Corollary xor_zero_l: forall x, xor zero x = x.

Lemma bitwise_binop_shru: forall f f' x y n, (forall x y i, 0 <= i < zwordsize -> testbit (f x y) i = f' (testbit x i) (testbit y i)) -> f' false false = false -> f (shru x n) (shru y n) = shru (f x y) n.