From a0b31c88aa2bcd50524cbc48d16eb78c62da3445 Mon Sep 17 00:00:00 2001
From: letouzey
Date: Tue, 28 Jun 2011 23:30:10 +0000
Subject: Deletion of useless Zsqrt_def

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14245 85f007b7-540e-0410-9357-904b9bb8a0f7
---
 theories/Numbers/Integer/BigZ/ZMake.v           | 4 ++--
 theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v | 4 ++--
 2 files changed, 4 insertions(+), 4 deletions(-)

(limited to 'theories/Numbers/Integer')

diff --git a/theories/Numbers/Integer/BigZ/ZMake.v b/theories/Numbers/Integer/BigZ/ZMake.v
index 173a8f1777..0bcf22e328 100644
--- a/theories/Numbers/Integer/BigZ/ZMake.v
+++ b/theories/Numbers/Integer/BigZ/ZMake.v
@@ -383,13 +383,13 @@ Module Make (N:NType) <: ZType.
   | Neg nx => Neg N.zero
   end.
 
- Theorem spec_sqrt: forall x, to_Z (sqrt x) = Zsqrt (to_Z x).
+ Theorem spec_sqrt: forall x, to_Z (sqrt x) = Z.sqrt (to_Z x).
  Proof.
   destruct x as [p|p]; simpl.
   apply N.spec_sqrt.
   rewrite N.spec_0.
   destruct (Z_le_lt_eq_dec _ _ (N.spec_pos p)) as [LT|EQ].
-  rewrite Zsqrt_neg; auto with zarith.
+  rewrite Z.sqrt_neg; auto with zarith.
   now rewrite <- EQ.
  Qed.
 
diff --git a/theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v b/theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v
index 390b52ebee..dd83b65da1 100644
--- a/theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v
+++ b/theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v
@@ -311,12 +311,12 @@ Qed.
 Lemma sqrt_spec : forall n, 0<=n ->
  (sqrt n)*(sqrt n) <= n /\ n < (succ (sqrt n))*(succ (sqrt n)).
 Proof.
- intros n. zify. apply Zsqrt_spec.
+ intros n. zify. apply Z.sqrt_spec.
 Qed.
 
 Lemma sqrt_neg : forall n, n<0 -> sqrt n == 0.
 Proof.
- intros n. zify. apply Zsqrt_neg.
+ intros n. zify. apply Z.sqrt_neg.
 Qed.
 
 (** Log2 *)
-- 
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