X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Flogic%2Fequality.ma;h=3b242c66709d6562debbc465a00e930cd4fb370e;hb=894c3e4038c93b484896e81132eae55046e47605;hp=95cb973074df0794ff8bd0003b357e965a2ef866;hpb=b273fb8dacc8ce058ffa4677846085864ace6b36;p=helm.git

diff --git a/helm/software/matita/library/logic/equality.ma b/helm/software/matita/library/logic/equality.ma
index 95cb97307..3b242c667 100644
--- a/helm/software/matita/library/logic/equality.ma
+++ b/helm/software/matita/library/logic/equality.ma
@@ -60,6 +60,21 @@ theorem eq_elim_r:
 intros. elim (sym_eq ? ? ? H1).assumption.
 qed.
 
+theorem eq_f: \forall  A,B:Type.\forall f:A\to B.
+\forall x,y:A. x=y \to f x = f y.
+intros.elim H.apply refl_eq.
+qed.
+
+theorem eq_f': \forall  A,B:Type.\forall f:A\to B.
+\forall x,y:A. x=y \to f y = f x.
+intros.elim H.apply refl_eq.
+qed.
+
+(* 
+coercion cic:/matita/logic/equality/sym_eq.con.
+coercion cic:/matita/logic/equality/eq_f.con.
+*)
+
 default "equality"
  cic:/matita/logic/equality/eq.ind
  cic:/matita/logic/equality/sym_eq.con
@@ -67,19 +82,8 @@ default "equality"
  cic:/matita/logic/equality/eq_ind.con
  cic:/matita/logic/equality/eq_elim_r.con
  cic:/matita/logic/equality/eq_f.con
- cic:/matita/logic/equality/eq_OF_eq.con. (* \x.sym (eq_f x) *)
-
+ cic:/matita/logic/equality/eq_f'.con. (* \x.sym (eq_f x) *)
  
-theorem eq_f: \forall  A,B:Type.\forall f:A\to B.
-\forall x,y:A. x=y \to f x = f y.
-intros.elim H.reflexivity.
-qed.
-
-theorem eq_f1: \forall  A,B:Type.\forall f:A\to B.
-\forall x,y:A. x=y \to f y = f x.
-intros.elim H.reflexivity.
-qed.
-
 theorem eq_f2: \forall  A,B,C:Type.\forall f:A\to B \to C.
 \forall x1,x2:A. \forall y1,y2:B.
 x1=x2 \to y1=y2 \to f x1 y1 = f x2 y2.