A few experiments (with horrible results) using notation...

[helm.git] / helm / matita / library / algebra / semigroups.ma

diff --git a/helm/matita/library/algebra/semigroups.ma b/helm/matita/library/algebra/semigroups.ma
index bea3ae584a3c456af650c82b443628f64a575a38..93a139ca760e5113f6b87d00a8f09d5552861e48 100644 (file)
--- a/helm/matita/library/algebra/semigroups.ma
+++ b/helm/matita/library/algebra/semigroups.ma
@@ -27,11 +27,21 @@ record SemiGroup : Type ≝
  
 coercion cic:/matita/algebra/semigroups/carrier.con.
 
+notation "hvbox(a break * \sub S b)" 
+  left associative with precedence 55
+for @{ 'ptimes $S $a $b }.
+
+interpretation "Semigroup operation" 'times a b =
+ (cic:/matita/algebra/semigroups/op.con _ a b).
+
+interpretation "Semigroup operation" 'ptimes S a b =
+ (cic:/matita/algebra/semigroups/op.con S a b).
+
 definition is_left_unit ≝
- λS:SemiGroup. λe:S. ∀x:S. op S e x = x.
+ λS:SemiGroup. λe:S. ∀x:S. e * x = x.
  
 definition is_right_unit ≝
- λS:SemiGroup. λe:S. ∀x:S. op S x e = x.
+ λS:SemiGroup. λe:S. ∀x:S. x * e = x.
 
 theorem is_left_unit_to_is_right_unit_to_eq:
  ∀S:SemiGroup. ∀e1,e2:S.