theorem f_equal: \forall A,B:Type.\forall f:A\to B.
\forall x,y:A. eq A x y \to eq B (f x) (f y).
-intros.elim H.apply refl_equal.
+intros.elim H.reflexivity.
qed.
theorem f_equal2: \forall A,B,C:Type.\forall f:A\to B \to C.
\forall x1,x2:A. \forall y1,y2:B.
eq A x1 x2\to eq B y1 y2\to eq C (f x1 y1) (f x2 y2).
-intros.elim H1.elim H.apply refl_equal.
+intros.elim H1.elim H.reflexivity.
qed.