X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Falgebra%2Fsemigroups.ma;h=7d68dbb360f9cdcef6dd4fdf3325cdd32fbc2b62;hb=e78cf74f8976cf0ca554f64baa9979d0423ee927;hp=5b461d1a4f43edba6acc9e4dd448f0eceb157243;hpb=55b82bd235d82ff7f0a40d980effe1efde1f5073;p=helm.git

diff --git a/helm/software/matita/library/algebra/semigroups.ma b/helm/software/matita/library/algebra/semigroups.ma
index 5b461d1a4..7d68dbb36 100644
--- a/helm/software/matita/library/algebra/semigroups.ma
+++ b/helm/software/matita/library/algebra/semigroups.ma
@@ -12,42 +12,27 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/algebra/semigroups".
-
 include "higher_order_defs/functions.ma".
 
 (* Magmas *)
 
-record Magma : Type ≝
+record Magma : Type≝
  { carrier:> Type;
    op: carrier → carrier → carrier
  }.
 
-notation < "M" for @{ 'carrier $M }.
-interpretation "carrier coercion" 'carrier S =
- (cic:/matita/algebra/semigroups/carrier.con S).
-
-notation "hvbox(a break \middot b)" 
-  left associative with precedence 55
-for @{ 'magma_op $a $b }.
-
-interpretation "magma operation" 'magma_op a b =
- (cic:/matita/algebra/semigroups/op.con _ a b).
+interpretation "magma operation" 'middot a b = (op ? a b).
 
 (* Semigroups *)
 
-record isSemiGroup (M:Magma) : Prop ≝
- { associative: associative ? (op M) }.
+record isSemiGroup (M:Magma) : Prop≝
+ { op_associative: associative ? (op M) }.
 
-record SemiGroup : Type ≝
+record SemiGroup : Type≝
  { magma:> Magma;
    semigroup_properties:> isSemiGroup magma
  }.
  
-notation < "S" for @{ 'magma $S }.
-interpretation "magma coercion" 'magma S =
- (cic:/matita/algebra/semigroups/magma.con S).
- 
 definition is_left_unit ≝
  λS:SemiGroup. λe:S. ∀x:S. e·x = x.
  
@@ -59,6 +44,6 @@ theorem is_left_unit_to_is_right_unit_to_eq:
   is_left_unit ? e → is_right_unit ? e' → e=e'.
  intros;
  rewrite < (H e');
- rewrite < (H1 e) in \vdash (? ? % ?);
+ rewrite < (H1 e) in \vdash (? ? % ?).
  reflexivity.
 qed.