Definition projP1 (H : sig P) := let (x, h) := H in x.Definition projP2 (H : sig P) :=
   let (x, h) as H return (P (projP1 H)) := H in h.

Lemma Zmult_simpl : forall n m p q : Z, n = m -> p = q -> (n * p)%Z = (m * q)%Z.