End Nat2Pos.
(**********************************************************************)
(** Properties of the shifted injection from Peano natural numbers to binary positive numbers *)
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.
End Pos2SuccNat.