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_cotrans_pos : forall x y : Z, (0 < x + y)%Z -> {(0 < x)%Z} + {(0 < y)%Z}.