Definition plt (x y: positive) : {Plt x y} + {~ Plt x y}.Definition Ple: positive -> positive -> Prop := Pos.le.

(* Specifications: *)
Lemma Ple_refl: forall (p: positive), Ple p p.
Lemma Ple_trans: forall (p q r: positive), Ple p q -> Ple q r -> Ple p r.
Lemma Plt_Ple: forall (p q: positive), Plt p q -> Ple p q.
Lemma Ple_succ: forall (p: positive), Ple p (Pos.succ p).
Lemma Plt_Ple_trans: forall (p q r: positive), Plt p q -> Ple q r -> Plt p r.
Lemma Plt_strict: forall p, ~ Plt p p.