Lemma divls_mul_params_sound: forall d m p, divls_mul_params d = Some(p, m) -> 0 <= m < Int64.modulus /\ 0 <= p < 64 /\ forall n, Int64.min_signed <= n <= Int64.max_signed -> Z.quot n d = Z.div (m * n) (two_p (64 + p)) + (if zlt n 0 then 1 else 0).