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 quadro_leq_inf : forall a b c d : Z, {(c <= a)%Z /\ (d <= b)%Z} + {~ ((c <= a)%Z /\ (d <= b)%Z)}.