From 12daccee87b77ca0ee0a79878205c166091bc731 Mon Sep 17 00:00:00 2001
From: Guillaume Melquiond <guillaume.melquiond@inria.fr>
Date: Mon, 3 Oct 2011 11:15:39 +0200
Subject: [PATCH] Add a realization of real.square.

Remark about the theory: if one considers that the square root is always
nonnegative (by definition in Coq), then Lemma Sqrt_positive has an
extraneous hypothesis.
---
 realizations/coq/real/Square.v | 49 ++++++++++++++++++++++++++++++++++
 1 file changed, 49 insertions(+)
 create mode 100644 realizations/coq/real/Square.v

diff --git a/realizations/coq/real/Square.v b/realizations/coq/real/Square.v
new file mode 100644
index 000000000..ce9cb4eff
--- /dev/null
+++ b/realizations/coq/real/Square.v
@@ -0,0 +1,49 @@
+(* This file is generated by Why3's Coq driver *)
+(* Beware! Only edit allowed sections below    *)
+Require Import ZArith.
+Require Import Rbase.
+Require Import R_sqrt.
+(*Add Rec LoadPath "/home/guillaume/bin/why3/share/why3/theories".*)
+(*Add Rec LoadPath "/home/guillaume/bin/why3/share/why3/modules".*)
+Require real.Real.
+Definition sqr(x:R): R := (x * x)%R.
+
+Definition sqrt: R -> R.
+(* YOU MAY EDIT THE PROOF BELOW *)
+exact sqrt.
+Defined.
+(* DO NOT EDIT BELOW *)
+
+
+(* YOU MAY EDIT THE CONTEXT BELOW *)
+
+(* DO NOT EDIT BELOW *)
+
+Lemma Sqrt_positive : forall (x:R), (0%R <= x)%R -> (0%R <= (sqrt x))%R.
+(* YOU MAY EDIT THE PROOF BELOW *)
+intros x _.
+apply sqrt_pos.
+Qed.
+(* DO NOT EDIT BELOW *)
+
+(* YOU MAY EDIT THE CONTEXT BELOW *)
+
+(* DO NOT EDIT BELOW *)
+
+Lemma Sqrt_square : forall (x:R), (0%R <= x)%R -> ((sqr (sqrt x)) = x).
+(* YOU MAY EDIT THE PROOF BELOW *)
+exact sqrt_sqrt.
+Qed.
+(* DO NOT EDIT BELOW *)
+
+(* YOU MAY EDIT THE CONTEXT BELOW *)
+
+(* DO NOT EDIT BELOW *)
+
+Lemma Square_sqrt : forall (x:R), (0%R <= x)%R -> ((sqrt (x * x)%R) = x).
+(* YOU MAY EDIT THE PROOF BELOW *)
+exact sqrt_square.
+Qed.
+(* DO NOT EDIT BELOW *)
+
+
-- 
2.24.1