Corollary to_Z_bounded : forall x, (0 <= φ  x  < wB)%Z.

Theorem Zmod_distr: forall a b r t, 0 <= a <= b -> 0 <= r -> 0 <= t < 2 ^a -> (2 ^a * r + t) mod (2 ^ b) = (2 ^a * r) mod (2 ^ b) + t.