diff options
| author | letouzey | 2010-11-02 15:10:52 +0000 |
|---|---|---|
| committer | letouzey | 2010-11-02 15:10:52 +0000 |
| commit | cce4c64a95e5f835cfd28bb3589c535903cbd011 (patch) | |
| tree | 23d4dfb0f7c2a504c57d5c7be50ba59f5b06768d /theories/Numbers/Natural | |
| parent | 8e5cae9a9f8edbedc2fb2451d32dc18af89cfa40 (diff) | |
NZSqrt : since spec is complete, no need for morphism axiom sqrt_wd
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13609 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Numbers/Natural')
| -rw-r--r-- | theories/Numbers/Natural/Binary/NBinary.v | 1 | ||||
| -rw-r--r-- | theories/Numbers/Natural/Peano/NPeano.v | 1 | ||||
| -rw-r--r-- | theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v | 2 |
3 files changed, 0 insertions, 4 deletions
diff --git a/theories/Numbers/Natural/Binary/NBinary.v b/theories/Numbers/Natural/Binary/NBinary.v index 34b44d3c60..cc57171b32 100644 --- a/theories/Numbers/Natural/Binary/NBinary.v +++ b/theories/Numbers/Natural/Binary/NBinary.v @@ -165,7 +165,6 @@ Definition log2_nonpos := Nlog2_nonpos. (** Sqrt *) -Program Instance sqrt_wd : Proper (eq==>eq) Nsqrt. Definition sqrt_spec n (H:0<=n) := Nsqrt_spec n. Lemma sqrt_neg : forall a, a<0 -> Nsqrt a = 0. Proof. destruct a; discriminate. Qed. diff --git a/theories/Numbers/Natural/Peano/NPeano.v b/theories/Numbers/Natural/Peano/NPeano.v index 6502cfa555..a828ec821c 100644 --- a/theories/Numbers/Natural/Peano/NPeano.v +++ b/theories/Numbers/Natural/Peano/NPeano.v @@ -448,7 +448,6 @@ Definition log2_spec := log2_spec. Definition log2_nonpos := log2_nonpos. Definition log2 := log2. -Program Instance sqrt_wd : Proper (eq==>eq) sqrt. Definition sqrt_spec a (Ha:0<=a) := sqrt_spec a. Lemma sqrt_neg : forall a, a<0 -> sqrt a = 0. inversion 1. Qed. Definition sqrt := sqrt. diff --git a/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v b/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v index 3620045d1e..547f51b3d5 100644 --- a/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v +++ b/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v @@ -229,8 +229,6 @@ Qed. (** Sqrt *) -Program Instance sqrt_wd : Proper (eq==>eq) sqrt. - Lemma sqrt_spec : forall n, 0<=n -> (sqrt n)*(sqrt n) <= n /\ n < (succ (sqrt n))*(succ (sqrt n)). Proof. |