Definition swap (i: int) : int :=
 Int.or (Int.shl (Int.and i (Int.repr 255)) (Int.repr 24))
   (Int.or (Int.shl (Int.and (Shr 8 i) (Int.repr 255)) (Int.repr 16))
      (Int.or (Int.shl (Int.and (Shr 16 i) (Int.repr 255)) (Int.repr 8))
         (Shr 24 i))).

Lemma map_swap_involutive: forall l, map swap (map swap l) = l.