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 double_not_equal_zero : forall c d : Z, ~ (c = 0%Z /\ d = 0%Z) -> c <> d \/ c <> 0%Z.