From ca1305a0187653edcf63e46b84c65130ac78d117 Mon Sep 17 00:00:00 2001
From: Frédéric Besson
Date: Fri, 20 Dec 2013 01:22:45 +0100
Subject: micromega: removal of spurious Export; addition of Lia.v
 encapsulating lia and nia.

---
 doc/refman/Micromega.tex              |  4 ++--
 plugins/micromega/Lia.v               | 39 +++++++++++++++++++++++++++++++++++
 plugins/micromega/Psatz.v             |  2 +-
 plugins/micromega/vo.itarget          |  1 +
 test-suite/micromega/heap3_vcgen_25.v |  2 +-
 test-suite/micromega/zomicron.v       |  2 +-
 6 files changed, 45 insertions(+), 5 deletions(-)
 create mode 100644 plugins/micromega/Lia.v

diff --git a/doc/refman/Micromega.tex b/doc/refman/Micromega.tex
index 5f9ed443c4..7bdbd6d84e 100644
--- a/doc/refman/Micromega.tex
+++ b/doc/refman/Micromega.tex
@@ -132,7 +132,7 @@ Theorem~\ref{thm:psatz}, the goal is valid.
 \tacindex{lia}
 \label{sec:lia}
 
-The tactic {\tt lia} offers an alternative to the {\tt omega} and {\tt romega} tactic (see
+The tactic {\tt lia} ({\tt Require Lia.}) offers an alternative to the {\tt omega} and {\tt romega} tactic (see
 Chapter~\ref{OmegaChapter}). 
 %
 Rougthly speaking, the deductive power of {\tt lia} is the combined deductive power of {\tt ring\_simplify} and {\tt omega}.
@@ -145,7 +145,7 @@ following so-called \emph{omega nightmare}~\cite{TheOmegaPaper}.
        -10 <= 7 * x - 9 * y <= 4 ->   False.
 \end{coq_example*}
 \begin{coq_eval}
-intro x; lia;
+intro x; lia.
 \end{coq_eval}
 The estimation of the relative efficiency of lia \emph{vs} {\tt omega}
 and {\tt romega} is under evaluation.
diff --git a/plugins/micromega/Lia.v b/plugins/micromega/Lia.v
new file mode 100644
index 0000000000..4553f03e30
--- /dev/null
+++ b/plugins/micromega/Lia.v
@@ -0,0 +1,39 @@
+(************************************************************************)
+(*  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: *)
diff --git a/plugins/micromega/Psatz.v b/plugins/micromega/Psatz.v
index 5090542c6a..804a16b793 100644
--- a/plugins/micromega/Psatz.v
+++ b/plugins/micromega/Psatz.v
@@ -18,7 +18,7 @@ Require Import RMicromega.
 Require Import QArith.
 Require Import ZArith.
 Require Import Rdefinitions.
-Require Export RingMicromega.
+Require Import RingMicromega.
 Require Import VarMap.
 Require Tauto.
 Declare ML Module "micromega_plugin".
diff --git a/plugins/micromega/vo.itarget b/plugins/micromega/vo.itarget
index fb75bf20c8..bf6a1a7db2 100644
--- a/plugins/micromega/vo.itarget
+++ b/plugins/micromega/vo.itarget
@@ -10,3 +10,4 @@ Tauto.vo
 VarMap.vo
 ZCoeff.vo
 ZMicromega.vo
+Lia.vo
\ No newline at end of file
diff --git a/test-suite/micromega/heap3_vcgen_25.v b/test-suite/micromega/heap3_vcgen_25.v
index efb5c7fd5c..00522f50aa 100644
--- a/test-suite/micromega/heap3_vcgen_25.v
+++ b/test-suite/micromega/heap3_vcgen_25.v
@@ -7,7 +7,7 @@
 (************************************************************************)
 
 Require Import ZArith.
-Require Import Psatz.
+Require Import Lia.
 
 Open Scope Z_scope.
 
diff --git a/test-suite/micromega/zomicron.v b/test-suite/micromega/zomicron.v
index 3b24602336..0ec1dbfbcd 100644
--- a/test-suite/micromega/zomicron.v
+++ b/test-suite/micromega/zomicron.v
@@ -1,5 +1,5 @@
 Require Import ZArith.
-Require Import Psatz.
+Require Import Lia.
 Open Scope Z_scope.
 
 Lemma two_x_eq_1 : forall x, 2 * x = 1 -> False.
-- 
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