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(*         *   The Coq Proof Assistant / The Coq Development Team       *)
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(** 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 *)
(** * Transitivity *)

Theorem le_gt_trans n m p : m <= n -> m > p -> n > p.