X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Flibrary%2Falgebra%2Fmonoids.ma;h=a80ee5fb06e40723f2f9e6051c255b9a3fa2a36d;hb=1c0aa5a6fe9b54787046c7e0270760ad197ee460;hp=c3f3cc48e8841b8139a915399030355744755038;hpb=7f2444c2670cadafddd8785b687ef312158376b0;p=helm.git

diff --git a/matita/library/algebra/monoids.ma b/matita/library/algebra/monoids.ma
index c3f3cc48e..a80ee5fb0 100644
--- a/matita/library/algebra/monoids.ma
+++ b/matita/library/algebra/monoids.ma
@@ -21,12 +21,8 @@ record PreMonoid : Type ≝
    e: magma
  }.
 
-notation < "M" for @{ 'pmmagma $M }.
-interpretation "premonoid magma coercion" 'pmmagma M =
- (cic:/matita/algebra/monoids/magma.con M).
-
 record isMonoid (M:PreMonoid) : Prop ≝
- { is_semi_group: isSemiGroup M;
+ { is_semi_group:> isSemiGroup M;
    e_is_left_unit:
     is_left_unit (mk_SemiGroup ? is_semi_group) (e M);
    e_is_right_unit:
@@ -38,18 +34,6 @@ record Monoid : Type ≝
    monoid_properties:> isMonoid premonoid 
  }.
 
-notation < "M" for @{ 'semigroup $M }.
-interpretation "premonoid coercion" 'premonoid M =
- (cic:/matita/algebra/monoids/premonoid.con M).
- 
-notation < "M" for @{ 'typeofmonoid $M }.
-interpretation "premonoid coercion" 'typeofmonoid M =
- (cic:/matita/algebra/monoids/Type_of_Monoid.con M).
- 
-notation < "M" for @{ 'magmaofmonoid $M }.
-interpretation "premonoid coercion" 'magmaofmonoid M =
- (cic:/matita/algebra/monoids/Magma_of_Monoid.con M).
- 
 notation "1" with precedence 89
 for @{ 'munit }.
 
@@ -75,7 +59,7 @@ theorem is_left_inverse_to_is_right_inverse_to_eq:
  generalize in match (eq_f ? ? (λy.y·(r x)) ? ? H2);
  simplify; fold simplify (op M);
  intro; clear H2;
- generalize in match (associative ? (is_semi_group ? (monoid_properties M)));
+ generalize in match (op_associative ? (is_semi_group ? (monoid_properties M)));
  intro;
  rewrite > H2 in H3; clear H2;
  rewrite > H1 in H3;