X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Falgebra%2Fgroups.ma;h=f72711aaab9d33880f00caf8b312d6a780e79121;hb=0137a346eaaf9ae7a0b23c7a3b4c6628073b7dfb;hp=29324c4aa748f9d4cf4f8b6d215c6d23f59bb2e0;hpb=80ea6f314e89d9d280338c41860cb04949319629;p=helm.git

diff --git a/helm/software/matita/library/algebra/groups.ma b/helm/software/matita/library/algebra/groups.ma
index 29324c4aa..f72711aaa 100644
--- a/helm/software/matita/library/algebra/groups.ma
+++ b/helm/software/matita/library/algebra/groups.ma
@@ -177,8 +177,7 @@ notation "hvbox(x \sub H)" with precedence 79
 for @{ 'subgroupimage $H $x }.
 
 interpretation "Subgroup image" 'subgroupimage H x =
- (cic:/matita/algebra/groups/image.con _ _
-   (cic:/matita/algebra/groups/morphism_OF_subgroup.con _ H) x).
+ (image _ _ (morphism_OF_subgroup _ H) x).
 
 definition member_of_subgroup ≝
  λG.λH:subgroup G.λx:G.∃y.x=y \sub H.
@@ -190,11 +189,10 @@ notation "hvbox(x break \notin H)" with precedence 79
 for @{ 'not_member_of $x $H }.
 
 interpretation "Member of subgroup" 'member_of x H =
- (cic:/matita/algebra/groups/member_of_subgroup.con _ H x).
+ (member_of_subgroup _ H x).
  
 interpretation "Not member of subgroup" 'not_member_of x H =
- (cic:/matita/logic/connectives/Not.con
-  (cic:/matita/algebra/groups/member_of_subgroup.con _ H x)).
+ (Not (member_of_subgroup _ H x)).
 
 (* Left cosets *)
 
@@ -205,21 +203,20 @@ record left_coset (G:Group) : Type ≝
 
 (* Here I would prefer 'magma_op, but this breaks something in the next definition *)
 interpretation "Left_coset" 'times x C =
- (cic:/matita/algebra/groups/left_coset.ind#xpointer(1/1/1) _ x C).
+ (mk_left_coset _ x C).
 
 definition member_of_left_coset ≝
  λG:Group.λC:left_coset G.λx:G.
   ∃y.x=(element ? C)·y \sub (subgrp ? C).
 
 interpretation "Member of left_coset" 'member_of x C =
- (cic:/matita/algebra/groups/member_of_left_coset.con _ C x).
+ (member_of_left_coset _ C x).
 
 definition left_coset_eq ≝
  λG.λC,C':left_coset G.
   ∀x.((element ? C)·x \sub (subgrp ? C)) ∈ C'.
   
-interpretation "Left cosets equality" 'eq C C' =
- (cic:/matita/algebra/groups/left_coset_eq.con _ C C').
+interpretation "Left cosets equality" 'eq t C C' = (left_coset_eq t C C').
 
 definition left_coset_disjoint ≝
  λG.λC,C':left_coset G.
@@ -230,7 +227,7 @@ notation "hvbox(a break \par b)"
 for @{ 'disjoint $a $b }.
 
 interpretation "Left cosets disjoint" 'disjoint C C' =
- (cic:/matita/algebra/groups/left_coset_disjoint.con _ C C').
+ (left_coset_disjoint _ C C').
 
 (* The following should be a one-shot alias! *)
 alias symbol "member_of" (instance 0) = "Member of subgroup".
@@ -287,7 +284,7 @@ theorem in_x_mk_left_coset_x_H:
  ∀G.∀x:Type_OF_Group G.∀H:subgroup G.x ∈ (x*H).
 intros;
 simplify;
-apply (ex_intro ? ? 1);
+apply (ex_intro ? ? ⅇ);
 rewrite > morphism_to_eq_f_1_1;
 rewrite > (e_is_right_unit ? G);
 reflexivity.