Definition Ile x y := Ident.lt x y \/ Ident.eq x y.

(* Specifications: *)
Lemma Ile_refl x : Ile x x.
Lemma Ilt_Zpos i j : Ident.lt i j <-> Z.lt (Zpos (id2pos i)) ((Zpos (id2pos j))).
Lemma nat_of_P_id2pos_le x y : Ile x y -> nat_of_P (id2pos x) <= nat_of_P (id2pos y).