we removed some coercion detours and we added some coercions we really would like...

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

diff --git a/helm/software/matita/library/algebra/finite_groups.ma b/helm/software/matita/library/algebra/finite_groups.ma
index 6da0a7256b0eb0517ca203228041d58a4e6ed72e..30408be37d28e7db2cd5047c913bca0087729c3d 100644 (file)
--- a/helm/software/matita/library/algebra/finite_groups.ma
+++ b/helm/software/matita/library/algebra/finite_groups.ma
@@ -327,7 +327,7 @@ theorem finite_enumerable_SemiGroup_to_left_cancellable_to_right_cancellable_to_
  ∀G:finite_enumerable_SemiGroup.
   left_cancellable ? (op G) →
   right_cancellable ? (op G) →
-   ∃e:G. isMonoid (mk_PreMonoid G e).
+   ∃e:G. IsMonoid (mk_PreMonoid G e).
 intros;
 letin f ≝(λn.ι(G \sub O · G \sub n));
 cut (∀n.n ≤ order ? (is_finite_enumerable G) → ∃m.f m = n);
@@ -346,24 +346,24 @@ cut (∀n.n ≤ order ? (is_finite_enumerable G) → ∃m.f m = n);
     clearbody GOGO;
     rewrite < HH in GOGO;
     rewrite < HH in GOGO:(? ? % ?);
-    rewrite > (op_associative ? G) in GOGO;
+    rewrite > (op_is_associative ? G) in GOGO;
     letin GaGa ≝(H ? ? ? GOGO);
     clearbody GaGa;
     clear GOGO;
     constructor 1;
     [ simplify;
-      apply (semigroup_properties G)
+      apply (is_semi_group G)
     | unfold is_left_unit; intro;
       letin GaxGax ≝(refl_eq ? (G \sub a ·x));
       clearbody GaxGax; (* demo *)
       rewrite < GaGa in GaxGax:(? ? % ?);
-      rewrite > (op_associative ? (semigroup_properties G)) in GaxGax;
+      rewrite > (op_is_associative ? G) in GaxGax;
       apply (H ? ? ? GaxGax)
     | unfold is_right_unit; intro;
       letin GaxGax ≝(refl_eq ? (x·G \sub a));
       clearbody GaxGax;
       rewrite < GaGa in GaxGax:(? ? % ?);
-      rewrite < (op_associative ? (semigroup_properties G)) in GaxGax;
+      rewrite < (op_is_associative ? G) in GaxGax;
       apply (H1 ? ? ? GaxGax)
     ]
   ]