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

Lemma Z_add_is_or: forall i, 0 <= i -> forall x y, (forall j, 0 <= j <= i -> Z.testbit x j && Z.testbit y j = false) -> Z.testbit (x + y) i = Z.testbit x i || Z.testbit y i.