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 Zle_resp_neg : forall x y : Z, (x <= 0)%Z -> (y <= 0)%Z -> (x + y <= 0)%Z.