(* Nleb and N.compare *)
(* NB: No need to prove that Nleb a b = true <-> N.compare a b <> Gt, this statement is in fact Nleb_Nle! *)

(* Specifications: *)
Lemma Nltb_Ncompare a b : Nleb a b = false <-> N.compare a b = Gt.
Lemma Ncompare_Gt_Nltb a b : N.compare a b = Gt -> Nleb a b = false.
Notation Nmin_choice := N.min_dec (only parsing).