X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fcontribs%2FCoRN-Decl%2Fdevel%2Floeb%2Fper%2Fcsetfun.ma;fp=matita%2Fcontribs%2FCoRN-Decl%2Fdevel%2Floeb%2Fper%2Fcsetfun.ma;h=88fcfbeb9322f633babd7c468ba78d787cdef683;hp=0000000000000000000000000000000000000000;hb=f61af501fb4608cc4fb062a0864c774e677f0d76;hpb=58ae1809c352e71e7b5530dc41e2bfc834e1aef1 diff --git a/matita/contribs/CoRN-Decl/devel/loeb/per/csetfun.ma b/matita/contribs/CoRN-Decl/devel/loeb/per/csetfun.ma new file mode 100644 index 000000000..88fcfbeb9 --- /dev/null +++ b/matita/contribs/CoRN-Decl/devel/loeb/per/csetfun.ma @@ -0,0 +1,134 @@ +(**************************************************************************) +(* ___ *) +(* ||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 *) +(* *) +(**************************************************************************) + +(* This file was automatically generated: do not edit *********************) + +set "baseuri" "cic:/matita/CoRN-Decl/devel/loeb/per/csetfun". + +include "CoRN.ma". + +include "algebra/CSetoids.ma". + +include "algebra/CSetoidFun.ma". + +inline "cic:/CoRN/devel/loeb/per/csetfun/ap_fun.con". + +inline "cic:/CoRN/devel/loeb/per/csetfun/eq_fun.con". + +inline "cic:/CoRN/devel/loeb/per/csetfun/irrefl_apfun.con". + +inline "cic:/CoRN/devel/loeb/per/csetfun/cotrans_apfun.con". + +inline "cic:/CoRN/devel/loeb/per/csetfun/ta_apfun.con". + +inline "cic:/CoRN/devel/loeb/per/csetfun/sym_apfun.con". + +inline "cic:/CoRN/devel/loeb/per/csetfun/FS_is_CSetoid.con". + +inline "cic:/CoRN/devel/loeb/per/csetfun/FS_as_CSetoid.con". + +(* UNEXPORTED +Print associative. +*) + +inline "cic:/CoRN/devel/loeb/per/csetfun/comp.con". + +inline "cic:/CoRN/devel/loeb/per/csetfun/comp_as_bin_op.con". + +inline "cic:/CoRN/devel/loeb/per/csetfun/assoc_comp.con". + +include "algebra/CSemiGroups.ma". + +inline "cic:/CoRN/devel/loeb/per/csetfun/FS_as_CSemiGroup.con". + +include "algebra/CMonoids.ma". + +inline "cic:/CoRN/devel/loeb/per/csetfun/FS_id.con". + +inline "cic:/CoRN/devel/loeb/per/csetfun/id_is_rht_unit.con". + +inline "cic:/CoRN/devel/loeb/per/csetfun/id_is_lft_unit.con". + +inline "cic:/CoRN/devel/loeb/per/csetfun/FS_is_CMonoid.con". + +inline "cic:/CoRN/devel/loeb/per/csetfun/FS_as_CMonoid.con". + +inline "cic:/CoRN/devel/loeb/per/csetfun/PS_as_CMonoid.con". + +include "algebra/CGroups.ma". + +inline "cic:/CoRN/devel/loeb/per/csetfun/Inv_is_bij.con". + +(* Lemma Inv_is_bij : + forall (A B : CSetoid) (f : CSetoid_fun A B) (H : bijective f), + bijective (Inv f H). +intros A B f. +case f. +unfold fun_strext in |- *. +intros f0 H5. +unfold bijective in |- *. +intro H. +elim H. +clear H. +unfold injective in |- *. +unfold surjective in |- *. +intros H0 H1. +split. +unfold Inv in |- *. +simpl in |- *. +unfold invfun in |- *. +simpl in |- *. +unfold sigT_rect in |- *. +intros a0 a1 H2. +case H1. +case (H1 a1). +intros x H3 y H4. +simpl in H3. +simpl in H4. +simpl in H0. +simpl in H1. +apply H5. +astepl a0. +astepr a1. +exact H2. + +simpl in |- *. +unfold invfun in |- *. +simpl in |- *. +unfold sigT_rect in |- *. +intros b. +exists (f0 b). +case (H1 (f0 b)). +simpl in |- *. +intros x H2. +simpl in H0. +simpl in H1. +apply not_ap_imp_eq. +red in |- *. +intro H3. +set (H4 := H0 x b H3) in *. +set (H6 := ap_imp_neq B (f0 x) (f0 b) H4) in *. +intuition. +Qed.*) + +inline "cic:/CoRN/devel/loeb/per/csetfun/PS_Inv.con". + +inline "cic:/CoRN/devel/loeb/per/csetfun/Inv_as_un_op.con". + +inline "cic:/CoRN/devel/loeb/per/csetfun/PS_is_CGroup.con". + +inline "cic:/CoRN/devel/loeb/per/csetfun/PS_as_CGroup.con". + +(* In het algemeen niet Abels! *) +