Documentation Verification Report

Basic

πŸ“ Source: Mathlib/Analysis/SpecialFunctions/ContinuousFunctionalCalculus/Rpow/Basic.lean

Statistics

MetricCount
DefinitionsinstPowNNReal, instPowReal, nnrpow, rpow, nnrpow, cfcRpow
6
TheoremsisUnit_nnrpow_iff, isUnit_rpow_iff, isUnit_sqrt_iff, mul_self_eq, mul_self_eq_mul_self_iff, nnrpow_add, nnrpow_def, nnrpow_eq_cfcβ‚™_real, nnrpow_eq_nnrpow_pi, nnrpow_eq_nnrpow_prod, nnrpow_eq_pow, nnrpow_eq_rpow, nnrpow_inv_eq, nnrpow_inv_nnrpow, nnrpow_map_pi, nnrpow_map_prod, nnrpow_nnrpow, nnrpow_nnrpow_inv, nnrpow_nonneg, nnrpow_one, nnrpow_sqrt, nnrpow_sqrt_two, nnrpow_three, nnrpow_two, nnrpow_zero, one_rpow, rpow_add, rpow_algebraMap, rpow_def, rpow_eq_cfc_real, rpow_eq_pow, rpow_eq_rpow_pi, rpow_eq_rpow_prod, rpow_intCast, rpow_inv_rpow, rpow_map_pi, rpow_map_prod, rpow_mul_rpow_neg, rpow_natCast, rpow_neg, rpow_neg_mul_rpow, rpow_neg_one_eq_cfc_inv, rpow_neg_one_eq_inv, rpow_nonneg, rpow_one, rpow_rpow, rpow_rpow_inv, rpow_rpow_of_exponent_nonneg, rpow_sqrt, rpow_sqrt_nnreal, rpow_zero, spectrum_rpow, sq_eq_sq_iff, sq_sqrt, sqrt_algebraMap, sqrt_eq_cfc, sqrt_eq_iff, sqrt_eq_nnrpow, sqrt_eq_one_iff, sqrt_eq_one_iff', sqrt_eq_real_sqrt, sqrt_eq_rpow, sqrt_eq_zero_iff, sqrt_map_pi, sqrt_map_prod, sqrt_mul_self, sqrt_mul_sqrt_self, sqrt_nnrpow, sqrt_nnrpow_two, sqrt_nonneg, sqrt_one, sqrt_rpow, sqrt_rpow_nnreal, sqrt_sq, sqrt_unique, sqrt_zero, zero_nnrpow, zero_rpow, isStrictlyPositive_TFAE, isStrictlyPositive_iff_eq_mul_star_self, isStrictlyPositive_iff_eq_star_mul_self, isStrictlyPositive_iff_exists_isStrictlyPositive_and_eq_mul_self, isStrictlyPositive_iff_exists_isUnit_and_isSelfAdjoint_and_eq_mul_self, isStrictlyPositive_iff_isSelfAdjoint_and_spectrum_pos, isStrictlyPositive_iff_isStrictlyPositive_sqrt_and_eq_sqrt_mul_sqrt, isStrictlyPositive_iff_isUnit_sqrt_and_eq_sqrt_mul_sqrt, nonneg_TFAE, nonneg_iff_eq_mul_star_self, nonneg_iff_eq_sqrt_mul_sqrt, nonneg_iff_eq_star_mul_self, nonneg_iff_exists_isSelfAdjoint_and_eq_mul_self, nonneg_iff_exists_nonneg_and_eq_mul_self, nonneg_iff_isSelfAdjoint_and_negPart_eq_zero, nnrpow, rpow, cfcNNRpow, cfcRpow, cfcSqrt, continuous_nnrpow_const, monotone_nnrpow_const, nnrpow_def, val_cfcRpow, val_inv_cfcRpow
103
Total109

CFC

Definitions

NameCategoryTheorems
instPowNNReal πŸ“–CompOp
36 mathmath: monotone_nnrpow, abs_nnrpow_two, nnrpow_one, abs_nnrpow, nnrpow_sqrt_two, nnrpow_map_pi, nnrpow_def, nnrpow_inv_nnrpow, sqrt_eq_nnrpow, abs_nnrpow_two_mul, IsStrictlyPositive.nnrpow, continuousOn_nnrpow, nnrpow_zero, nnrpow_sqrt, IsUnit.cfcNNRpow, nnrpow_inv_eq, nnrpow_nnrpow, zero_nnrpow, nnrpow_le_nnrpow, nnrpow_eq_pow, nnrpow_eq_nnrpow_pi, nnrpow_three, exists_measure_nnrpow_eq_integral_cfcβ‚™_rpowIntegrand₀₁, sqrt_nnrpow_two, sqrt_nnrpow, nnrpow_eq_cfcβ‚™_real, nnrpow_eq_nnrpow_prod, nnrpow_nnrpow_inv, nnrpow_eq_rpow, nnrpow_nonneg, isUnit_nnrpow_iff, nnnorm_nnrpow, norm_nnrpow, nnrpow_map_prod, nnrpow_two, nnrpow_add
instPowReal πŸ“–CompOp
45 mathmath: IsUnit.cfcRpow, rpow_inv_rpow, Units.val_cfcRpow, rpow_eq_pow, sqrt_rpow, rpow_def, rpow_algebraMap, rpow_one, rpow_neg, sqrt_eq_rpow, rpow_rpow_inv, rpow_rpow, IsStrictlyPositive.rpow, rpow_natCast, rpow_map_prod, rpow_eq_rpow_pi, monotone_rpow, rpow_neg_one_eq_cfc_inv, Units.val_inv_cfcRpow, rpow_neg_one_eq_inv, rpow_le_rpow, rpow_sqrt_nnreal, CStarAlgebra.rpow_neg_one_le_rpow_neg_one, spectrum_rpow, rpow_nonneg, rpow_add, nnnorm_rpow, rpow_intCast, CStarAlgebra.rpow_neg_one_le_one, isUnit_rpow_iff, rpow_rpow_of_exponent_nonneg, one_rpow, sqrt_rpow_nnreal, norm_rpow, rpow_map_pi, nnrpow_eq_rpow, rpow_zero, rpow_neg_mul_rpow, continuousOn_rpow, rpow_eq_rpow_prod, rpow_mul_rpow_neg, conjugate_rpow_neg_one_half, le_iff_norm_sqrt_mul_rpow, rpow_eq_cfc_real, rpow_sqrt
nnrpow πŸ“–CompOp
5 mathmath: nnrpow_map_pi, nnrpow_eq_pow, nnrpow_eq_nnrpow_pi, nnrpow_eq_nnrpow_prod, nnrpow_map_prod
rpow πŸ“–CompOp
6 mathmath: rpow_eq_pow, rpow_map_prod, zero_rpow, rpow_eq_rpow_pi, rpow_map_pi, rpow_eq_rpow_prod

Theorems

NameKindAssumesProvesValidatesDepends On
isUnit_nnrpow_iff πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
IsUnit
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
NNReal
instPowNNReal
Ring.toNonUnitalRing
Algebra.toModule
Real
Real.instCommSemiring
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
IsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalRing.toNonUnitalNonAssocRing
StarRing.toStarAddMonoid
Field.toSemifield
Real.instField
instStarRingReal
Real.metricSpace
IsTopologicalRing.toIsTopologicalSemiring
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
MetricSpace.toPseudoMetricSpace
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
NonUnitalNormedCommRing.toNonUnitalCommRing
NormedCommRing.toNonUnitalNormedCommRing
Real.normedCommRing
instIsTopologicalRingReal
instContinuousStarReal
Real.instCompleteSpace
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
Real.instCompleteSpace
nnrpow_eq_rpow
pos_of_ne_zero
NNReal.instCanonicallyOrderedAdd
isUnit_rpow_iff
Nat.cast_zero
isUnit_rpow_iff πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
IsUnit
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
Real
instPowReal
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Mathlib.Tactic.Nontriviality.subsingleton_or_nontrivial_elim
Unique.instSubsingleton
spectrum.isUnit_of_zero_notMem
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
Nonneg.instContinuousFunctionalCalculus
isUnit_cfc_iff
rpow_def
not_isUnit_zero
cfc_apply_of_not_continuousOn
IsUnit.cfcRpow
isUnit_sqrt_iff πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
IsUnit
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
sqrt
Ring.toNonUnitalRing
Algebra.toModule
Real
Real.instCommSemiring
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
IsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
StarRing.toStarAddMonoid
Field.toSemifield
Real.instField
instStarRingReal
Real.metricSpace
IsTopologicalRing.toIsTopologicalSemiring
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
MetricSpace.toPseudoMetricSpace
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
NonUnitalNormedCommRing.toNonUnitalCommRing
NormedCommRing.toNonUnitalNormedCommRing
Real.normedCommRing
instIsTopologicalRingReal
instContinuousStarReal
Real.instCompleteSpace
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
Real.instCompleteSpace
Nat.instAtLeastTwoHAddOfNat
sqrt_eq_rpow
isUnit_rpow_iff
one_div
RCLike.charZero_rclike
mul_self_eq πŸ“–mathematicalsqrt
Preorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
sqrt_mul_sqrt_self
mul_self_eq_mul_self_iff πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
sqrt_unique
sqrt_mul_self
nnrpow_add πŸ“–mathematicalNNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderNNReal
instZeroNNReal
instPowNNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
instSemiringNNReal
Distrib.toMul
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
NNReal.instIsScalarTowerOfReal
NNReal.smulCommClass_left
Nonneg.instNonUnitalContinuousFunctionalCalculus
cfcβ‚™_mul
NNReal.continuousOn_rpow_const
NNReal.rpow_add'
ne_of_gt
add_pos
IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono
AddLeftCancelSemigroup.toIsLeftCancelAdd
IsOrderedAddMonoid.toAddLeftMono
Real.instIsOrderedAddMonoid
nnrpow_def πŸ“–mathematicalβ€”NNReal
instPowNNReal
cfcβ‚™
Preorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
instCommSemiringNNReal
instNontrivialNNReal
instStarRingNNReal
instMetricSpaceNNReal
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
NNReal.instModuleOfReal
NonUnitalNonAssocSemiring.toAddCommMonoid
NNReal.instIsScalarTowerOfReal
DistribMulAction.toMulAction
Real
Real.instMonoid
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
Real.semiring
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
NonUnitalNonAssocRing.toAddCommGroup
DistribSMul.toSMulZeroClass
NonUnitalNonAssocSemiring.toDistribSMul
NNReal.smulCommClass_left
Nonneg.instNonUnitalContinuousFunctionalCalculus
NNReal.nnrpow
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
nnrpow_eq_cfcβ‚™_real πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
NNReal
instPowNNReal
cfcβ‚™
Real
IsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
StarRing.toStarAddMonoid
Real.instCommSemiring
Real.instNontrivial
instStarRingReal
Real.metricSpace
IsTopologicalRing.toIsTopologicalSemiring
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
MetricSpace.toPseudoMetricSpace
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
NonUnitalNormedCommRing.toNonUnitalCommRing
NormedCommRing.toNonUnitalNormedCommRing
Real.normedCommRing
instIsTopologicalRingReal
instContinuousStarReal
Real.instPow
NNReal.toReal
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
NNReal.instIsScalarTowerOfReal
NNReal.smulCommClass_left
Nonneg.instNonUnitalContinuousFunctionalCalculus
nnrpow_def
cfcβ‚™_nnreal_eq_real
cfcβ‚™_congr
sup_of_le_left
nnrpow_eq_nnrpow_pi πŸ“–mathematicalStarOrderedRing
NonUnitalRing.toNonUnitalSemiring
SMulCommClass
Real
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
NonUnitalNonAssocRing.toAddCommGroup
NonUnitalRing.toNonUnitalNonAssocRing
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
Real.instMonoid
Module.toDistribMulAction
Real.semiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocSemiring.toDistribSMul
IsScalarTower
NonUnitalContinuousFunctionalCalculus
IsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
StarRing.toStarAddMonoid
Real.instCommSemiring
Real.instNontrivial
instStarRingReal
Real.metricSpace
IsTopologicalRing.toIsTopologicalSemiring
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
MetricSpace.toPseudoMetricSpace
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
NonUnitalNormedCommRing.toNonUnitalCommRing
NormedCommRing.toNonUnitalNormedCommRing
Real.normedCommRing
instIsTopologicalRingReal
instContinuousStarReal
IsTopologicalRing
T2Space
NonnegSpectrumClass
Real.partialOrder
nnrpow
Pi.partialOrder
Pi.nonUnitalRing
Pi.topologicalSpace
Pi.instStarRingForall
Pi.module
Pi.smulCommClass'
SemigroupAction.toSMul
Monoid.toSemigroup
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
MulAction.toSemigroupAction
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
Pi.isScalarTower'
NNReal
Pi.instPow
instPowNNReal
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Pi.isScalarTower'
Pi.smulCommClass'
nnrpow_map_pi
nnrpow_eq_nnrpow_prod πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
nnrpow
Prod.instPartialOrder
Prod.instNonUnitalRing
instTopologicalSpaceProd
Prod.instStarRing
Prod.instModule
Real
Real.semiring
NonUnitalNonAssocSemiring.toAddCommMonoid
Prod.smulCommClassBoth
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
SemigroupAction.toSMul
Monoid.toSemigroup
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
MulAction.toSemigroupAction
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
Prod.isScalarTowerBoth
Prod.instStarOrderedRing
NonUnitalRing.toNonUnitalSemiring
NNReal
Prod.instPow
instPowNNReal
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Prod.isScalarTowerBoth
Prod.smulCommClassBoth
nnrpow_map_prod
nnrpow_eq_pow πŸ“–mathematicalβ€”nnrpow
NNReal
instPowNNReal
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
nnrpow_eq_rpow πŸ“–mathematicalNNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderNNReal
instZeroNNReal
instPowNNReal
Ring.toNonUnitalRing
Algebra.toModule
Real
Real.instCommSemiring
Ring.toSemiring
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
IsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
StarRing.toStarAddMonoid
Field.toSemifield
Real.instField
instStarRingReal
Real.metricSpace
IsTopologicalRing.toIsTopologicalSemiring
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
MetricSpace.toPseudoMetricSpace
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
NonUnitalNormedCommRing.toNonUnitalCommRing
NormedCommRing.toNonUnitalNormedCommRing
Real.normedCommRing
instIsTopologicalRingReal
instContinuousStarReal
Real.instCompleteSpace
instPowReal
NNReal.toReal
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
Real.instCompleteSpace
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
NNReal.instIsScalarTowerOfReal
NNReal.smulCommClass_left
Nonneg.instNonUnitalContinuousFunctionalCalculus
nnrpow_def
Nonneg.instContinuousFunctionalCalculus
rpow_def
IsDomain.toNontrivial
instIsDomain
NNReal.instCompleteSpace
cfcβ‚™_eq_cfc
NNReal.instContinuousMapZero.UniqueHom
NNReal.continuousOn_rpow_const
nnrpow_inv_eq πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
NNReal
instPowNNReal
NNReal.instInv
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
nnrpow_inv_nnrpow
nnrpow_nnrpow_inv
nnrpow_inv_nnrpow πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
NNReal
instPowNNReal
NNReal.instInv
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
nnrpow_nnrpow
inv_mul_cancelβ‚€
nnrpow_one
nnrpow_map_pi πŸ“–mathematicalStarOrderedRing
NonUnitalRing.toNonUnitalSemiring
SMulCommClass
Real
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
NonUnitalNonAssocRing.toAddCommGroup
NonUnitalRing.toNonUnitalNonAssocRing
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
Real.instMonoid
Module.toDistribMulAction
Real.semiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocSemiring.toDistribSMul
IsScalarTower
NonUnitalContinuousFunctionalCalculus
IsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
StarRing.toStarAddMonoid
Real.instCommSemiring
Real.instNontrivial
instStarRingReal
Real.metricSpace
IsTopologicalRing.toIsTopologicalSemiring
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
MetricSpace.toPseudoMetricSpace
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
NonUnitalNormedCommRing.toNonUnitalCommRing
NormedCommRing.toNonUnitalNormedCommRing
Real.normedCommRing
instIsTopologicalRingReal
instContinuousStarReal
IsTopologicalRing
T2Space
NonnegSpectrumClass
Real.partialOrder
nnrpow
Pi.partialOrder
Pi.nonUnitalRing
Pi.topologicalSpace
Pi.instStarRingForall
Pi.module
Pi.smulCommClass'
SemigroupAction.toSMul
Monoid.toSemigroup
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
MulAction.toSemigroupAction
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
Pi.isScalarTower'
NNReal
instPowNNReal
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Pi.isScalarTower'
Pi.smulCommClass'
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
NNReal.instIsScalarTowerOfReal
NNReal.smulCommClass_left
Nonneg.instNonUnitalContinuousFunctionalCalculus
cfcβ‚™_map_pi
IsScalarTower.left
NNReal.instContinuousMapZero.UniqueHom
NNReal.continuousOn_rpow_const
nnrpow_map_prod πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
nnrpow
Prod.instPartialOrder
Prod.instNonUnitalRing
instTopologicalSpaceProd
Prod.instStarRing
Prod.instModule
Real
Real.semiring
NonUnitalNonAssocSemiring.toAddCommMonoid
Prod.smulCommClassBoth
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
SemigroupAction.toSMul
Monoid.toSemigroup
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
MulAction.toSemigroupAction
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
Prod.isScalarTowerBoth
Prod.instStarOrderedRing
NonUnitalRing.toNonUnitalSemiring
NNReal
instPowNNReal
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Prod.isScalarTowerBoth
Prod.smulCommClassBoth
Prod.instStarOrderedRing
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
NNReal.instIsScalarTowerOfReal
NNReal.smulCommClass_left
Nonneg.instNonUnitalContinuousFunctionalCalculus
cfcβ‚™_map_prod
IsScalarTower.left
NNReal.instContinuousMapZero.UniqueHom
Continuous.continuousOn
NNReal.continuous_nnrpow_const
Prod.le_def
nnrpow_nnrpow πŸ“–mathematicalβ€”NNReal
instPowNNReal
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
instSemiringNNReal
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
eq_zero_or_pos
NNReal.instCanonicallyOrderedAdd
nnrpow_zero
MulZeroClass.mul_zero
zero_nnrpow
MulZeroClass.zero_mul
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
NNReal.instIsScalarTowerOfReal
NNReal.smulCommClass_left
Nonneg.instNonUnitalContinuousFunctionalCalculus
cfcβ‚™_comp
NNReal.instContinuousMapZero.UniqueHom
NNReal.continuousOn_rpow_const
Set.image_congr
NNReal.eq
Real.rpow_mul
cfcβ‚™_apply_of_not_predicate
cfcβ‚™_apply_zero
nnrpow_nnrpow_inv πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
NNReal
instPowNNReal
NNReal.instInv
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
nnrpow_nnrpow
mul_inv_cancelβ‚€
nnrpow_one
nnrpow_nonneg πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
NNReal
instPowNNReal
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
cfcβ‚™_predicate
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
Nonneg.instNonUnitalContinuousFunctionalCalculus
nnrpow_one πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
NNReal
instPowNNReal
instOneNNReal
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
NNReal.instIsScalarTowerOfReal
NNReal.smulCommClass_left
Nonneg.instNonUnitalContinuousFunctionalCalculus
cfcβ‚™.congr_simp
NNReal.rpow_one
cfcβ‚™_id
nnrpow_sqrt πŸ“–mathematicalβ€”NNReal
instPowNNReal
sqrt
NNReal.instDiv
instOfNatAtLeastTwo
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
instSemiringNNReal
Nat.instAtLeastTwoHAddOfNat
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Nat.instAtLeastTwoHAddOfNat
sqrt_eq_nnrpow
nnrpow_nnrpow
one_div_mul_eq_div
nnrpow_sqrt_two πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
NNReal
instPowNNReal
sqrt
instOfNatAtLeastTwo
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
instSemiringNNReal
Nat.instAtLeastTwoHAddOfNat
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Nat.instAtLeastTwoHAddOfNat
nnrpow_sqrt
div_self
IsStrictOrderedRing.toCharZero
NNReal.instIsStrictOrderedRing
nnrpow_one
nnrpow_three πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
NNReal
instPowNNReal
instOfNatAtLeastTwo
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
instSemiringNNReal
Nat.instAtLeastTwoHAddOfNat
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Nat.instAtLeastTwoHAddOfNat
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
NNReal.instIsScalarTowerOfReal
NNReal.smulCommClass_left
Nonneg.instNonUnitalContinuousFunctionalCalculus
cfcβ‚™.congr_simp
NNReal.rpow_ofNat
pow_three
cfcβ‚™_mul
continuousOn_id'
ContinuousOn.fun_mul
IsTopologicalSemiring.toContinuousMul
MulZeroClass.mul_zero
mul_assoc
cfcβ‚™_id
nnrpow_two πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
NNReal
instPowNNReal
instOfNatAtLeastTwo
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
instSemiringNNReal
Nat.instAtLeastTwoHAddOfNat
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Nat.instAtLeastTwoHAddOfNat
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
NNReal.instIsScalarTowerOfReal
NNReal.smulCommClass_left
Nonneg.instNonUnitalContinuousFunctionalCalculus
cfcβ‚™.congr_simp
NNReal.rpow_ofNat
pow_two
cfcβ‚™_mul
continuousOn_id'
cfcβ‚™_id
nnrpow_zero πŸ“–mathematicalβ€”NNReal
instPowNNReal
instZeroNNReal
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
NNReal.instIsScalarTowerOfReal
NNReal.smulCommClass_left
Nonneg.instNonUnitalContinuousFunctionalCalculus
cfcβ‚™.congr_simp
NNReal.rpow_zero
cfcβ‚™_apply_of_not_map_zero
NeZero.charZero_one
IsStrictOrderedRing.toCharZero
NNReal.instIsStrictOrderedRing
one_rpow πŸ“–mathematicalβ€”Real
instPowReal
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
Nonneg.instContinuousFunctionalCalculus
cfc_apply_one
NNReal.one_rpow
map_one
MonoidHomClass.toOneHomClass
MonoidWithZeroHomClass.toMonoidHomClass
RingHomClass.toMonoidWithZeroHomClass
RingHom.instRingHomClass
rpow_add πŸ“–mathematicalIsUnit
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
Real
instPowReal
Real.instAdd
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
spectrum.zero_notMem
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
Nonneg.instContinuousFunctionalCalculus
cfc_mul
NNReal.continuousOn_rpow_const
cfc_congr
NNReal.rpow_add
rpow_algebraMap πŸ“–mathematicalβ€”Real
instPowReal
DFunLike.coe
RingHom
NNReal
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNReal
Ring.toSemiring
RingHom.instFunLike
algebraMap
NNReal.instAlgebraOfReal
NNReal.instPowReal
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
Nonneg.instContinuousFunctionalCalculus
rpow_def
cfc_algebraMap
rpow_def πŸ“–mathematicalβ€”Real
instPowReal
cfc
NNReal
Preorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
instCommSemiringNNReal
instStarRingNNReal
instMetricSpaceNNReal
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
NNReal.instAlgebraOfReal
Ring.toSemiring
Nonneg.instContinuousFunctionalCalculus
NNReal.instPowReal
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
rpow_eq_cfc_real πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Real
instPowReal
cfc
IsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
StarRing.toStarAddMonoid
Real.instCommSemiring
instStarRingReal
Real.metricSpace
IsTopologicalRing.toIsTopologicalSemiring
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
MetricSpace.toPseudoMetricSpace
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
NonUnitalNormedCommRing.toNonUnitalCommRing
NormedCommRing.toNonUnitalNormedCommRing
Real.normedCommRing
instIsTopologicalRingReal
instContinuousStarReal
Real.instPow
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
Nonneg.instContinuousFunctionalCalculus
rpow_def
cfc_nnreal_eq_real
cfc_congr
rpow_eq_pow πŸ“–mathematicalβ€”rpow
Real
instPowReal
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
rpow_eq_rpow_pi πŸ“–mathematicalStarOrderedRing
Semiring.toNonUnitalSemiring
Ring.toSemiring
ContinuousFunctionalCalculus
Real
IsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
StarRing.toStarAddMonoid
Real.instCommSemiring
instStarRingReal
Real.metricSpace
IsTopologicalRing.toIsTopologicalSemiring
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
MetricSpace.toPseudoMetricSpace
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
NonUnitalNormedCommRing.toNonUnitalCommRing
NormedCommRing.toNonUnitalNormedCommRing
Real.normedCommRing
instIsTopologicalRingReal
instContinuousStarReal
IsTopologicalRing
T2Space
NonnegSpectrumClass
Real.partialOrder
Ring.toNonUnitalRing
Algebra.toModule
IsUnit
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
rpow
Pi.partialOrder
Pi.ring
Pi.instStarRingForall
Pi.topologicalSpace
Pi.algebra
Pi.instPow
instPowReal
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
rpow_map_pi
rpow_eq_rpow_prod πŸ“–mathematicalIsUnit
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
rpow
Prod.instPartialOrder
Prod.instRing
Prod.instStarRing
instTopologicalSpaceProd
Prod.algebra
Real
Real.instCommSemiring
Prod.instPow
instPowReal
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
rpow_map_prod
rpow_intCast πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Units.val
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
Real
instPowReal
Real.instIntCast
Units
DivInvMonoid.toZPow
Units.instDivInvMonoid
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
Nonneg.instContinuousFunctionalCalculus
cfc_zpow
NNReal.instContinuousInvβ‚€
rpow_def
cfc_congr
NNReal.rpow_intCast
rpow_inv_rpow πŸ“–mathematicalIsUnit
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Real
instPowReal
Real.instInv
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
inv_inv
rpow_rpow_inv
inv_ne_zero
rpow_map_pi πŸ“–mathematicalStarOrderedRing
Semiring.toNonUnitalSemiring
Ring.toSemiring
ContinuousFunctionalCalculus
Real
IsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
StarRing.toStarAddMonoid
Real.instCommSemiring
instStarRingReal
Real.metricSpace
IsTopologicalRing.toIsTopologicalSemiring
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
MetricSpace.toPseudoMetricSpace
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
NonUnitalNormedCommRing.toNonUnitalCommRing
NormedCommRing.toNonUnitalNormedCommRing
Real.normedCommRing
instIsTopologicalRingReal
instContinuousStarReal
IsTopologicalRing
T2Space
NonnegSpectrumClass
Real.partialOrder
Ring.toNonUnitalRing
Algebra.toModule
IsUnit
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
rpow
Pi.partialOrder
Pi.ring
Pi.instStarRingForall
Pi.topologicalSpace
Pi.algebra
instPowReal
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
spectrum.zero_notMem
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
Nonneg.instContinuousFunctionalCalculus
cfc_map_pi
NNReal.instIsScalarTowerOfReal
IsScalarTower.left
Pi.isScalarTower
NNReal.instContinuousMap.UniqueHom
NNReal.continuousOn_rpow_const
rpow_map_prod πŸ“–mathematicalIsUnit
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
rpow
Prod.instPartialOrder
Prod.instRing
Prod.instStarRing
instTopologicalSpaceProd
Prod.algebra
Real
Real.instCommSemiring
instPowReal
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
spectrum.zero_notMem
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
Nonneg.instContinuousFunctionalCalculus
cfc_map_prod
NNReal.instIsScalarTowerOfReal
IsScalarTower.left
NNReal.instContinuousMap.UniqueHom
NNReal.continuousOn_rpow_const
Prod.le_def
rpow_mul_rpow_neg πŸ“–mathematicalIsUnit
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
Real
instPowReal
Real.instNeg
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
rpow_add
add_neg_cancel
rpow_zero
rpow_natCast πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Real
instPowReal
Real.instNatCast
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
Nonneg.instContinuousFunctionalCalculus
cfc_pow_id
rpow_def
NNReal.rpow_natCast
rpow_neg πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Units.val
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
Real
instPowReal
Real.instNeg
Units
Units.instInv
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
NNReal.continuousOn_rpow_const
spectrum.zero_notMem
Units.isUnit
inv_eq_zero
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
Nonneg.instContinuousFunctionalCalculus
cfc_inv_id
NNReal.instContinuousInvβ‚€
rpow_def
cfc_comp'
NNReal.instContinuousMap.UniqueHom
Units.continuousOn_invβ‚€_spectrum
cfc_congr
NNReal.rpow_neg
NNReal.inv_rpow
rpow_neg_mul_rpow πŸ“–mathematicalIsUnit
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
Real
instPowReal
Real.instNeg
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
rpow_add
neg_add_cancel
rpow_zero
rpow_neg_one_eq_cfc_inv πŸ“–mathematicalβ€”Real
instPowReal
NormedRing.toRing
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedRing.toPseudoMetricSpace
NormedRing.toSeminormedRing
NormedAlgebra.toAlgebra
Real.normedField
Real.instNeg
Real.instOne
cfc
NNReal
Preorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
instCommSemiringNNReal
instStarRingNNReal
instMetricSpaceNNReal
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
NNReal.instAlgebraOfReal
Ring.toSemiring
Nonneg.instContinuousFunctionalCalculus
NNReal.instInv
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
cfc_congr
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
Nonneg.instContinuousFunctionalCalculus
NNReal.rpow_neg_one
rpow_neg_one_eq_inv πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Units.val
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
Real
instPowReal
Real.instNeg
Real.instOne
Units
Units.instInv
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Units.inv_eq_of_mul_eq_one_left
rpow_one
rpow_neg_mul_rpow
Units.isUnit
rpow_nonneg πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Real
instPowReal
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
cfc_predicate
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
Nonneg.instContinuousFunctionalCalculus
rpow_one πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Real
instPowReal
Real.instOne
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
Nonneg.instContinuousFunctionalCalculus
cfc.congr_simp
NNReal.rpow_one
cfc_id'
rpow_rpow πŸ“–mathematicalIsUnit
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Real
instPowReal
Real.instMul
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
spectrum.zero_notMem
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
Nonneg.instContinuousFunctionalCalculus
cfc_comp
NNReal.instContinuousMap.UniqueHom
NNReal.continuousOn_rpow_const
cfc_congr
NNReal.rpow_mul
rpow_rpow_inv πŸ“–mathematicalIsUnit
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Real
instPowReal
Real.instInv
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
rpow_rpow
mul_inv_cancelβ‚€
rpow_one
rpow_rpow_of_exponent_nonneg πŸ“–mathematicalReal
Real.instLE
Real.instZero
Preorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
instPowReal
Real.instMul
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
Nonneg.instContinuousFunctionalCalculus
cfc_comp
NNReal.instContinuousMap.UniqueHom
NNReal.continuousOn_rpow_const
cfc_congr
NNReal.rpow_mul
rpow_sqrt πŸ“–mathematicalIsUnit
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Real
instPowReal
sqrt
Ring.toNonUnitalRing
Algebra.toModule
Real.instCommSemiring
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
IsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
StarRing.toStarAddMonoid
Field.toSemifield
Real.instField
instStarRingReal
Real.metricSpace
IsTopologicalRing.toIsTopologicalSemiring
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
MetricSpace.toPseudoMetricSpace
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
NonUnitalNormedCommRing.toNonUnitalCommRing
NormedCommRing.toNonUnitalNormedCommRing
Real.normedCommRing
instIsTopologicalRingReal
instContinuousStarReal
Real.instCompleteSpace
DivInvMonoid.toDiv
Real.instDivInvMonoid
instOfNatAtLeastTwo
Real.instNatCast
Nat.instAtLeastTwoHAddOfNat
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
Real.instCompleteSpace
Nat.instAtLeastTwoHAddOfNat
sqrt_eq_rpow
div_eq_mul_inv
one_mul
rpow_rpow
RCLike.charZero_rclike
inv_mul_eq_div
rpow_sqrt_nnreal πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Real
instPowReal
sqrt
Ring.toNonUnitalRing
Algebra.toModule
Real.instCommSemiring
Ring.toSemiring
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
IsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
StarRing.toStarAddMonoid
Field.toSemifield
Real.instField
instStarRingReal
Real.metricSpace
IsTopologicalRing.toIsTopologicalSemiring
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
MetricSpace.toPseudoMetricSpace
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
NonUnitalNormedCommRing.toNonUnitalCommRing
NormedCommRing.toNonUnitalNormedCommRing
Real.normedCommRing
instIsTopologicalRingReal
instContinuousStarReal
Real.instCompleteSpace
NNReal.toReal
DivInvMonoid.toDiv
Real.instDivInvMonoid
instOfNatAtLeastTwo
Real.instNatCast
Nat.instAtLeastTwoHAddOfNat
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
Real.instCompleteSpace
Nat.instAtLeastTwoHAddOfNat
sqrt_nonneg
rpow_zero
zero_div
NNReal.zero_le_coe
sqrt_eq_rpow
rpow_rpow_of_exponent_nonneg
one_div
PosMulReflectLE.toPosMulReflectLT
PosMulStrictMono.toPosMulReflectLE
IsStrictOrderedRing.toPosMulStrictMono
Real.instIsStrictOrderedRing
Real.instIsOrderedRing
one_div_mul_eq_div
rpow_zero πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Real
instPowReal
Real.instZero
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
Nonneg.instContinuousFunctionalCalculus
cfc.congr_simp
NNReal.rpow_zero
cfc_const_one
spectrum_rpow πŸ“–mathematicalContinuousOn
NNReal
NNReal.instTopologicalSpace
Real
NNReal.instPowReal
spectrum
instCommSemiringNNReal
NNReal.instAlgebraOfReal
Ring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
instPowReal
Set.image
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
cfc_map_spectrum
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
Nonneg.instContinuousFunctionalCalculus
sq_eq_sq_iff πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
sq
mul_self_eq_mul_self_iff
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
Real.instCompleteSpace
sq_sqrt πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
sqrt
Ring.toNonUnitalRing
Algebra.toModule
Real
Real.instCommSemiring
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
IsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
StarRing.toStarAddMonoid
Field.toSemifield
Real.instField
instStarRingReal
Real.metricSpace
IsTopologicalRing.toIsTopologicalSemiring
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
MetricSpace.toPseudoMetricSpace
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
NonUnitalNormedCommRing.toNonUnitalCommRing
NormedCommRing.toNonUnitalNormedCommRing
Real.normedCommRing
instIsTopologicalRingReal
instContinuousStarReal
Real.instCompleteSpace
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
Real.instCompleteSpace
pow_two
sqrt_mul_sqrt_self
sqrt_algebraMap πŸ“–mathematicalβ€”sqrt
Ring.toNonUnitalRing
Algebra.toModule
Real
Real.instCommSemiring
Ring.toSemiring
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
IsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
StarRing.toStarAddMonoid
Field.toSemifield
Real.instField
instStarRingReal
Real.metricSpace
IsTopologicalRing.toIsTopologicalSemiring
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
MetricSpace.toPseudoMetricSpace
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
NonUnitalNormedCommRing.toNonUnitalCommRing
NormedCommRing.toNonUnitalNormedCommRing
Real.normedCommRing
instIsTopologicalRingReal
instContinuousStarReal
Real.instCompleteSpace
DFunLike.coe
RingHom
NNReal
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNReal
RingHom.instFunLike
algebraMap
NNReal.instAlgebraOfReal
OrderIso
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderNNReal
instFunLikeOrderIso
NNReal.sqrt
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
Real.instCompleteSpace
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
Nonneg.instContinuousFunctionalCalculus
sqrt_eq_cfc
cfc_algebraMap
sqrt_eq_cfc πŸ“–mathematicalβ€”sqrt
Ring.toNonUnitalRing
Algebra.toModule
Real
Real.instCommSemiring
Ring.toSemiring
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
IsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
StarRing.toStarAddMonoid
Field.toSemifield
Real.instField
instStarRingReal
Real.metricSpace
IsTopologicalRing.toIsTopologicalSemiring
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
MetricSpace.toPseudoMetricSpace
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
NonUnitalNormedCommRing.toNonUnitalCommRing
NormedCommRing.toNonUnitalNormedCommRing
Real.normedCommRing
instIsTopologicalRingReal
instContinuousStarReal
Real.instCompleteSpace
cfc
NNReal
Preorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
instCommSemiringNNReal
instStarRingNNReal
instMetricSpaceNNReal
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
NNReal.instAlgebraOfReal
Nonneg.instContinuousFunctionalCalculus
DFunLike.coe
OrderIso
instPartialOrderNNReal
instFunLikeOrderIso
NNReal.sqrt
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
Real.instCompleteSpace
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
Nonneg.instContinuousFunctionalCalculus
Nonneg.instNonUnitalContinuousFunctionalCalculus
IsDomain.toNontrivial
instIsDomain
NNReal.instCompleteSpace
cfcβ‚™_eq_cfc
NNReal.instContinuousMapZero.UniqueHom
Continuous.continuousOn
NNReal.continuous_sqrt
NNReal.sqrt_zero
sqrt_eq_iff πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
sqrt
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
mul_self_eq
sqrt_unique
sqrt_eq_nnrpow πŸ“–mathematicalβ€”sqrt
NNReal
instPowNNReal
NNReal.instDiv
instOneNNReal
instOfNatAtLeastTwo
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
instSemiringNNReal
Nat.instAtLeastTwoHAddOfNat
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Nat.instAtLeastTwoHAddOfNat
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
Nonneg.instNonUnitalContinuousFunctionalCalculus
NNReal.eq
Nat.cast_one
NNReal.sqrt_eq_rpow
sqrt_eq_one_iff πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
sqrt
Ring.toNonUnitalRing
Algebra.toModule
Real
Real.instCommSemiring
Ring.toSemiring
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
IsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
StarRing.toStarAddMonoid
Field.toSemifield
Real.instField
instStarRingReal
Real.metricSpace
IsTopologicalRing.toIsTopologicalSemiring
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
MetricSpace.toPseudoMetricSpace
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
NonUnitalNormedCommRing.toNonUnitalCommRing
NormedCommRing.toNonUnitalNormedCommRing
Real.normedCommRing
instIsTopologicalRingReal
instContinuousStarReal
Real.instCompleteSpace
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
Real.instCompleteSpace
sqrt_eq_iff
instZeroLEOneClass
mul_one
sqrt_eq_one_iff' πŸ“–mathematicalβ€”sqrt
Ring.toNonUnitalRing
Algebra.toModule
Real
Real.instCommSemiring
Ring.toSemiring
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
IsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
StarRing.toStarAddMonoid
Field.toSemifield
Real.instField
instStarRingReal
Real.metricSpace
IsTopologicalRing.toIsTopologicalSemiring
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
MetricSpace.toPseudoMetricSpace
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
NonUnitalNormedCommRing.toNonUnitalCommRing
NormedCommRing.toNonUnitalNormedCommRing
Real.normedCommRing
instIsTopologicalRingReal
instContinuousStarReal
Real.instCompleteSpace
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
Real.instCompleteSpace
sqrt_eq_one_iff
NeZero.one
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
Nonneg.instNonUnitalContinuousFunctionalCalculus
cfcβ‚™_def
sqrt.eq_1
sqrt_one
sqrt_eq_real_sqrt πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
sqrt
cfcβ‚™
Real
IsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
StarRing.toStarAddMonoid
Real.instCommSemiring
Real.instNontrivial
instStarRingReal
Real.metricSpace
IsTopologicalRing.toIsTopologicalSemiring
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
MetricSpace.toPseudoMetricSpace
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
NonUnitalNormedCommRing.toNonUnitalCommRing
NormedCommRing.toNonUnitalNormedCommRing
Real.normedCommRing
instIsTopologicalRingReal
instContinuousStarReal
Real.sqrt
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
cfcβ‚™_congr
Real.mul_self_sqrt
NonnegSpectrumClass.quasispectrum_nonneg_of_nonneg
sqrt_eq_iff
cfcβ‚™_nonneg
Real.instStarOrderedRing
NormMulClass.toNoZeroDivisors
NormedDivisionRing.toNormMulClass
Real.sqrt_nonneg
cfcβ‚™_id'
IsSelfAdjoint.of_nonneg
cfcβ‚™_mul
ContinuousOn.sqrt
continuousOn_id'
Real.sqrt_zero
sqrt_eq_rpow πŸ“–mathematicalβ€”sqrt
Ring.toNonUnitalRing
Algebra.toModule
Real
Real.instCommSemiring
Ring.toSemiring
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
IsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
StarRing.toStarAddMonoid
Field.toSemifield
Real.instField
instStarRingReal
Real.metricSpace
IsTopologicalRing.toIsTopologicalSemiring
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
MetricSpace.toPseudoMetricSpace
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
NonUnitalNormedCommRing.toNonUnitalCommRing
NormedCommRing.toNonUnitalNormedCommRing
Real.normedCommRing
instIsTopologicalRingReal
instContinuousStarReal
Real.instCompleteSpace
instPowReal
DivInvMonoid.toDiv
Real.instDivInvMonoid
Real.instOne
instOfNatAtLeastTwo
Real.instNatCast
Nat.instAtLeastTwoHAddOfNat
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Nat.instAtLeastTwoHAddOfNat
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
Real.instCompleteSpace
nnrpow_eq_rpow
one_div
PosMulReflectLE.toPosMulReflectLT
PosMulStrictMono.toPosMulReflectLE
LinearOrderedCommMonoidWithZero.toPosMulStrictMono
NNReal.instIsOrderedRing
sqrt_eq_nnrpow
sqrt_eq_zero_iff πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
sqrtβ€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
sqrt_eq_iff
MulZeroClass.mul_zero
sqrt_map_pi πŸ“–mathematicalStarOrderedRing
NonUnitalRing.toNonUnitalSemiring
SMulCommClass
Real
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
NonUnitalNonAssocRing.toAddCommGroup
NonUnitalRing.toNonUnitalNonAssocRing
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
Real.instMonoid
Module.toDistribMulAction
Real.semiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocSemiring.toDistribSMul
IsScalarTower
NonUnitalContinuousFunctionalCalculus
IsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
StarRing.toStarAddMonoid
Real.instCommSemiring
Real.instNontrivial
instStarRingReal
Real.metricSpace
IsTopologicalRing.toIsTopologicalSemiring
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
MetricSpace.toPseudoMetricSpace
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
NonUnitalNormedCommRing.toNonUnitalCommRing
NormedCommRing.toNonUnitalNormedCommRing
Real.normedCommRing
instIsTopologicalRingReal
instContinuousStarReal
IsTopologicalRing
T2Space
NonnegSpectrumClass
Real.partialOrder
sqrt
Pi.partialOrder
Pi.nonUnitalRing
Pi.topologicalSpace
Pi.instStarRingForall
Pi.module
Pi.smulCommClass'
SemigroupAction.toSMul
Monoid.toSemigroup
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
MulAction.toSemigroupAction
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
Pi.isScalarTower'
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Pi.isScalarTower'
Pi.smulCommClass'
Nat.instAtLeastTwoHAddOfNat
sqrt_eq_nnrpow
nnrpow_map_pi
sqrt_map_prod πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
sqrt
Prod.instPartialOrder
Prod.instNonUnitalRing
instTopologicalSpaceProd
Prod.instStarRing
Prod.instModule
Real
Real.semiring
NonUnitalNonAssocSemiring.toAddCommMonoid
Prod.smulCommClassBoth
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
SemigroupAction.toSMul
Monoid.toSemigroup
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
MulAction.toSemigroupAction
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
Prod.isScalarTowerBoth
Prod.instStarOrderedRing
NonUnitalRing.toNonUnitalSemiring
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Prod.isScalarTowerBoth
Prod.smulCommClassBoth
Prod.instStarOrderedRing
Nat.instAtLeastTwoHAddOfNat
sqrt_eq_nnrpow
nnrpow_map_prod
sqrt_mul_self πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
sqrt
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Nat.instAtLeastTwoHAddOfNat
nnrpow_two
sqrt_nnrpow_two
sqrt_mul_sqrt_self πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
sqrt
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Nat.instAtLeastTwoHAddOfNat
nnrpow_two
nnrpow_sqrt_two
sqrt_nnrpow πŸ“–mathematicalβ€”sqrt
NNReal
instPowNNReal
NNReal.instDiv
instOfNatAtLeastTwo
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
instSemiringNNReal
Nat.instAtLeastTwoHAddOfNat
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Nat.instAtLeastTwoHAddOfNat
sqrt_eq_nnrpow
div_eq_mul_inv
one_mul
nnrpow_nnrpow
sqrt_nnrpow_two πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
sqrt
NNReal
instPowNNReal
instOfNatAtLeastTwo
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
instSemiringNNReal
Nat.instAtLeastTwoHAddOfNat
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Nat.instAtLeastTwoHAddOfNat
sqrt_nnrpow
div_self
IsStrictOrderedRing.toCharZero
NNReal.instIsStrictOrderedRing
nnrpow_one
sqrt_nonneg πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
sqrt
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
cfcβ‚™_predicate
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
Nonneg.instNonUnitalContinuousFunctionalCalculus
sqrt_one πŸ“–mathematicalβ€”sqrt
Ring.toNonUnitalRing
Algebra.toModule
Real
Real.instCommSemiring
Ring.toSemiring
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
IsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
StarRing.toStarAddMonoid
Field.toSemifield
Real.instField
instStarRingReal
Real.metricSpace
IsTopologicalRing.toIsTopologicalSemiring
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
MetricSpace.toPseudoMetricSpace
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
NonUnitalNormedCommRing.toNonUnitalCommRing
NormedCommRing.toNonUnitalNormedCommRing
Real.normedCommRing
instIsTopologicalRingReal
instContinuousStarReal
Real.instCompleteSpace
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
Real.instCompleteSpace
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
Nonneg.instContinuousFunctionalCalculus
sqrt_eq_cfc
cfc_apply_one
NNReal.sqrt_one
map_one
MonoidHomClass.toOneHomClass
MonoidWithZeroHomClass.toMonoidHomClass
RingHomClass.toMonoidWithZeroHomClass
RingHom.instRingHomClass
sqrt_rpow πŸ“–mathematicalIsUnit
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
sqrt
Ring.toNonUnitalRing
Algebra.toModule
Real
Real.instCommSemiring
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
IsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
StarRing.toStarAddMonoid
Field.toSemifield
Real.instField
instStarRingReal
Real.metricSpace
IsTopologicalRing.toIsTopologicalSemiring
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
MetricSpace.toPseudoMetricSpace
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
NonUnitalNormedCommRing.toNonUnitalCommRing
NormedCommRing.toNonUnitalNormedCommRing
Real.normedCommRing
instIsTopologicalRingReal
instContinuousStarReal
Real.instCompleteSpace
instPowReal
DivInvMonoid.toDiv
Real.instDivInvMonoid
instOfNatAtLeastTwo
Real.instNatCast
Nat.instAtLeastTwoHAddOfNat
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
Real.instCompleteSpace
Nat.instAtLeastTwoHAddOfNat
sqrt_eq_rpow
div_eq_mul_inv
one_mul
rpow_rpow
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
Nonneg.instContinuousFunctionalCalculus
sqrt.congr_simp
cfc_apply_of_not_predicate
sqrt_eq_cfc
cfc_apply_zero
NNReal.sqrt_zero
map_zero
MonoidWithZeroHomClass.toZeroHomClass
RingHomClass.toMonoidWithZeroHomClass
RingHom.instRingHomClass
sqrt_rpow_nnreal πŸ“–mathematicalβ€”sqrt
Ring.toNonUnitalRing
Algebra.toModule
Real
Real.instCommSemiring
Ring.toSemiring
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
IsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
StarRing.toStarAddMonoid
Field.toSemifield
Real.instField
instStarRingReal
Real.metricSpace
IsTopologicalRing.toIsTopologicalSemiring
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
MetricSpace.toPseudoMetricSpace
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
NonUnitalNormedCommRing.toNonUnitalCommRing
NormedCommRing.toNonUnitalNormedCommRing
Real.normedCommRing
instIsTopologicalRingReal
instContinuousStarReal
Real.instCompleteSpace
instPowReal
NNReal.toReal
DivInvMonoid.toDiv
Real.instDivInvMonoid
instOfNatAtLeastTwo
Real.instNatCast
Nat.instAtLeastTwoHAddOfNat
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
Real.instCompleteSpace
Nat.instAtLeastTwoHAddOfNat
eq_zero_or_pos
NNReal.instCanonicallyOrderedAdd
sqrt.congr_simp
rpow_zero
sqrt_one
zero_div
div_pos
PosMulReflectLE.toPosMulReflectLT
PosMulStrictMono.toPosMulReflectLE
LinearOrderedCommMonoidWithZero.toPosMulStrictMono
Mathlib.Meta.Positivity.pos_of_isNat
NNReal.instIsOrderedRing
Mathlib.Meta.NormNum.isNat_ofNat
Mathlib.Meta.NormNum.instAtLeastTwo
nnrpow_eq_rpow
sqrt_nnrpow
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
Nonneg.instContinuousFunctionalCalculus
cfc_apply_of_not_predicate
sqrt_eq_cfc
cfc_apply_zero
NNReal.sqrt_zero
map_zero
MonoidWithZeroHomClass.toZeroHomClass
RingHomClass.toMonoidWithZeroHomClass
RingHom.instRingHomClass
sqrt_sq πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
sqrt
Ring.toNonUnitalRing
Algebra.toModule
Real
Real.instCommSemiring
Ring.toSemiring
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
IsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
StarRing.toStarAddMonoid
Field.toSemifield
Real.instField
instStarRingReal
Real.metricSpace
IsTopologicalRing.toIsTopologicalSemiring
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
MetricSpace.toPseudoMetricSpace
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
NonUnitalNormedCommRing.toNonUnitalCommRing
NormedCommRing.toNonUnitalNormedCommRing
Real.normedCommRing
instIsTopologicalRingReal
instContinuousStarReal
Real.instCompleteSpace
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
Real.instCompleteSpace
pow_two
sqrt_mul_self
sqrt_unique πŸ“–mathematicalDistrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
Preorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
sqrtβ€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
sqrt_mul_self
sqrt_zero πŸ“–mathematicalβ€”sqrt
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
cfcβ‚™_apply_zero
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
Nonneg.instNonUnitalContinuousFunctionalCalculus
zero_nnrpow πŸ“–mathematicalβ€”NNReal
instPowNNReal
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
cfcβ‚™_apply_zero
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
NNReal.instIsScalarTowerOfReal
NNReal.smulCommClass_left
Nonneg.instNonUnitalContinuousFunctionalCalculus
zero_rpow πŸ“–mathematicalβ€”rpow
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
Nonneg.instContinuousFunctionalCalculus
cfc_apply_zero
NNReal.zero_rpow
map_zero
MonoidWithZeroHomClass.toZeroHomClass
RingHomClass.toMonoidWithZeroHomClass
RingHom.instRingHomClass

CStarAlgebra

Theorems

NameKindAssumesProvesValidatesDepends On
isStrictlyPositive_TFAE πŸ“–mathematicalβ€”List.TFAE
IsStrictlyPositive
Preorder.toLE
PartialOrder.toPreorder
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
CFC.sqrt
Ring.toNonUnitalRing
Algebra.toModule
Real
Real.instCommSemiring
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
IsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
StarRing.toStarAddMonoid
Field.toSemifield
Real.instField
instStarRingReal
Real.metricSpace
IsTopologicalRing.toIsTopologicalSemiring
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
MetricSpace.toPseudoMetricSpace
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
NonUnitalNormedCommRing.toNonUnitalCommRing
NormedCommRing.toNonUnitalNormedCommRing
Real.normedCommRing
instIsTopologicalRingReal
instContinuousStarReal
Real.instCompleteSpace
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
IsUnit
Star.star
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
IsStrictlyPositive.iff_of_unital
IsStrictlyPositive.isSelfAdjoint
StarOrderedRing.isStrictlyPositive_iff_spectrum_pos
Real.instStarOrderedRing
IsSelfAdjoint.of_nonneg
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
Real.instCompleteSpace
IsStrictlyPositive.sqrt
CFC.sqrt_mul_sqrt_self
IsStrictlyPositive.isUnit
IsUnit.isStrictlyPositive
CFC.sqrt_nonneg
IsUnit.star
star_star
mul_star_self_nonneg
IsUnit.mul
List.tfae_of_cycle
isStrictlyPositive_iff_eq_mul_star_self πŸ“–mathematicalβ€”IsStrictlyPositive
Preorder.toLE
PartialOrder.toPreorder
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
IsUnit
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
Star.star
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
StarRing.toStarAddMonoid
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
List.TFAE.out
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
Real.instCompleteSpace
isStrictlyPositive_TFAE
isStrictlyPositive_iff_eq_star_mul_self πŸ“–mathematicalβ€”IsStrictlyPositive
Preorder.toLE
PartialOrder.toPreorder
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
IsUnit
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
Star.star
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
StarRing.toStarAddMonoid
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
List.TFAE.out
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
Real.instCompleteSpace
isStrictlyPositive_TFAE
isStrictlyPositive_iff_exists_isStrictlyPositive_and_eq_mul_self πŸ“–mathematicalβ€”IsStrictlyPositive
Preorder.toLE
PartialOrder.toPreorder
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
List.TFAE.out
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
Real.instCompleteSpace
isStrictlyPositive_TFAE
isStrictlyPositive_iff_exists_isUnit_and_isSelfAdjoint_and_eq_mul_self πŸ“–mathematicalβ€”IsStrictlyPositive
Preorder.toLE
PartialOrder.toPreorder
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
IsUnit
IsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
StarRing.toStarAddMonoid
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
List.TFAE.out
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
Real.instCompleteSpace
isStrictlyPositive_TFAE
isStrictlyPositive_iff_isSelfAdjoint_and_spectrum_pos πŸ“–mathematicalβ€”IsStrictlyPositive
Preorder.toLE
PartialOrder.toPreorder
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
IsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
StarRing.toStarAddMonoid
Real
Real.instLT
Real.instZero
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
List.TFAE.out
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
Real.instCompleteSpace
isStrictlyPositive_TFAE
isStrictlyPositive_iff_isStrictlyPositive_sqrt_and_eq_sqrt_mul_sqrt πŸ“–mathematicalβ€”IsStrictlyPositive
Preorder.toLE
PartialOrder.toPreorder
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
CFC.sqrt
Ring.toNonUnitalRing
Algebra.toModule
Real
Real.instCommSemiring
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
IsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
StarRing.toStarAddMonoid
Field.toSemifield
Real.instField
instStarRingReal
Real.metricSpace
IsTopologicalRing.toIsTopologicalSemiring
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
MetricSpace.toPseudoMetricSpace
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
NonUnitalNormedCommRing.toNonUnitalCommRing
NormedCommRing.toNonUnitalNormedCommRing
Real.normedCommRing
instIsTopologicalRingReal
instContinuousStarReal
Real.instCompleteSpace
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
List.TFAE.out
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
Real.instCompleteSpace
isStrictlyPositive_TFAE
isStrictlyPositive_iff_isUnit_sqrt_and_eq_sqrt_mul_sqrt πŸ“–mathematicalβ€”IsStrictlyPositive
Preorder.toLE
PartialOrder.toPreorder
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
IsUnit
CFC.sqrt
Ring.toNonUnitalRing
Algebra.toModule
Real
Real.instCommSemiring
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
IsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
StarRing.toStarAddMonoid
Field.toSemifield
Real.instField
instStarRingReal
Real.metricSpace
IsTopologicalRing.toIsTopologicalSemiring
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
MetricSpace.toPseudoMetricSpace
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
NonUnitalNormedCommRing.toNonUnitalCommRing
NormedCommRing.toNonUnitalNormedCommRing
Real.normedCommRing
instIsTopologicalRingReal
instContinuousStarReal
Real.instCompleteSpace
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
List.TFAE.out
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
Real.instCompleteSpace
isStrictlyPositive_TFAE
nonneg_TFAE πŸ“–mathematicalβ€”List.TFAE
Preorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
CFC.sqrt
IsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
StarRing.toStarAddMonoid
Star.star
PosPart.posPart
instPosPart
NegPart.negPart
instNegPart
QuasispectrumRestricts
NNReal
Real
instCommSemiringNNReal
Real.instCommSemiring
NNReal.instModuleOfReal
NNReal.instAlgebraOfReal
CommSemiring.toSemiring
Algebra.id
DFunLike.coe
ContinuousMap
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
Real.pseudoMetricSpace
NNReal.instTopologicalSpace
ContinuousMap.instFunLike
ContinuousMap.realToNNReal
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
nonneg_iff_isSelfAdjoint_and_quasispectrumRestricts
CFC.posPart_eq_self
LE.le.isSelfAdjoint
CFC.negPart_eq_zero_iff
CFC.sqrt_mul_sqrt_self
CFC.sqrt_nonneg
star_star
mul_star_self_nonneg
List.tfae_of_cycle
nonneg_iff_eq_mul_star_self πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
Star.star
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
StarRing.toStarAddMonoid
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
List.TFAE.out
nonneg_TFAE
nonneg_iff_eq_sqrt_mul_sqrt πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
CFC.sqrt
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
List.TFAE.out
nonneg_TFAE
nonneg_iff_eq_star_mul_self πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
Star.star
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
StarRing.toStarAddMonoid
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
List.TFAE.out
nonneg_TFAE
nonneg_iff_exists_isSelfAdjoint_and_eq_mul_self πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
IsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
StarRing.toStarAddMonoid
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
List.TFAE.out
nonneg_TFAE
nonneg_iff_exists_nonneg_and_eq_mul_self πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
List.TFAE.out
nonneg_TFAE
nonneg_iff_isSelfAdjoint_and_negPart_eq_zero πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
IsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
StarRing.toStarAddMonoid
NegPart.negPart
instNegPart
β€”Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
List.TFAE.out
nonneg_TFAE

IsStrictlyPositive

Theorems

NameKindAssumesProvesValidatesDepends On
nnrpow πŸ“–mathematicalIsStrictlyPositive
Preorder.toLE
PartialOrder.toPreorder
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NNReal
CFC.instPowNNReal
Ring.toNonUnitalRing
Algebra.toModule
Real
Real.instCommSemiring
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
IsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalRing.toNonUnitalNonAssocRing
StarRing.toStarAddMonoid
Field.toSemifield
Real.instField
instStarRingReal
Real.metricSpace
IsTopologicalRing.toIsTopologicalSemiring
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
MetricSpace.toPseudoMetricSpace
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
NonUnitalNormedCommRing.toNonUnitalCommRing
NormedCommRing.toNonUnitalNormedCommRing
Real.normedCommRing
instIsTopologicalRingReal
instContinuousStarReal
Real.instCompleteSpace
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
rpow πŸ“–mathematicalIsStrictlyPositive
Preorder.toLE
PartialOrder.toPreorder
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Real
CFC.instPowReal
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal

IsUnit

Theorems

NameKindAssumesProvesValidatesDepends On
cfcNNRpow πŸ“–mathematicalIsUnit
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NNReal
CFC.instPowNNReal
Ring.toNonUnitalRing
Algebra.toModule
Real
Real.instCommSemiring
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
IsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalRing.toNonUnitalNonAssocRing
StarRing.toStarAddMonoid
Field.toSemifield
Real.instField
instStarRingReal
Real.metricSpace
IsTopologicalRing.toIsTopologicalSemiring
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
MetricSpace.toPseudoMetricSpace
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
NonUnitalNormedCommRing.toNonUnitalCommRing
NormedCommRing.toNonUnitalNormedCommRing
Real.normedCommRing
instIsTopologicalRingReal
instContinuousStarReal
Real.instCompleteSpace
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
Real.instCompleteSpace
CFC.isUnit_nnrpow_iff
cfcRpow πŸ“–mathematicalIsUnit
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Real
CFC.instPowReal
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Units.isUnit
cfcSqrt πŸ“–mathematicalIsUnit
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
Preorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
CFC.sqrt
Ring.toNonUnitalRing
Algebra.toModule
Real
Real.instCommSemiring
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
IsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
StarRing.toStarAddMonoid
Field.toSemifield
Real.instField
instStarRingReal
Real.metricSpace
IsTopologicalRing.toIsTopologicalSemiring
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
MetricSpace.toPseudoMetricSpace
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
NonUnitalNormedCommRing.toNonUnitalCommRing
NormedCommRing.toNonUnitalNormedCommRing
Real.normedCommRing
instIsTopologicalRingReal
instContinuousStarReal
Real.instCompleteSpace
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Algebra.to_smulCommClass
IsScalarTower.right
ContinuousFunctionalCalculus.toNonUnital
Real.instCompleteSpace
CFC.isUnit_sqrt_iff

NNReal

Definitions

NameCategoryTheorems
nnrpow πŸ“–CompOp
4 mathmath: CFC.nnrpow_def, nnrpow_def, monotone_nnrpow_const, continuous_nnrpow_const

Theorems

NameKindAssumesProvesValidatesDepends On
continuous_nnrpow_const πŸ“–mathematicalβ€”Continuous
NNReal
instTopologicalSpace
nnrpow
β€”continuous_rpow_const
zero_le_coe
monotone_nnrpow_const πŸ“–mathematicalβ€”Monotone
NNReal
PartialOrder.toPreorder
instPartialOrderNNReal
nnrpow
β€”monotone_rpow_of_nonneg
zero_le_coe
nnrpow_def πŸ“–mathematicalβ€”nnrpow
NNReal
Real
instPowReal
toReal
β€”β€”

Units

Definitions

NameCategoryTheorems
cfcRpow πŸ“–CompOp
2 mathmath: val_cfcRpow, val_inv_cfcRpow

Theorems

NameKindAssumesProvesValidatesDepends On
val_cfcRpow πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
val
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
cfcRpow
Real
CFC.instPowReal
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
val_inv_cfcRpow πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
val
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
Units
instInv
cfcRpow
Real
CFC.instPowReal
Real.instNeg
β€”IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal

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