN-Decl/tactics/DiffTactics2.ma index 9abd9ae08..8b2fa6832 100644 --- a/helm/software/matita/contribs/CoRN-Decl/tactics/DiffTactics2.ma +++ b/helm/software/matita/contribs/CoRN-Decl/tactics/DiffTactics2.ma @@ -25,12 +25,12 @@ include "CoRN.ma". include "ftc/Differentiability.ma". (* UNEXPORTED -Section Automatizing_Continuity. +Section Automatizing_Continuity *) -inline "cic:/CoRN/tactics/DiffTactics2/a.var". +inline "cic:/CoRN/tactics/DiffTactics2/Automatizing_Continuity/a.var" "Automatizing_Continuity__". -inline "cic:/CoRN/tactics/DiffTactics2/b.var". +inline "cic:/CoRN/tactics/DiffTactics2/Automatizing_Continuity/b.var" "Automatizing_Continuity__". inline "cic:/CoRN/tactics/DiffTactics2/cont_function.ind". @@ -39,7 +39,7 @@ inline "cic:/CoRN/tactics/DiffTactics2/cont_to_pfunct.con". inline "cic:/CoRN/tactics/DiffTactics2/continuous_cont.con". (* UNEXPORTED -End Automatizing_Continuity. +End Automatizing_Continuity *) (* UNEXPORTED @@ -95,12 +95,12 @@ Ltac New_Contin := *) (* UNEXPORTED -Section Automatizing_Derivatives. +Section Automatizing_Derivatives *) -inline "cic:/CoRN/tactics/DiffTactics2/a.var". +inline "cic:/CoRN/tactics/DiffTactics2/Automatizing_Derivatives/a.var" "Automatizing_Derivatives__". -inline "cic:/CoRN/tactics/DiffTactics2/b.var". +inline "cic:/CoRN/tactics/DiffTactics2/Automatizing_Derivatives/b.var" "Automatizing_Derivatives__". inline "cic:/CoRN/tactics/DiffTactics2/deriv_function.ind". @@ -113,7 +113,7 @@ inline "cic:/CoRN/tactics/DiffTactics2/deriv_restr.con". inline "cic:/CoRN/tactics/DiffTactics2/diffble_restr.con". (* UNEXPORTED -End Automatizing_Derivatives. +End Automatizing_Derivatives *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/tactics/FieldReflection.ma b/helm/software/matita/contribs/CoRN-Decl/tactics/FieldReflection.ma index 70b61dea5..459f7d132 100644 --- a/helm/software/matita/contribs/CoRN-Decl/tactics/FieldReflection.ma +++ b/helm/software/matita/contribs/CoRN-Decl/tactics/FieldReflection.ma @@ -27,18 +27,18 @@ include "algebra/CFields.ma". include "tactics/AlgReflection.ma". (* UNEXPORTED -Section Field_Interpretation_Function. +Section Field_Interpretation_Function *) -inline "cic:/CoRN/tactics/FieldReflection/F.var". +inline "cic:/CoRN/tactics/FieldReflection/Field_Interpretation_Function/F.var" "Field_Interpretation_Function__". -inline "cic:/CoRN/tactics/FieldReflection/val.var". +inline "cic:/CoRN/tactics/FieldReflection/Field_Interpretation_Function/val.var" "Field_Interpretation_Function__". -inline "cic:/CoRN/tactics/FieldReflection/unop.var". +inline "cic:/CoRN/tactics/FieldReflection/Field_Interpretation_Function/unop.var" "Field_Interpretation_Function__". -inline "cic:/CoRN/tactics/FieldReflection/binop.var". +inline "cic:/CoRN/tactics/FieldReflection/Field_Interpretation_Function/binop.var" "Field_Interpretation_Function__". -inline "cic:/CoRN/tactics/FieldReflection/pfun.var". +inline "cic:/CoRN/tactics/FieldReflection/Field_Interpretation_Function/pfun.var" "Field_Interpretation_Function__". inline "cic:/CoRN/tactics/FieldReflection/interpF.ind". @@ -79,22 +79,22 @@ inline "cic:/CoRN/tactics/FieldReflection/refl_interpF.con". inline "cic:/CoRN/tactics/FieldReflection/interpF_wd.con". (* UNEXPORTED -End Field_Interpretation_Function. +End Field_Interpretation_Function *) (* UNEXPORTED -Section Field_NormCorrect. +Section Field_NormCorrect *) -inline "cic:/CoRN/tactics/FieldReflection/F.var". +inline "cic:/CoRN/tactics/FieldReflection/Field_NormCorrect/F.var" "Field_NormCorrect__". -inline "cic:/CoRN/tactics/FieldReflection/val.var". +inline "cic:/CoRN/tactics/FieldReflection/Field_NormCorrect/val.var" "Field_NormCorrect__". -inline "cic:/CoRN/tactics/FieldReflection/unop.var". +inline "cic:/CoRN/tactics/FieldReflection/Field_NormCorrect/unop.var" "Field_NormCorrect__". -inline "cic:/CoRN/tactics/FieldReflection/binop.var". +inline "cic:/CoRN/tactics/FieldReflection/Field_NormCorrect/binop.var" "Field_NormCorrect__". -inline "cic:/CoRN/tactics/FieldReflection/pfun.var". +inline "cic:/CoRN/tactics/FieldReflection/Field_NormCorrect/pfun.var" "Field_NormCorrect__". (* NOTATION Notation II := (interpF F val unop binop pfun). @@ -211,7 +211,7 @@ inline "cic:/CoRN/tactics/FieldReflection/Tactic_lemma_zero_F.con". inline "cic:/CoRN/tactics/FieldReflection/Tactic_lemmaF.con". (* UNEXPORTED -End Field_NormCorrect. +End Field_NormCorrect *) (* end hide *) diff --git a/helm/software/matita/contribs/CoRN-Decl/tactics/GroupReflection.ma b/helm/software/matita/contribs/CoRN-Decl/tactics/GroupReflection.ma index 6b377af2a..c314cc089 100644 --- a/helm/software/matita/contribs/CoRN-Decl/tactics/GroupReflection.ma +++ b/helm/software/matita/contribs/CoRN-Decl/tactics/GroupReflection.ma @@ -27,18 +27,18 @@ include "algebra/CAbGroups.ma". include "tactics/AlgReflection.ma". (* UNEXPORTED -Section Group_Interpretation_Function. +Section Group_Interpretation_Function *) -inline "cic:/CoRN/tactics/GroupReflection/G.var". +inline "cic:/CoRN/tactics/GroupReflection/Group_Interpretation_Function/G.var" "Group_Interpretation_Function__". -inline "cic:/CoRN/tactics/GroupReflection/val.var". +inline "cic:/CoRN/tactics/GroupReflection/Group_Interpretation_Function/val.var" "Group_Interpretation_Function__". -inline "cic:/CoRN/tactics/GroupReflection/unop.var". +inline "cic:/CoRN/tactics/GroupReflection/Group_Interpretation_Function/unop.var" "Group_Interpretation_Function__". -inline "cic:/CoRN/tactics/GroupReflection/binop.var". +inline "cic:/CoRN/tactics/GroupReflection/Group_Interpretation_Function/binop.var" "Group_Interpretation_Function__". -inline "cic:/CoRN/tactics/GroupReflection/pfun.var". +inline "cic:/CoRN/tactics/GroupReflection/Group_Interpretation_Function/pfun.var" "Group_Interpretation_Function__". inline "cic:/CoRN/tactics/GroupReflection/interpG.ind". @@ -129,22 +129,22 @@ inline "cic:/CoRN/tactics/GroupReflection/refl_interpG.con". inline "cic:/CoRN/tactics/GroupReflection/interpG_wd.con". (* UNEXPORTED -End Group_Interpretation_Function. +End Group_Interpretation_Function *) (* UNEXPORTED -Section Group_NormCorrect. +Section Group_NormCorrect *) -inline "cic:/CoRN/tactics/GroupReflection/G.var". +inline "cic:/CoRN/tactics/GroupReflection/Group_NormCorrect/G.var" "Group_NormCorrect__". -inline "cic:/CoRN/tactics/GroupReflection/val.var". +inline "cic:/CoRN/tactics/GroupReflection/Group_NormCorrect/val.var" "Group_NormCorrect__". -inline "cic:/CoRN/tactics/GroupReflection/unop.var". +inline "cic:/CoRN/tactics/GroupReflection/Group_NormCorrect/unop.var" "Group_NormCorrect__". -inline "cic:/CoRN/tactics/GroupReflection/binop.var". +inline "cic:/CoRN/tactics/GroupReflection/Group_NormCorrect/binop.var" "Group_NormCorrect__". -inline "cic:/CoRN/tactics/GroupReflection/pfun.var". +inline "cic:/CoRN/tactics/GroupReflection/Group_NormCorrect/pfun.var" "Group_NormCorrect__". (* NOTATION Notation II := (interpG G val unop binop pfun). @@ -239,7 +239,7 @@ inline "cic:/CoRN/tactics/GroupReflection/NormG_corr_G.con". inline "cic:/CoRN/tactics/GroupReflection/Tactic_lemmaG.con". (* UNEXPORTED -End Group_NormCorrect. +End Group_NormCorrect *) (* end hide *) diff --git a/helm/software/matita/contribs/CoRN-Decl/tactics/RingReflection.ma b/helm/software/matita/contribs/CoRN-Decl/tactics/RingReflection.ma index d9c85b33b..74f7b0be3 100644 --- a/helm/software/matita/contribs/CoRN-Decl/tactics/RingReflection.ma +++ b/helm/software/matita/contribs/CoRN-Decl/tactics/RingReflection.ma @@ -27,18 +27,18 @@ include "algebra/CRings.ma". include "tactics/AlgReflection.ma". (* UNEXPORTED -Section Ring_Interpretation_Function. +Section Ring_Interpretation_Function *) -inline "cic:/CoRN/tactics/RingReflection/R.var". +inline "cic:/CoRN/tactics/RingReflection/Ring_Interpretation_Function/R.var" "Ring_Interpretation_Function__". -inline "cic:/CoRN/tactics/RingReflection/val.var". +inline "cic:/CoRN/tactics/RingReflection/Ring_Interpretation_Function/val.var" "Ring_Interpretation_Function__". -inline "cic:/CoRN/tactics/RingReflection/unop.var". +inline "cic:/CoRN/tactics/RingReflection/Ring_Interpretation_Function/unop.var" "Ring_Interpretation_Function__". -inline "cic:/CoRN/tactics/RingReflection/binop.var". +inline "cic:/CoRN/tactics/RingReflection/Ring_Interpretation_Function/binop.var" "Ring_Interpretation_Function__". -inline "cic:/CoRN/tactics/RingReflection/pfun.var". +inline "cic:/CoRN/tactics/RingReflection/Ring_Interpretation_Function/pfun.var" "Ring_Interpretation_Function__". inline "cic:/CoRN/tactics/RingReflection/interpR.ind". @@ -145,22 +145,22 @@ inline "cic:/CoRN/tactics/RingReflection/refl_interpR.con". inline "cic:/CoRN/tactics/RingReflection/interpR_wd.con". (* UNEXPORTED -End Ring_Interpretation_Function. +End Ring_Interpretation_Function *) (* UNEXPORTED -Section Ring_NormCorrect. +Section Ring_NormCorrect *) -inline "cic:/CoRN/tactics/RingReflection/R.var". +inline "cic:/CoRN/tactics/RingReflection/Ring_NormCorrect/R.var" "Ring_NormCorrect__". -inline "cic:/CoRN/tactics/RingReflection/val.var". +inline "cic:/CoRN/tactics/RingReflection/Ring_NormCorrect/val.var" "Ring_NormCorrect__". -inline "cic:/CoRN/tactics/RingReflection/unop.var". +inline "cic:/CoRN/tactics/RingReflection/Ring_NormCorrect/unop.var" "Ring_NormCorrect__". -inline "cic:/CoRN/tactics/RingReflection/binop.var". +inline "cic:/CoRN/tactics/RingReflection/Ring_NormCorrect/binop.var" "Ring_NormCorrect__". -inline "cic:/CoRN/tactics/RingReflection/pfun.var". +inline "cic:/CoRN/tactics/RingReflection/Ring_NormCorrect/pfun.var" "Ring_NormCorrect__". (* NOTATION Notation II := (interpR R val unop binop pfun). @@ -317,7 +317,7 @@ inline "cic:/CoRN/tactics/RingReflection/NormR_corr.con". inline "cic:/CoRN/tactics/RingReflection/Tactic_lemmaR.con". (* UNEXPORTED -End Ring_NormCorrect. +End Ring_NormCorrect *) (* end hide *) diff --git a/helm/software/matita/contribs/CoRN-Decl/transc/InvTrigonom.ma b/helm/software/matita/contribs/CoRN-Decl/transc/InvTrigonom.ma index 7e6d8f719..5296d75cb 100644 --- a/helm/software/matita/contribs/CoRN-Decl/transc/InvTrigonom.ma +++ b/helm/software/matita/contribs/CoRN-Decl/transc/InvTrigonom.ma @@ -106,7 +106,7 @@ Hint Resolve Continuous_ArcCos Continuous_ArcTan: continuous. *) (* UNEXPORTED -Section Inverses. +Section Inverses *) (*#* **Composition properties @@ -203,66 +203,66 @@ Transparent Cos. *) (* UNEXPORTED -Section ArcTan_Range. +Section ArcTan_Range *) -inline "cic:/CoRN/transc/InvTrigonom/x.var". +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/x.var" "Inverses__ArcTan_Range__". (* begin hide *) -inline "cic:/CoRN/transc/InvTrigonom/min.con". +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min.con" "Inverses__ArcTan_Range__". -inline "cic:/CoRN/transc/InvTrigonom/max.con". +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max.con" "Inverses__ArcTan_Range__". -inline "cic:/CoRN/transc/InvTrigonom/min1.con". +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min1.con" "Inverses__ArcTan_Range__". -inline "cic:/CoRN/transc/InvTrigonom/min2.con". +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min2.con" "Inverses__ArcTan_Range__". -inline "cic:/CoRN/transc/InvTrigonom/min3.con". +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min3.con" "Inverses__ArcTan_Range__". -inline "cic:/CoRN/transc/InvTrigonom/min4.con". +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min4.con" "Inverses__ArcTan_Range__". -inline "cic:/CoRN/transc/InvTrigonom/max1.con". +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max1.con" "Inverses__ArcTan_Range__". -inline "cic:/CoRN/transc/InvTrigonom/max2.con". +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max2.con" "Inverses__ArcTan_Range__". -inline "cic:/CoRN/transc/InvTrigonom/max3.con". +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max3.con" "Inverses__ArcTan_Range__". -inline "cic:/CoRN/transc/InvTrigonom/max4.con". +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max4.con" "Inverses__ArcTan_Range__". -inline "cic:/CoRN/transc/InvTrigonom/min5.con". +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min5.con" "Inverses__ArcTan_Range__". -inline "cic:/CoRN/transc/InvTrigonom/min6.con". +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min6.con" "Inverses__ArcTan_Range__". -inline "cic:/CoRN/transc/InvTrigonom/max5.con". +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max5.con" "Inverses__ArcTan_Range__". -inline "cic:/CoRN/transc/InvTrigonom/max6.con". +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max6.con" "Inverses__ArcTan_Range__". -inline "cic:/CoRN/transc/InvTrigonom/a.con". +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a.con" "Inverses__ArcTan_Range__". -inline "cic:/CoRN/transc/InvTrigonom/a1.con". +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a1.con" "Inverses__ArcTan_Range__". -inline "cic:/CoRN/transc/InvTrigonom/a2.con". +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a2.con" "Inverses__ArcTan_Range__". -inline "cic:/CoRN/transc/InvTrigonom/a3.con". +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a3.con" "Inverses__ArcTan_Range__". -inline "cic:/CoRN/transc/InvTrigonom/a4.con". +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a4.con" "Inverses__ArcTan_Range__". -inline "cic:/CoRN/transc/InvTrigonom/a5.con". +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a5.con" "Inverses__ArcTan_Range__". -inline "cic:/CoRN/transc/InvTrigonom/b.con". +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b.con" "Inverses__ArcTan_Range__". -inline "cic:/CoRN/transc/InvTrigonom/b1.con". +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b1.con" "Inverses__ArcTan_Range__". -inline "cic:/CoRN/transc/InvTrigonom/b2.con". +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b2.con" "Inverses__ArcTan_Range__". -inline "cic:/CoRN/transc/InvTrigonom/b3.con". +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b3.con" "Inverses__ArcTan_Range__". -inline "cic:/CoRN/transc/InvTrigonom/b4.con". +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b4.con" "Inverses__ArcTan_Range__". -inline "cic:/CoRN/transc/InvTrigonom/b5.con". +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b5.con" "Inverses__ArcTan_Range__". -inline "cic:/CoRN/transc/InvTrigonom/ab.con". +inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/ab.con" "Inverses__ArcTan_Range__". inline "cic:/CoRN/transc/InvTrigonom/ArcTan_range_lemma.con". @@ -275,7 +275,7 @@ Transparent ArcTang. inline "cic:/CoRN/transc/InvTrigonom/ArcTan_range.con". (* UNEXPORTED -End ArcTan_Range. +End ArcTan_Range *) (* UNEXPORTED @@ -291,6 +291,6 @@ Opaque ArcTang. inline "cic:/CoRN/transc/InvTrigonom/Tan_ArcTan_inv.con". (* UNEXPORTED -End Inverses. +End Inverses *) diff --git a/helm/software/matita/contribs/CoRN-Decl/transc/Pi.ma b/helm/software/matita/contribs/CoRN-Decl/transc/Pi.ma index 3f077c443..af134caa1 100644 --- a/helm/software/matita/contribs/CoRN-Decl/transc/Pi.ma +++ b/helm/software/matita/contribs/CoRN-Decl/transc/Pi.ma @@ -21,7 +21,7 @@ include "CoRN.ma". include "transc/SinCos.ma". (* UNEXPORTED -Section Properties_of_Pi. +Section Properties_of_Pi *) (*#* printing Pi %\ensuremath{\pi}% #π# *) @@ -113,7 +113,7 @@ inline "cic:/CoRN/transc/Pi/HalfPi_gt_pi_seq.con". inline "cic:/CoRN/transc/Pi/pos_Pi.con". (* UNEXPORTED -End Properties_of_Pi. +End Properties_of_Pi *) (* UNEXPORTED @@ -121,7 +121,7 @@ Hint Resolve Cos_HalfPi: algebra. *) (* UNEXPORTED -Section Pi_and_Order. +Section Pi_and_Order *) (*#* **Properties of Pi @@ -180,7 +180,7 @@ inline "cic:/CoRN/transc/Pi/invQuarterPi_less_HalfPi.con". inline "cic:/CoRN/transc/Pi/invQuarterPi_less_QuarterPi.con". (* UNEXPORTED -End Pi_and_Order. +End Pi_and_Order *) (* UNEXPORTED @@ -201,7 +201,7 @@ Ltac PiSolve := try apply less_leEq; auto with piorder. (* end hide *) (* UNEXPORTED -Section Sin_And_Cos. +Section Sin_And_Cos *) (*#* **More formulas @@ -275,7 +275,7 @@ inline "cic:/CoRN/transc/Pi/Cos_periodic.con". inline "cic:/CoRN/transc/Pi/Tan_periodic.con". (* UNEXPORTED -End Sin_And_Cos. +End Sin_And_Cos *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/transc/PowerSeries.ma b/helm/software/matita/contribs/CoRN-Decl/transc/PowerSeries.ma index ffd7d4720..ab927ca4e 100644 --- a/helm/software/matita/contribs/CoRN-Decl/transc/PowerSeries.ma +++ b/helm/software/matita/contribs/CoRN-Decl/transc/PowerSeries.ma @@ -40,7 +40,7 @@ prove some important properties of these entities. *) (* UNEXPORTED -Section Power_Series. +Section Power_Series *) (*#* **General results @@ -50,13 +50,13 @@ Let [a : nat -> IR]. %\end{convention}% *) -inline "cic:/CoRN/transc/PowerSeries/J.var". +inline "cic:/CoRN/transc/PowerSeries/Power_Series/J.var" "Power_Series__". -inline "cic:/CoRN/transc/PowerSeries/x0.var". +inline "cic:/CoRN/transc/PowerSeries/Power_Series/x0.var" "Power_Series__". -inline "cic:/CoRN/transc/PowerSeries/Hx0.var". +inline "cic:/CoRN/transc/PowerSeries/Power_Series/Hx0.var" "Power_Series__". -inline "cic:/CoRN/transc/PowerSeries/a.var". +inline "cic:/CoRN/transc/PowerSeries/Power_Series/a.var" "Power_Series__". inline "cic:/CoRN/transc/PowerSeries/FPowerSeries.con". @@ -67,11 +67,11 @@ is the Dirichlet criterium. (* begin show *) -inline "cic:/CoRN/transc/PowerSeries/Ha.var". +inline "cic:/CoRN/transc/PowerSeries/Power_Series/Ha.var" "Power_Series__". -inline "cic:/CoRN/transc/PowerSeries/r.con". +inline "cic:/CoRN/transc/PowerSeries/Power_Series/r.con" "Power_Series__". -inline "cic:/CoRN/transc/PowerSeries/Hr.con". +inline "cic:/CoRN/transc/PowerSeries/Power_Series/Hr.con" "Power_Series__". (* end show *) @@ -93,7 +93,7 @@ inline "cic:/CoRN/transc/PowerSeries/included_FPowerSeries'.con". (* begin show *) -inline "cic:/CoRN/transc/PowerSeries/Ha'.var". +inline "cic:/CoRN/transc/PowerSeries/Power_Series/Ha'.var" "Power_Series__". (* end show *) @@ -102,7 +102,7 @@ inline "cic:/CoRN/transc/PowerSeries/FPowerSeries'_conv'.con". inline "cic:/CoRN/transc/PowerSeries/FPowerSeries'_conv.con". (* UNEXPORTED -End Power_Series. +End Power_Series *) (* UNEXPORTED @@ -110,7 +110,7 @@ Hint Resolve FPowerSeries'_cont: continuous. *) (* UNEXPORTED -Section More_on_PowerSeries. +Section More_on_PowerSeries *) (*#* @@ -119,25 +119,25 @@ respectively by [a] and by [fun n => (a (S n))]. %\end{convention}% *) -inline "cic:/CoRN/transc/PowerSeries/x0.var". +inline "cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/x0.var" "More_on_PowerSeries__". -inline "cic:/CoRN/transc/PowerSeries/a.var". +inline "cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/a.var" "More_on_PowerSeries__". (* begin hide *) -inline "cic:/CoRN/transc/PowerSeries/F.con". +inline "cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/F.con" "More_on_PowerSeries__". -inline "cic:/CoRN/transc/PowerSeries/G.con". +inline "cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/G.con" "More_on_PowerSeries__". (* end hide *) (* begin show *) -inline "cic:/CoRN/transc/PowerSeries/Hf.var". +inline "cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/Hf.var" "More_on_PowerSeries__". -inline "cic:/CoRN/transc/PowerSeries/Hf'.var". +inline "cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/Hf'.var" "More_on_PowerSeries__". -inline "cic:/CoRN/transc/PowerSeries/Hg.var". +inline "cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/Hg.var" "More_on_PowerSeries__". (* end show *) @@ -154,11 +154,11 @@ Opaque nring fac. inline "cic:/CoRN/transc/PowerSeries/Derivative_FPowerSeries1'.con". (* UNEXPORTED -End More_on_PowerSeries. +End More_on_PowerSeries *) (* UNEXPORTED -Section Definitions. +Section Definitions *) (*#* **Function definitions through power series @@ -219,7 +219,7 @@ inline "cic:/CoRN/transc/PowerSeries/log_defn_lemma.con". inline "cic:/CoRN/transc/PowerSeries/Logarithm.con". (* UNEXPORTED -End Definitions. +End Definitions *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/transc/RealPowers.ma b/helm/software/matita/contribs/CoRN-Decl/transc/RealPowers.ma index 015d267fe..7e8950fee 100644 --- a/helm/software/matita/contribs/CoRN-Decl/transc/RealPowers.ma +++ b/helm/software/matita/contribs/CoRN-Decl/transc/RealPowers.ma @@ -129,7 +129,7 @@ Hint Resolve power_div: algebra. *) (* UNEXPORTED -Section Power_Function. +Section Power_Function *) (*#* **Power Function @@ -141,11 +141,11 @@ on partial functions which preserves continuity. %\end{convention}% *) -inline "cic:/CoRN/transc/RealPowers/J.var". +inline "cic:/CoRN/transc/RealPowers/Power_Function/J.var" "Power_Function__". -inline "cic:/CoRN/transc/RealPowers/F.var". +inline "cic:/CoRN/transc/RealPowers/Power_Function/F.var" "Power_Function__". -inline "cic:/CoRN/transc/RealPowers/G.var". +inline "cic:/CoRN/transc/RealPowers/Power_Function/G.var" "Power_Function__". inline "cic:/CoRN/transc/RealPowers/FPower.con". @@ -154,7 +154,7 @@ inline "cic:/CoRN/transc/RealPowers/FPower_domain.con". inline "cic:/CoRN/transc/RealPowers/Continuous_power.con". (* UNEXPORTED -End Power_Function. +End Power_Function *) (* NOTATION @@ -162,7 +162,7 @@ Notation "F {!} G" := (FPower F G) (at level 20). *) (* UNEXPORTED -Section More_on_Power_Function. +Section More_on_Power_Function *) (* UNEXPORTED @@ -188,7 +188,7 @@ inline "cic:/CoRN/transc/RealPowers/Derivative_power.con". inline "cic:/CoRN/transc/RealPowers/Diffble_power.con". (* UNEXPORTED -End More_on_Power_Function. +End More_on_Power_Function *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/transc/SinCos.ma b/helm/software/matita/contribs/CoRN-Decl/transc/SinCos.ma index 4a226195f..314d0f5fa 100644 --- a/helm/software/matita/contribs/CoRN-Decl/transc/SinCos.ma +++ b/helm/software/matita/contribs/CoRN-Decl/transc/SinCos.ma @@ -23,7 +23,7 @@ include "CoRN.ma". include "transc/Trigonometric.ma". (* UNEXPORTED -Section Sum_and_so_on. +Section Sum_and_so_on *) (* UNEXPORTED @@ -32,13 +32,13 @@ Opaque Sine Cosine. (* begin hide *) -inline "cic:/CoRN/transc/SinCos/F.con". +inline "cic:/CoRN/transc/SinCos/Sum_and_so_on/F.con" "Sum_and_so_on__". -inline "cic:/CoRN/transc/SinCos/G.con". +inline "cic:/CoRN/transc/SinCos/Sum_and_so_on/G.con" "Sum_and_so_on__". -inline "cic:/CoRN/transc/SinCos/F'.con". +inline "cic:/CoRN/transc/SinCos/Sum_and_so_on/F'.con" "Sum_and_so_on__". -inline "cic:/CoRN/transc/SinCos/G'.con". +inline "cic:/CoRN/transc/SinCos/Sum_and_so_on/G'.con" "Sum_and_so_on__". (* end hide *) @@ -103,7 +103,7 @@ Hint Resolve FFT: algebra. inline "cic:/CoRN/transc/SinCos/FFT'.con". (* UNEXPORTED -End Sum_and_so_on. +End Sum_and_so_on *) (* UNEXPORTED @@ -124,7 +124,7 @@ Opaque Min Sine Cosine. *) (* UNEXPORTED -Section Basic_Properties. +Section Basic_Properties *) (*#* **Basic properties @@ -167,7 +167,7 @@ inline "cic:/CoRN/transc/SinCos/Sin_less_One.con". inline "cic:/CoRN/transc/SinCos/AbsIR_Sin_less_One.con". (* UNEXPORTED -End Basic_Properties. +End Basic_Properties *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/transc/TaylorSeries.ma b/helm/software/matita/contribs/CoRN-Decl/transc/TaylorSeries.ma index 74966e1d9..89153db18 100644 --- a/helm/software/matita/contribs/CoRN-Decl/transc/TaylorSeries.ma +++ b/helm/software/matita/contribs/CoRN-Decl/transc/TaylorSeries.ma @@ -40,20 +40,20 @@ point of [J]. *) (* UNEXPORTED -Section Definitions. +Section Definitions *) -inline "cic:/CoRN/transc/TaylorSeries/J.var". +inline "cic:/CoRN/transc/TaylorSeries/Definitions/J.var" "Definitions__". -inline "cic:/CoRN/transc/TaylorSeries/pJ.var". +inline "cic:/CoRN/transc/TaylorSeries/Definitions/pJ.var" "Definitions__". -inline "cic:/CoRN/transc/TaylorSeries/F.var". +inline "cic:/CoRN/transc/TaylorSeries/Definitions/F.var" "Definitions__". -inline "cic:/CoRN/transc/TaylorSeries/diffF.var". +inline "cic:/CoRN/transc/TaylorSeries/Definitions/diffF.var" "Definitions__". -inline "cic:/CoRN/transc/TaylorSeries/a.var". +inline "cic:/CoRN/transc/TaylorSeries/Definitions/a.var" "Definitions__". -inline "cic:/CoRN/transc/TaylorSeries/Ha.var". +inline "cic:/CoRN/transc/TaylorSeries/Definitions/Ha.var" "Definitions__". inline "cic:/CoRN/transc/TaylorSeries/Taylor_Series'.con". @@ -63,9 +63,9 @@ derivatives of [F]. %\end{convention}% *) -inline "cic:/CoRN/transc/TaylorSeries/f.var". +inline "cic:/CoRN/transc/TaylorSeries/Definitions/f.var" "Definitions__". -inline "cic:/CoRN/transc/TaylorSeries/derF.var". +inline "cic:/CoRN/transc/TaylorSeries/Definitions/derF.var" "Definitions__". inline "cic:/CoRN/transc/TaylorSeries/Taylor_Series.con". @@ -80,11 +80,11 @@ inline "cic:/CoRN/transc/TaylorSeries/Taylor_Rem_char.con". inline "cic:/CoRN/transc/TaylorSeries/abs_Taylor_Rem_char.con". (* UNEXPORTED -End Definitions. +End Definitions *) (* UNEXPORTED -Section Convergence_in_IR. +Section Convergence_in_IR *) (*#* **Convergence @@ -95,17 +95,17 @@ derivatives of [F] that guarantees convergence of its Taylor series to [F]. *) -inline "cic:/CoRN/transc/TaylorSeries/H.var". +inline "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/H.var" "Convergence_in_IR__". -inline "cic:/CoRN/transc/TaylorSeries/F.var". +inline "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/F.var" "Convergence_in_IR__". -inline "cic:/CoRN/transc/TaylorSeries/a.var". +inline "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/a.var" "Convergence_in_IR__". -inline "cic:/CoRN/transc/TaylorSeries/Ha.var". +inline "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/Ha.var" "Convergence_in_IR__". -inline "cic:/CoRN/transc/TaylorSeries/f.var". +inline "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/f.var" "Convergence_in_IR__". -inline "cic:/CoRN/transc/TaylorSeries/derF.var". +inline "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/derF.var" "Convergence_in_IR__". inline "cic:/CoRN/transc/TaylorSeries/Taylor_Series_imp_cont.con". @@ -115,7 +115,7 @@ inline "cic:/CoRN/transc/TaylorSeries/Taylor_bnd.con". (* begin show *) -inline "cic:/CoRN/transc/TaylorSeries/bndf.var". +inline "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/bndf.var" "Convergence_in_IR__". (* end show *) @@ -125,7 +125,7 @@ Opaque nexp_op fac. (* begin hide *) -inline "cic:/CoRN/transc/TaylorSeries/H1.con". +inline "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/H1.con" "Convergence_in_IR__". (* UNEXPORTED Transparent nexp_op. @@ -173,7 +173,7 @@ will separately assume convergence. (* begin show *) -inline "cic:/CoRN/transc/TaylorSeries/Hf.var". +inline "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/Hf.var" "Convergence_in_IR__". (* end show *) @@ -188,11 +188,11 @@ Opaque mult. inline "cic:/CoRN/transc/TaylorSeries/Taylor_Series_conv_to_fun.con". (* UNEXPORTED -End Convergence_in_IR. +End Convergence_in_IR *) (* UNEXPORTED -Section Other_Results. +Section Other_Results *) (*#* @@ -220,39 +220,39 @@ provided that their derivatives coincide at a given point and their Taylor series converge to themselves. *) -inline "cic:/CoRN/transc/TaylorSeries/F.var". +inline "cic:/CoRN/transc/TaylorSeries/Other_Results/F.var" "Other_Results__". -inline "cic:/CoRN/transc/TaylorSeries/G.var". +inline "cic:/CoRN/transc/TaylorSeries/Other_Results/G.var" "Other_Results__". -inline "cic:/CoRN/transc/TaylorSeries/a.var". +inline "cic:/CoRN/transc/TaylorSeries/Other_Results/a.var" "Other_Results__". -inline "cic:/CoRN/transc/TaylorSeries/f.var". +inline "cic:/CoRN/transc/TaylorSeries/Other_Results/f.var" "Other_Results__". -inline "cic:/CoRN/transc/TaylorSeries/g.var". +inline "cic:/CoRN/transc/TaylorSeries/Other_Results/g.var" "Other_Results__". -inline "cic:/CoRN/transc/TaylorSeries/derF.var". +inline "cic:/CoRN/transc/TaylorSeries/Other_Results/derF.var" "Other_Results__". -inline "cic:/CoRN/transc/TaylorSeries/derG.var". +inline "cic:/CoRN/transc/TaylorSeries/Other_Results/derG.var" "Other_Results__". -inline "cic:/CoRN/transc/TaylorSeries/bndf.var". +inline "cic:/CoRN/transc/TaylorSeries/Other_Results/bndf.var" "Other_Results__". -inline "cic:/CoRN/transc/TaylorSeries/bndg.var". +inline "cic:/CoRN/transc/TaylorSeries/Other_Results/bndg.var" "Other_Results__". (* begin show *) -inline "cic:/CoRN/transc/TaylorSeries/Heq.var". +inline "cic:/CoRN/transc/TaylorSeries/Other_Results/Heq.var" "Other_Results__". (* end show *) (* begin hide *) -inline "cic:/CoRN/transc/TaylorSeries/Hf.con". +inline "cic:/CoRN/transc/TaylorSeries/Other_Results/Hf.con" "Other_Results__". (* end hide *) inline "cic:/CoRN/transc/TaylorSeries/Taylor_unique_crit.con". (* UNEXPORTED -End Other_Results. +End Other_Results *) diff --git a/helm/software/matita/contribs/CoRN-Decl/transc/TrigMon.ma b/helm/software/matita/contribs/CoRN-Decl/transc/TrigMon.ma index 7307c4f5a..a80658438 100644 --- a/helm/software/matita/contribs/CoRN-Decl/transc/TrigMon.ma +++ b/helm/software/matita/contribs/CoRN-Decl/transc/TrigMon.ma @@ -70,7 +70,7 @@ inline "cic:/CoRN/transc/TrigMon/Cos_resp_less.con". inline "cic:/CoRN/transc/TrigMon/Sin_resp_less.con". (* UNEXPORTED -Section Tangent. +Section Tangent *) (*#* **Derivative of Tangent @@ -94,7 +94,7 @@ inline "cic:/CoRN/transc/TrigMon/Tan_resp_less.con". inline "cic:/CoRN/transc/TrigMon/Tan_resp_leEq.con". (* UNEXPORTED -End Tangent. +End Tangent *) (* UNEXPORTED diff --git a/helm/software/matita/contribs/CoRN-Decl/transc/Trigonometric.ma b/helm/software/matita/contribs/CoRN-Decl/transc/Trigonometric.ma index de100d310..b4f59a9a8 100644 --- a/helm/software/matita/contribs/CoRN-Decl/transc/Trigonometric.ma +++ b/helm/software/matita/contribs/CoRN-Decl/transc/Trigonometric.ma @@ -28,7 +28,7 @@ In this section, we explore the properties of the trigonometric functions which *) (* UNEXPORTED -Section Lemmas. +Section Lemmas *) (*#* First, we need a lemma on mappings. *) @@ -36,11 +36,11 @@ Section Lemmas. inline "cic:/CoRN/transc/Trigonometric/maps_translation.con". (* UNEXPORTED -End Lemmas. +End Lemmas *) (* UNEXPORTED -Section Sine_and_Cosine. +Section Sine_and_Cosine *) (*#* Sine, cosine and tangent at [Zero]. *) @@ -92,7 +92,7 @@ Hint Resolve Continuous_Sin Continuous_Cos: continuous. *) (* UNEXPORTED -Section Sine_of_Sum. +Section Sine_of_Sum *) (*#* @@ -110,13 +110,13 @@ situations). (* begin hide *) -inline "cic:/CoRN/transc/Trigonometric/F.con". +inline "cic:/CoRN/transc/Trigonometric/Sine_and_Cosine/Sine_of_Sum/F.con" "Sine_and_Cosine__Sine_of_Sum__". -inline "cic:/CoRN/transc/Trigonometric/G.con". +inline "cic:/CoRN/transc/Trigonometric/Sine_and_Cosine/Sine_of_Sum/G.con" "Sine_and_Cosine__Sine_of_Sum__". -inline "cic:/CoRN/transc/Trigonometric/F'.con". +inline "cic:/CoRN/transc/Trigonometric/Sine_and_Cosine/Sine_of_Sum/F'.con" "Sine_and_Cosine__Sine_of_Sum__". -inline "cic:/CoRN/transc/Trigonometric/G'.con". +inline "cic:/CoRN/transc/Trigonometric/Sine_and_Cosine/Sine_of_Sum/G'.con" "Sine_and_Cosine__Sine_of_Sum__". (* end hide *) @@ -201,7 +201,7 @@ inline "cic:/CoRN/transc/Trigonometric/Sin_plus_der_rht.con". inline "cic:/CoRN/transc/Trigonometric/Sin_plus_fun.con". (* UNEXPORTED -End Sine_of_Sum. +End Sine_of_Sum *) (* UNEXPORTED @@ -211,6 +211,6 @@ Opaque Sine Cosine. inline "cic:/CoRN/transc/Trigonometric/Cos_plus_fun.con". (* UNEXPORTED -End Sine_and_Cosine. +End Sine_and_Cosine *) diff --git a/helm/software/matita/library/logic/coimplication.ma b/helm/software/matita/library/logic/coimplication.ma new file mode 100644 index 000000000..9edb4949c --- /dev/null +++ b/helm/software/matita/library/logic/coimplication.ma @@ -0,0 +1,47 @@ +(**************************************************************************) +(* ___ *) +(* ||M|| *) +(* ||A|| A project by Andrea Asperti *) +(* ||T|| *) +(* ||I|| Developers: *) +(* ||T|| The HELM team. *) +(* ||A|| http://helm.cs.unibo.it *) +(* \ / *) +(* \ / This file is distributed under the terms of the *) +(* v GNU General Public License Version 2 *) +(* *) +(**************************************************************************) + +set "baseuri" "cic:/matita/logic/coimplication". + +include "logic/connectives.ma". + +definition Iff : Prop \to Prop \to Prop \def + \lambda A,B. (A \to B) \land (B \to A). + + (*CSC: the URI must disappear: there is a bug now *) +interpretation "logical iff" 'iff x y = (cic:/matita/logic/coimplication/Iff.con x y). + +notation > "hvbox(a break \liff b)" + left associative with precedence 25 +for @{ 'iff $a $b }. + +notation < "hvbox(a break \leftrightarrow b)" + left associative with precedence 25 +for @{ 'iff $a $b }. + +theorem iff_intro: \forall A,B. (A \to B) \to (B \to A) \to (A \liff B). + unfold Iff. intros. split; intros; auto. +qed. + +theorem iff_refl: \forall A. A \liff A. + intros. apply iff_intro; intros; auto. +qed. + +theorem iff_sym: \forall A,B. A \liff B \to B \liff A. + intros. decompose. apply iff_intro; intros; auto. +qed. + +theorem iff_trans: \forall A,B,C. A \liff B \to B \liff C \to A \liff C. + intros. decompose. apply iff_intro; intros; auto. +qed. diff --git a/helm/software/matita/matitaScript.ml b/helm/software/matita/matitaScript.ml index 0e5121309..12f26036b 100644 --- a/helm/software/matita/matitaScript.ml +++ b/helm/software/matita/matitaScript.ml @@ -288,7 +288,7 @@ let rec eval_macro include_paths (buffer : GText.buffer) guistuff lexicon_status let t_and_ty = Cic.Cast (term,ty) in guistuff.mathviewer#show_entry (`Cic (t_and_ty,metasenv)); [], "", parsed_text_length - | TA.Inline (_,suri) -> + | TA.Inline (_,suri,prefix) -> let dbd = LibraryDb.instance () in let uris = let sql_pat =