X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Falgebra%2Fmonoids.ma;h=fe35eeb6709fea8092269d6035f470f6136c9523;hb=070b11daefc90ecc20ebee73acc550aeac1c627b;hp=63b6430ec90facf077bfbd3b4b346a9e124d7cc9;hpb=35337934554027181913e87de11ff77745a77ebe;p=helm.git

diff --git a/helm/software/matita/library/algebra/monoids.ma b/helm/software/matita/library/algebra/monoids.ma
index 63b6430ec..fe35eeb67 100644
--- a/helm/software/matita/library/algebra/monoids.ma
+++ b/helm/software/matita/library/algebra/monoids.ma
@@ -12,8 +12,6 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/algebra/monoids/".
-
 include "algebra/semigroups.ma".
 
 record PreMonoid : Type ≝
@@ -21,10 +19,6 @@ 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;
    e_is_left_unit:
@@ -38,33 +32,17 @@ 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 }.
-
-interpretation "Monoid unit" 'munit =
- (cic:/matita/algebra/monoids/e.con _).
+interpretation "Monoid unit" 'neutral = (e _).
   
 definition is_left_inverse ≝
  λM:Monoid.
   λopp: M → M.
-   ∀x:M. (opp x)·x = 1.
+   ∀x:M. (opp x)·x = ⅇ.
    
 definition is_right_inverse ≝
  λM:Monoid.
   λopp: M → M.
-   ∀x:M. x·(opp x) = 1.
+   ∀x:M. x·(opp x) = ⅇ.
 
 theorem is_left_inverse_to_is_right_inverse_to_eq:
  ∀M:Monoid. ∀l,r.