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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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(*                                                                      *)
(* Micromega: A reflexive tactic using the Positivstellensatz           *)
(*                                                                      *)
(*  Frédéric Besson (Irisa/Inria) 2006-2011                             *)
(*                                                                      *)
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Require  FSetPositive FSetEqProperties.
(*Declare ML Module "micromega_plugin".*)
Ltac flatten_bool :=
repeat match goal with
[ id : (_ && _)%bool = true |- _ ] =>  destruct (andb_prop _ _ id); clear id
|  [ id : (_ || _)%bool = true |- _ ] =>  destruct (orb_prop _ _ id); clear id
end.
Ltac inv H := inversion H ; try subst ; clear H.
Open Scope Z_scope.

Lemma ZSORaddon :
SORaddon 0 1 Z.add Z.mul Z.sub Z.opp  (@eq Z) Z.le (* ring elements *)
0%Z 1%Z Z.add Z.mul Z.sub Z.opp (* coefficients *)
Zeq_bool Z.leb
(fun x => x) (fun x => x) (pow_N 1 Z.mul).