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