Definition plt (x y: positive) : {Plt x y} + {~ Plt x y}.

(* Specifications: *)
Lemma Plt_Ple_trans:
forall (p q r: positive), Plt p q -> Ple q r -> Plt p r.
Lemma Plt_Ple_trans:
forall (p q r: positive), Plt p q -> Ple q r -> Plt p r.