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(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012 *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
(* *)
(* Micromega: A reflexive tactic using the Positivstellensatz *)
(* *)
(* Frédéric Besson (Irisa/Inria) 2013 *)
(* *)
(************************************************************************)
Require Import ZMicromega.
Require Import ZArith.
Require Import RingMicromega.
Require Import VarMap.
Require Tauto.
Declare ML Module "micromega_plugin".
Ltac lia :=
zify ; unfold Z.succ in * ;
(*cbv delta - [Z.add Z.sub Z.opp Z.mul Z.pow Z.gt Z.ge Z.le Z.lt iff not] ;*) xlia ;
intros __wit __varmap __ff ;
change (Tauto.eval_f (Zeval_formula (@find Z Z0 __varmap)) __ff) ;
apply (ZTautoChecker_sound __ff __wit); vm_compute ; reflexivity.
Ltac nia :=
zify ; unfold Z.succ in * ;
xnlia ;
intros __wit __varmap __ff ;
change (Tauto.eval_f (Zeval_formula (@find Z Z0 __varmap)) __ff) ;
apply (ZTautoChecker_sound __ff __wit); vm_compute ; reflexivity.
(* Local Variables: *)
(* coding: utf-8 *)
(* End: *)
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