diff options
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 34b44d3c6..cc57171b3 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 6502cfa55..a828ec821 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 3620045d1..547f51b3d 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. |