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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) *)
(*   \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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(*                      Evgeny Makarov, INRIA, 2007                     *)
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Require Export ZMul.
Module ZOrderProp (Import Z : ZAxiomsMiniSig').
Include ZMulProp Z.
(** Instances of earlier theorems for m == 0 *)

(* Specifications: *)
Theorem neg_pos_cases : forall n, n ~= 0 <-> n < 0 \/ n > 0.
Theorem nonpos_pos_cases : forall n, n <= 0 \/ n > 0.
Theorem neg_nonneg_cases : forall n, n < 0 \/ n >= 0.
Theorem nonpos_nonneg_cases : forall n, n <= 0 \/ n >= 0.
Ltac zinduct n := induction_maker n ltac:(apply order_induction_0).