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