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_pos_pos : forall x y : Z, (0 < x)%Z -> (0 < y)%Z -> (0 < x * y)%Z.