intros. elim (sym_eq ? ? ? H1).assumption.
qed.
+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.
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/symmetric_eq.con
+ cic:/matita/logic/equality/sym_eq.con
cic:/matita/logic/equality/transitive_eq.con
cic:/matita/logic/equality/eq_ind.con
cic:/matita/logic/equality/eq_elim_r.con
+ cic:/matita/logic/equality/eq_rec.con
+ cic:/matita/logic/equality/eq_elim_r'.con
+ cic:/matita/logic/equality/eq_rect.con
+ cic:/matita/logic/equality/eq_elim_r''.con
cic:/matita/logic/equality/eq_f.con
+(* *)
+ cic:/matita/logic/equality/eq_OF_eq.con.
+(* *)
+(*
cic:/matita/logic/equality/eq_f'.con. (* \x.sym (eq_f x) *)
+ *)
theorem eq_f2: \forall A,B,C:Type.\forall f:A\to B \to C.
\forall x1,x2:A. \forall y1,y2:B.