Documentation Verification Report

Order

📁 Source: Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/Order.lean

Statistics

MetricCount
DefinitionsinstPartialOrder
1
Theoremsconjugate_rpow_neg_one_half, exists_pos_algebraMap_le_iff, conjugate_le_norm_smul, conjugate_le_norm_smul', inr_mem_Icc_iff_nnnorm_le, inr_mem_Icc_iff_norm_le, instNonnegSpectrumClassComplexNonUnital, instOrderClosedTopology, inv_le_iff, inv_le_inv, inv_le_inv_iff, inv_le_one, inv_le_one_iff_one_le, isClosed_nonneg, isUnit_of_le, le_inv_iff, le_one_of_one_le_inv, mem_Icc_algebraMap_iff_nnnorm_le, mem_Icc_algebraMap_iff_norm_le, mem_Icc_iff_nnnorm_le_one, mem_Icc_iff_norm_le_one, mul_star_le_algebraMap_norm_sq, nnnorm_le_iff_of_nonneg, nnnorm_le_natCast_iff_of_nonneg, nnnorm_le_nnnorm_of_nonneg_of_le, nnnorm_le_one_iff_of_nonneg, nnnorm_mem_spectrum_of_nonneg, norm_le_iff_le_algebraMap, norm_le_natCast_iff_of_nonneg, norm_le_norm_of_nonneg_of_le, norm_le_one_iff_of_nonneg, norm_mem_spectrum_of_nonneg, norm_or_neg_norm_mem_spectrum, one_le_inv_iff_le_one, pow_antitone, pow_monotone, pow_nonneg, preimage_inr_Icc_zero_one, rpow_neg_one_le_one, rpow_neg_one_le_rpow_neg_one, star_left_conjugate_le_norm_smul, star_mul_le_algebraMap_norm_sq, star_right_conjugate_le_norm_smul, le_algebraMap_norm_self, neg_algebraMap_norm_le_self, toReal_spectralRadius_eq_norm, add_nonneg, nonneg_add, of_le, inr_le_iff, inr_nonneg_iff, instStarOrderedRing, nnreal_cfcₙ_eq_cfc_inr, cfc_nnreal_le_iff, cfc_tsub, cfcₙ_tsub, isStrictlyPositive_add, le_iff_norm_sqrt_mul_rpow, le_iff_norm_sqrt_mul_sqrt_inv
59
Total60

CFC

Theorems

NameKindAssumesProvesValidatesDepends On
conjugate_rpow_neg_one_half 📖mathematicalIsStrictlyPositive
Preorder.toLE
PartialOrder.toPreorder
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
NormedRing.toRing
CStarAlgebra.toNormedRing
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
Real
instPowReal
CStarAlgebra.toStarRing
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedRing.toPseudoMetricSpace
NormedRing.toSeminormedRing
NormedAlgebra.toAlgebra
Real.normedField
NormedAlgebra.complexToReal
CStarAlgebra.toNormedAlgebra
IsSelfAdjoint.instContinuousFunctionalCalculus
Complex
Complex.instNormedField
IsStarNormal.instContinuousFunctionalCalculus
CStarAlgebra.instNonnegSpectrumClass'
CStarAlgebra.toNonUnitalCStarAlgebra
Real.instNeg
DivInvMonoid.toDiv
Real.instDivInvMonoid
Real.instOne
instOfNatAtLeastTwo
Real.instNatCast
Nat.instAtLeastTwoHAddOfNat
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
IsSelfAdjoint.instContinuousFunctionalCalculus
IsStarNormal.instContinuousFunctionalCalculus
CStarAlgebra.instNonnegSpectrumClass'
Nat.instAtLeastTwoHAddOfNat
CanLift.prf
instCanLiftUnitsValIsUnit
IsStrictlyPositive.isUnit
rpow_one
IsStrictlyPositive.nonneg
rpow_add
Units.isUnit
Mathlib.Meta.NormNum.IsNat.to_eq
Mathlib.Meta.NormNum.IsInt.to_isNat
Mathlib.Meta.NormNum.IsRat.to_isInt
Mathlib.Meta.NormNum.isRat_add
Mathlib.Meta.NormNum.IsNNRat.to_isRat
Mathlib.Meta.NormNum.IsRat.to_isNNRat
Mathlib.Meta.NormNum.isRat_neg
Mathlib.Meta.NormNum.isNNRat_div
Mathlib.Meta.NormNum.isNNRat_mul
Mathlib.Meta.NormNum.IsNat.to_isNNRat
Mathlib.Meta.NormNum.isNat_ofNat
Nat.cast_one
Mathlib.Meta.NormNum.isNNRat_inv_pos
RCLike.charZero_rclike
Mathlib.Meta.NormNum.instAtLeastTwo
Nat.cast_zero
rpow_zero
exists_pos_algebraMap_le_iff 📖mathematicalIsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
StarRing.toStarAddMonoid
Real
Real.instLT
Real.instZero
Preorder.toLE
PartialOrder.toPreorder
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
Real.instCommSemiring
Ring.toSemiring
RingHom.instFunLike
algebraMap
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
isCompact_iff_compactSpace
ContinuousFunctionalCalculus.compactSpace_spectrum
algebraMap_le_iff_le_spectrum
Real.instStarOrderedRing
LT.lt.trans_le
IsCompact.exists_isMinOn
instClosedIicTopology
HasSolidNorm.orderClosedTopology
instHasSolidNormReal
Real.instIsOrderedAddMonoid
spectrum_nonempty
continuousOn_id

CStarAlgebra

Theorems

NameKindAssumesProvesValidatesDepends On
conjugate_le_norm_smul 📖mathematicalIsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
NonUnitalNormedRing.toNonUnitalRing
NonUnitalCStarAlgebra.toNonUnitalNormedRing
StarRing.toStarAddMonoid
NonUnitalCStarAlgebra.toStarRing
Preorder.toLE
PartialOrder.toPreorder
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
Star.star
Real
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
ESeminormedAddMonoid.toAddMonoid
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
NormedAddCommGroup.toSeminormedAddCommGroup
NonUnitalNormedRing.toNormedAddCommGroup
ESeminormedAddCommMonoid.toESeminormedAddMonoid
ENormedAddCommMonoid.toESeminormedAddCommMonoid
NormedAddCommGroup.toENormedAddCommMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
Real.instMonoid
Module.toDistribMulAction
Real.semiring
ESeminormedAddCommMonoid.toAddCommMonoid
NonUnitalSeminormedRing.toPseudoMetricSpace
NonUnitalNormedRing.toNonUnitalSeminormedRing
NormedSpace.toModule
Real.normedField
NonUnitalSeminormedRing.toSeminormedAddCommGroup
NormedSpace.complexToReal
NonUnitalCStarAlgebra.toNormedSpace
Norm.norm
NonUnitalNormedRing.toNorm
star_left_conjugate_le_norm_smul
conjugate_le_norm_smul' 📖mathematicalIsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
NonUnitalNormedRing.toNonUnitalRing
NonUnitalCStarAlgebra.toNonUnitalNormedRing
StarRing.toStarAddMonoid
NonUnitalCStarAlgebra.toStarRing
Preorder.toLE
PartialOrder.toPreorder
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
Star.star
Real
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
ESeminormedAddMonoid.toAddMonoid
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
NormedAddCommGroup.toSeminormedAddCommGroup
NonUnitalNormedRing.toNormedAddCommGroup
ESeminormedAddCommMonoid.toESeminormedAddMonoid
ENormedAddCommMonoid.toESeminormedAddCommMonoid
NormedAddCommGroup.toENormedAddCommMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
Real.instMonoid
Module.toDistribMulAction
Real.semiring
ESeminormedAddCommMonoid.toAddCommMonoid
NonUnitalSeminormedRing.toPseudoMetricSpace
NonUnitalNormedRing.toNonUnitalSeminormedRing
NormedSpace.toModule
Real.normedField
NonUnitalSeminormedRing.toSeminormedAddCommGroup
NormedSpace.complexToReal
NonUnitalCStarAlgebra.toNormedSpace
Norm.norm
NonUnitalNormedRing.toNorm
star_right_conjugate_le_norm_smul
inr_mem_Icc_iff_nnnorm_le 📖mathematicalUnitization
Complex
Set
Set.instMembership
Set.Icc
PartialOrder.toPreorder
Unitization.instPartialOrder
Unitization.instZero
Complex.instZero
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
NonUnitalNormedRing.toNonUnitalRing
NonUnitalCStarAlgebra.toNonUnitalNormedRing
Unitization.instOne
Complex.instOne
Unitization.inr
Preorder.toLE
NNReal
instPartialOrderNNReal
NNNorm.nnnorm
SeminormedAddGroup.toNNNorm
SeminormedAddCommGroup.toSeminormedAddGroup
NonUnitalSeminormedRing.toSeminormedAddCommGroup
NonUnitalNormedRing.toNonUnitalSeminormedRing
instOneNNReal
inr_mem_Icc_iff_norm_le
inr_mem_Icc_iff_norm_le 📖mathematicalUnitization
Complex
Set
Set.instMembership
Set.Icc
PartialOrder.toPreorder
Unitization.instPartialOrder
Unitization.instZero
Complex.instZero
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
NonUnitalNormedRing.toNonUnitalRing
NonUnitalCStarAlgebra.toNonUnitalNormedRing
Unitization.instOne
Complex.instOne
Unitization.inr
Preorder.toLE
Real
Real.instLE
Norm.norm
NonUnitalNormedRing.toNorm
Real.instOne
NonUnitalCStarAlgebra.toIsScalarTower
NonUnitalCStarAlgebra.toSMulCommClass
CStarRing.instRegularNormedAlgebra
NonUnitalCStarAlgebra.toCStarRing
Unitization.norm_inr
Unitization.inr_nonneg_iff
norm_le_one_iff_of_nonneg
Unitization.instStarOrderedRing
instNonnegSpectrumClassComplexNonUnital 📖mathematicalNonnegSpectrumClass
Complex
Complex.instCommSemiring
Complex.partialOrder
NonUnitalNormedRing.toNonUnitalRing
NonUnitalCStarAlgebra.toNonUnitalNormedRing
NormedSpace.toModule
Complex.instNormedField
NonUnitalSeminormedRing.toSeminormedAddCommGroup
NonUnitalNormedRing.toNonUnitalSeminormedRing
NonUnitalCStarAlgebra.toNormedSpace
spectrum_nonneg_of_nonneg
NonUnitalCStarAlgebra.toIsScalarTower
NonUnitalCStarAlgebra.toSMulCommClass
IsScalarTower.left
instNonnegSpectrumClassComplexUnital
Unitization.instStarOrderedRing
Unitization.inr_nonneg_iff
Unitization.quasispectrum_eq_spectrum_inr'
instOrderClosedTopology 📖mathematicalOrderClosedTopology
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
NonUnitalSeminormedRing.toPseudoMetricSpace
NonUnitalNormedRing.toNonUnitalSeminormedRing
NonUnitalCStarAlgebra.toNonUnitalNormedRing
PartialOrder.toPreorder
isClosed_le_of_isClosed_nonneg
StarOrderedRing.toIsOrderedAddMonoid
IsTopologicalAddGroup.to_continuousSub
SeminormedAddCommGroup.toIsTopologicalAddGroup
isClosed_nonneg
inv_le_iff 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NormedRing.toRing
toNormedRing
Units.val
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
Units
Units.instInv
inv_inv
inv_le_inv_iff
CFC.inv_nonneg_of_nonneg
Nonneg.instContinuousFunctionalCalculus
IsSelfAdjoint.instContinuousFunctionalCalculus
IsStarNormal.instContinuousFunctionalCalculus
instNonnegSpectrumClass'
inv_le_inv 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NormedRing.toRing
toNormedRing
Units.val
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
Units
Units.instInv
LE.le.trans
CFC.inv_nonneg_of_nonneg
Nonneg.instContinuousFunctionalCalculus
IsSelfAdjoint.instContinuousFunctionalCalculus
IsStarNormal.instContinuousFunctionalCalculus
instNonnegSpectrumClass'
Algebra.to_smulCommClass
IsScalarTower.right
IsSelfAdjoint.instNonUnitalContinuousFunctionalCalculus
IsStarNormal.instNonUnitalContinuousFunctionalCalculus
le_iff_norm_sqrt_mul_sqrt_inv
inv_inv
sq_le_one_iff₀
IsStrictOrderedRing.toPosMulStrictMono
Real.instIsStrictOrderedRing
Real.instZeroLEOneClass
norm_nonneg
sq
CStarRing.norm_self_mul_star
toCStarRing
StarMul.star_mul
IsSelfAdjoint.of_nonneg
CFC.sqrt_nonneg
CStarRing.norm_star_mul_self
inv_le_inv_iff 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NormedRing.toRing
toNormedRing
Units.val
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
Units
Units.instInv
inv_le_inv
CFC.inv_nonneg_of_nonneg
Nonneg.instContinuousFunctionalCalculus
IsSelfAdjoint.instContinuousFunctionalCalculus
IsStarNormal.instContinuousFunctionalCalculus
instNonnegSpectrumClass'
inv_le_one 📖mathematicalUnits
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
NormedRing.toRing
toNormedRing
Preorder.toLE
Units.instPreorder
PartialOrder.toPreorder
Units.instOne
Units.val
Units.instInv
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
inv_le_one_iff_one_le
LE.le.trans
zero_le_one
instZeroLEOneClass
inv_le_one_iff_one_le 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NormedRing.toRing
toNormedRing
Units.val
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
Units
Units.instInv
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Units.instPreorder
Units.instOne
inv_one
inv_le_iff
instZeroLEOneClass
isClosed_nonneg 📖mathematicalIsClosed
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
NonUnitalSeminormedRing.toPseudoMetricSpace
NonUnitalNormedRing.toNonUnitalSeminormedRing
NonUnitalCStarAlgebra.toNonUnitalNormedRing
setOf
Preorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
NonUnitalNormedRing.toNonUnitalRing
NonUnitalCStarAlgebra.toStarModule
Unitization.instStarOrderedRing
IsScalarTower.right
NonUnitalCStarAlgebra.toIsScalarTower
NonUnitalCStarAlgebra.toSMulCommClass
IsScalarTower.complexToReal
IsScalarTower.left
Algebra.to_smulCommClass
IsSelfAdjoint.instNonUnitalContinuousFunctionalCalculus
IsStarNormal.instNonUnitalContinuousFunctionalCalculus
instNonnegSpectrumClass'
SpectrumRestricts.nnreal_iff_nnnorm
le_rfl
IsClosed.inter
isClosed_eq
TopologicalSpace.t2Space_of_metrizableSpace
EMetricSpace.metrizableSpace
CStarRing.instRegularNormedAlgebra
NonUnitalCStarAlgebra.toCStarRing
Continuous.star
NormedStarGroup.to_continuousStar
CStarRing.to_normedStarGroup
Unitization.instCStarRing
toCStarRing
continuous_id'
isClosed_le
OrderTopology.to_orderClosedTopology
NNReal.instOrderTopology
Continuous.nnnorm
Continuous.sub
IsTopologicalAddGroup.to_continuousSub
SeminormedAddCommGroup.toIsTopologicalAddGroup
Continuous.comp'
continuous_algebraMap
IsBoundedSMul.continuousSMul
NormedSpace.toIsBoundedSMul
NNReal.continuous_coe
Topology.IsClosedEmbedding.isClosed_iff_image_isClosed
Isometry.isClosedEmbedding
NonUnitalCStarAlgebra.toCompleteSpace
Unitization.isometry_inr
Set.ext
Topology.IsClosedEmbedding.isClosed_range
isUnit_of_le 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
IsStrictlyPositive
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
NormedRing.toRing
toNormedRing
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
IsUnitIsStrictlyPositive.isUnit
IsStrictlyPositive.nonneg
spectrum.zero_notMem_iff
Mathlib.Tactic.Nontriviality.subsingleton_or_nontrivial_elim
spectrum.of_subsingleton
LE.le.trans
zero_notMem_iff
NNReal.instCanonicallyOrderedAdd
SpectrumRestricts.nnreal_lt_iff
SpectrumRestricts.nnreal_of_nonneg
instNonnegSpectrumClass'
NNReal.coe_zero
CFC.exists_pos_algebraMap_le_iff
IsSelfAdjoint.instContinuousFunctionalCalculus
IsStarNormal.instContinuousFunctionalCalculus
IsSelfAdjoint.of_nonneg
le_inv_iff 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NormedRing.toRing
toNormedRing
Units.val
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
Units
Units.instInv
inv_inv
inv_le_inv_iff
CFC.inv_nonneg_of_nonneg
Nonneg.instContinuousFunctionalCalculus
IsSelfAdjoint.instContinuousFunctionalCalculus
IsStarNormal.instContinuousFunctionalCalculus
instNonnegSpectrumClass'
le_one_of_one_le_inv 📖Preorder.toLE
PartialOrder.toPreorder
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
NormedRing.toRing
toNormedRing
Units.val
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
Units
Units.instInv
inv_inv
inv_le_one
mem_Icc_algebraMap_iff_nnnorm_le 📖mathematicalSet
Set.instMembership
Set.Icc
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NormedRing.toRing
toNormedRing
DFunLike.coe
RingHom
NNReal
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNReal
Ring.toSemiring
RingHom.instFunLike
algebraMap
NNReal.instAlgebraOfReal
NormedAlgebra.toAlgebra
Real
Real.normedField
NormedRing.toSeminormedRing
NormedAlgebra.complexToReal
toNormedAlgebra
Preorder.toLE
instPartialOrderNNReal
NNNorm.nnnorm
SeminormedAddGroup.toNNNorm
SeminormedAddCommGroup.toSeminormedAddGroup
NonUnitalSeminormedRing.toSeminormedAddCommGroup
NonUnitalNormedRing.toNonUnitalSeminormedRing
NonUnitalCStarAlgebra.toNonUnitalNormedRing
toNonUnitalCStarAlgebra
mem_Icc_algebraMap_iff_norm_le
mem_Icc_algebraMap_iff_norm_le 📖mathematicalReal
Real.instLE
Real.instZero
Set
Set.instMembership
Set.Icc
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NormedRing.toRing
toNormedRing
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
Real.instCommSemiring
Ring.toSemiring
RingHom.instFunLike
algebraMap
NormedAlgebra.toAlgebra
Real.normedField
NormedRing.toSeminormedRing
NormedAlgebra.complexToReal
toNormedAlgebra
Preorder.toLE
Norm.norm
NormedRing.toNorm
Set.mem_Icc
norm_le_iff_le_algebraMap
mem_Icc_iff_nnnorm_le_one 📖mathematicalSet
Set.instMembership
Set.Icc
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NormedRing.toRing
toNormedRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Preorder.toLE
NNReal
instPartialOrderNNReal
NNNorm.nnnorm
SeminormedAddGroup.toNNNorm
SeminormedAddCommGroup.toSeminormedAddGroup
NonUnitalSeminormedRing.toSeminormedAddCommGroup
NonUnitalNormedRing.toNonUnitalSeminormedRing
NonUnitalCStarAlgebra.toNonUnitalNormedRing
toNonUnitalCStarAlgebra
instOneNNReal
mem_Icc_iff_norm_le_one
mem_Icc_iff_norm_le_one 📖mathematicalSet
Set.instMembership
Set.Icc
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NormedRing.toRing
toNormedRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Preorder.toLE
Real
Real.instLE
Norm.norm
NormedRing.toNorm
Real.instOne
map_one
MonoidHomClass.toOneHomClass
MonoidWithZeroHomClass.toMonoidHomClass
RingHomClass.toMonoidWithZeroHomClass
RingHom.instRingHomClass
mem_Icc_algebraMap_iff_norm_le
zero_le_one
Real.instZeroLEOneClass
mul_star_le_algebraMap_norm_sq 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NormedRing.toRing
toNormedRing
Star.star
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
StarRing.toStarAddMonoid
toStarRing
DFunLike.coe
RingHom
Real
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
Real.instCommSemiring
Ring.toSemiring
RingHom.instFunLike
algebraMap
NormedAlgebra.toAlgebra
Real.normedField
NormedRing.toSeminormedRing
NormedAlgebra.complexToReal
toNormedAlgebra
Monoid.toNatPow
Real.instMonoid
Norm.norm
NormedRing.toNorm
IsSelfAdjoint.le_algebraMap_norm_self
pow_two
CStarRing.norm_self_mul_star
toCStarRing
nnnorm_le_iff_of_nonneg 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NormedRing.toRing
toNormedRing
NNReal
instPartialOrderNNReal
NNNorm.nnnorm
SeminormedAddGroup.toNNNorm
SeminormedAddCommGroup.toSeminormedAddGroup
NonUnitalSeminormedRing.toSeminormedAddCommGroup
NonUnitalNormedRing.toNonUnitalSeminormedRing
NonUnitalCStarAlgebra.toNonUnitalNormedRing
toNonUnitalCStarAlgebra
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNReal
Ring.toSemiring
RingHom.instFunLike
algebraMap
NNReal.instAlgebraOfReal
NormedAlgebra.toAlgebra
Real
Real.normedField
NormedRing.toSeminormedRing
NormedAlgebra.complexToReal
toNormedAlgebra
NNReal.coe_le_coe
norm_le_iff_le_algebraMap
nnnorm_le_natCast_iff_of_nonneg 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NormedRing.toRing
toNormedRing
NNReal
instPartialOrderNNReal
NNNorm.nnnorm
SeminormedAddGroup.toNNNorm
SeminormedAddCommGroup.toSeminormedAddGroup
NonUnitalSeminormedRing.toSeminormedAddCommGroup
NonUnitalNormedRing.toNonUnitalSeminormedRing
NonUnitalCStarAlgebra.toNonUnitalNormedRing
toNonUnitalCStarAlgebra
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
instSemiringNNReal
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
map_natCast
RingHom.instRingHomClass
nnnorm_le_iff_of_nonneg
nnnorm_le_nnnorm_of_nonneg_of_le 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
NonUnitalNormedRing.toNonUnitalRing
NonUnitalCStarAlgebra.toNonUnitalNormedRing
NNReal
instPartialOrderNNReal
NNNorm.nnnorm
SeminormedAddGroup.toNNNorm
SeminormedAddCommGroup.toSeminormedAddGroup
NonUnitalSeminormedRing.toSeminormedAddCommGroup
NonUnitalNormedRing.toNonUnitalSeminormedRing
norm_le_norm_of_nonneg_of_le
nnnorm_le_one_iff_of_nonneg 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NormedRing.toRing
toNormedRing
NNReal
instPartialOrderNNReal
NNNorm.nnnorm
SeminormedAddGroup.toNNNorm
SeminormedAddCommGroup.toSeminormedAddGroup
NonUnitalSeminormedRing.toSeminormedAddCommGroup
NonUnitalNormedRing.toNonUnitalSeminormedRing
NonUnitalCStarAlgebra.toNonUnitalNormedRing
toNonUnitalCStarAlgebra
instOneNNReal
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
NNReal.coe_le_coe
norm_le_one_iff_of_nonneg
nnnorm_mem_spectrum_of_nonneg 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NormedRing.toRing
toNormedRing
NNReal
Set
Set.instMembership
spectrum
instCommSemiringNNReal
NNReal.instAlgebraOfReal
Ring.toSemiring
NormedAlgebra.toAlgebra
Real
Real.normedField
NormedRing.toSeminormedRing
NormedAlgebra.complexToReal
toNormedAlgebra
NNNorm.nnnorm
SeminormedAddGroup.toNNNorm
SeminormedAddCommGroup.toSeminormedAddGroup
NonUnitalSeminormedRing.toSeminormedAddCommGroup
NonUnitalNormedRing.toNonUnitalSeminormedRing
NonUnitalCStarAlgebra.toNonUnitalNormedRing
toNonUnitalCStarAlgebra
IsSelfAdjoint.of_nonneg
SpectrumRestricts.spectralRadius_eq
IsScalarTower.complexToReal
IsScalarTower.left
IsSelfAdjoint.spectrumRestricts
IsStarNormal.instContinuousFunctionalCalculus
IsSelfAdjoint.spectralRadius_eq_nnnorm
NNReal.spectralRadius_mem_spectrum
toCompleteSpace
Set.Nonempty.image
spectrum.nonempty
SpectrumRestricts.image
SpectrumRestricts.nnreal_of_nonneg
instNonnegSpectrumClass'
norm_le_iff_le_algebraMap 📖mathematicalReal
Real.instLE
Real.instZero
Preorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NormedRing.toRing
toNormedRing
Norm.norm
NormedRing.toNorm
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
Real.instCommSemiring
Ring.toSemiring
RingHom.instFunLike
algebraMap
NormedAlgebra.toAlgebra
Real.normedField
NormedRing.toSeminormedRing
NormedAlgebra.complexToReal
toNormedAlgebra
le_algebraMap_iff_spectrum_le
instIsTopologicalRingReal
instContinuousStarReal
Real.instStarOrderedRing
IsSelfAdjoint.instContinuousFunctionalCalculus
IsStarNormal.instContinuousFunctionalCalculus
instNonnegSpectrumClass'
IsSelfAdjoint.of_nonneg
subsingleton_or_nontrivial
norm_zero
spectrum.of_subsingleton
instIsEmptyFalse
LE.le.trans
Real.le_norm_self
spectrum.norm_le_norm_of_mem
toCompleteSpace
CStarRing.instNormOneClassOfNontrivial
toCStarRing
norm_mem_spectrum_of_nonneg
norm_le_natCast_iff_of_nonneg 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NormedRing.toRing
toNormedRing
Real
Real.instLE
Norm.norm
NormedRing.toNorm
Real.instNatCast
AddMonoidWithOne.toNatCast
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
map_natCast
RingHom.instRingHomClass
norm_le_iff_le_algebraMap
Nat.cast_nonneg
Real.instIsOrderedRing
norm_le_norm_of_nonneg_of_le 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
NonUnitalNormedRing.toNonUnitalRing
NonUnitalCStarAlgebra.toNonUnitalNormedRing
Real
Real.instLE
Norm.norm
NonUnitalNormedRing.toNorm
NonUnitalCStarAlgebra.toIsScalarTower
NonUnitalCStarAlgebra.toSMulCommClass
CStarRing.instRegularNormedAlgebra
NonUnitalCStarAlgebra.toCStarRing
LE.le.trans
NonUnitalCStarAlgebra.toStarModule
IsSelfAdjoint.of_nonneg
Unitization.instStarOrderedRing
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
IsScalarTower.complexToReal
IsScalarTower.left
IsSelfAdjoint.instContinuousFunctionalCalculus
IsStarNormal.instContinuousFunctionalCalculus
cfc_id
cfc_mono
Real.instStarOrderedRing
Real.norm_of_nonneg
spectrum_nonneg_of_nonneg
instNonnegSpectrumClass'
spectrum.norm_le_norm_of_mem
Unitization.instCompleteSpace
Complex.instCompleteSpace
NonUnitalCStarAlgebra.toCompleteSpace
Unitization.instNormOneClass
continuousOn_id'
continuousOn_const
cfc_const
cfc_le_iff
norm_mem_spectrum_of_nonneg
Unitization.instNontrivialLeft
Complex.instNontrivial
AddTorsor.nonempty
Unitization.norm_inr
Unitization.inr_le_iff
norm_le_one_iff_of_nonneg 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NormedRing.toRing
toNormedRing
Real
Real.instLE
Norm.norm
NormedRing.toNorm
Real.instOne
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
map_one
MonoidHomClass.toOneHomClass
MonoidWithZeroHomClass.toMonoidHomClass
RingHomClass.toMonoidWithZeroHomClass
RingHom.instRingHomClass
norm_le_iff_le_algebraMap
zero_le_one
Real.instZeroLEOneClass
norm_mem_spectrum_of_nonneg 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NormedRing.toRing
toNormedRing
Real
Set
Set.instMembership
spectrum
Real.instCommSemiring
NormedAlgebra.toAlgebra
Real.normedField
NormedRing.toSeminormedRing
NormedAlgebra.complexToReal
toNormedAlgebra
Norm.norm
NormedRing.toNorm
spectrum.algebraMap_mem
NNReal.instIsScalarTowerOfReal
IsScalarTower.left
nnnorm_mem_spectrum_of_nonneg
norm_or_neg_norm_mem_spectrum 📖mathematicalIsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NormedRing.toRing
toNormedRing
StarRing.toStarAddMonoid
toStarRing
Real
Set
Set.instMembership
spectrum
Real.instCommSemiring
NormedAlgebra.toAlgebra
Real.normedField
NormedRing.toSeminormedRing
NormedAlgebra.complexToReal
toNormedAlgebra
Norm.norm
NormedRing.toNorm
Real.instNeg
IsSelfAdjoint.spectrumRestricts
IsStarNormal.instContinuousFunctionalCalculus
IsSelfAdjoint.toReal_spectralRadius_eq_norm
Real.spectralRadius_mem_spectrum_or
toCompleteSpace
Set.Nonempty.image
spectrum.nonempty
SpectrumRestricts.image
IsScalarTower.complexToReal
IsScalarTower.left
one_le_inv_iff_le_one 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NormedRing.toRing
toNormedRing
Units.val
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Units
Units.instInv
Units.instPreorder
Units.instOne
inv_one
le_inv_iff
instZeroLEOneClass
pow_antitone 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NormedRing.toRing
toNormedRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Antitone
Nat.instPreorder
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
IsSelfAdjoint.instContinuousFunctionalCalculus
IsStarNormal.instContinuousFunctionalCalculus
cfc_pow_id
IsSelfAdjoint.of_nonneg
cfc_le_iff
Real.instStarOrderedRing
instNonnegSpectrumClass'
ContinuousOn.pow
IsTopologicalSemiring.toContinuousMul
continuousOn_id'
pow_le_pow_of_le_one
IsOrderedRing.toPosMulMono
Real.instIsOrderedRing
spectrum_nonneg_of_nonneg
CFC.le_one_iff
pow_monotone 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
NormedRing.toRing
toNormedRing
Monotone
Nat.instPreorder
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
LE.le.trans
zero_le_one
instZeroLEOneClass
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
IsSelfAdjoint.instContinuousFunctionalCalculus
IsStarNormal.instContinuousFunctionalCalculus
cfc_pow_id
IsSelfAdjoint.of_nonneg
cfc_le_iff
Real.instStarOrderedRing
instNonnegSpectrumClass'
ContinuousOn.pow
IsTopologicalSemiring.toContinuousMul
continuousOn_id'
pow_le_pow_right₀
Real.instZeroLEOneClass
IsOrderedRing.toPosMulMono
Real.instIsOrderedRing
CFC.one_le_iff
pow_nonneg 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NormedRing.toRing
toNormedRing
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
Nonneg.instContinuousFunctionalCalculus
IsSelfAdjoint.instContinuousFunctionalCalculus
IsStarNormal.instContinuousFunctionalCalculus
instNonnegSpectrumClass'
cfc_pow_id
cfc_nonneg_of_predicate
preimage_inr_Icc_zero_one 📖mathematicalSet.preimage
Unitization
Complex
Unitization.inr
Complex.instZero
Set.Icc
PartialOrder.toPreorder
Unitization.instPartialOrder
Unitization.instZero
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
NonUnitalNormedRing.toNonUnitalRing
NonUnitalCStarAlgebra.toNonUnitalNormedRing
Unitization.instOne
Complex.instOne
Set
Set.instInter
setOf
Preorder.toLE
Metric.closedBall
NonUnitalSeminormedRing.toPseudoMetricSpace
NonUnitalNormedRing.toNonUnitalSeminormedRing
Real
Real.instOne
Set.ext
dist_zero_right
rpow_neg_one_le_one 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
NormedRing.toRing
toNormedRing
Real
CFC.instPowReal
toStarRing
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedRing.toPseudoMetricSpace
NormedRing.toSeminormedRing
NormedAlgebra.toAlgebra
Real.normedField
NormedAlgebra.complexToReal
toNormedAlgebra
IsSelfAdjoint.instContinuousFunctionalCalculus
Complex
Complex.instNormedField
IsStarNormal.instContinuousFunctionalCalculus
instNonnegSpectrumClass'
toNonUnitalCStarAlgebra
Real.instNeg
Real.instOne
IsSelfAdjoint.instContinuousFunctionalCalculus
IsStarNormal.instContinuousFunctionalCalculus
instNonnegSpectrumClass'
CanLift.prf
instCanLiftUnitsValIsUnit
isUnit_of_le
instZeroLEOneClass
CFC.rpow_neg_one_eq_inv
LE.le.trans
zero_le_one
inv_le_one
rpow_neg_one_le_rpow_neg_one 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
IsStrictlyPositive
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
NormedRing.toRing
toNormedRing
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Real
CFC.instPowReal
toStarRing
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedRing.toPseudoMetricSpace
NormedRing.toSeminormedRing
NormedAlgebra.toAlgebra
Real.normedField
NormedAlgebra.complexToReal
toNormedAlgebra
IsSelfAdjoint.instContinuousFunctionalCalculus
Complex
Complex.instNormedField
IsStarNormal.instContinuousFunctionalCalculus
instNonnegSpectrumClass'
toNonUnitalCStarAlgebra
Real.instNeg
Real.instOne
IsSelfAdjoint.instContinuousFunctionalCalculus
IsStarNormal.instContinuousFunctionalCalculus
instNonnegSpectrumClass'
CanLift.prf
instCanLiftUnitsValIsUnit
isUnit_of_le
IsStrictlyPositive.isUnit
CFC.rpow_neg_one_eq_inv
IsStrictlyPositive.nonneg
LE.le.trans
inv_le_inv
star_left_conjugate_le_norm_smul 📖mathematicalIsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
NonUnitalNormedRing.toNonUnitalRing
NonUnitalCStarAlgebra.toNonUnitalNormedRing
StarRing.toStarAddMonoid
NonUnitalCStarAlgebra.toStarRing
Preorder.toLE
PartialOrder.toPreorder
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
Star.star
Real
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
ESeminormedAddMonoid.toAddMonoid
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
NormedAddCommGroup.toSeminormedAddCommGroup
NonUnitalNormedRing.toNormedAddCommGroup
ESeminormedAddCommMonoid.toESeminormedAddMonoid
ENormedAddCommMonoid.toESeminormedAddCommMonoid
NormedAddCommGroup.toENormedAddCommMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
Real.instMonoid
Module.toDistribMulAction
Real.semiring
ESeminormedAddCommMonoid.toAddCommMonoid
NonUnitalSeminormedRing.toPseudoMetricSpace
NonUnitalNormedRing.toNonUnitalSeminormedRing
NormedSpace.toModule
Real.normedField
NonUnitalSeminormedRing.toSeminormedAddCommGroup
NormedSpace.complexToReal
NonUnitalCStarAlgebra.toNormedSpace
Norm.norm
NonUnitalNormedRing.toNorm
NonUnitalCStarAlgebra.toIsScalarTower
NonUnitalCStarAlgebra.toSMulCommClass
CStarRing.instRegularNormedAlgebra
NonUnitalCStarAlgebra.toCStarRing
IsScalarTower.complexToReal
IsScalarTower.left
star_left_conjugate_le_conjugate
NonUnitalCStarAlgebra.toStarModule
Unitization.instStarOrderedRing
IsSelfAdjoint.le_algebraMap_norm_self
Algebra.algebraMap_eq_smul_one
Algebra.mul_smul_comm
mul_one
Algebra.smul_mul_assoc
Unitization.inr_le_iff
IsSelfAdjoint.conjugate'
IsSelfAdjoint.smul
StarModule.complexToReal
IsSelfAdjoint.all
instTrivialStarReal
IsSelfAdjoint.star_mul_self
Unitization.inr_mul
Unitization.inr_star
Unitization.inr_smul
Unitization.norm_inr
IsSelfAdjoint.inr
star_mul_le_algebraMap_norm_sq 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NormedRing.toRing
toNormedRing
Star.star
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
StarRing.toStarAddMonoid
toStarRing
DFunLike.coe
RingHom
Real
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
Real.instCommSemiring
Ring.toSemiring
RingHom.instFunLike
algebraMap
NormedAlgebra.toAlgebra
Real.normedField
NormedRing.toSeminormedRing
NormedAlgebra.complexToReal
toNormedAlgebra
Monoid.toNatPow
Real.instMonoid
Norm.norm
NormedRing.toNorm
IsSelfAdjoint.le_algebraMap_norm_self
pow_two
CStarRing.norm_star_mul_self
toCStarRing
star_right_conjugate_le_norm_smul 📖mathematicalIsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
NonUnitalNormedRing.toNonUnitalRing
NonUnitalCStarAlgebra.toNonUnitalNormedRing
StarRing.toStarAddMonoid
NonUnitalCStarAlgebra.toStarRing
Preorder.toLE
PartialOrder.toPreorder
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
Star.star
Real
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
ESeminormedAddMonoid.toAddMonoid
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
NormedAddCommGroup.toSeminormedAddCommGroup
NonUnitalNormedRing.toNormedAddCommGroup
ESeminormedAddCommMonoid.toESeminormedAddMonoid
ENormedAddCommMonoid.toESeminormedAddCommMonoid
NormedAddCommGroup.toENormedAddCommMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
Real.instMonoid
Module.toDistribMulAction
Real.semiring
ESeminormedAddCommMonoid.toAddCommMonoid
NonUnitalSeminormedRing.toPseudoMetricSpace
NonUnitalNormedRing.toNonUnitalSeminormedRing
NormedSpace.toModule
Real.normedField
NonUnitalSeminormedRing.toSeminormedAddCommGroup
NormedSpace.complexToReal
NonUnitalCStarAlgebra.toNormedSpace
Norm.norm
NonUnitalNormedRing.toNorm
star_star
star_left_conjugate_le_norm_smul

IsSelfAdjoint

Theorems

NameKindAssumesProvesValidatesDepends On
le_algebraMap_norm_self 📖mathematicalIsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NormedRing.toRing
CStarAlgebra.toNormedRing
StarRing.toStarAddMonoid
CStarAlgebra.toStarRing
Preorder.toLE
PartialOrder.toPreorder
DFunLike.coe
RingHom
Real
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
Real.instCommSemiring
Ring.toSemiring
RingHom.instFunLike
algebraMap
NormedAlgebra.toAlgebra
Real.normedField
NormedRing.toSeminormedRing
NormedAlgebra.complexToReal
CStarAlgebra.toNormedAlgebra
Norm.norm
NormedRing.toNorm
le_algebraMap_of_spectrum_le
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Real.instStarOrderedRing
instContinuousFunctionalCalculus
IsStarNormal.instContinuousFunctionalCalculus
Real.le_norm_self
spectrum.norm_le_norm_of_mem
CStarAlgebra.toCompleteSpace
CStarRing.instNormOneClassOfNontrivial
CStarAlgebra.toCStarRing
neg_algebraMap_norm_le_self 📖mathematicalIsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NormedRing.toRing
CStarAlgebra.toNormedRing
StarRing.toStarAddMonoid
CStarAlgebra.toStarRing
Preorder.toLE
PartialOrder.toPreorder
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
NormedAddCommGroup.toAddCommGroup
NonUnitalNormedRing.toNormedAddCommGroup
NonUnitalCStarAlgebra.toNonUnitalNormedRing
CStarAlgebra.toNonUnitalCStarAlgebra
DFunLike.coe
RingHom
Real
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
Real.instCommSemiring
Ring.toSemiring
RingHom.instFunLike
algebraMap
NormedAlgebra.toAlgebra
Real.normedField
NormedRing.toSeminormedRing
NormedAlgebra.complexToReal
CStarAlgebra.toNormedAlgebra
Norm.norm
NormedRing.toNorm
neg_le
IsOrderedAddMonoid.toAddLeftMono
IsOrderedCancelAddMonoid.toIsOrderedAddMonoid
IsOrderedAddMonoid.toIsOrderedCancelAddMonoid
StarOrderedRing.toIsOrderedAddMonoid
covariant_swap_add_of_covariant_add
norm_neg
le_algebraMap_norm_self
neg
toReal_spectralRadius_eq_norm 📖mathematicalIsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NormedRing.toRing
CStarAlgebra.toNormedRing
StarRing.toStarAddMonoid
CStarAlgebra.toStarRing
ENNReal.toReal
spectralRadius
Real
Real.normedField
NormedAlgebra.toAlgebra
NormedRing.toSeminormedRing
NormedAlgebra.complexToReal
CStarAlgebra.toNormedAlgebra
Norm.norm
NormedRing.toNorm
SpectrumRestricts.spectralRadius_eq
IsScalarTower.complexToReal
IsScalarTower.left
spectrumRestricts
IsStarNormal.instContinuousFunctionalCalculus
spectralRadius_eq_nnnorm

IsStrictlyPositive

Theorems

NameKindAssumesProvesValidatesDepends On
add_nonneg 📖mathematicalIsStrictlyPositive
Preorder.toLE
PartialOrder.toPreorder
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
NormedRing.toRing
CStarAlgebra.toNormedRing
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
of_le
le_add_iff_nonneg_right
IsOrderedAddMonoid.toAddLeftMono
IsOrderedCancelAddMonoid.toIsOrderedAddMonoid
IsOrderedAddMonoid.toIsOrderedCancelAddMonoid
StarOrderedRing.toIsOrderedAddMonoid
IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT
AddLeftCancelSemigroup.toIsLeftCancelAdd
IsOrderedCancelAddMonoid.toAddLeftReflectLT
nonneg_add 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NormedRing.toRing
CStarAlgebra.toNormedRing
IsStrictlyPositive
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
add_nonneg
add_comm
of_le 📖IsStrictlyPositive
Preorder.toLE
PartialOrder.toPreorder
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
NormedRing.toRing
CStarAlgebra.toNormedRing
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
LE.le.trans
nonneg
CStarAlgebra.isUnit_of_le

Unitization

Definitions

NameCategoryTheorems
instPartialOrder 📖CompOp
7 mathmath: CStarAlgebra.preimage_inr_Icc_zero_one, CStarAlgebra.inr_mem_Icc_iff_norm_le, inr_le_iff, instStarOrderedRing, nnreal_cfcₙ_eq_cfc_inr, CStarAlgebra.inr_mem_Icc_iff_nnnorm_le, inr_nonneg_iff

Theorems

NameKindAssumesProvesValidatesDepends On
inr_le_iff 📖mathematicalIsSelfAdjoint
InvolutiveStar.toStar
StarAddMonoid.toInvolutiveStar
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
NonUnitalNormedRing.toNonUnitalRing
NonUnitalCStarAlgebra.toNonUnitalNormedRing
StarRing.toStarAddMonoid
NonUnitalCStarAlgebra.toStarRing
Unitization
Complex
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
inr
Complex.instZero
sub_nonneg
covariant_swap_add_of_covariant_add
IsOrderedAddMonoid.toAddLeftMono
IsOrderedCancelAddMonoid.toIsOrderedAddMonoid
IsOrderedAddMonoid.toIsOrderedCancelAddMonoid
StarOrderedRing.toIsOrderedAddMonoid
NonUnitalCStarAlgebra.toIsScalarTower
NonUnitalCStarAlgebra.toSMulCommClass
NonUnitalCStarAlgebra.toStarModule
instStarOrderedRing
IsScalarTower.complexToReal
IsScalarTower.left
StarOrderedRing.nonneg_iff_spectrum_nonneg
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Real.instStarOrderedRing
IsSelfAdjoint.instContinuousFunctionalCalculus
IsStarNormal.instContinuousFunctionalCalculus
CStarAlgebra.instNonnegSpectrumClass'
IsSelfAdjoint.sub
inr_sub
quasispectrum_eq_spectrum_inr'
StarOrderedRing.nonneg_iff_quasispectrum_nonneg
Real.instNontrivial
NormMulClass.toNoZeroDivisors
NormedDivisionRing.toNormMulClass
SMulCommClass.complexToReal
IsSelfAdjoint.instNonUnitalContinuousFunctionalCalculus
IsStarNormal.instNonUnitalContinuousFunctionalCalculus
inr_nonneg_iff 📖mathematicalUnitization
Complex
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
instZero
Complex.instZero
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
NonUnitalNormedRing.toNonUnitalRing
NonUnitalCStarAlgebra.toNonUnitalNormedRing
inr
inr_le_iff
inr_zero
isSelfAdjoint_inr
IsSelfAdjoint.of_nonneg
NonUnitalCStarAlgebra.toIsScalarTower
NonUnitalCStarAlgebra.toSMulCommClass
NonUnitalCStarAlgebra.toStarModule
instStarOrderedRing
instStarOrderedRing 📖mathematicalStarOrderedRing
Unitization
Complex
Semiring.toNonUnitalSemiring
instSemiring
Complex.instCommSemiring
NonUnitalRing.toNonUnitalSemiring
NonUnitalNormedRing.toNonUnitalRing
NonUnitalCStarAlgebra.toNonUnitalNormedRing
NormedSpace.toModule
Complex.instNormedField
NonUnitalSeminormedRing.toSeminormedAddCommGroup
NonUnitalNormedRing.toNonUnitalSeminormedRing
NonUnitalCStarAlgebra.toNormedSpace
NonUnitalCStarAlgebra.toIsScalarTower
NonUnitalCStarAlgebra.toSMulCommClass
instPartialOrder
instStarRing
Complex.instStarRing
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
NonUnitalCStarAlgebra.toStarRing
NonUnitalCStarAlgebra.toStarModule
CStarAlgebra.spectralOrderedRing
nnreal_cfcₙ_eq_cfc_inr 📖mathematicalNNReal
instZeroNNReal
inr
Complex
Complex.instZero
cfcₙ
Preorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
NonUnitalNormedRing.toNonUnitalRing
NonUnitalCStarAlgebra.toNonUnitalNormedRing
instCommSemiringNNReal
instNontrivialNNReal
instStarRingNNReal
instMetricSpaceNNReal
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
NonUnitalCStarAlgebra.toStarRing
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
NonUnitalSeminormedRing.toPseudoMetricSpace
NonUnitalNormedRing.toNonUnitalSeminormedRing
NNReal.instModuleOfReal
NonUnitalNonAssocSemiring.toAddCommMonoid
NormedSpace.toModule
Real
Real.normedField
NonUnitalSeminormedRing.toSeminormedAddCommGroup
NormedSpace.complexToReal
NonUnitalCStarAlgebra.toNormedSpace
NNReal.instIsScalarTowerOfReal
DistribMulAction.toMulAction
Real.instMonoid
AddCommMonoid.toAddMonoid
ESeminormedAddCommMonoid.toAddCommMonoid
ENormedAddCommMonoid.toESeminormedAddCommMonoid
NormedAddCommGroup.toENormedAddCommMonoid
NonUnitalNormedRing.toNormedAddCommGroup
Module.toDistribMulAction
Real.semiring
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
NonUnitalNonAssocRing.toAddCommGroup
DistribSMul.toSMulZeroClass
NonUnitalNonAssocSemiring.toDistribSMul
IsScalarTower.complexToReal
NormedAddCommGroup.toAddCommGroup
Complex.instNormedField
NonUnitalCStarAlgebra.toIsScalarTower
NNReal.smulCommClass_left
SMulCommClass.complexToReal
NonUnitalCStarAlgebra.toSMulCommClass
Nonneg.instNonUnitalContinuousFunctionalCalculus
IsSelfAdjoint.instNonUnitalContinuousFunctionalCalculus
IsStarNormal.instNonUnitalContinuousFunctionalCalculus
CStarAlgebra.instNonnegSpectrumClass'
cfc
Unitization
instPartialOrder
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
instRing
Complex.commRing
instUniformSpace
DenselyNormedField.toNontriviallyNormedField
Complex.instDenselyNormedField
instStarRing
Complex.instCommSemiring
Complex.instStarRing
NonUnitalCStarAlgebra.toStarModule
NNReal.instAlgebraOfReal
Ring.toSemiring
instAlgebra
Real.instCommSemiring
NonUnitalRing.toNonUnitalSemiring
NormedAlgebra.toAlgebra
SeminormedCommRing.toSeminormedRing
NormedCommRing.toSeminormedCommRing
CommCStarAlgebra.toNormedCommRing
instCommCStarAlgebraComplex
RCLike.toNormedAlgebra
Complex.instRCLike
CommSemiring.toSemiring
Complex.addCommGroup
Complex.instModuleSelf
NonUnitalSemiring.toNonUnitalNonAssocSemiring
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
IsScalarTower.left
Complex.instSemiring
Nonneg.instContinuousFunctionalCalculus
instStarOrderedRing
IsSelfAdjoint.instContinuousFunctionalCalculus
Algebra.id
IsStarNormal.instContinuousFunctionalCalculus
instCStarAlgebra
CStarAlgebra.toNonUnitalCStarAlgebra
cfcₙ_eq_cfc_inr
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
NNReal.instIsScalarTowerOfReal
IsScalarTower.complexToReal
NonUnitalCStarAlgebra.toIsScalarTower
NNReal.smulCommClass_left
SMulCommClass.complexToReal
NonUnitalCStarAlgebra.toSMulCommClass
NNReal.instCompleteSpace
IsScalarTower.left
Nonneg.instNonUnitalContinuousFunctionalCalculus
IsSelfAdjoint.instNonUnitalContinuousFunctionalCalculus
IsStarNormal.instNonUnitalContinuousFunctionalCalculus
CStarAlgebra.instNonnegSpectrumClass'
Nonneg.instContinuousFunctionalCalculus
NonUnitalCStarAlgebra.toStarModule
instStarOrderedRing
IsSelfAdjoint.instContinuousFunctionalCalculus
IsStarNormal.instContinuousFunctionalCalculus
NNReal.instContinuousMapZero.UniqueHom
NonUnitalSeminormedRing.toIsTopologicalRing
IsScalarTower.right
Algebra.to_smulCommClass
TopologicalSpace.t2Space_of_metrizableSpace
EMetricSpace.metrizableSpace
CStarRing.instRegularNormedAlgebra
NonUnitalCStarAlgebra.toCStarRing
inr_nonneg_iff

(root)

Theorems

NameKindAssumesProvesValidatesDepends On
cfc_nnreal_le_iff 📖mathematicalSpectrumRestricts
NNReal
Real
NNReal.instSemifield
Field.toSemifield
Real.instField
NNReal.instAlgebraOfReal
Ring.toSemiring
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Algebra.id
Real.instCommSemiring
DFunLike.coe
ContinuousMap
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
Real.pseudoMetricSpace
NNReal.instTopologicalSpace
ContinuousMap.instFunLike
ContinuousMap.realToNNReal
ContinuousOn
spectrum
instCommSemiringNNReal
Preorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
cfc
instStarRingNNReal
instMetricSpaceNNReal
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
Nonneg.instContinuousFunctionalCalculus
instPartialOrderNNReal
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
ContinuousOn.ofReal_map_toNNReal
Set.mapsTo_image
SpectrumRestricts.image
NNReal.instIsScalarTowerOfReal
IsScalarTower.left
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
Nonneg.instContinuousFunctionalCalculus
cfc_nnreal_eq_real
cfc_le_iff
Real.instStarOrderedRing
IsSelfAdjoint.of_nonneg
Set.image_congr
cfc_tsub 📖mathematicalNNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderNNReal
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
ContinuousOn
NNReal.instTopologicalSpace
spectrum
instCommSemiringNNReal
NNReal.instAlgebraOfReal
Ring.toSemiring
cfc
instStarRingNNReal
instMetricSpaceNNReal
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
Nonneg.instContinuousFunctionalCalculus
NNReal.instSub
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
SpectrumRestricts.nnreal_of_nonneg
NNReal.coe_sub
SpectrumRestricts.apply_mem
NNReal.instIsScalarTowerOfReal
IsScalarTower.left
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
Nonneg.instContinuousFunctionalCalculus
cfc_nnreal_eq_real
cfc_congr
cfc_sub
Continuous.comp_continuousOn
continuous_subtype_val
ContinuousOn.comp
Continuous.continuousOn
continuous_real_toNNReal
Set.mapsTo_image
SpectrumRestricts.image
cfcₙ_tsub 📖mathematicalNNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderNNReal
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalRing.toNonUnitalNonAssocRing
ContinuousOn
NNReal.instTopologicalSpace
quasispectrum
instCommSemiringNNReal
NNReal.instModuleOfReal
NonUnitalNonAssocSemiring.toAddCommMonoid
instZeroNNReal
cfcₙ
instNontrivialNNReal
instStarRingNNReal
instMetricSpaceNNReal
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
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.instSub
SubNegMonoid.toSub
Real.instNontrivial
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
QuasispectrumRestricts.nnreal_of_nonneg
NNReal.coe_sub
QuasispectrumRestricts.apply_mem
NNReal.instIsScalarTowerOfReal
IsScalarTower.left
NNReal.instIsTopologicalSemiring
NNReal.instContinuousStar
NNReal.smulCommClass_left
Nonneg.instNonUnitalContinuousFunctionalCalculus
cfcₙ_nnreal_eq_real
cfcₙ_congr
cfcₙ_sub
Continuous.comp_continuousOn
continuous_subtype_val
ContinuousOn.comp
Continuous.continuousOn
continuous_real_toNNReal
Set.mapsTo_image
QuasispectrumRestricts.image
Real.toNNReal_zero
isStrictlyPositive_add 📖mathematicalIsStrictlyPositive
Preorder.toLE
PartialOrder.toPreorder
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
NormedRing.toRing
CStarAlgebra.toNormedRing
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
le_iff_norm_sqrt_mul_rpow 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NormedRing.toRing
CStarAlgebra.toNormedRing
IsStrictlyPositive
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
Real
Real.instLE
Norm.norm
NormedRing.toNorm
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
CFC.sqrt
NonUnitalNormedRing.toNonUnitalRing
NonUnitalCStarAlgebra.toNonUnitalNormedRing
CStarAlgebra.toNonUnitalCStarAlgebra
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedRing.toPseudoMetricSpace
NormedRing.toSeminormedRing
CStarAlgebra.toStarRing
NormedSpace.toModule
Real.normedField
NonUnitalSeminormedRing.toSeminormedAddCommGroup
NonUnitalNormedRing.toNonUnitalSeminormedRing
NormedSpace.complexToReal
NonUnitalCStarAlgebra.toNormedSpace
Algebra.to_smulCommClass
Semifield.toCommSemiring
Field.toSemifield
NormedField.toField
SeminormedRing.toRing
NormedAlgebra.toAlgebra
NormedAlgebra.complexToReal
CStarAlgebra.toNormedAlgebra
IsScalarTower.right
IsSelfAdjoint.instNonUnitalContinuousFunctionalCalculus
Complex
Complex.instNormedField
IsStarNormal.instNonUnitalContinuousFunctionalCalculus
CStarAlgebra.instNonnegSpectrumClass'
CFC.instPowReal
IsSelfAdjoint.instContinuousFunctionalCalculus
IsStarNormal.instContinuousFunctionalCalculus
Real.instNeg
DivInvMonoid.toDiv
Real.instDivInvMonoid
Real.instOne
instOfNatAtLeastTwo
Real.instNatCast
Nat.instAtLeastTwoHAddOfNat
Algebra.to_smulCommClass
IsScalarTower.right
IsSelfAdjoint.instNonUnitalContinuousFunctionalCalculus
IsStarNormal.instNonUnitalContinuousFunctionalCalculus
CStarAlgebra.instNonnegSpectrumClass'
IsSelfAdjoint.instContinuousFunctionalCalculus
IsStarNormal.instContinuousFunctionalCalculus
Nat.instAtLeastTwoHAddOfNat
CanLift.prf
instCanLiftUnitsValIsUnit
IsStrictlyPositive.isUnit
conjugate_nonneg_of_nonneg
CFC.rpow_nonneg
sq_le_one_iff₀
IsStrictOrderedRing.toPosMulStrictMono
Real.instIsStrictOrderedRing
Real.instZeroLEOneClass
norm_nonneg
sq
CStarRing.norm_star_mul_self
CStarAlgebra.toCStarRing
StarMul.star_mul
IsSelfAdjoint.of_nonneg
CFC.sqrt_nonneg
mul_assoc
CFC.sqrt_mul_sqrt_self
NonUnitalSeminormedRing.toIsTopologicalRing
TopologicalSpace.t2Space_of_metrizableSpace
EMetricSpace.metrizableSpace
CStarAlgebra.norm_le_one_iff_of_nonneg
IsSelfAdjoint.conjugate_le_conjugate
CFC.conjugate_rpow_neg_one_half
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
CFC.sqrt_eq_rpow
CFC.rpow_add
Units.isUnit
Mathlib.Meta.NormNum.IsNat.to_eq
Mathlib.Meta.NormNum.IsInt.to_isNat
Mathlib.Meta.NormNum.IsRat.to_isInt
Mathlib.Meta.NormNum.isRat_add
Mathlib.Meta.NormNum.IsNNRat.to_isRat
Mathlib.Meta.NormNum.isNNRat_div
Mathlib.Meta.NormNum.isNNRat_mul
Mathlib.Meta.NormNum.IsNat.to_isNNRat
Mathlib.Meta.NormNum.isNat_ofNat
Nat.cast_one
Mathlib.Meta.NormNum.isNNRat_inv_pos
RCLike.charZero_rclike
Mathlib.Meta.NormNum.instAtLeastTwo
Mathlib.Meta.NormNum.isRat_neg
Nat.cast_zero
CFC.rpow_zero
IsStrictlyPositive.nonneg
one_mul
mul_one
LE.le.trans
conjugate_le_conjugate_of_nonneg
le_iff_norm_sqrt_mul_sqrt_inv 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NormedRing.toRing
CStarAlgebra.toNormedRing
Units.val
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
Real
Real.instLE
Norm.norm
NormedRing.toNorm
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
CFC.sqrt
NonUnitalNormedRing.toNonUnitalRing
NonUnitalCStarAlgebra.toNonUnitalNormedRing
CStarAlgebra.toNonUnitalCStarAlgebra
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedRing.toPseudoMetricSpace
NormedRing.toSeminormedRing
CStarAlgebra.toStarRing
NormedSpace.toModule
Real.normedField
NonUnitalSeminormedRing.toSeminormedAddCommGroup
NonUnitalNormedRing.toNonUnitalSeminormedRing
NormedSpace.complexToReal
NonUnitalCStarAlgebra.toNormedSpace
Algebra.to_smulCommClass
Semifield.toCommSemiring
Field.toSemifield
NormedField.toField
SeminormedRing.toRing
NormedAlgebra.toAlgebra
NormedAlgebra.complexToReal
CStarAlgebra.toNormedAlgebra
IsScalarTower.right
IsSelfAdjoint.instNonUnitalContinuousFunctionalCalculus
Complex
Complex.instNormedField
IsStarNormal.instNonUnitalContinuousFunctionalCalculus
CStarAlgebra.instNonnegSpectrumClass'
Units
Units.instInv
Real.instOne
Algebra.to_smulCommClass
IsScalarTower.right
IsSelfAdjoint.instNonUnitalContinuousFunctionalCalculus
IsStarNormal.instNonUnitalContinuousFunctionalCalculus
CStarAlgebra.instNonnegSpectrumClass'
IsSelfAdjoint.instContinuousFunctionalCalculus
IsStarNormal.instContinuousFunctionalCalculus
Nat.instAtLeastTwoHAddOfNat
ContinuousFunctionalCalculus.toNonUnital
IsTopologicalRing.toIsTopologicalSemiring
instIsTopologicalRingReal
instContinuousStarReal
Real.instCompleteSpace
CFC.sqrt_eq_rpow
NonUnitalSeminormedRing.toIsTopologicalRing
TopologicalSpace.t2Space_of_metrizableSpace
EMetricSpace.metrizableSpace
CFC.rpow_neg_one_eq_inv
CFC.rpow_rpow
NeZero.charZero_one
RCLike.charZero_rclike
le_iff_norm_sqrt_mul_rpow
IsUnit.isStrictlyPositive
Units.isUnit
one_div
neg_mul
one_mul

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