+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.
+