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(*         *      The Rocq Prover / The Rocq Development Team           *)
(*  v      *         Copyright INRIA, CNRS and contributors             *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
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(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
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(** Equality is decidable on [nat] *)
Local Open Scope nat_scope.
Notation not_eq_sym := not_eq_sym (only parsing).
Implicit Types m n p q : nat.
Definition le_or_le_S := le_le_S_dec.
Definition Pcompare := gt_eq_gt_dec.

(* Specifications: *)
Lemma le_dec : forall n m, {n <= m} + {m <= n}.
Proof le_ge_dec.