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(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
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(*         *     GNU Lesser General Public License Version 2.1          *)
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(** Strict order on natural numbers.  This file is mostly OBSOLETE now, see module [PeanoNat.Nat] instead.  [lt] is defined in library [Init/Peano.v] as: << Definition lt (n m:nat) := S n <= m. Infix "<" := lt : nat_scope. >> *)
Local Open Scope nat_scope.
(** * Irreflexivity *)
Notation lt_irrefl := Nat.lt_irrefl (only parsing). (* ~ x < x *)
Hint Resolve lt_irrefl: arith.
(** * Relationship between [le] and [lt] *)
Hint Immediate lt_le_S: arith.
Hint Immediate lt_n_Sm_le: arith.
Hint Immediate le_lt_n_Sm: arith.

Theorem lt_not_le n m : n < m -> ~ m <= n.