Fixpoint iterShr8 u n :=
  match n with O => u
   | S n' => Int.shru (iterShr8 u n') (Int.repr 8)
  end.

Lemma unsigned_xor_Byte_Int xi yi: Byte.unsigned (Byte.xor xi yi) = Int.unsigned (Int.xor (Int.repr (Byte.unsigned xi)) (Int.repr (Byte.unsigned yi))).