X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Flibrary%2Flogic%2Fequality.ma;h=3b242c66709d6562debbc465a00e930cd4fb370e;hb=3ee4674162a39cb65b08d492278738008057566d;hp=b87dc6c95656dcf5de3c3ceb00e9ed105067c6b8;hpb=7f2444c2670cadafddd8785b687ef312158376b0;p=helm.git

diff --git a/matita/library/logic/equality.ma b/matita/library/logic/equality.ma
index b87dc6c95..3b242c667 100644
--- a/matita/library/logic/equality.ma
+++ b/matita/library/logic/equality.ma
@@ -60,18 +60,30 @@ 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
  cic:/matita/logic/equality/trans_eq.con
  cic:/matita/logic/equality/eq_ind.con
- cic:/matita/logic/equality/eq_elim_r.con. 
+ cic:/matita/logic/equality/eq_elim_r.con
+ cic:/matita/logic/equality/eq_f.con
+ 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_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.