ZPow

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

Statistics

Metric	Count
Definitions	0
Theorems zpow, zpow, zpow, zpow, derivWithin_zpow, deriv_zpow, deriv_zpow', differentiableAt_zpow, differentiableOn_zpow, differentiableWithinAt_zpow, hasDerivAt_zpow, hasDerivWithinAt_zpow, hasStrictDerivAt_zpow, iter_deriv_inv, iter_deriv_inv', iter_deriv_inv_linear, iter_deriv_inv_linear_sub, iter_deriv_pow, iter_deriv_pow', iter_deriv_zpow, iter_deriv_zpow'	21
Total	21

Differentiable

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
zpow 📖	mathematical	Differentiable NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing	DivInvMonoid.toZPow DivisionRing.toDivInvMonoid NormedDivisionRing.toDivisionRing NormedField.toNormedDivisionRing	—	DifferentiableAt.zpow

DifferentiableAt

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
zpow 📖	mathematical	DifferentiableAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing	DivInvMonoid.toZPow DivisionRing.toDivInvMonoid NormedDivisionRing.toDivisionRing NormedField.toNormedDivisionRing	—	comp differentiableAt_zpow

DifferentiableOn

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
zpow 📖	mathematical	DifferentiableOn NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing	DivInvMonoid.toZPow DivisionRing.toDivInvMonoid NormedDivisionRing.toDivisionRing NormedField.toNormedDivisionRing	—	DifferentiableWithinAt.zpow

DifferentiableWithinAt

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
zpow 📖	mathematical	DifferentiableWithinAt NormedAddCommGroup.toAddCommGroup NormedSpace.toModule NontriviallyNormedField.toNormedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing	DivInvMonoid.toZPow DivisionRing.toDivInvMonoid NormedDivisionRing.toDivisionRing NormedField.toNormedDivisionRing	—	DifferentiableAt.comp_differentiableWithinAt differentiableAt_zpow

(root)

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
derivWithin_zpow 📖	mathematical	UniqueDiffWithinAt DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing	derivWithin DivInvMonoid.toZPow DivisionRing.toDivInvMonoid NormedDivisionRing.toDivisionRing NormedField.toNormedDivisionRing Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing AddGroupWithOne.toIntCast Ring.toAddGroupWithOne NormedRing.toRing NormedCommRing.toNormedRing	—	HasDerivWithinAt.derivWithin hasDerivWithinAt_zpow
deriv_zpow 📖	mathematical	—	deriv NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing NontriviallyNormedField.toNormedField NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing DivInvMonoid.toZPow DivisionRing.toDivInvMonoid NormedDivisionRing.toDivisionRing NormedField.toNormedDivisionRing Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing AddGroupWithOne.toIntCast Ring.toAddGroupWithOne NormedRing.toRing NormedCommRing.toNormedRing	—	HasDerivAt.deriv hasDerivAt_zpow deriv_zero_of_not_differentiableAt differentiableAt_zpow zero_zpow LT.lt.ne LT.lt.trans sub_one_lt Int.instZeroLEOneClass IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono AddLeftCancelSemigroup.toIsLeftCancelAdd Int.instAddLeftMono MulZeroClass.mul_zero
deriv_zpow' 📖	mathematical	—	deriv NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing NontriviallyNormedField.toNormedField NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing DivInvMonoid.toZPow DivisionRing.toDivInvMonoid NormedDivisionRing.toDivisionRing NormedField.toNormedDivisionRing Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing AddGroupWithOne.toIntCast Ring.toAddGroupWithOne NormedRing.toRing NormedCommRing.toNormedRing	—	deriv_zpow
differentiableAt_zpow 📖	mathematical	—	DifferentiableAt NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing NontriviallyNormedField.toNormedField NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing DivInvMonoid.toZPow DivisionRing.toDivInvMonoid NormedDivisionRing.toDivisionRing NormedField.toNormedDivisionRing	—	NormedField.continuousAt_zpow DifferentiableAt.continuousAt IsTopologicalSemiring.toContinuousAdd IsTopologicalRing.toIsTopologicalSemiring IsTopologicalDivisionRing.toIsTopologicalRing NormedDivisionRing.to_isTopologicalDivisionRing ContinuousMul.to_continuousSMul IsTopologicalSemiring.toContinuousMul HasDerivAt.differentiableAt hasDerivAt_zpow
differentiableOn_zpow 📖	mathematical	Set Set.instMembership MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing NontriviallyNormedField.toNormedField	DifferentiableOn NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing DivInvMonoid.toZPow DivisionRing.toDivInvMonoid NormedDivisionRing.toDivisionRing NormedField.toNormedDivisionRing	—	differentiableWithinAt_zpow
differentiableWithinAt_zpow 📖	mathematical	—	DifferentiableWithinAt NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing NontriviallyNormedField.toNormedField NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing DivInvMonoid.toZPow DivisionRing.toDivInvMonoid NormedDivisionRing.toDivisionRing NormedField.toNormedDivisionRing	—	DifferentiableAt.differentiableWithinAt differentiableAt_zpow
hasDerivAt_zpow 📖	mathematical	—	HasDerivAt NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing NontriviallyNormedField.toNormedField NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing ContinuousMul.to_continuousSMul 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 DivInvMonoid.toZPow DivisionRing.toDivInvMonoid Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring AddGroupWithOne.toIntCast Ring.toAddGroupWithOne NormedRing.toRing NormedCommRing.toNormedRing	—	HasStrictDerivAt.hasDerivAt hasStrictDerivAt_zpow
hasDerivWithinAt_zpow 📖	mathematical	—	HasDerivWithinAt NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing NontriviallyNormedField.toNormedField NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing ContinuousMul.to_continuousSMul 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 DivInvMonoid.toZPow DivisionRing.toDivInvMonoid Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring AddGroupWithOne.toIntCast Ring.toAddGroupWithOne NormedRing.toRing NormedCommRing.toNormedRing	—	HasDerivAt.hasDerivWithinAt hasDerivAt_zpow
hasStrictDerivAt_zpow 📖	mathematical	—	HasStrictDerivAt NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing NontriviallyNormedField.toNormedField NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing ContinuousMul.to_continuousSMul 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 DivInvMonoid.toZPow DivisionRing.toDivInvMonoid Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring AddGroupWithOne.toIntCast Ring.toAddGroupWithOne NormedRing.toRing NormedCommRing.toNormedRing	—	ContinuousMul.to_continuousSMul IsTopologicalSemiring.toContinuousMul IsTopologicalRing.toIsTopologicalSemiring IsTopologicalDivisionRing.toIsTopologicalRing NormedDivisionRing.to_isTopologicalDivisionRing CanLift.prf instCanLiftIntNatCastLeOfNat LT.lt.le HasStrictDerivAt.congr_simp zpow_natCast Int.cast_natCast Nat.cast_zero Int.instAddLeftMono Int.instZeroLEOneClass Int.instCharZero hasStrictDerivAt_pow lt_trichotomy LT.lt.not_ge IsBoundedSMul.continuousSMul NormedSpace.toIsBoundedSMul HasStrictDerivAt.scomp IsScalarTower.right hasStrictDerivAt_inv zpow_ne_zero neg_pos IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono AddLeftCancelSemigroup.toIsLeftCancelAdd sq mul_inv inv_inv Int.cast_neg neg_mul neg_mul_neg zpow_add₀ mul_assoc Mathlib.Tactic.Abel.unfold_sub Mathlib.Tactic.Abel.subst_into_addg Mathlib.Tactic.Abel.term_atomg Mathlib.Tactic.Abel.subst_into_negg Mathlib.Tactic.Abel.term_neg neg_zero Mathlib.Tactic.Abel.term_add_constg zero_add Mathlib.Tactic.Abel.term_add_termg Mathlib.Meta.NormNum.IsNat.to_eq Mathlib.Meta.NormNum.isNat_add Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Meta.NormNum.IsInt.to_isNat Mathlib.Meta.NormNum.isInt_add Mathlib.Meta.NormNum.isInt_neg Mathlib.Meta.NormNum.IsNat.to_isInt add_zero zpow_neg zpow_zero Int.cast_zero MulZeroClass.zero_mul
iter_deriv_inv 📖	mathematical	—	Nat.iterate deriv NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing NontriviallyNormedField.toNormedField NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing InvOneClass.toInv DivInvOneMonoid.toInvOneClass DivisionMonoid.toDivInvOneMonoid DivisionCommMonoid.toDivisionMonoid CommGroupWithZero.toDivisionCommMonoid Semifield.toCommGroupWithZero Field.toSemifield NormedField.toField Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring NegZeroClass.toNeg SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne NormedRing.toRing NormedCommRing.toNormedRing AddMonoidWithOne.toNatCast Nat.factorial DivInvMonoid.toZPow DivisionRing.toDivInvMonoid NormedDivisionRing.toDivisionRing NormedField.toNormedDivisionRing	—	zpow_neg zpow_one Nat.cast_one Finset.prod_congr Int.cast_natCast iter_deriv_zpow Finset.prod_neg Finset.prod_Ico_eq_prod_range Finset.card_range neg_add_rev add_tsub_cancel_right Nat.instOrderedSub IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT AddLeftCancelSemigroup.toIsLeftCancelAdd contravariant_lt_of_covariant_le IsOrderedAddMonoid.toAddLeftMono Nat.instIsOrderedAddMonoid Nat.cast_prod Nat.cast_add
iter_deriv_inv' 📖	mathematical	—	Nat.iterate deriv NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing NontriviallyNormedField.toNormedField NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing InvOneClass.toInv DivInvOneMonoid.toInvOneClass DivisionMonoid.toDivInvOneMonoid DivisionCommMonoid.toDivisionMonoid CommGroupWithZero.toDivisionCommMonoid Semifield.toCommGroupWithZero Field.toSemifield NormedField.toField Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring NegZeroClass.toNeg SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne NormedRing.toRing NormedCommRing.toNormedRing AddMonoidWithOne.toNatCast Nat.factorial DivInvMonoid.toZPow DivisionRing.toDivInvMonoid NormedDivisionRing.toDivisionRing NormedField.toNormedDivisionRing	—	iter_deriv_inv
iter_deriv_inv_linear 📖	mathematical	—	Nat.iterate deriv NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing NontriviallyNormedField.toNormedField NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing InvOneClass.toInv DivInvOneMonoid.toInvOneClass DivisionMonoid.toDivInvOneMonoid DivisionCommMonoid.toDivisionMonoid CommGroupWithZero.toDivisionCommMonoid Semifield.toCommGroupWithZero Field.toSemifield NormedField.toField Distrib.toAdd NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing Distrib.toMul Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring NegZeroClass.toNeg SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne NormedRing.toRing NormedCommRing.toNormedRing AddMonoidWithOne.toNatCast Nat.factorial DivInvMonoid.toZPow DivisionRing.toDivInvMonoid NormedDivisionRing.toDivisionRing NormedField.toNormedDivisionRing	—	pow_zero Nat.cast_one mul_one CharP.cast_eq_zero CharP.ofCharZero Int.instCharZero sub_zero zpow_neg zpow_one one_mul Nat.factorial_succ add_comm Function.iterate_add_apply Function.iterate_one deriv_const_mul_field' Nat.cast_add MulZeroClass.zero_mul zero_add deriv_const' MulZeroClass.mul_zero Nat.cast_mul zero_pow deriv_comp_add_const Mathlib.Tactic.FieldSimp.eq_eq_cancel_eq IsCancelMulZero.toIsLeftCancelMulZero instIsCancelMulZero Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul Mathlib.Tactic.FieldSimp.NF.mul_eq_eval Mathlib.Tactic.FieldSimp.NF.atom_eq_eval Mathlib.Tactic.FieldSimp.subst_add Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval_cons_neg Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div div_one Mathlib.Tactic.FieldSimp.NF.eval_cons Mathlib.Tactic.FieldSimp.zpow'_one Mathlib.Tactic.FieldSimp.NF.div_eq_eval Mathlib.Tactic.FieldSimp.NF.div_eq_eval₁ Mathlib.Tactic.FieldSimp.NF.one_div_eq_eval Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval Mathlib.Tactic.FieldSimp.NF.mul_eq_eval₃ Mathlib.Tactic.FieldSimp.NF.mul_eq_eval₂ Mathlib.Tactic.FieldSimp.NF.eval_cons_eq_eval_of_eq_of_eq Mathlib.Tactic.FieldSimp.NF.eval_cons_of_pow_eq_zero one_ne_zero NeZero.one GroupWithZero.toNontrivial deriv_comp_mul_left deriv_zpow' Int.cast_sub Int.cast_neg Int.cast_one Int.cast_natCast Mathlib.Tactic.FieldSimp.subst_sub Mathlib.Tactic.FieldSimp.NF.one_eq_eval mul_neg Mathlib.Tactic.FieldSimp.NF.mul_eq_eval₁ Nat.instAtLeastTwoHAddOfNat Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.neg_congr Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat 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.atom_pf Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.pow_prod_atom Mathlib.Tactic.Ring.pow_zero 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_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.add_pf_add_lt Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Tactic.Ring.add_pf_add_gt Mathlib.Tactic.Ring.atom_pf' Mathlib.Tactic.Ring.add_pf_add_overlap Mathlib.Meta.NormNum.isInt_add Mathlib.Tactic.RingNF.int_rawCast_neg Mathlib.Tactic.RingNF.nat_rawCast_1 pow_one Mathlib.Tactic.RingNF.mul_neg add_zero Mathlib.Tactic.RingNF.add_neg Mathlib.Tactic.Ring.mul_one Mathlib.Tactic.RingNF.mul_assoc_rev Mathlib.Tactic.Ring.add_congr Mathlib.Tactic.Ring.pow_one_cast
iter_deriv_inv_linear_sub 📖	mathematical	—	Nat.iterate deriv NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing NontriviallyNormedField.toNormedField NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing InvOneClass.toInv DivInvOneMonoid.toInvOneClass DivisionMonoid.toDivInvOneMonoid DivisionCommMonoid.toDivisionMonoid CommGroupWithZero.toDivisionCommMonoid Semifield.toCommGroupWithZero Field.toSemifield NormedField.toField SubNegMonoid.toSub AddGroup.toSubNegMonoid NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring NegZeroClass.toNeg SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne NormedRing.toRing NormedCommRing.toNormedRing AddMonoidWithOne.toNatCast Nat.factorial DivInvMonoid.toZPow DivisionRing.toDivInvMonoid NormedDivisionRing.toDivisionRing NormedField.toNormedDivisionRing	—	sub_eq_add_neg iter_deriv_inv_linear
iter_deriv_pow 📖	mathematical	—	Nat.iterate deriv NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing NontriviallyNormedField.toNormedField NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing Finset.prod CommRing.toCommMonoid Field.toCommRing Finset.range SubNegMonoid.toSub AddGroup.toSubNegMonoid NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup AddMonoidWithOne.toNatCast AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne NormedRing.toRing NormedCommRing.toNormedRing	—	iter_deriv_zpow Finset.prod_congr Int.cast_natCast le_or_gt Finset.prod_eq_zero Finset.mem_range sub_self MulZeroClass.zero_mul
iter_deriv_pow' 📖	mathematical	—	Nat.iterate deriv NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing NontriviallyNormedField.toNormedField NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing Finset.prod CommRing.toCommMonoid Field.toCommRing Finset.range SubNegMonoid.toSub AddGroup.toSubNegMonoid NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup AddMonoidWithOne.toNatCast AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne NormedRing.toRing NormedCommRing.toNormedRing	—	iter_deriv_pow
iter_deriv_zpow 📖	mathematical	—	Nat.iterate deriv NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing NontriviallyNormedField.toNormedField NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing DivInvMonoid.toZPow DivisionRing.toDivInvMonoid NormedDivisionRing.toDivisionRing NormedField.toNormedDivisionRing Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing Finset.prod CommRing.toCommMonoid Field.toCommRing NormedField.toField Finset.range SubNegMonoid.toSub AddGroup.toSubNegMonoid NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup AddGroupWithOne.toIntCast Ring.toAddGroupWithOne NormedRing.toRing NormedCommRing.toNormedRing AddMonoidWithOne.toNatCast AddGroupWithOne.toAddMonoidWithOne	—	iter_deriv_zpow'
iter_deriv_zpow' 📖	mathematical	—	Nat.iterate deriv NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing NormedField.toNormedCommRing NontriviallyNormedField.toNormedField NormedSpace.toModule NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing NormedField.toNormedSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing DivInvMonoid.toZPow DivisionRing.toDivInvMonoid NormedDivisionRing.toDivisionRing NormedField.toNormedDivisionRing Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing Finset.prod CommRing.toCommMonoid Field.toCommRing NormedField.toField Finset.range SubNegMonoid.toSub AddGroup.toSubNegMonoid NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup AddGroupWithOne.toIntCast Ring.toAddGroupWithOne NormedRing.toRing NormedCommRing.toNormedRing AddMonoidWithOne.toNatCast AddGroupWithOne.toAddMonoidWithOne	—	Finset.prod_range_zero sub_zero one_mul Function.iterate_succ_apply' deriv_const_mul_field' deriv_zpow' Int.cast_sub Int.cast_natCast Finset.prod_range_succ mul_assoc

---

← Back to Index