Module Pos2SuccNat.
(** Composition of [Pos.to_nat] and [Pos.of_succ_nat] is successor on [positive] *)
(** Composition of [Pos.to_nat], [Pos.of_succ_nat] and [Pos.pred] is identity on [positive] *)

Theorem pred_id p : Pos.pred (Pos.of_succ_nat (Pos.to_nat p)) = p.