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 Zgt_mult_conv_absorb_l : forall a x y : Z, (a < 0)%Z -> (a * x > a * y)%Z -> (x < y)%Z.