Admitted.

(* TODO also requires that 0 <= b0, b1, b2, b3 < 256 *)
Lemma xor_is_or_4_bytes: forall b0 b1 b2 b3,
(Int.xor (Int.xor (Int.xor b0
(Int.shl b1 (Int.repr 8)))
(Int.shl b2 (Int.repr 16)))
(Int.shl b3 (Int.repr 24))) =
(Int.or  (Int.or  (Int.or  b0
(Int.shl b1 (Int.repr 8)))
(Int.shl b2 (Int.repr 16)))
(Int.shl b3 (Int.repr 24))).