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_resp_Zle : forall a x y : Z, (0 < a)%Z -> (a * y <= a * x)%Z -> (y <= x)%Z.