(************************************************************************)
(*         *   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)         *)
(************************************************************************)
(** Theorems about [gt] in [nat].  This file is DEPRECATED now, see module [PeanoNat.Nat] instead, which favor [lt] over [gt].  [gt] is defined in [Init/Peano.v] as: << Definition gt (n m:nat) := m < n. >> *)
Local Open Scope nat_scope.
(** * Order and successor *)
Proof Nat.lt_0_succ _.
Proof Nat.lt_succ_diag_r _.
(** * Irreflexivity *)
Proof Nat.lt_irrefl _.
(** * Asymmetry *)
Proof Nat.lt_asymm _ _.
(** * Relating strict and large orders *)

Lemma le_not_gt n m : n <= m -> ~ n > m.