Definition change_x0y0 :=
  change_x0 E (F -> G) eq_E_dec t x0 (change_x0 F G eq_F_dec (t x0) y0 z0).

(* Specifications: *)
Lemma here2 : change_x0y0 x0 y0 = z0.
Lemma elsewhere2_x : forall x : E, x <> x0 -> change_x0y0 x = t x.
Lemma elsewhere2_y : forall y : F, y <> y0 -> (fun x : E => change_x0y0 x y) = (fun x : E => t x y).
Lemma elsewhere2 : forall (x : E) (y : F), x <> x0 \/ y <> y0 -> change_x0y0 x y = t x y.
Lemma here2 : change_x0y0 x0 y0 = z0.