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(*         *      The Rocq Prover / The Rocq Development Team           *)
(*  v      *         Copyright INRIA, CNRS and contributors             *)
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(*         *     GNU Lesser General Public License Version 2.1          *)
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(** * Conversions from [N] to [nat] *)
Module N2Nat.
(** [N.to_nat] is a bijection between [N] and [nat], with [N.of_nat] as reciprocal. See [Nat2N.id] below for the dual equation. *)

Lemma inj_pred a : N.to_nat (N.pred a) = Nat.pred (N.to_nat a).