Qed. Hint Resolve If_eq.

(* Specifications: *)
Lemma IfIf :
forall (T : Set) (b1 b2 : bool) (x x' y y' : T),
If T b1 (If T b2 x y) (If T b2 x' y') =
If T b2 (If T b1 x x') (If T b1 y y').