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