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 Zlt_mult_mult : forall a b c d : Z, (0 < a)%Z -> (0 < d)%Z -> (a < b)%Z -> (c < d)%Z -> (a * c < b * d)%Z.