Infix "<?" := ltb.
Infix "<=?" := leb.
(** For compatibility, some decidability fonctions (informative). *)

(** Specifications *)
(** First, we ask [i2z] to be injective. Said otherwise, our ad-hoc equality [==] and the generic [=] are in fact equivalent. We define [==] nonetheless since the translation to [Z] for using automatic tactic is easier. *)
Axiom i2z_eq : forall n p : t, n == p -> n = p.