+theorem eq_elim_r':
+ \forall A:Type.\forall x:A. \forall P: A \to Set.
+ P x \to \forall y:A. y=x \to P y.
+intros. elim (sym_eq ? ? ? H).assumption.
+qed.
+
+theorem eq_elim_r'':
+ \forall A:Type.\forall x:A. \forall P: A \to Type.
+ P x \to \forall y:A. y=x \to P y.
+intros. elim (sym_eq ? ? ? H).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.
+(* *)
+