Comp

📁 Source: Mathlib/Analysis/Calculus/FDeriv/Comp.lean

Statistics

Metric	Count
Definitions	0
Theorems comp, comp_differentiableOn, fun_comp, iterate, comp, comp_differentiableWithinAt, fun_comp', iterate, comp, fun_comp, iterate, comp, comp', iterate, comp, comp_hasFDerivWithinAt, iterate, comp, iterate, comp, comp_hasFDerivAt, comp_hasFDerivAt_of_eq, comp_of_tendsto, iterate, comp, iterate, fderivWithin_comp, fderivWithin_comp', fderivWithin_comp_of_eq, fderivWithin_comp_of_eq', fderivWithin_comp₃, fderivWithin_fderivWithin, fderiv_comp, fderiv_comp', fderiv_comp_fderivWithin	35
Total	35

Differentiable

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
comp 📖	—	Differentiable NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace	—	—	DifferentiableAt.comp
comp_differentiableOn 📖	—	Differentiable NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace DifferentiableOn	—	—	DifferentiableOn.comp differentiableOn Set.mapsTo_univ
fun_comp 📖	—	Differentiable NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace	—	—	DifferentiableAt.comp
iterate 📖	mathematical	Differentiable NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace	Nat.iterate	—	differentiable_id comp

DifferentiableAt

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
comp 📖	—	DifferentiableAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace	—	—	HasFDerivAt.differentiableAt RingHomCompTriple.ids HasFDerivAt.comp hasFDerivAt
comp_differentiableWithinAt 📖	—	DifferentiableAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace DifferentiableWithinAt	—	—	DifferentiableWithinAt.comp differentiableWithinAt Set.mapsTo_univ
fun_comp' 📖	—	DifferentiableAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace	—	—	HasFDerivAt.differentiableAt RingHomCompTriple.ids HasFDerivAt.comp hasFDerivAt
iterate 📖	mathematical	DifferentiableAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace	Nat.iterate	—	HasFDerivAt.differentiableAt HasFDerivAt.iterate hasFDerivAt

DifferentiableOn

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
comp 📖	—	DifferentiableOn NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace Set.MapsTo	—	—	DifferentiableWithinAt.comp
fun_comp 📖	—	DifferentiableOn NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace Set.MapsTo	—	—	DifferentiableWithinAt.comp
iterate 📖	mathematical	DifferentiableOn NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace Set.MapsTo	Nat.iterate	—	differentiableOn_id comp

DifferentiableWithinAt

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
comp 📖	—	DifferentiableWithinAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace Set.MapsTo	—	—	HasFDerivWithinAt.differentiableWithinAt RingHomCompTriple.ids HasFDerivWithinAt.comp hasFDerivWithinAt
comp' 📖	mathematical	DifferentiableWithinAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace	Set Set.instInter Set.preimage	—	comp mono Set.inter_subset_left Set.inter_subset_right
iterate 📖	mathematical	DifferentiableWithinAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace Set.MapsTo	Nat.iterate	—	HasFDerivWithinAt.differentiableWithinAt HasFDerivWithinAt.iterate hasFDerivWithinAt

HasFDerivAt

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
comp 📖	mathematical	HasFDerivAt SeminormedAddCommGroup.toAddCommGroup NormedAddCommGroup.toSeminormedAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace	ContinuousLinearMap.comp DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid RingHomCompTriple.ids	—	HasFDerivAtFilter.comp continuousAt IsTopologicalAddGroup.toContinuousAdd SeminormedAddCommGroup.toIsTopologicalAddGroup IsBoundedSMul.continuousSMul NormedSpace.toIsBoundedSMul
comp_hasFDerivWithinAt 📖	mathematical	HasFDerivAt SeminormedAddCommGroup.toAddCommGroup NormedAddCommGroup.toSeminormedAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace HasFDerivWithinAt	ContinuousLinearMap.comp DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid RingHomCompTriple.ids	—	HasFDerivAtFilter.comp HasFDerivWithinAt.continuousWithinAt IsTopologicalAddGroup.toContinuousAdd SeminormedAddCommGroup.toIsTopologicalAddGroup IsBoundedSMul.continuousSMul NormedSpace.toIsBoundedSMul
iterate 📖	mathematical	HasFDerivAt SeminormedAddCommGroup.toAddCommGroup NormedAddCommGroup.toSeminormedAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace	Nat.iterate ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField RingHom.id Semiring.toNonAssocSemiring ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid Monoid.toNatPow MonoidWithZero.toMonoid ContinuousLinearMap.monoidWithZero	—	HasFDerivAtFilter.iterate ContinuousAt.tendsto continuousAt IsTopologicalAddGroup.toContinuousAdd SeminormedAddCommGroup.toIsTopologicalAddGroup IsBoundedSMul.continuousSMul NormedSpace.toIsBoundedSMul

HasFDerivAtFilter

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
comp 📖	mathematical	HasFDerivAtFilter SeminormedAddCommGroup.toAddCommGroup NormedAddCommGroup.toSeminormedAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace Filter.Tendsto	ContinuousLinearMap.comp DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid RingHomCompTriple.ids	—	Asymptotics.IsBigO.trans_isLittleO ContinuousLinearMap.isBigO_comp RingHomIsometric.ids isLittleO Asymptotics.IsLittleO.trans_isBigO Asymptotics.IsLittleO.comp_tendsto isBigO_sub of_isLittleO RingHomCompTriple.ids Asymptotics.IsLittleO.triangle Asymptotics.IsLittleO.congr_left map_sub DistribMulActionSemiHomClass.toAddMonoidHomClass SemilinearMapClass.distribMulActionSemiHomClass ContinuousSemilinearMapClass.toSemilinearMapClass ContinuousLinearMap.continuousSemilinearMapClass
iterate 📖	mathematical	HasFDerivAtFilter SeminormedAddCommGroup.toAddCommGroup NormedAddCommGroup.toSeminormedAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace Filter.Tendsto	Nat.iterate ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField RingHom.id Semiring.toNonAssocSemiring ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid Monoid.toNatPow MonoidWithZero.toMonoid ContinuousLinearMap.monoidWithZero	—	hasFDerivAtFilter_id Function.iterate_succ pow_succ comp

HasFDerivWithinAt

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
comp 📖	mathematical	HasFDerivWithinAt SeminormedAddCommGroup.toAddCommGroup NormedAddCommGroup.toSeminormedAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace Set.MapsTo	ContinuousLinearMap.comp DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid RingHomCompTriple.ids	—	HasFDerivAtFilter.comp ContinuousWithinAt.tendsto_nhdsWithin continuousWithinAt IsTopologicalAddGroup.toContinuousAdd SeminormedAddCommGroup.toIsTopologicalAddGroup IsBoundedSMul.continuousSMul NormedSpace.toIsBoundedSMul
comp_hasFDerivAt 📖	mathematical	HasFDerivWithinAt SeminormedAddCommGroup.toAddCommGroup NormedAddCommGroup.toSeminormedAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace HasFDerivAt Filter.Eventually Set Set.instMembership nhds	ContinuousLinearMap.comp DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid RingHomCompTriple.ids	—	HasFDerivAtFilter.comp tendsto_nhdsWithin_iff HasFDerivAt.continuousAt IsTopologicalAddGroup.toContinuousAdd SeminormedAddCommGroup.toIsTopologicalAddGroup IsBoundedSMul.continuousSMul NormedSpace.toIsBoundedSMul
comp_hasFDerivAt_of_eq 📖	mathematical	HasFDerivWithinAt SeminormedAddCommGroup.toAddCommGroup NormedAddCommGroup.toSeminormedAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace HasFDerivAt Filter.Eventually Set Set.instMembership nhds	ContinuousLinearMap.comp DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid RingHomCompTriple.ids	—	RingHomCompTriple.ids comp_hasFDerivAt
comp_of_tendsto 📖	mathematical	HasFDerivWithinAt SeminormedAddCommGroup.toAddCommGroup NormedAddCommGroup.toSeminormedAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace Filter.Tendsto nhdsWithin	ContinuousLinearMap.comp DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid RingHomCompTriple.ids	—	HasFDerivAtFilter.comp
iterate 📖	mathematical	HasFDerivWithinAt SeminormedAddCommGroup.toAddCommGroup NormedAddCommGroup.toSeminormedAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace Set.MapsTo	Nat.iterate ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField RingHom.id Semiring.toNonAssocSemiring ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid Monoid.toNatPow MonoidWithZero.toMonoid ContinuousLinearMap.monoidWithZero	—	HasFDerivAtFilter.iterate nhdsWithin.eq_1 Filter.tendsto_inf continuousWithinAt IsTopologicalAddGroup.toContinuousAdd SeminormedAddCommGroup.toIsTopologicalAddGroup IsBoundedSMul.continuousSMul NormedSpace.toIsBoundedSMul Filter.Tendsto.mono_left Filter.tendsto_principal_principal inf_le_right

HasStrictFDerivAt

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
comp 📖	mathematical	HasStrictFDerivAt SeminormedAddCommGroup.toAddCommGroup NormedAddCommGroup.toSeminormedAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace	ContinuousLinearMap.comp DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid RingHomCompTriple.ids	—	of_isLittleO RingHomCompTriple.ids Asymptotics.IsLittleO.triangle Asymptotics.IsLittleO.trans_isBigO Asymptotics.IsLittleO.comp_tendsto isLittleO ContinuousAt.prodMap' continuousAt IsTopologicalAddGroup.toContinuousAdd SeminormedAddCommGroup.toIsTopologicalAddGroup IsBoundedSMul.continuousSMul NormedSpace.toIsBoundedSMul isBigO_sub ContinuousLinearMap.map_sub Asymptotics.IsBigO.trans_isLittleO ContinuousLinearMap.isBigO_comp RingHomIsometric.ids
iterate 📖	mathematical	HasStrictFDerivAt SeminormedAddCommGroup.toAddCommGroup NormedAddCommGroup.toSeminormedAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace	Nat.iterate ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField RingHom.id Semiring.toNonAssocSemiring ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid Monoid.toNatPow MonoidWithZero.toMonoid ContinuousLinearMap.monoidWithZero	—	hasStrictFDerivAt_id Function.iterate_succ pow_succ comp

(root)

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
fderivWithin_comp 📖	mathematical	DifferentiableWithinAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace Set.MapsTo UniqueDiffWithinAt DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField	fderivWithin ContinuousLinearMap.comp RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid RingHomCompTriple.ids SeminormedAddCommGroup.toAddCommGroup	—	HasFDerivWithinAt.fderivWithin RingHomCompTriple.ids IsTopologicalAddGroup.toContinuousAdd SeminormedAddCommGroup.toIsTopologicalAddGroup IsBoundedSMul.continuousSMul NormedSpace.toIsBoundedSMul TopologicalSpace.t2Space_of_metrizableSpace EMetricSpace.metrizableSpace HasFDerivWithinAt.comp DifferentiableWithinAt.hasFDerivWithinAt
fderivWithin_comp' 📖	mathematical	DifferentiableWithinAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace Set.MapsTo UniqueDiffWithinAt DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField	fderivWithin ContinuousLinearMap.comp RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid RingHomCompTriple.ids SeminormedAddCommGroup.toAddCommGroup	—	fderivWithin_comp
fderivWithin_comp_of_eq 📖	mathematical	DifferentiableWithinAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace Set.MapsTo UniqueDiffWithinAt DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField	fderivWithin ContinuousLinearMap.comp RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid RingHomCompTriple.ids SeminormedAddCommGroup.toAddCommGroup	—	RingHomCompTriple.ids fderivWithin_comp
fderivWithin_comp_of_eq' 📖	mathematical	DifferentiableWithinAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace Set.MapsTo UniqueDiffWithinAt DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField	fderivWithin ContinuousLinearMap.comp RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid RingHomCompTriple.ids SeminormedAddCommGroup.toAddCommGroup	—	RingHomCompTriple.ids fderivWithin_comp
fderivWithin_comp₃ 📖	mathematical	DifferentiableWithinAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace Set.MapsTo UniqueDiffWithinAt DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField	fderivWithin ContinuousLinearMap.comp RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid RingHomCompTriple.ids SeminormedAddCommGroup.toAddCommGroup	—	RingHomCompTriple.ids HasFDerivWithinAt.fderivWithin IsTopologicalAddGroup.toContinuousAdd SeminormedAddCommGroup.toIsTopologicalAddGroup IsBoundedSMul.continuousSMul NormedSpace.toIsBoundedSMul TopologicalSpace.t2Space_of_metrizableSpace EMetricSpace.metrizableSpace HasFDerivWithinAt.comp DifferentiableWithinAt.hasFDerivWithinAt Set.MapsTo.comp
fderivWithin_fderivWithin 📖	mathematical	DifferentiableWithinAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace Set.MapsTo UniqueDiffWithinAt DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField	DFunLike.coe ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid ContinuousLinearMap.funLike fderivWithin	—	RingHomCompTriple.ids fderivWithin_comp ContinuousLinearMap.coe_comp'
fderiv_comp 📖	mathematical	DifferentiableAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace	fderiv ContinuousLinearMap.comp DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid RingHomCompTriple.ids SeminormedAddCommGroup.toAddCommGroup	—	HasFDerivAt.fderiv RingHomCompTriple.ids IsTopologicalAddGroup.toContinuousAdd SeminormedAddCommGroup.toIsTopologicalAddGroup IsBoundedSMul.continuousSMul NormedSpace.toIsBoundedSMul TopologicalSpace.t2Space_of_metrizableSpace EMetricSpace.metrizableSpace HasFDerivAt.comp DifferentiableAt.hasFDerivAt
fderiv_comp' 📖	mathematical	DifferentiableAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace	fderiv ContinuousLinearMap.comp DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid RingHomCompTriple.ids SeminormedAddCommGroup.toAddCommGroup	—	fderiv_comp
fderiv_comp_fderivWithin 📖	mathematical	DifferentiableAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace DifferentiableWithinAt UniqueDiffWithinAt DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField	fderivWithin ContinuousLinearMap.comp RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid RingHomCompTriple.ids fderiv SeminormedAddCommGroup.toAddCommGroup	—	HasFDerivWithinAt.fderivWithin RingHomCompTriple.ids IsTopologicalAddGroup.toContinuousAdd SeminormedAddCommGroup.toIsTopologicalAddGroup IsBoundedSMul.continuousSMul NormedSpace.toIsBoundedSMul TopologicalSpace.t2Space_of_metrizableSpace EMetricSpace.metrizableSpace HasFDerivAt.comp_hasFDerivWithinAt DifferentiableAt.hasFDerivAt DifferentiableWithinAt.hasFDerivWithinAt

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