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

Lemma bitwise_binop_shl: 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 (shl x n) (shl y n) = shl (f x y) n.