X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FCoRN-Decl%2Falgebra%2FCAbGroups.ma;h=5548ff0a618ad3960ce9e9ffc08dd1f4631693fa;hb=82d0bc4291648c88e9f248fc5a67518e938eacdf;hp=b137c572c77ddaf81f2476a1912fe9fda2875be0;hpb=3199f2a8428b5d19a3a803c1b03d9f90e4120f74;p=helm.git diff --git a/helm/software/matita/contribs/CoRN-Decl/algebra/CAbGroups.ma b/helm/software/matita/contribs/CoRN-Decl/algebra/CAbGroups.ma index b137c572c..5548ff0a6 100644 --- a/helm/software/matita/contribs/CoRN-Decl/algebra/CAbGroups.ma +++ b/helm/software/matita/contribs/CoRN-Decl/algebra/CAbGroups.ma @@ -16,12 +16,12 @@ set "baseuri" "cic:/matita/CoRN-Decl/algebra/CAbGroups". -(* INCLUDE -CGroups -*) +include "CoRN.ma". + +include "algebra/CGroups.ma". (* UNEXPORTED -Section Abelian_Groups. +Section Abelian_Groups *) (*#* @@ -29,48 +29,50 @@ Section Abelian_Groups. Now we introduce commutativity and add some results. *) -inline cic:/CoRN/algebra/CAbGroups/is_CAbGroup.con. +inline "cic:/CoRN/algebra/CAbGroups/is_CAbGroup.con". + +inline "cic:/CoRN/algebra/CAbGroups/CAbGroup.ind". -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. +alias id "G" = "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/AbGroup_Axioms/G.var". (*#* %\begin{convention}% Let [G] be an Abelian Group. %\end{convention}% *) -inline cic:/CoRN/algebra/CAbGroups/CAbGroup_is_CAbGroup.con. +inline "cic:/CoRN/algebra/CAbGroups/CAbGroup_is_CAbGroup.con". -inline cic:/CoRN/algebra/CAbGroups/cag_commutes.con. +inline "cic:/CoRN/algebra/CAbGroups/cag_commutes.con". -inline cic:/CoRN/algebra/CAbGroups/cag_commutes_unfolded.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. +alias id "G" = "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/G.var". -inline cic:/CoRN/algebra/CAbGroups/P.var. +alias id "P" = "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/P.var". -inline cic:/CoRN/algebra/CAbGroups/Punit.var. +alias id "Punit" = "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/Punit.var". -inline cic:/CoRN/algebra/CAbGroups/op_pres_P.var. +alias id "op_pres_P" = "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/op_pres_P.var". -inline cic:/CoRN/algebra/CAbGroups/inv_pres_P.var. +alias id "inv_pres_P" = "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/inv_pres_P.var". (*#* %\begin{convention}% @@ -79,18 +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/isabgrp_scrr.con". -inline cic:/CoRN/algebra/CAbGroups/Build_SubCAbGroup.con. +inline "cic:/CoRN/algebra/CAbGroups/Build_SubCAbGroup.con". (* UNEXPORTED -End SubCAbGroups. +End SubCAbGroups *) (* UNEXPORTED -Section Various. +Section Various *) (*#* @@ -101,35 +103,35 @@ Section Various. Hint Resolve cag_commutes_unfolded: algebra. *) -inline cic:/CoRN/algebra/CAbGroups/G.var. +alias id "G" = "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/Various/G.var". (*#* %\begin{convention}% Let [G] be an Abelian Group. %\end{convention}% *) -inline cic:/CoRN/algebra/CAbGroups/cag_op_inv.con. +inline "cic:/CoRN/algebra/CAbGroups/cag_op_inv.con". (* UNEXPORTED Hint Resolve cag_op_inv: algebra. *) -inline cic:/CoRN/algebra/CAbGroups/assoc_1.con. +inline "cic:/CoRN/algebra/CAbGroups/assoc_1.con". -inline cic:/CoRN/algebra/CAbGroups/minus_plus.con. +inline "cic:/CoRN/algebra/CAbGroups/minus_plus.con". -inline cic:/CoRN/algebra/CAbGroups/op_lft_resp_ap.con. +inline "cic:/CoRN/algebra/CAbGroups/op_lft_resp_ap.con". -inline cic:/CoRN/algebra/CAbGroups/cag_ap_cancel_lft.con. +inline "cic:/CoRN/algebra/CAbGroups/cag_ap_cancel_lft.con". -inline cic:/CoRN/algebra/CAbGroups/plus_cancel_ap_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 @@ -141,7 +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 *) (*#* @@ -161,11 +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. +alias id "S" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/S.var". -inline cic:/CoRN/algebra/CAbGroups/unit.var. +alias id "unit" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/unit.var". -inline cic:/CoRN/algebra/CAbGroups/plus.var. +alias id "plus" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/plus.var". (*#* %\begin{convention}% @@ -177,38 +179,38 @@ 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. +alias id "plus_lext" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/plus_lext.var". -inline cic:/CoRN/algebra/CAbGroups/plus_lunit.var. +alias id "plus_lunit" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/plus_lunit.var". -inline cic:/CoRN/algebra/CAbGroups/plus_comm.var. +alias id "plus_comm" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/plus_comm.var". -inline cic:/CoRN/algebra/CAbGroups/plus_assoc.var. +alias id "plus_assoc" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/plus_assoc.var". -inline cic:/CoRN/algebra/CAbGroups/inv.var. +alias id "inv" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/inv.var". -inline cic:/CoRN/algebra/CAbGroups/inv_inv.var. +alias id "inv_inv" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/inv_inv.var". -inline cic:/CoRN/algebra/CAbGroups/plus_rext.con. +inline "cic:/CoRN/algebra/CAbGroups/plus_rext.con". -inline cic:/CoRN/algebra/CAbGroups/plus_runit.con. +inline "cic:/CoRN/algebra/CAbGroups/plus_runit.con". -inline cic:/CoRN/algebra/CAbGroups/plus_is_fun.con. +inline "cic:/CoRN/algebra/CAbGroups/plus_is_fun.con". -inline cic:/CoRN/algebra/CAbGroups/inv_inv'.con. +inline "cic:/CoRN/algebra/CAbGroups/inv_inv'.con". -inline cic:/CoRN/algebra/CAbGroups/plus_fun.con. +inline "cic:/CoRN/algebra/CAbGroups/plus_fun.con". -inline cic:/CoRN/algebra/CAbGroups/Build_CSemiGroup'.con. +inline "cic:/CoRN/algebra/CAbGroups/Build_CSemiGroup'.con". -inline cic:/CoRN/algebra/CAbGroups/Build_CMonoid'.con. +inline "cic:/CoRN/algebra/CAbGroups/Build_CMonoid'.con". -inline cic:/CoRN/algebra/CAbGroups/Build_CGroup'.con. +inline "cic:/CoRN/algebra/CAbGroups/Build_CGroup'.con". -inline cic:/CoRN/algebra/CAbGroups/Build_CAbGroup'.con. +inline "cic:/CoRN/algebra/CAbGroups/Build_CAbGroup'.con". (* UNEXPORTED -End Nice_Char. +End Nice_Char *) (*#* ** Iteration @@ -217,32 +219,32 @@ 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. +alias id "G" = "cic:/CoRN/algebra/CAbGroups/Group_Extras/G.var". -inline cic:/CoRN/algebra/CAbGroups/nmult.con. +inline "cic:/CoRN/algebra/CAbGroups/nmult.con". -inline cic:/CoRN/algebra/CAbGroups/nmult_wd.con. +inline "cic:/CoRN/algebra/CAbGroups/nmult_wd.con". -inline cic:/CoRN/algebra/CAbGroups/nmult_one.con. +inline "cic:/CoRN/algebra/CAbGroups/nmult_one.con". -inline cic:/CoRN/algebra/CAbGroups/nmult_Zero.con. +inline "cic:/CoRN/algebra/CAbGroups/nmult_Zero.con". -inline cic:/CoRN/algebra/CAbGroups/nmult_plus.con. +inline "cic:/CoRN/algebra/CAbGroups/nmult_plus.con". -inline cic:/CoRN/algebra/CAbGroups/nmult_mult.con. +inline "cic:/CoRN/algebra/CAbGroups/nmult_mult.con". -inline cic:/CoRN/algebra/CAbGroups/nmult_inv.con. +inline "cic:/CoRN/algebra/CAbGroups/nmult_inv.con". -inline cic:/CoRN/algebra/CAbGroups/nmult_plus'.con. +inline "cic:/CoRN/algebra/CAbGroups/nmult_plus'.con". (* UNEXPORTED Hint Resolve nmult_wd nmult_Zero nmult_inv nmult_plus nmult_plus': algebra. *) -inline cic:/CoRN/algebra/CAbGroups/zmult.con. +inline "cic:/CoRN/algebra/CAbGroups/zmult.con". (* Lemma Zeq_imp_nat_eq : forall m n:nat, m = n -> m = n. @@ -260,30 +262,30 @@ auto with zarith. Qed. *) -inline cic:/CoRN/algebra/CAbGroups/zmult_char.con. +inline "cic:/CoRN/algebra/CAbGroups/zmult_char.con". -inline cic:/CoRN/algebra/CAbGroups/zmult_wd.con. +inline "cic:/CoRN/algebra/CAbGroups/zmult_wd.con". -inline cic:/CoRN/algebra/CAbGroups/zmult_one.con. +inline "cic:/CoRN/algebra/CAbGroups/zmult_one.con". -inline cic:/CoRN/algebra/CAbGroups/zmult_min_one.con. +inline "cic:/CoRN/algebra/CAbGroups/zmult_min_one.con". -inline cic:/CoRN/algebra/CAbGroups/zmult_zero.con. +inline "cic:/CoRN/algebra/CAbGroups/zmult_zero.con". -inline cic:/CoRN/algebra/CAbGroups/zmult_Zero.con. +inline "cic:/CoRN/algebra/CAbGroups/zmult_Zero.con". (* UNEXPORTED Hint Resolve zmult_zero: algebra. *) -inline cic:/CoRN/algebra/CAbGroups/zmult_plus.con. +inline "cic:/CoRN/algebra/CAbGroups/zmult_plus.con". -inline cic:/CoRN/algebra/CAbGroups/zmult_mult.con. +inline "cic:/CoRN/algebra/CAbGroups/zmult_mult.con". -inline cic:/CoRN/algebra/CAbGroups/zmult_plus'.con. +inline "cic:/CoRN/algebra/CAbGroups/zmult_plus'.con". (* UNEXPORTED -End Group_Extras. +End Group_Extras *) (* UNEXPORTED