From 16240e35eb14a5029291eae6e08cbdd88728b535 Mon Sep 17 00:00:00 2001
From: Ralf Jung <jung@mpi-sws.org>
Date: Mon, 22 Aug 2016 11:53:26 +0200
Subject: [PATCH] use Psatz without using axioms about real numbers
---
_CoqProject | 1 +
prelude/psatz_axiomfree.v | 39 +++++++++++++++++++++++++++++++++++++++
prelude/tactics.v | 2 +-
3 files changed, 41 insertions(+), 1 deletion(-)
create mode 100644 prelude/psatz_axiomfree.v
diff --git a/_CoqProject b/_CoqProject
index 05c4e0532..903bf1256 100644
--- a/_CoqProject
+++ b/_CoqProject
@@ -21,6 +21,7 @@ prelude/listset.v
prelude/streams.v
prelude/gmap.v
prelude/base.v
+prelude/psatz_axiomfree.v
prelude/tactics.v
prelude/prelude.v
prelude/listset_nodup.v
diff --git a/prelude/psatz_axiomfree.v b/prelude/psatz_axiomfree.v
new file mode 100644
index 000000000..9b1d430e9
--- /dev/null
+++ b/prelude/psatz_axiomfree.v
@@ -0,0 +1,39 @@
+(** This file is a hack that lets us use Psatz without importing all sorts of
+ axioms about real numbers. It has been created by copying the file
+ Psatz.v from the Coq distribution, removing everything defined after the lia
+ tactic, and removing the two lines importing RMicromega and Rdefinitions.
+ The original license header follows. *)
+
+(************************************************************************)
+(* v * The Coq Proof Assistant / The Coq Development Team *)
+(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *)
+(* \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) 2006-2008 *)
+(* *)
+(************************************************************************)
+
+From Coq Require Import ZMicromega.
+From Coq Require Import QMicromega.
+From Coq Require Import QArith.
+From Coq Require Import ZArith.
+From Coq Require Import RingMicromega.
+From Coq Require Import VarMap.
+From Coq Require Tauto.
+Declare ML Module "micromega_plugin".
+
+Ltac preprocess :=
+ zify ; unfold Z.succ in * ; unfold Z.pred in *.
+
+Ltac lia :=
+ preprocess;
+ xlia ;
+ abstract (
+ intros __wit __varmap __ff ;
+ change (Tauto.eval_f (Zeval_formula (@find Z Z0 __varmap)) __ff) ;
+ apply (ZTautoChecker_sound __ff __wit); vm_cast_no_check (eq_refl true)).
diff --git a/prelude/tactics.v b/prelude/tactics.v
index 246e51cde..2a41f7646 100644
--- a/prelude/tactics.v
+++ b/prelude/tactics.v
@@ -3,7 +3,7 @@
(** This file collects general purpose tactics that are used throughout
the development. *)
From Coq Require Import Omega.
-From Coq Require Export Psatz.
+From iris.prelude Require Export psatz_axiomfree.
From iris.prelude Require Export decidable.
Lemma f_equal_dep {A B} (f g : ∀ x : A, B x) x : f = g → f x = g x.
--
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