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_lt_eq_S : forall x y : Z, (x <= y)%Z -> (y < x + 1)%Z -> y = x.