Module SuccNat2Pos.
(** Composition of [Pos.of_succ_nat] and [Pos.to_nat] is successor on [nat] *)
(** [Pos.of_succ_nat] is hence injective *)
(** Another formulation *)
(** Successor and comparison are morphisms with respect to [Pos.of_succ_nat] *)

Lemma inj_compare n m :
(n ?= m) = (Pos.of_succ_nat n ?= Pos.of_succ_nat m)%positive.