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_neq_Zlt : forall a b : Z, (a <= b)%Z -> b <> a -> (a < b)%Z.