proposition: Lemma elsewhere2_y : forall y : F, y <> y0 -> (fun x : E => change_x0y0 x y) = (fun x : E => t x y).
proof: Proof. intros; apply funct_eq. intros; unfold change_x0y0 in |- *. case (eq_E_dec e x0); intros. rewrite e0. rewrite (here E (F -> G) eq_E_dec t x0 (change_x0 F G eq_F_dec (t x0) y0 z0)) . rewrite elsewhere; auto. rewrite (elsewhere E (F -> G) eq_E_dec t x0 (change_x0 F G eq_F_dec (t x0) y0 z0) e) ; auto. Qed.
imports: table