From 90ce6473f26b10bb7e0400fb4f358fa734da69f4 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
---
theories/psatz_axiomfree.v | 39 ++++++++++++++++++++++++++++++++++++++
theories/tactics.v | 2 +-
2 files changed, 40 insertions(+), 1 deletion(-)
create mode 100644 theories/psatz_axiomfree.v
diff --git a/theories/psatz_axiomfree.v b/theories/psatz_axiomfree.v
new file mode 100644
index 00000000..9b1d430e
--- /dev/null
+++ b/theories/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/theories/tactics.v b/theories/tactics.v
index b1b9224e..705045be 100644
--- a/theories/tactics.v
+++ b/theories/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 stdpp Require Export psatz_axiomfree.
From stdpp 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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