diff options
Diffstat (limited to 'theories/Numbers/Integer/SpecViaZ')
| -rw-r--r-- | theories/Numbers/Integer/SpecViaZ/ZSig.v | 2 | ||||
| -rw-r--r-- | theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v | 2 |
2 files changed, 3 insertions, 1 deletions
diff --git a/theories/Numbers/Integer/SpecViaZ/ZSig.v b/theories/Numbers/Integer/SpecViaZ/ZSig.v index a9945e848c..ffa91706f7 100644 --- a/theories/Numbers/Integer/SpecViaZ/ZSig.v +++ b/theories/Numbers/Integer/SpecViaZ/ZSig.v @@ -49,6 +49,7 @@ Module Type ZType. Parameter mul : t -> t -> t. Parameter square : t -> t. Parameter power_pos : t -> positive -> t. + Parameter power : t -> N -> t. Parameter sqrt : t -> t. Parameter div_eucl : t -> t -> t * t. Parameter div : t -> t -> t. @@ -72,6 +73,7 @@ Module Type ZType. Parameter spec_mul: forall x y, [mul x y] = [x] * [y]. Parameter spec_square: forall x, [square x] = [x] * [x]. 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, 0 <= [x] -> [sqrt x] ^ 2 <= [x] < ([sqrt x] + 1) ^ 2. Parameter spec_div_eucl: forall x y, diff --git a/theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v b/theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v index 3d53707eb8..bcecb6a8a2 100644 --- a/theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v +++ b/theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v @@ -255,5 +255,5 @@ Qed. End ZTypeIsZAxioms. Module ZType_ZAxioms (Z : ZType) - <: ZAxiomsSig <: ZDivSig <: HasCompare Z <: HasEqBool Z + <: ZAxiomsSig <: ZDivSig <: HasCompare Z <: HasEqBool Z <: HasMinMax Z := Z <+ ZTypeIsZAxioms. |
