diff options
Diffstat (limited to 'theories/Numbers/Natural/SpecViaZ/NSig.v')
| -rw-r--r-- | theories/Numbers/Natural/SpecViaZ/NSig.v | 3 |
1 files changed, 3 insertions, 0 deletions
diff --git a/theories/Numbers/Natural/SpecViaZ/NSig.v b/theories/Numbers/Natural/SpecViaZ/NSig.v index 85639aa6a..3f60cbf1a 100644 --- a/theories/Numbers/Natural/SpecViaZ/NSig.v +++ b/theories/Numbers/Natural/SpecViaZ/NSig.v @@ -51,6 +51,7 @@ Module Type NType. Parameter power_pos : t -> positive -> t. Parameter power : t -> N -> t. Parameter sqrt : t -> t. + Parameter log2 : t -> t. Parameter div_eucl : t -> t -> t * t. Parameter div : t -> t -> t. Parameter modulo : t -> t -> t. @@ -74,6 +75,8 @@ Module Type NType. Parameter spec_power_pos: forall x n, [power_pos x n] = [x] ^ Zpos n. Parameter spec_power: forall x n, [power x n] = [x] ^ Z_of_N n. Parameter spec_sqrt: forall x, [sqrt x] ^ 2 <= [x] < ([sqrt x] + 1) ^ 2. + Parameter spec_log2_0: forall x, [x] = 0 -> [log2 x] = 0. + Parameter spec_log2: forall x, [x]<>0 -> 2^[log2 x] <= [x] < 2^([log2 x]+1). Parameter spec_div_eucl: forall x y, let (q,r) := div_eucl x y in ([q], [r]) = Zdiv_eucl [x] [y]. Parameter spec_div: forall x y, [div x y] = [x] / [y]. |