1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 (* This file was automatically generated: do not edit *********************)
17 set "baseuri" "cic:/matita/CoRN-Decl/devel/loeb/per/csetfun".
21 include "algebra/CSetoids.ma".
23 include "algebra/CSetoidFun.ma".
25 inline "cic:/CoRN/devel/loeb/per/csetfun/ap_fun.con".
27 inline "cic:/CoRN/devel/loeb/per/csetfun/eq_fun.con".
29 inline "cic:/CoRN/devel/loeb/per/csetfun/irrefl_apfun.con".
31 inline "cic:/CoRN/devel/loeb/per/csetfun/cotrans_apfun.con".
33 inline "cic:/CoRN/devel/loeb/per/csetfun/ta_apfun.con".
35 inline "cic:/CoRN/devel/loeb/per/csetfun/sym_apfun.con".
37 inline "cic:/CoRN/devel/loeb/per/csetfun/FS_is_CSetoid.con".
39 inline "cic:/CoRN/devel/loeb/per/csetfun/FS_as_CSetoid.con".
45 inline "cic:/CoRN/devel/loeb/per/csetfun/comp.con".
47 inline "cic:/CoRN/devel/loeb/per/csetfun/comp_as_bin_op.con".
49 inline "cic:/CoRN/devel/loeb/per/csetfun/assoc_comp.con".
51 include "algebra/CSemiGroups.ma".
53 inline "cic:/CoRN/devel/loeb/per/csetfun/FS_as_CSemiGroup.con".
55 include "algebra/CMonoids.ma".
57 inline "cic:/CoRN/devel/loeb/per/csetfun/FS_id.con".
59 inline "cic:/CoRN/devel/loeb/per/csetfun/id_is_rht_unit.con".
61 inline "cic:/CoRN/devel/loeb/per/csetfun/id_is_lft_unit.con".
63 inline "cic:/CoRN/devel/loeb/per/csetfun/FS_is_CMonoid.con".
65 inline "cic:/CoRN/devel/loeb/per/csetfun/FS_as_CMonoid.con".
67 inline "cic:/CoRN/devel/loeb/per/csetfun/PS_as_CMonoid.con".
69 include "algebra/CGroups.ma".
71 inline "cic:/CoRN/devel/loeb/per/csetfun/Inv_is_bij.con".
74 forall (A B : CSetoid) (f : CSetoid_fun A B) (H : bijective f),
78 unfold fun_strext in |- *.
80 unfold bijective in |- *.
84 unfold injective in |- *.
85 unfold surjective in |- *.
90 unfold invfun in |- *.
92 unfold sigT_rect in |- *.
107 unfold invfun in |- *.
109 unfold sigT_rect in |- *.
120 set (H4 := H0 x b H3) in *.
121 set (H6 := ap_imp_neq B (f0 x) (f0 b) H4) in *.
125 inline "cic:/CoRN/devel/loeb/per/csetfun/PS_Inv.con".
127 inline "cic:/CoRN/devel/loeb/per/csetfun/Inv_as_un_op.con".
129 inline "cic:/CoRN/devel/loeb/per/csetfun/PS_is_CGroup.con".
131 inline "cic:/CoRN/devel/loeb/per/csetfun/PS_as_CGroup.con".
133 (* In het algemeen niet Abels! *)