Min.v

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(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
(* <O___,, *       (see CREDITS file for the list of authors)           *)
(*   \VV/  **************************************************************)
(*    //   *    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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THIS FILE IS DEPRECATED. Use PeanoNat.Nat instead.

Require Import PeanoNat.

Local Open Scope nat_scope.
Implicit Types m n p : nat.

Notation min := Nat.min (only parsing).

Definition min_0_l := Nat.min_0_l.
Definition min_0_r := Nat.min_0_r.
Definition succ_min_distr := Nat.succ_min_distr.
Definition plus_min_distr_l := Nat.add_min_distr_l.
Definition plus_min_distr_r := Nat.add_min_distr_r.
Definition min_case_strong := Nat.min_case_strong.
Definition min_spec := Nat.min_spec.
Definition min_dec := Nat.min_dec.
Definition min_case := Nat.min_case.
Definition min_idempotent := Nat.min_id.
Definition min_assoc := Nat.min_assoc.
Definition min_comm := Nat.min_comm.
Definition min_l := Nat.min_l.
Definition min_r := Nat.min_r.
Definition le_min_l := Nat.le_min_l.
Definition le_min_r := Nat.le_min_r.
Definition min_glb_l := Nat.min_glb_l.
Definition min_glb_r := Nat.min_glb_r.
Definition min_glb := Nat.min_glb.

(* begin hide *)
(* Compatibility *)
Notation min_case2 := min_case (only parsing).
Notation min_SS := Nat.succ_min_distr (only parsing).
(* end hide *)