diff options
| author |  letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2011-06-28 23:30:10 +0000 |
|---|---|---|
| committer | letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2011-06-28 23:30:10 +0000 |
| commit | a0b31c88aa2bcd50524cbc48d16eb78c62da3445 (patch) | |
| tree | ebf4533e46fb630e520a745f2b3df41d489a33ec /theories/Numbers/Natural | |
| parent | 2941378aee6586bcff9f8a117f11e5c5c2327607 (diff) | |
Deletion of useless Zsqrt_def
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14245 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Numbers/Natural')
| -rw-r--r-- | theories/Numbers/Natural/BigN/NMake.v | 2 | ||||
| -rw-r--r-- | theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v | 2 |
2 files changed, 2 insertions, 2 deletions
diff --git a/theories/Numbers/Natural/BigN/NMake.v b/theories/Numbers/Natural/BigN/NMake.v index aabbf87f2..66b39aca9 100644 --- a/theories/Numbers/Natural/BigN/NMake.v +++ b/theories/Numbers/Natural/BigN/NMake.v @@ -771,7 +771,7 @@ Module Make (W0:CyclicType) <: NType. intros x. rewrite sqrt_fold. destr_t x as (n,x). exact (ZnZ.spec_sqrt x). Qed. - Theorem spec_sqrt: forall x, [sqrt x] = Zsqrt [x]. + Theorem spec_sqrt: forall x, [sqrt x] = Z.sqrt [x]. Proof. intros x. symmetry. apply Z.sqrt_unique. diff --git a/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v b/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v index 57277b489..9bed794f2 100644 --- a/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v +++ b/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v @@ -263,7 +263,7 @@ 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. |