Exponential

📁 Source: Mathlib/Analysis/SpecialFunctions/Exponential.lean

Statistics

Metric	Count
Definitions	0
Theorems exp_eq_exp_ℂ, exp, exp_eq_exp_ℝ, hasDerivAt_exp, hasDerivAt_exp_of_mem_ball, hasDerivAt_exp_smul_const, hasDerivAt_exp_smul_const', hasDerivAt_exp_smul_const_of_mem_ball, hasDerivAt_exp_smul_const_of_mem_ball', hasDerivAt_exp_zero, hasDerivAt_exp_zero_of_radius_pos, hasFDerivAt_exp, hasFDerivAt_exp_of_mem_ball, hasFDerivAt_exp_smul_const, hasFDerivAt_exp_smul_const', hasFDerivAt_exp_smul_const_of_mem_ball, hasFDerivAt_exp_smul_const_of_mem_ball', hasFDerivAt_exp_zero, hasFDerivAt_exp_zero_of_radius_pos, hasStrictDerivAt_exp, hasStrictDerivAt_exp_of_mem_ball, hasStrictDerivAt_exp_smul_const, hasStrictDerivAt_exp_smul_const', hasStrictDerivAt_exp_smul_const_of_mem_ball, hasStrictDerivAt_exp_smul_const_of_mem_ball', hasStrictDerivAt_exp_zero, hasStrictDerivAt_exp_zero_of_radius_pos, hasStrictFDerivAt_exp, hasStrictFDerivAt_exp_of_mem_ball, hasStrictFDerivAt_exp_smul_const, hasStrictFDerivAt_exp_smul_const', hasStrictFDerivAt_exp_smul_const_of_mem_ball, hasStrictFDerivAt_exp_smul_const_of_mem_ball', hasStrictFDerivAt_exp_zero, hasStrictFDerivAt_exp_zero_of_radius_pos	35
Total	35

Complex

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
exp_eq_exp_ℂ 📖	mathematical	—	exp NormedSpace.exp Complex instRing UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing instNormedField IsTopologicalDivisionRing.toIsTopologicalRing NormedDivisionRing.toDivisionRing NormedField.toNormedDivisionRing NormedDivisionRing.to_isTopologicalDivisionRing	—	IsTopologicalDivisionRing.toIsTopologicalRing NormedDivisionRing.to_isTopologicalDivisionRing Real.instIsStrictOrderedRing isAbsoluteValueNorm instIsComplete exp_def NormedSpace.exp_eq_tsum_div instCharZero tendsto_nhds_unique instT2Space Filter.atTop_neBot instIsDirectedOrder IsStrictOrderedRing.toIsOrderedRing Nat.instIsStrictOrderedRing instArchimedeanNat CauSeq.tendsto_limit HasSum.tendsto_sum_nat Summable.hasSum NormedSpace.expSeries_div_summable instCompleteSpace

HasSum

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
exp 📖	mathematical	HasSum ESeminormedAddCommMonoid.toAddCommMonoid UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing SummationFilter.unconditional	HasProd CommRing.toCommMonoid NormedCommRing.toCommRing NormedSpace.exp NormedRing.toRing NormedCommRing.toNormedRing NonUnitalSeminormedRing.toIsTopologicalRing NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing	—	Filter.Tendsto.congr NonUnitalSeminormedRing.toIsTopologicalRing NormedSpace.exp_sum Filter.Tendsto.exp

Real

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
exp_eq_exp_ℝ 📖	mathematical	—	exp NormedSpace.exp Real instRing UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace pseudoMetricSpace instIsTopologicalRingReal	—	instIsTopologicalRingReal IsTopologicalDivisionRing.toIsTopologicalRing NormedDivisionRing.to_isTopologicalDivisionRing Complex.exp_eq_exp_ℂ

(root)

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
hasDerivAt_exp 📖	mathematical	—	HasDerivAt DenselyNormedField.toNontriviallyNormedField RCLike.toDenselyNormedField NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing DenselyNormedField.toNormedField NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing ContinuousMul.to_continuousSMul NontriviallyNormedField.toNormedField MulZeroClass.toMul MulZeroOneClass.toMulZeroClass MonoidWithZero.toMulZeroOneClass Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField IsTopologicalSemiring.toContinuousMul NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring IsTopologicalRing.toIsTopologicalSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing IsTopologicalDivisionRing.toIsTopologicalRing NormedDivisionRing.toDivisionRing NormedField.toNormedDivisionRing NormedDivisionRing.to_isTopologicalDivisionRing NormedSpace.exp NormedRing.toRing NormedCommRing.toNormedRing	—	HasStrictDerivAt.hasDerivAt IsTopologicalDivisionRing.toIsTopologicalRing NormedDivisionRing.to_isTopologicalDivisionRing hasStrictDerivAt_exp
hasDerivAt_exp_of_mem_ball 📖	mathematical	Set Set.instMembership Metric.eball EMetricSpace.toPseudoEMetricSpace MetricSpace.toEMetricSpace NormedField.toMetricSpace NontriviallyNormedField.toNormedField MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing FormalMultilinearSeries.radius NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedField.toNormedSpace NormedSpace.expSeries NormedField.toField NormedRing.toRing NormedCommRing.toNormedRing Algebra.id Semifield.toCommSemiring Field.toSemifield UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing IsTopologicalDivisionRing.toIsTopologicalRing NormedDivisionRing.toDivisionRing NormedField.toNormedDivisionRing NormedDivisionRing.to_isTopologicalDivisionRing	HasDerivAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing ContinuousMul.to_continuousSMul MulZeroClass.toMul MulZeroOneClass.toMulZeroClass MonoidWithZero.toMulZeroOneClass Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring IsTopologicalSemiring.toContinuousMul NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring IsTopologicalRing.toIsTopologicalSemiring NormedSpace.exp	—	IsTopologicalDivisionRing.toIsTopologicalRing NormedDivisionRing.to_isTopologicalDivisionRing HasStrictDerivAt.hasDerivAt hasStrictDerivAt_exp_of_mem_ball
hasDerivAt_exp_smul_const 📖	mathematical	—	HasDerivAt DenselyNormedField.toNontriviallyNormedField RCLike.toDenselyNormedField NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NormedRing.toNonUnitalNormedRing NormedSpace.toModule DenselyNormedField.toNormedField NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalNormedRing.toNonUnitalSeminormedRing NormedAlgebra.toNormedSpace NormedRing.toSeminormedRing UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace IsBoundedSMul.continuousSMul SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NonAssocRing.toNonUnitalNonAssocRing Ring.toNonAssocRing NormedRing.toRing 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 NontriviallyNormedField.toNormedField Module.toDistribMulAction AddCommGroup.toAddCommMonoid NormedSpace.toIsBoundedSMul NormedSpace.exp NonUnitalSeminormedRing.toIsTopologicalRing Algebra.toSMul Semifield.toCommSemiring Ring.toSemiring SeminormedRing.toRing NormedAlgebra.toAlgebra Distrib.toMul NonUnitalNonAssocSemiring.toDistrib	—	hasDerivAt_exp_smul_const_of_mem_ball RCLike.charZero_rclike edist_lt_top NonUnitalSeminormedRing.toIsTopologicalRing NormedSpace.expSeries_radius_eq_top IsBoundedSMul.continuousSMul NormedSpace.toIsBoundedSMul
hasDerivAt_exp_smul_const' 📖	mathematical	—	HasDerivAt DenselyNormedField.toNontriviallyNormedField RCLike.toDenselyNormedField NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NormedRing.toNonUnitalNormedRing NormedSpace.toModule DenselyNormedField.toNormedField NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalNormedRing.toNonUnitalSeminormedRing NormedAlgebra.toNormedSpace NormedRing.toSeminormedRing UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace IsBoundedSMul.continuousSMul SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NonAssocRing.toNonUnitalNonAssocRing Ring.toNonAssocRing NormedRing.toRing 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 NontriviallyNormedField.toNormedField Module.toDistribMulAction AddCommGroup.toAddCommMonoid NormedSpace.toIsBoundedSMul NormedSpace.exp NonUnitalSeminormedRing.toIsTopologicalRing Algebra.toSMul Semifield.toCommSemiring Ring.toSemiring SeminormedRing.toRing NormedAlgebra.toAlgebra Distrib.toMul NonUnitalNonAssocSemiring.toDistrib	—	hasDerivAt_exp_smul_const_of_mem_ball' RCLike.charZero_rclike edist_lt_top NonUnitalSeminormedRing.toIsTopologicalRing NormedSpace.expSeries_radius_eq_top IsBoundedSMul.continuousSMul NormedSpace.toIsBoundedSMul
hasDerivAt_exp_smul_const_of_mem_ball 📖	mathematical	Set Set.instMembership Metric.eball EMetricSpace.toPseudoEMetricSpace MetricSpace.toEMetricSpace NormedRing.toMetricSpace MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonAssocRing.toNonUnitalNonAssocRing Ring.toNonAssocRing NormedRing.toRing FormalMultilinearSeries.radius NonUnitalNormedRing.toNormedAddCommGroup NormedRing.toNonUnitalNormedRing NormedAlgebra.toNormedSpace NontriviallyNormedField.toNormedField NormedRing.toSeminormedRing NormedSpace.expSeries NormedField.toField NormedAlgebra.toAlgebra UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace NonUnitalSeminormedRing.toIsTopologicalRing NonUnitalNormedRing.toNonUnitalSeminormedRing Algebra.toSMul Semifield.toCommSemiring Field.toSemifield Ring.toSemiring SeminormedRing.toRing	HasDerivAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup IsBoundedSMul.continuousSMul SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing 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 Module.toDistribMulAction AddCommGroup.toAddCommMonoid NormedSpace.toIsBoundedSMul NormedSpace.exp Distrib.toMul NonUnitalNonAssocSemiring.toDistrib	—	NonUnitalSeminormedRing.toIsTopologicalRing HasStrictDerivAt.hasDerivAt hasStrictDerivAt_exp_smul_const_of_mem_ball
hasDerivAt_exp_smul_const_of_mem_ball' 📖	mathematical	Set Set.instMembership Metric.eball EMetricSpace.toPseudoEMetricSpace MetricSpace.toEMetricSpace NormedRing.toMetricSpace MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonAssocRing.toNonUnitalNonAssocRing Ring.toNonAssocRing NormedRing.toRing FormalMultilinearSeries.radius NonUnitalNormedRing.toNormedAddCommGroup NormedRing.toNonUnitalNormedRing NormedAlgebra.toNormedSpace NontriviallyNormedField.toNormedField NormedRing.toSeminormedRing NormedSpace.expSeries NormedField.toField NormedAlgebra.toAlgebra UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace NonUnitalSeminormedRing.toIsTopologicalRing NonUnitalNormedRing.toNonUnitalSeminormedRing Algebra.toSMul Semifield.toCommSemiring Field.toSemifield Ring.toSemiring SeminormedRing.toRing	HasDerivAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup IsBoundedSMul.continuousSMul SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing 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 Module.toDistribMulAction AddCommGroup.toAddCommMonoid NormedSpace.toIsBoundedSMul NormedSpace.exp Distrib.toMul NonUnitalNonAssocSemiring.toDistrib	—	NonUnitalSeminormedRing.toIsTopologicalRing HasStrictDerivAt.hasDerivAt hasStrictDerivAt_exp_smul_const_of_mem_ball'
hasDerivAt_exp_zero 📖	mathematical	—	HasDerivAt DenselyNormedField.toNontriviallyNormedField RCLike.toDenselyNormedField NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing DenselyNormedField.toNormedField NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing ContinuousMul.to_continuousSMul NontriviallyNormedField.toNormedField MulZeroClass.toMul MulZeroOneClass.toMulZeroClass MonoidWithZero.toMulZeroOneClass Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField IsTopologicalSemiring.toContinuousMul NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring IsTopologicalRing.toIsTopologicalSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing IsTopologicalDivisionRing.toIsTopologicalRing NormedDivisionRing.toDivisionRing NormedField.toNormedDivisionRing NormedDivisionRing.to_isTopologicalDivisionRing NormedSpace.exp NormedRing.toRing NormedCommRing.toNormedRing AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring	—	HasStrictDerivAt.hasDerivAt IsTopologicalDivisionRing.toIsTopologicalRing NormedDivisionRing.to_isTopologicalDivisionRing hasStrictDerivAt_exp_zero
hasDerivAt_exp_zero_of_radius_pos 📖	mathematical	ENNReal Preorder.toLT PartialOrder.toPreorder ENNReal.instPartialOrder instZeroENNReal FormalMultilinearSeries.radius NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing NontriviallyNormedField.toNormedField NormedField.toNormedSpace NormedSpace.expSeries NormedField.toField NormedRing.toRing NormedCommRing.toNormedRing Algebra.id Semifield.toCommSemiring Field.toSemifield UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing IsTopologicalDivisionRing.toIsTopologicalRing NormedDivisionRing.toDivisionRing NormedField.toNormedDivisionRing NormedDivisionRing.to_isTopologicalDivisionRing	HasDerivAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing ContinuousMul.to_continuousSMul MulZeroClass.toMul MulZeroOneClass.toMulZeroClass MonoidWithZero.toMulZeroOneClass Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring IsTopologicalSemiring.toContinuousMul NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring IsTopologicalRing.toIsTopologicalSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedSpace.exp AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring	—	IsTopologicalDivisionRing.toIsTopologicalRing NormedDivisionRing.to_isTopologicalDivisionRing HasStrictDerivAt.hasDerivAt hasStrictDerivAt_exp_zero_of_radius_pos
hasFDerivAt_exp 📖	mathematical	—	HasFDerivAt DenselyNormedField.toNontriviallyNormedField RCLike.toDenselyNormedField SeminormedAddCommGroup.toAddCommGroup NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedSpace.toModule DenselyNormedField.toNormedField NormedAlgebra.toNormedSpace SeminormedCommRing.toSeminormedRing UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace NormedSpace.exp NormedRing.toRing NormedCommRing.toNormedRing NonUnitalSeminormedRing.toIsTopologicalRing ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField RingHom.id Semiring.toNonAssocSemiring ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing ContinuousLinearMap.instSMul NonUnitalNonAssocSemiring.toDistribSMul NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing Algebra.to_smulCommClass Semifield.toCommSemiring Ring.toSemiring SeminormedRing.toRing NormedAlgebra.toAlgebra UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass Ring.uniformContinuousConstSMul SeminormedAddCommGroup.to_isUniformAddGroup IsTopologicalSemiring.toContinuousMul NonAssocRing.toNonUnitalNonAssocRing Ring.toNonAssocRing IsTopologicalRing.toIsTopologicalSemiring ContinuousLinearMap.one	—	HasStrictFDerivAt.hasFDerivAt NonUnitalSeminormedRing.toIsTopologicalRing Algebra.to_smulCommClass UniformContinuousConstSMul.to_continuousConstSMul Ring.uniformContinuousConstSMul SeminormedAddCommGroup.to_isUniformAddGroup IsTopologicalSemiring.toContinuousMul IsTopologicalRing.toIsTopologicalSemiring hasStrictFDerivAt_exp
hasFDerivAt_exp_of_mem_ball 📖	mathematical	Set Set.instMembership Metric.eball EMetricSpace.toPseudoEMetricSpace MetricSpace.toEMetricSpace NormedRing.toMetricSpace NormedCommRing.toNormedRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing FormalMultilinearSeries.radius NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedAlgebra.toNormedSpace NontriviallyNormedField.toNormedField SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedSpace.expSeries NormedField.toField NormedRing.toRing NormedAlgebra.toAlgebra UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace NonUnitalSeminormedRing.toIsTopologicalRing NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing	HasFDerivAt SeminormedAddCommGroup.toAddCommGroup NonUnitalSeminormedRing.toSeminormedAddCommGroup NormedSpace.toModule NormedSpace.exp ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield RingHom.id Semiring.toNonAssocSemiring ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousLinearMap.instSMul NonUnitalNonAssocSemiring.toDistribSMul Algebra.to_smulCommClass Semifield.toCommSemiring Ring.toSemiring SeminormedRing.toRing UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass Ring.uniformContinuousConstSMul SeminormedAddCommGroup.to_isUniformAddGroup IsTopologicalSemiring.toContinuousMul NonAssocRing.toNonUnitalNonAssocRing Ring.toNonAssocRing IsTopologicalRing.toIsTopologicalSemiring ContinuousLinearMap.one	—	NonUnitalSeminormedRing.toIsTopologicalRing LE.le.trans_lt zero_le ENNReal.instCanonicallyOrderedAdd Algebra.to_smulCommClass UniformContinuousConstSMul.to_continuousConstSMul Ring.uniformContinuousConstSMul SeminormedAddCommGroup.to_isUniformAddGroup IsTopologicalSemiring.toContinuousMul IsTopologicalRing.toIsTopologicalSemiring hasFDerivAt_iff_isLittleO_nhds_zero Metric.eball_mem_nhds Filter.mp_mem Filter.univ_mem' NormedSpace.exp_add_of_mem_ball NormedSpace.exp_zero zero_add ContinuousLinearMap.id_apply smul_eq_mul Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Nat.cast_one Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.add_pf_add_gt Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.add_pf_add_lt Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.zero_mul Asymptotics.IsLittleO.congr' Asymptotics.IsLittleO.const_mul_left hasFDerivAt_exp_zero_of_radius_pos Filter.EventuallyEq.refl
hasFDerivAt_exp_smul_const 📖	mathematical	—	HasFDerivAt DenselyNormedField.toNontriviallyNormedField RCLike.toDenselyNormedField SeminormedAddCommGroup.toAddCommGroup NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedSpace.toModule DenselyNormedField.toNormedField NormedAlgebra.toNormedSpace SeminormedCommRing.toSeminormedRing UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace NonUnitalNormedRing.toNonUnitalSeminormedRing NormedRing.toNonUnitalNormedRing NormedRing.toSeminormedRing NormedSpace.exp NormedRing.toRing NonUnitalSeminormedRing.toIsTopologicalRing Algebra.toSMul CommRing.toCommSemiring NormedCommRing.toCommRing Ring.toSemiring ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField RingHom.id Semiring.toNonAssocSemiring ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing ContinuousLinearMap.instSMul NonUnitalNonAssocSemiring.toDistribSMul NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonAssocRing.toNonUnitalNonAssocRing Ring.toNonAssocRing Algebra.to_smulCommClass Semifield.toCommSemiring SeminormedRing.toRing NormedAlgebra.toAlgebra UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass Ring.uniformContinuousConstSMul SeminormedAddCommGroup.to_isUniformAddGroup IsTopologicalSemiring.toContinuousMul IsTopologicalRing.toIsTopologicalSemiring ContinuousLinearMap.smulRight CommSemiring.toSemiring Algebra.toModule ContinuousLinearMap.one	—	hasFDerivAt_exp_smul_const_of_mem_ball RCLike.charZero_rclike edist_lt_top NonUnitalSeminormedRing.toIsTopologicalRing NormedSpace.expSeries_radius_eq_top IsBoundedSMul.continuousSMul NormedSpace.toIsBoundedSMul
hasFDerivAt_exp_smul_const' 📖	mathematical	—	HasFDerivAt DenselyNormedField.toNontriviallyNormedField RCLike.toDenselyNormedField SeminormedAddCommGroup.toAddCommGroup NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedSpace.toModule DenselyNormedField.toNormedField NormedAlgebra.toNormedSpace SeminormedCommRing.toSeminormedRing UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NormedRing.toNonUnitalNormedRing NonUnitalNormedRing.toNonUnitalSeminormedRing NormedRing.toSeminormedRing NormedSpace.exp NormedRing.toRing NonUnitalSeminormedRing.toIsTopologicalRing Algebra.toSMul CommRing.toCommSemiring NormedCommRing.toCommRing Ring.toSemiring ContinuousLinearMap.smulRight ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing AddCommGroup.toAddCommMonoid DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField Semiring.toModule IsScalarTower.right Semifield.toCommSemiring SeminormedRing.toRing NormedAlgebra.toAlgebra ContinuousMul.to_continuousSMul MulZeroClass.toMul MulZeroOneClass.toMulZeroClass MonoidWithZero.toMulZeroOneClass Semiring.toMonoidWithZero IsTopologicalSemiring.toContinuousMul NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring IsTopologicalRing.toIsTopologicalSemiring NonAssocRing.toNonUnitalNonAssocRing Ring.toNonAssocRing CommSemiring.toSemiring Algebra.toModule ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring ContinuousLinearMap.one	—	hasFDerivAt_exp_smul_const_of_mem_ball' RCLike.charZero_rclike edist_lt_top NonUnitalSeminormedRing.toIsTopologicalRing NormedSpace.expSeries_radius_eq_top IsBoundedSMul.continuousSMul NormedSpace.toIsBoundedSMul
hasFDerivAt_exp_smul_const_of_mem_ball 📖	mathematical	Set Set.instMembership Metric.eball EMetricSpace.toPseudoEMetricSpace MetricSpace.toEMetricSpace NormedRing.toMetricSpace MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonAssocRing.toNonUnitalNonAssocRing Ring.toNonAssocRing NormedRing.toRing FormalMultilinearSeries.radius NonUnitalNormedRing.toNormedAddCommGroup NormedRing.toNonUnitalNormedRing NormedAlgebra.toNormedSpace NontriviallyNormedField.toNormedField NormedRing.toSeminormedRing NormedSpace.expSeries NormedField.toField NormedAlgebra.toAlgebra UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace NonUnitalSeminormedRing.toIsTopologicalRing NonUnitalNormedRing.toNonUnitalSeminormedRing Algebra.toSMul CommRing.toCommSemiring NormedCommRing.toCommRing Ring.toSemiring	HasFDerivAt SeminormedAddCommGroup.toAddCommGroup NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedSpace.toModule SeminormedCommRing.toSeminormedRing NormedSpace.exp ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield RingHom.id Semiring.toNonAssocSemiring ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing ContinuousLinearMap.instSMul NonUnitalNonAssocSemiring.toDistribSMul Algebra.to_smulCommClass Semifield.toCommSemiring SeminormedRing.toRing UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass Ring.uniformContinuousConstSMul SeminormedAddCommGroup.to_isUniformAddGroup IsTopologicalSemiring.toContinuousMul IsTopologicalRing.toIsTopologicalSemiring ContinuousLinearMap.smulRight CommSemiring.toSemiring Algebra.toModule ContinuousLinearMap.one	—	NonUnitalSeminormedRing.toIsTopologicalRing LE.le.trans_lt zero_le ENNReal.instCanonicallyOrderedAdd Algebra.to_smulCommClass UniformContinuousConstSMul.to_continuousConstSMul Ring.uniformContinuousConstSMul SeminormedAddCommGroup.to_isUniformAddGroup IsTopologicalSemiring.toContinuousMul IsTopologicalRing.toIsTopologicalSemiring hasFDerivAt_iff_isLittleO_nhds_zero zero_smul Filter.Tendsto.smul_const Filter.tendsto_id Filter.Tendsto.eventually Metric.eball_mem_nhds Filter.mp_mem Filter.univ_mem' Commute.smul_right IsScalarTower.right Commute.smul_left Commute.refl add_smul NormedSpace.exp_add_of_commute_of_mem_ball zero_add NormedSpace.exp_zero ContinuousLinearMap.smulRight_apply ContinuousLinearMap.one_apply ContinuousLinearMap.smul_apply smul_eq_mul mul_sub_left_distrib mul_one Asymptotics.IsLittleO.congr' Asymptotics.IsLittleO.const_mul_left hasFDerivAt_exp_zero_of_radius_pos HasFDerivAt.comp ContinuousLinearMap.hasFDerivAt Filter.EventuallyEq.refl
hasFDerivAt_exp_smul_const_of_mem_ball' 📖	mathematical	Set Set.instMembership Metric.eball EMetricSpace.toPseudoEMetricSpace MetricSpace.toEMetricSpace NormedRing.toMetricSpace MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonAssocRing.toNonUnitalNonAssocRing Ring.toNonAssocRing NormedRing.toRing FormalMultilinearSeries.radius NonUnitalNormedRing.toNormedAddCommGroup NormedRing.toNonUnitalNormedRing NormedAlgebra.toNormedSpace NontriviallyNormedField.toNormedField NormedRing.toSeminormedRing NormedSpace.expSeries NormedField.toField NormedAlgebra.toAlgebra UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace NonUnitalSeminormedRing.toIsTopologicalRing NonUnitalNormedRing.toNonUnitalSeminormedRing Algebra.toSMul CommRing.toCommSemiring NormedCommRing.toCommRing Ring.toSemiring	HasFDerivAt SeminormedAddCommGroup.toAddCommGroup NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedSpace.toModule SeminormedCommRing.toSeminormedRing NormedAddCommGroup.toAddCommGroup NormedSpace.exp ContinuousLinearMap.smulRight ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing AddCommGroup.toAddCommMonoid DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield Semiring.toModule IsScalarTower.right Semifield.toCommSemiring SeminormedRing.toRing ContinuousMul.to_continuousSMul MulZeroClass.toMul MulZeroOneClass.toMulZeroClass MonoidWithZero.toMulZeroOneClass Semiring.toMonoidWithZero IsTopologicalSemiring.toContinuousMul NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring IsTopologicalRing.toIsTopologicalSemiring CommSemiring.toSemiring Algebra.toModule ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring ContinuousLinearMap.one	—	NonUnitalSeminormedRing.toIsTopologicalRing IsScalarTower.right ContinuousMul.to_continuousSMul IsTopologicalSemiring.toContinuousMul IsTopologicalRing.toIsTopologicalSemiring Algebra.to_smulCommClass UniformContinuousConstSMul.to_continuousConstSMul Ring.uniformContinuousConstSMul SeminormedAddCommGroup.to_isUniformAddGroup ContinuousLinearMap.ext Commute.exp_right TopologicalSpace.t2Space_of_metrizableSpace EMetricSpace.metrizableSpace Commute.smul_right Commute.smul_left Commute.refl hasFDerivAt_exp_smul_const_of_mem_ball
hasFDerivAt_exp_zero 📖	mathematical	—	HasFDerivAt DenselyNormedField.toNontriviallyNormedField RCLike.toDenselyNormedField SeminormedAddCommGroup.toAddCommGroup NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalNormedRing.toNonUnitalSeminormedRing NormedRing.toNonUnitalNormedRing NormedSpace.toModule DenselyNormedField.toNormedField NormedAlgebra.toNormedSpace NormedRing.toSeminormedRing UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace NormedSpace.exp NormedRing.toRing NonUnitalSeminormedRing.toIsTopologicalRing ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField RingHom.id Semiring.toNonAssocSemiring ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NonUnitalNormedRing.toNormedAddCommGroup ContinuousLinearMap.one MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonAssocRing.toNonUnitalNonAssocRing Ring.toNonAssocRing	—	HasStrictFDerivAt.hasFDerivAt NonUnitalSeminormedRing.toIsTopologicalRing hasStrictFDerivAt_exp_zero
hasFDerivAt_exp_zero_of_radius_pos 📖	mathematical	ENNReal Preorder.toLT PartialOrder.toPreorder ENNReal.instPartialOrder instZeroENNReal FormalMultilinearSeries.radius NonUnitalNormedRing.toNormedAddCommGroup NormedRing.toNonUnitalNormedRing NormedAlgebra.toNormedSpace NontriviallyNormedField.toNormedField NormedRing.toSeminormedRing NormedSpace.expSeries NormedField.toField NormedRing.toRing NormedAlgebra.toAlgebra UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace NonUnitalSeminormedRing.toIsTopologicalRing NonUnitalNormedRing.toNonUnitalSeminormedRing	HasFDerivAt SeminormedAddCommGroup.toAddCommGroup NonUnitalSeminormedRing.toSeminormedAddCommGroup NormedSpace.toModule NormedSpace.exp ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield RingHom.id Semiring.toNonAssocSemiring ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousLinearMap.one MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonAssocRing.toNonUnitalNonAssocRing Ring.toNonAssocRing	—	NonUnitalSeminormedRing.toIsTopologicalRing HasStrictFDerivAt.hasFDerivAt hasStrictFDerivAt_exp_zero_of_radius_pos
hasStrictDerivAt_exp 📖	mathematical	—	HasStrictDerivAt DenselyNormedField.toNontriviallyNormedField RCLike.toDenselyNormedField NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing DenselyNormedField.toNormedField NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing ContinuousMul.to_continuousSMul NontriviallyNormedField.toNormedField MulZeroClass.toMul MulZeroOneClass.toMulZeroClass MonoidWithZero.toMulZeroOneClass Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField IsTopologicalSemiring.toContinuousMul NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring IsTopologicalRing.toIsTopologicalSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing IsTopologicalDivisionRing.toIsTopologicalRing NormedDivisionRing.toDivisionRing NormedField.toNormedDivisionRing NormedDivisionRing.to_isTopologicalDivisionRing NormedSpace.exp NormedRing.toRing NormedCommRing.toNormedRing	—	hasStrictDerivAt_exp_of_mem_ball RCLike.toCompleteSpace RCLike.charZero_rclike edist_lt_top NonUnitalSeminormedRing.toIsTopologicalRing NormedSpace.expSeries_radius_eq_top IsBoundedSMul.continuousSMul NormedSpace.toIsBoundedSMul
hasStrictDerivAt_exp_of_mem_ball 📖	mathematical	Set Set.instMembership Metric.eball EMetricSpace.toPseudoEMetricSpace MetricSpace.toEMetricSpace NormedField.toMetricSpace NontriviallyNormedField.toNormedField MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing FormalMultilinearSeries.radius NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedField.toNormedSpace NormedSpace.expSeries NormedField.toField NormedRing.toRing NormedCommRing.toNormedRing Algebra.id Semifield.toCommSemiring Field.toSemifield UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing IsTopologicalDivisionRing.toIsTopologicalRing NormedDivisionRing.toDivisionRing NormedField.toNormedDivisionRing NormedDivisionRing.to_isTopologicalDivisionRing	HasStrictDerivAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing ContinuousMul.to_continuousSMul MulZeroClass.toMul MulZeroOneClass.toMulZeroClass MonoidWithZero.toMulZeroOneClass Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring IsTopologicalSemiring.toContinuousMul NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring IsTopologicalRing.toIsTopologicalSemiring NormedSpace.exp	—	IsTopologicalDivisionRing.toIsTopologicalRing NormedDivisionRing.to_isTopologicalDivisionRing ContinuousMul.to_continuousSMul IsTopologicalSemiring.toContinuousMul IsTopologicalRing.toIsTopologicalSemiring NonUnitalSeminormedRing.toIsTopologicalRing Algebra.to_smulCommClass UniformContinuousConstSMul.to_continuousConstSMul Ring.uniformContinuousConstSMul SeminormedAddCommGroup.to_isUniformAddGroup HasStrictDerivAt.congr_simp mul_one HasStrictFDerivAt.hasStrictDerivAt hasStrictFDerivAt_exp_of_mem_ball
hasStrictDerivAt_exp_smul_const 📖	mathematical	—	HasStrictDerivAt DenselyNormedField.toNontriviallyNormedField RCLike.toDenselyNormedField NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NormedRing.toNonUnitalNormedRing NormedSpace.toModule DenselyNormedField.toNormedField NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalNormedRing.toNonUnitalSeminormedRing NormedAlgebra.toNormedSpace NormedRing.toSeminormedRing UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace IsBoundedSMul.continuousSMul SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NonAssocRing.toNonUnitalNonAssocRing Ring.toNonAssocRing NormedRing.toRing 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 NontriviallyNormedField.toNormedField Module.toDistribMulAction AddCommGroup.toAddCommMonoid NormedSpace.toIsBoundedSMul NormedSpace.exp NonUnitalSeminormedRing.toIsTopologicalRing Algebra.toSMul Semifield.toCommSemiring Ring.toSemiring SeminormedRing.toRing NormedAlgebra.toAlgebra Distrib.toMul NonUnitalNonAssocSemiring.toDistrib	—	hasStrictDerivAt_exp_smul_const_of_mem_ball RCLike.charZero_rclike edist_lt_top NonUnitalSeminormedRing.toIsTopologicalRing NormedSpace.expSeries_radius_eq_top IsBoundedSMul.continuousSMul NormedSpace.toIsBoundedSMul
hasStrictDerivAt_exp_smul_const' 📖	mathematical	—	HasStrictDerivAt DenselyNormedField.toNontriviallyNormedField RCLike.toDenselyNormedField NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NormedRing.toNonUnitalNormedRing NormedSpace.toModule DenselyNormedField.toNormedField NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalNormedRing.toNonUnitalSeminormedRing NormedAlgebra.toNormedSpace NormedRing.toSeminormedRing UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace IsBoundedSMul.continuousSMul SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NonAssocRing.toNonUnitalNonAssocRing Ring.toNonAssocRing NormedRing.toRing 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 NontriviallyNormedField.toNormedField Module.toDistribMulAction AddCommGroup.toAddCommMonoid NormedSpace.toIsBoundedSMul NormedSpace.exp NonUnitalSeminormedRing.toIsTopologicalRing Algebra.toSMul Semifield.toCommSemiring Ring.toSemiring SeminormedRing.toRing NormedAlgebra.toAlgebra Distrib.toMul NonUnitalNonAssocSemiring.toDistrib	—	hasStrictDerivAt_exp_smul_const_of_mem_ball' RCLike.charZero_rclike edist_lt_top NonUnitalSeminormedRing.toIsTopologicalRing NormedSpace.expSeries_radius_eq_top IsBoundedSMul.continuousSMul NormedSpace.toIsBoundedSMul
hasStrictDerivAt_exp_smul_const_of_mem_ball 📖	mathematical	Set Set.instMembership Metric.eball EMetricSpace.toPseudoEMetricSpace MetricSpace.toEMetricSpace NormedRing.toMetricSpace MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonAssocRing.toNonUnitalNonAssocRing Ring.toNonAssocRing NormedRing.toRing FormalMultilinearSeries.radius NonUnitalNormedRing.toNormedAddCommGroup NormedRing.toNonUnitalNormedRing NormedAlgebra.toNormedSpace NontriviallyNormedField.toNormedField NormedRing.toSeminormedRing NormedSpace.expSeries NormedField.toField NormedAlgebra.toAlgebra UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace NonUnitalSeminormedRing.toIsTopologicalRing NonUnitalNormedRing.toNonUnitalSeminormedRing Algebra.toSMul Semifield.toCommSemiring Field.toSemifield Ring.toSemiring SeminormedRing.toRing	HasStrictDerivAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup IsBoundedSMul.continuousSMul SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing 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 Module.toDistribMulAction AddCommGroup.toAddCommMonoid NormedSpace.toIsBoundedSMul NormedSpace.exp Distrib.toMul NonUnitalNonAssocSemiring.toDistrib	—	NonUnitalSeminormedRing.toIsTopologicalRing IsBoundedSMul.continuousSMul NormedSpace.toIsBoundedSMul Algebra.to_smulCommClass UniformContinuousConstSMul.to_continuousConstSMul Ring.uniformContinuousConstSMul SeminormedAddCommGroup.to_isUniformAddGroup IsTopologicalSemiring.toContinuousMul IsTopologicalRing.toIsTopologicalSemiring IsScalarTower.left HasStrictDerivAt.congr_simp one_smul HasStrictFDerivAt.hasStrictDerivAt hasStrictFDerivAt_exp_smul_const_of_mem_ball
hasStrictDerivAt_exp_smul_const_of_mem_ball' 📖	mathematical	Set Set.instMembership Metric.eball EMetricSpace.toPseudoEMetricSpace MetricSpace.toEMetricSpace NormedRing.toMetricSpace MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonAssocRing.toNonUnitalNonAssocRing Ring.toNonAssocRing NormedRing.toRing FormalMultilinearSeries.radius NonUnitalNormedRing.toNormedAddCommGroup NormedRing.toNonUnitalNormedRing NormedAlgebra.toNormedSpace NontriviallyNormedField.toNormedField NormedRing.toSeminormedRing NormedSpace.expSeries NormedField.toField NormedAlgebra.toAlgebra UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace NonUnitalSeminormedRing.toIsTopologicalRing NonUnitalNormedRing.toNonUnitalSeminormedRing Algebra.toSMul Semifield.toCommSemiring Field.toSemifield Ring.toSemiring SeminormedRing.toRing	HasStrictDerivAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup IsBoundedSMul.continuousSMul SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing 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 Module.toDistribMulAction AddCommGroup.toAddCommMonoid NormedSpace.toIsBoundedSMul NormedSpace.exp Distrib.toMul NonUnitalNonAssocSemiring.toDistrib	—	NonUnitalSeminormedRing.toIsTopologicalRing IsBoundedSMul.continuousSMul NormedSpace.toIsBoundedSMul IsScalarTower.right ContinuousMul.to_continuousSMul IsTopologicalSemiring.toContinuousMul IsTopologicalRing.toIsTopologicalSemiring IsScalarTower.left HasStrictDerivAt.congr_simp one_smul HasStrictFDerivAt.hasStrictDerivAt hasStrictFDerivAt_exp_smul_const_of_mem_ball'
hasStrictDerivAt_exp_zero 📖	mathematical	—	HasStrictDerivAt DenselyNormedField.toNontriviallyNormedField RCLike.toDenselyNormedField NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing DenselyNormedField.toNormedField NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing ContinuousMul.to_continuousSMul NontriviallyNormedField.toNormedField MulZeroClass.toMul MulZeroOneClass.toMulZeroClass MonoidWithZero.toMulZeroOneClass Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField IsTopologicalSemiring.toContinuousMul NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring IsTopologicalRing.toIsTopologicalSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing IsTopologicalDivisionRing.toIsTopologicalRing NormedDivisionRing.toDivisionRing NormedField.toNormedDivisionRing NormedDivisionRing.to_isTopologicalDivisionRing NormedSpace.exp NormedRing.toRing NormedCommRing.toNormedRing AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring	—	hasStrictDerivAt_exp_zero_of_radius_pos RCLike.toCompleteSpace RCLike.charZero_rclike NormedSpace.expSeries_radius_pos IsBoundedSMul.continuousSMul NormedSpace.toIsBoundedSMul
hasStrictDerivAt_exp_zero_of_radius_pos 📖	mathematical	ENNReal Preorder.toLT PartialOrder.toPreorder ENNReal.instPartialOrder instZeroENNReal FormalMultilinearSeries.radius NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing NontriviallyNormedField.toNormedField NormedField.toNormedSpace NormedSpace.expSeries NormedField.toField NormedRing.toRing NormedCommRing.toNormedRing Algebra.id Semifield.toCommSemiring Field.toSemifield UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing IsTopologicalDivisionRing.toIsTopologicalRing NormedDivisionRing.toDivisionRing NormedField.toNormedDivisionRing NormedDivisionRing.to_isTopologicalDivisionRing	HasStrictDerivAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing ContinuousMul.to_continuousSMul MulZeroClass.toMul MulZeroOneClass.toMulZeroClass MonoidWithZero.toMulZeroOneClass Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring IsTopologicalSemiring.toContinuousMul NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring IsTopologicalRing.toIsTopologicalSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedSpace.exp AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring	—	IsTopologicalDivisionRing.toIsTopologicalRing NormedDivisionRing.to_isTopologicalDivisionRing HasStrictFDerivAt.hasStrictDerivAt NonUnitalSeminormedRing.toIsTopologicalRing ContinuousMul.to_continuousSMul IsTopologicalSemiring.toContinuousMul IsTopologicalRing.toIsTopologicalSemiring hasStrictFDerivAt_exp_zero_of_radius_pos
hasStrictFDerivAt_exp 📖	mathematical	—	HasStrictFDerivAt DenselyNormedField.toNontriviallyNormedField RCLike.toDenselyNormedField SeminormedAddCommGroup.toAddCommGroup NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedSpace.toModule DenselyNormedField.toNormedField NormedAlgebra.toNormedSpace SeminormedCommRing.toSeminormedRing UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace NormedSpace.exp NormedRing.toRing NormedCommRing.toNormedRing NonUnitalSeminormedRing.toIsTopologicalRing ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField RingHom.id Semiring.toNonAssocSemiring ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing ContinuousLinearMap.instSMul NonUnitalNonAssocSemiring.toDistribSMul NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing Algebra.to_smulCommClass Semifield.toCommSemiring Ring.toSemiring SeminormedRing.toRing NormedAlgebra.toAlgebra UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass Ring.uniformContinuousConstSMul SeminormedAddCommGroup.to_isUniformAddGroup IsTopologicalSemiring.toContinuousMul NonAssocRing.toNonUnitalNonAssocRing Ring.toNonAssocRing IsTopologicalRing.toIsTopologicalSemiring ContinuousLinearMap.one	—	hasStrictFDerivAt_exp_of_mem_ball RCLike.charZero_rclike edist_lt_top NonUnitalSeminormedRing.toIsTopologicalRing NormedSpace.expSeries_radius_eq_top IsBoundedSMul.continuousSMul NormedSpace.toIsBoundedSMul
hasStrictFDerivAt_exp_of_mem_ball 📖	mathematical	Set Set.instMembership Metric.eball EMetricSpace.toPseudoEMetricSpace MetricSpace.toEMetricSpace NormedRing.toMetricSpace NormedCommRing.toNormedRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing FormalMultilinearSeries.radius NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedAlgebra.toNormedSpace NontriviallyNormedField.toNormedField SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedSpace.expSeries NormedField.toField NormedRing.toRing NormedAlgebra.toAlgebra UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace NonUnitalSeminormedRing.toIsTopologicalRing NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing	HasStrictFDerivAt SeminormedAddCommGroup.toAddCommGroup NonUnitalSeminormedRing.toSeminormedAddCommGroup NormedSpace.toModule NormedSpace.exp ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield RingHom.id Semiring.toNonAssocSemiring ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousLinearMap.instSMul NonUnitalNonAssocSemiring.toDistribSMul Algebra.to_smulCommClass Semifield.toCommSemiring Ring.toSemiring SeminormedRing.toRing UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass Ring.uniformContinuousConstSMul SeminormedAddCommGroup.to_isUniformAddGroup IsTopologicalSemiring.toContinuousMul NonAssocRing.toNonUnitalNonAssocRing Ring.toNonAssocRing IsTopologicalRing.toIsTopologicalSemiring ContinuousLinearMap.one	—	NonUnitalSeminormedRing.toIsTopologicalRing Algebra.to_smulCommClass UniformContinuousConstSMul.to_continuousConstSMul Ring.uniformContinuousConstSMul SeminormedAddCommGroup.to_isUniformAddGroup IsTopologicalSemiring.toContinuousMul IsTopologicalRing.toIsTopologicalSemiring NormedSpace.analyticAt_exp_of_mem_ball RingHomInvPair.ids RingHomIsometric.ids SeminormedAddCommGroup.toIsTopologicalAddGroup IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul smulCommClass_self HasFPowerSeriesAt.hasStrictFDerivAt HasFDerivAt.unique IsTopologicalSemiring.toContinuousAdd IsBoundedSMul.continuousSMul TopologicalSpace.t2Space_of_metrizableSpace EMetricSpace.metrizableSpace HasFPowerSeriesAt.hasFDerivAt hasFDerivAt_exp_of_mem_ball
hasStrictFDerivAt_exp_smul_const 📖	mathematical	—	HasStrictFDerivAt DenselyNormedField.toNontriviallyNormedField RCLike.toDenselyNormedField SeminormedAddCommGroup.toAddCommGroup NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedSpace.toModule DenselyNormedField.toNormedField NormedAlgebra.toNormedSpace SeminormedCommRing.toSeminormedRing UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace NonUnitalNormedRing.toNonUnitalSeminormedRing NormedRing.toNonUnitalNormedRing NormedRing.toSeminormedRing NormedSpace.exp NormedRing.toRing NonUnitalSeminormedRing.toIsTopologicalRing Algebra.toSMul CommRing.toCommSemiring NormedCommRing.toCommRing Ring.toSemiring ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField RingHom.id Semiring.toNonAssocSemiring ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing ContinuousLinearMap.instSMul NonUnitalNonAssocSemiring.toDistribSMul NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonAssocRing.toNonUnitalNonAssocRing Ring.toNonAssocRing Algebra.to_smulCommClass Semifield.toCommSemiring SeminormedRing.toRing NormedAlgebra.toAlgebra UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass Ring.uniformContinuousConstSMul SeminormedAddCommGroup.to_isUniformAddGroup IsTopologicalSemiring.toContinuousMul IsTopologicalRing.toIsTopologicalSemiring ContinuousLinearMap.smulRight CommSemiring.toSemiring Algebra.toModule ContinuousLinearMap.one	—	hasStrictFDerivAt_exp_smul_const_of_mem_ball RCLike.charZero_rclike edist_lt_top NonUnitalSeminormedRing.toIsTopologicalRing NormedSpace.expSeries_radius_eq_top IsBoundedSMul.continuousSMul NormedSpace.toIsBoundedSMul
hasStrictFDerivAt_exp_smul_const' 📖	mathematical	—	HasStrictFDerivAt DenselyNormedField.toNontriviallyNormedField RCLike.toDenselyNormedField SeminormedAddCommGroup.toAddCommGroup NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedSpace.toModule DenselyNormedField.toNormedField NormedAlgebra.toNormedSpace SeminormedCommRing.toSeminormedRing UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NormedRing.toNonUnitalNormedRing NonUnitalNormedRing.toNonUnitalSeminormedRing NormedRing.toSeminormedRing NormedSpace.exp NormedRing.toRing NonUnitalSeminormedRing.toIsTopologicalRing Algebra.toSMul CommRing.toCommSemiring NormedCommRing.toCommRing Ring.toSemiring ContinuousLinearMap.smulRight ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing AddCommGroup.toAddCommMonoid DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField Semiring.toModule IsScalarTower.right Semifield.toCommSemiring SeminormedRing.toRing NormedAlgebra.toAlgebra ContinuousMul.to_continuousSMul MulZeroClass.toMul MulZeroOneClass.toMulZeroClass MonoidWithZero.toMulZeroOneClass Semiring.toMonoidWithZero IsTopologicalSemiring.toContinuousMul NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring IsTopologicalRing.toIsTopologicalSemiring NonAssocRing.toNonUnitalNonAssocRing Ring.toNonAssocRing CommSemiring.toSemiring Algebra.toModule ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring ContinuousLinearMap.one	—	hasStrictFDerivAt_exp_smul_const_of_mem_ball' RCLike.charZero_rclike edist_lt_top NonUnitalSeminormedRing.toIsTopologicalRing NormedSpace.expSeries_radius_eq_top IsBoundedSMul.continuousSMul NormedSpace.toIsBoundedSMul
hasStrictFDerivAt_exp_smul_const_of_mem_ball 📖	mathematical	Set Set.instMembership Metric.eball EMetricSpace.toPseudoEMetricSpace MetricSpace.toEMetricSpace NormedRing.toMetricSpace MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonAssocRing.toNonUnitalNonAssocRing Ring.toNonAssocRing NormedRing.toRing FormalMultilinearSeries.radius NonUnitalNormedRing.toNormedAddCommGroup NormedRing.toNonUnitalNormedRing NormedAlgebra.toNormedSpace NontriviallyNormedField.toNormedField NormedRing.toSeminormedRing NormedSpace.expSeries NormedField.toField NormedAlgebra.toAlgebra UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace NonUnitalSeminormedRing.toIsTopologicalRing NonUnitalNormedRing.toNonUnitalSeminormedRing Algebra.toSMul CommRing.toCommSemiring NormedCommRing.toCommRing Ring.toSemiring	HasStrictFDerivAt SeminormedAddCommGroup.toAddCommGroup NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedSpace.toModule SeminormedCommRing.toSeminormedRing NormedSpace.exp ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield RingHom.id Semiring.toNonAssocSemiring ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing ContinuousLinearMap.instSMul NonUnitalNonAssocSemiring.toDistribSMul Algebra.to_smulCommClass Semifield.toCommSemiring SeminormedRing.toRing UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddCommMonoid.toAddMonoid DistribSMul.toSMulZeroClass Ring.uniformContinuousConstSMul SeminormedAddCommGroup.to_isUniformAddGroup IsTopologicalSemiring.toContinuousMul IsTopologicalRing.toIsTopologicalSemiring ContinuousLinearMap.smulRight CommSemiring.toSemiring Algebra.toModule ContinuousLinearMap.one	—	NonUnitalSeminormedRing.toIsTopologicalRing Algebra.to_smulCommClass UniformContinuousConstSMul.to_continuousConstSMul Ring.uniformContinuousConstSMul SeminormedAddCommGroup.to_isUniformAddGroup IsTopologicalSemiring.toContinuousMul IsTopologicalRing.toIsTopologicalSemiring NormedSpace.analyticAt_exp_of_mem_ball RingHomCompTriple.ids RingHomInvPair.ids RingHomIsometric.ids SeminormedAddCommGroup.toIsTopologicalAddGroup IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul smulCommClass_self HasStrictFDerivAt.comp HasFPowerSeriesAt.hasStrictFDerivAt ContinuousLinearMap.hasStrictFDerivAt hasFDerivAt_exp_smul_const_of_mem_ball HasFDerivAt.unique IsTopologicalSemiring.toContinuousAdd IsBoundedSMul.continuousSMul TopologicalSpace.t2Space_of_metrizableSpace EMetricSpace.metrizableSpace HasStrictFDerivAt.hasFDerivAt
hasStrictFDerivAt_exp_smul_const_of_mem_ball' 📖	mathematical	Set Set.instMembership Metric.eball EMetricSpace.toPseudoEMetricSpace MetricSpace.toEMetricSpace NormedRing.toMetricSpace MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonAssocRing.toNonUnitalNonAssocRing Ring.toNonAssocRing NormedRing.toRing FormalMultilinearSeries.radius NonUnitalNormedRing.toNormedAddCommGroup NormedRing.toNonUnitalNormedRing NormedAlgebra.toNormedSpace NontriviallyNormedField.toNormedField NormedRing.toSeminormedRing NormedSpace.expSeries NormedField.toField NormedAlgebra.toAlgebra UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace NonUnitalSeminormedRing.toIsTopologicalRing NonUnitalNormedRing.toNonUnitalSeminormedRing Algebra.toSMul CommRing.toCommSemiring NormedCommRing.toCommRing Ring.toSemiring	HasStrictFDerivAt SeminormedAddCommGroup.toAddCommGroup NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedSpace.toModule SeminormedCommRing.toSeminormedRing NormedAddCommGroup.toAddCommGroup NormedSpace.exp ContinuousLinearMap.smulRight ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing AddCommGroup.toAddCommMonoid DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield Semiring.toModule IsScalarTower.right Semifield.toCommSemiring SeminormedRing.toRing ContinuousMul.to_continuousSMul MulZeroClass.toMul MulZeroOneClass.toMulZeroClass MonoidWithZero.toMulZeroOneClass Semiring.toMonoidWithZero IsTopologicalSemiring.toContinuousMul NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring IsTopologicalRing.toIsTopologicalSemiring CommSemiring.toSemiring Algebra.toModule ContinuousLinearMap RingHom.id Semiring.toNonAssocSemiring ContinuousLinearMap.one	—	NonUnitalSeminormedRing.toIsTopologicalRing IsScalarTower.right ContinuousMul.to_continuousSMul IsTopologicalSemiring.toContinuousMul IsTopologicalRing.toIsTopologicalSemiring NormedSpace.analyticAt_exp_of_mem_ball Algebra.to_smulCommClass UniformContinuousConstSMul.to_continuousConstSMul Ring.uniformContinuousConstSMul SeminormedAddCommGroup.to_isUniformAddGroup ContinuousLinearMap.ext Commute.exp_right TopologicalSpace.t2Space_of_metrizableSpace EMetricSpace.metrizableSpace Commute.smul_right Commute.smul_left Commute.refl hasStrictFDerivAt_exp_smul_const_of_mem_ball
hasStrictFDerivAt_exp_zero 📖	mathematical	—	HasStrictFDerivAt DenselyNormedField.toNontriviallyNormedField RCLike.toDenselyNormedField SeminormedAddCommGroup.toAddCommGroup NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalNormedRing.toNonUnitalSeminormedRing NormedRing.toNonUnitalNormedRing NormedSpace.toModule DenselyNormedField.toNormedField NormedAlgebra.toNormedSpace NormedRing.toSeminormedRing UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace NormedSpace.exp NormedRing.toRing NonUnitalSeminormedRing.toIsTopologicalRing ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField RingHom.id Semiring.toNonAssocSemiring ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NonUnitalNormedRing.toNormedAddCommGroup ContinuousLinearMap.one MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonAssocRing.toNonUnitalNonAssocRing Ring.toNonAssocRing	—	hasStrictFDerivAt_exp_zero_of_radius_pos RCLike.charZero_rclike NormedSpace.expSeries_radius_pos IsBoundedSMul.continuousSMul NormedSpace.toIsBoundedSMul
hasStrictFDerivAt_exp_zero_of_radius_pos 📖	mathematical	ENNReal Preorder.toLT PartialOrder.toPreorder ENNReal.instPartialOrder instZeroENNReal FormalMultilinearSeries.radius NonUnitalNormedRing.toNormedAddCommGroup NormedRing.toNonUnitalNormedRing NormedAlgebra.toNormedSpace NontriviallyNormedField.toNormedField NormedRing.toSeminormedRing NormedSpace.expSeries NormedField.toField NormedRing.toRing NormedAlgebra.toAlgebra UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace NonUnitalSeminormedRing.toIsTopologicalRing NonUnitalNormedRing.toNonUnitalSeminormedRing	HasStrictFDerivAt SeminormedAddCommGroup.toAddCommGroup NonUnitalSeminormedRing.toSeminormedAddCommGroup NormedSpace.toModule NormedSpace.exp ContinuousLinearMap DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield RingHom.id Semiring.toNonAssocSemiring ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid ContinuousLinearMap.one MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonAssocRing.toNonUnitalNonAssocRing Ring.toNonAssocRing	—	NonUnitalSeminormedRing.toIsTopologicalRing RingHomInvPair.ids RingHomIsometric.ids SeminormedAddCommGroup.toIsTopologicalAddGroup UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul smulCommClass_self ContinuousLinearMap.ext NormedSpace.expSeries_apply_eq zero_add mul_one Nat.cast_one inv_one pow_one one_smul HasFPowerSeriesAt.hasStrictFDerivAt NormedSpace.hasFPowerSeriesAt_exp_zero_of_radius_pos

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