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 Zneq_stepl:forall (x y z:Z), (x<>y)%Z -> x=z -> (z<>y)%Z.