Local Lemma wmultZ_helper: forall a b k1 k2 p,
((a - k1 * p) * (b - k2 * p) = a * b - (k1 * b + k2 * a - k1 * k2 * p) * p)%Z.

Lemma zext_size_1: (* Note: not axiom free *)
forall sz (w: word (sz + 1)),
wmsb w false = false ->
exists sw, w = zext sw 1.