Procedural: higher-order unification needs a lot of hints !!

[helm.git] / helm / software / matita / library / algebra / groups.ma

diff --git a/helm/software/matita/library/algebra/groups.ma b/helm/software/matita/library/algebra/groups.ma
index d6e77ae8d0fa6a36404b7d084911e12602c234de..bfb639af78deabee531767ff1d4a39b7245e763b 100644 (file)
--- a/helm/software/matita/library/algebra/groups.ma
+++ b/helm/software/matita/library/algebra/groups.ma
@@ -33,7 +33,7 @@ record Group : Type ≝
    group_properties:> isGroup pregroup
  }.
 
-interpretation "Group inverse" 'invert x = (inv _ x).
+interpretation "Group inverse" 'invert x = (inv ? x).
 
 definition left_cancellable ≝
  λT:Type. λop: T -> T -> T.
@@ -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 t C C' =
- (cic:/matita/algebra/groups/left_coset_eq.con t 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".
@@ -267,7 +264,7 @@ apply H1;
 unfold member_of_subgroup;
 elim H2;
 apply (ex_intro ? ? (x'·a \sup -1));
-rewrite > f_morph;
+rewrite > f_morph; 
 apply (eq_op_x_y_op_z_y_to_eq ? (a \sub H));
 rewrite > (op_associative ? G);
 rewrite < H3;