Star

📁 Source: Mathlib/Analysis/Calculus/Deriv/Star.lean

Statistics

Metric	Count
Definitions	0
Theorems conj_conj, star_conj, conj_conj, star_conj, star', deriv_conj_conj, deriv_star_conj, differentiableAt_conj_conj_iff, differentiableAt_star_conj_iff, hasDerivAt_conj_conj_iff, hasDerivAt_star_conj_iff	11
Total	11

DifferentiableAt

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
conj_conj 📖	mathematical	DifferentiableAt NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing NontriviallyNormedField.toNormedField NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing	DifferentiableAt NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing NontriviallyNormedField.toNormedField NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring Semifield.toCommSemiring Field.toSemifield NormedField.toField RingHom.instFunLike starRingEnd	—	star_star StarMul.toStarModule NormedStarGroup.to_continuousStar
star_conj 📖	mathematical	DifferentiableAt NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing NontriviallyNormedField.toNormedField NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedAddCommGroup.toSeminormedAddCommGroup SeminormedAddCommGroup.toPseudoMetricSpace	DifferentiableAt NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing NontriviallyNormedField.toNormedField NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedAddCommGroup.toSeminormedAddCommGroup SeminormedAddCommGroup.toPseudoMetricSpace Star.star InvolutiveStar.toStar StarAddMonoid.toInvolutiveStar ESeminormedAddMonoid.toAddMonoid ESeminormedAddCommMonoid.toESeminormedAddMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring Semifield.toCommSemiring Field.toSemifield NormedField.toField RingHom.instFunLike starRingEnd	—	star_star StarMul.toStarModule NormedStarGroup.to_continuousStar

HasDerivAt

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
conj_conj 📖	mathematical	HasDerivAt NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing NontriviallyNormedField.toNormedField NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing ContinuousMul.to_continuousSMul Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing IsTopologicalSemiring.toContinuousMul IsTopologicalRing.toIsTopologicalSemiring IsTopologicalDivisionRing.toIsTopologicalRing NormedDivisionRing.toDivisionRing NormedField.toNormedDivisionRing NormedDivisionRing.to_isTopologicalDivisionRing	HasDerivAt NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing NontriviallyNormedField.toNormedField NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing ContinuousMul.to_continuousSMul Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing IsTopologicalSemiring.toContinuousMul IsTopologicalRing.toIsTopologicalSemiring IsTopologicalDivisionRing.toIsTopologicalRing NormedDivisionRing.toDivisionRing NormedField.toNormedDivisionRing NormedDivisionRing.to_isTopologicalDivisionRing DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring Semifield.toCommSemiring Field.toSemifield NormedField.toField RingHom.instFunLike starRingEnd	—	ContinuousMul.to_continuousSMul IsTopologicalSemiring.toContinuousMul IsTopologicalRing.toIsTopologicalSemiring IsTopologicalDivisionRing.toIsTopologicalRing NormedDivisionRing.to_isTopologicalDivisionRing star_conj StarMul.toStarModule NormedStarGroup.to_continuousStar
star_conj 📖	mathematical	HasDerivAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace IsBoundedSMul.continuousSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid AddCommGroup.toAddGroup DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField Module.toDistribMulAction AddCommGroup.toAddCommMonoid NormedSpace.toIsBoundedSMul	HasDerivAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace IsBoundedSMul.continuousSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid AddCommGroup.toAddGroup DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField Module.toDistribMulAction AddCommGroup.toAddCommMonoid NormedSpace.toIsBoundedSMul Star.star InvolutiveStar.toStar StarAddMonoid.toInvolutiveStar ESeminormedAddMonoid.toAddMonoid ESeminormedAddCommMonoid.toESeminormedAddMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring Semifield.toCommSemiring RingHom.instFunLike starRingEnd	—	IsBoundedSMul.continuousSMul NormedSpace.toIsBoundedSMul hasDerivAt_iff_hasFDerivAt RingHomInvPair.triples₂ RingHomInvPair.instStarRingEnd RingHomCompTriple.right_ids StarMul.toStarModule NormedStarGroup.to_continuousStar ContinuousLinearMap.ext_ring one_smul star_one HasFDerivAt.star_star hasFDerivAt

(root)

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
deriv_conj_conj 📖	mathematical	—	deriv NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing NontriviallyNormedField.toNormedField NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring Semifield.toCommSemiring Field.toSemifield NormedField.toField RingHom.instFunLike starRingEnd	—	deriv_star_conj StarMul.toStarModule NormedStarGroup.to_continuousStar
deriv_star_conj 📖	mathematical	—	deriv NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace Star.star InvolutiveStar.toStar StarAddMonoid.toInvolutiveStar ESeminormedAddMonoid.toAddMonoid ESeminormedAddCommMonoid.toESeminormedAddMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring Semifield.toCommSemiring Field.toSemifield NormedField.toField RingHom.instFunLike starRingEnd	—	RingHomCompTriple.comp_apply RingHomInvPair.triples₂ RingHomInvPair.instStarRingEnd HasDerivAt.deriv HasDerivAt.star_conj DifferentiableAt.hasDerivAt Iff.not differentiableAt_star_conj_iff deriv_zero_of_not_differentiableAt star_zero
differentiableAt_conj_conj_iff 📖	mathematical	—	DifferentiableAt NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing NontriviallyNormedField.toNormedField NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring Semifield.toCommSemiring Field.toSemifield NormedField.toField RingHom.instFunLike starRingEnd	—	differentiableAt_star_conj_iff StarMul.toStarModule NormedStarGroup.to_continuousStar
differentiableAt_star_conj_iff 📖	mathematical	—	DifferentiableAt NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing NontriviallyNormedField.toNormedField NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedAddCommGroup.toSeminormedAddCommGroup SeminormedAddCommGroup.toPseudoMetricSpace Star.star InvolutiveStar.toStar StarAddMonoid.toInvolutiveStar ESeminormedAddMonoid.toAddMonoid ESeminormedAddCommMonoid.toESeminormedAddMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring Semifield.toCommSemiring Field.toSemifield NormedField.toField RingHom.instFunLike starRingEnd	—	RingHomCompTriple.comp_apply RingHomInvPair.triples₂ RingHomInvPair.instStarRingEnd star_star DifferentiableAt.star_conj
hasDerivAt_conj_conj_iff 📖	mathematical	—	HasDerivAt NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing NontriviallyNormedField.toNormedField NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing ContinuousMul.to_continuousSMul Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing IsTopologicalSemiring.toContinuousMul IsTopologicalRing.toIsTopologicalSemiring IsTopologicalDivisionRing.toIsTopologicalRing NormedDivisionRing.toDivisionRing NormedField.toNormedDivisionRing NormedDivisionRing.to_isTopologicalDivisionRing DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring Semifield.toCommSemiring Field.toSemifield NormedField.toField RingHom.instFunLike starRingEnd	—	hasDerivAt_star_conj_iff StarMul.toStarModule NormedStarGroup.to_continuousStar
hasDerivAt_star_conj_iff 📖	mathematical	—	HasDerivAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace IsBoundedSMul.continuousSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid AddCommGroup.toAddGroup DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField Module.toDistribMulAction AddCommGroup.toAddCommMonoid NormedSpace.toIsBoundedSMul Star.star InvolutiveStar.toStar StarAddMonoid.toInvolutiveStar ESeminormedAddMonoid.toAddMonoid ESeminormedAddCommMonoid.toESeminormedAddMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring Semifield.toCommSemiring RingHom.instFunLike starRingEnd	—	IsBoundedSMul.continuousSMul NormedSpace.toIsBoundedSMul RingHomCompTriple.comp_apply RingHomInvPair.triples₂ RingHomInvPair.instStarRingEnd star_star HasDerivAt.star_conj

deriv

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
star' 📖	mathematical	—	deriv NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace Star.star InvolutiveStar.toStar StarAddMonoid.toInvolutiveStar ESeminormedAddMonoid.toAddMonoid ESeminormedAddCommMonoid.toESeminormedAddMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid	—	star

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