Documentation Verification Report

LogDeriv

📁 Source: Mathlib/Analysis/Calculus/LogDeriv.lean

Statistics

Metric	Count
Definitions `logDeriv`	1
Theorems `tendsto_mul_logDeriv_simple_zero`, `logDeriv_apply`, `logDeriv_comp`, `logDeriv_const`, `logDeriv_const_mul`, `logDeriv_div`, `logDeriv_eqOn_iff`, `logDeriv_eq_zero_of_not_differentiableAt`, `logDeriv_fun_pow`, `logDeriv_fun_zpow`, `logDeriv_id`, `logDeriv_id'`, `logDeriv_inv`, `logDeriv_mul`, `logDeriv_mul_const`, `logDeriv_pow`, `logDeriv_prod`, `logDeriv_zpow`	18
Total	19

AnalyticAt

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`tendsto_mul_logDeriv_simple_zero` 📖	mathematical	`AnalyticAt` `NonUnitalNormedRing.toNormedAddCommGroup` `NonUnitalNormedCommRing.toNonUnitalNormedRing` `NormedCommRing.toNonUnitalNormedCommRing` `NormedField.toNormedCommRing` `NontriviallyNormedField.toNormedField` `NormedField.toNormedSpace` `MulZeroClass.toZero` `NonUnitalNonAssocSemiring.toMulZeroClass` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing`	`Filter.Tendsto` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `NormedCommRing.toNonUnitalNormedCommRing` `NormedField.toNormedCommRing` `NontriviallyNormedField.toNormedField` `SubNegMonoid.toSub` `AddGroup.toSubNegMonoid` `NormedAddGroup.toAddGroup` `NormedAddCommGroup.toNormedAddGroup` `NonUnitalNormedRing.toNormedAddCommGroup` `NonUnitalNormedCommRing.toNonUnitalNormedRing` `logDeriv` `NormedAlgebra.id` `nhdsWithin` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedRing.toPseudoMetricSpace` `SeminormedCommRing.toSeminormedRing` `NormedCommRing.toSeminormedCommRing` `Compl.compl` `Set` `Set.instCompl` `Set.instSingletonSet` `nhds` `AddMonoidWithOne.toOne` `AddGroupWithOne.toAddMonoidWithOne` `Ring.toAddGroupWithOne` `NormedRing.toRing` `NormedCommRing.toNormedRing`	—	`IsBoundedSMul.continuousSMul` `NormedSpace.toIsBoundedSMul` `hasDerivAt_iff_tendsto_slope` `DifferentiableAt.hasDerivAt` `differentiableAt` `div_self` `sub_zero` `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.subst_sub` `Mathlib.Tactic.FieldSimp.NF.atom_eq_eval` `Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons` `one_mul` `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_eval₃` `Mathlib.Tactic.FieldSimp.NF.mul_eq_eval₃` `mul_one` `Mathlib.Tactic.FieldSimp.eq_div_of_subst` `Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div'` `Mathlib.Tactic.FieldSimp.NF.inv_eq_eval` `Mathlib.Tactic.FieldSimp.NF.div_eq_eval₁` `Mathlib.Tactic.FieldSimp.NF.one_div_eq_eval` `one_ne_zero` `NeZero.one` `GroupWithZero.toNontrivial` `Mathlib.Tactic.Ring.of_eq` `Mathlib.Tactic.Ring.div_congr` `Mathlib.Tactic.Ring.mul_congr` `Mathlib.Tactic.Ring.sub_congr` `Mathlib.Tactic.Ring.atom_pf` `Mathlib.Tactic.Ring.sub_pf` `Mathlib.Tactic.Ring.neg_add` `Mathlib.Tactic.Ring.neg_mul` `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_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.mul_pf_right` `Mathlib.Tactic.Ring.one_mul` `Mathlib.Tactic.Ring.mul_zero` `Mathlib.Tactic.Ring.add_pf_add_zero` `Mathlib.Tactic.Ring.mul_one` `Mathlib.Tactic.Ring.zero_mul` `Mathlib.Tactic.Ring.div_pf` `Mathlib.Tactic.Ring.inv_single` `Mathlib.Tactic.Ring.inv_mul` `Mathlib.Meta.NormNum.IsNat.to_raw_eq` `Mathlib.Meta.NormNum.isNat_inv_one` `Filter.Tendsto.div` `IsTopologicalDivisionRing.toContinuousInv₀` `NormedDivisionRing.to_isTopologicalDivisionRing` `IsTopologicalSemiring.toContinuousMul` `IsTopologicalRing.toIsTopologicalSemiring` `IsTopologicalDivisionRing.toIsTopologicalRing` `Filter.Tendsto.mono_left` `ContinuousAt.tendsto` `continuousAt` `deriv` `nhdsWithin_le_nhds`

(root)

Definitions

Name	Category	Theorems
`logDeriv` 📖	CompOp	45 math math: `logDeriv_tprod_eq_tsum`, `AnalyticAt.tendsto_mul_logDeriv_simple_zero`, `logDeriv_const`, `logDeriv_comp`, `Complex.logDeriv_tendsto`, `logDeriv_mul`, `ModularForm.tsum_logDeriv_eta_q`, `logDeriv_fun_pow`, `logDeriv_eqOn_iff`, `Real.LogDeriv_exp`, `tendsto_logDeriv_euler_sin_div`, `logDeriv_sin_div_eq_cot`, `logDeriv_div`, `Complex.logDeriv_sin`, `Complex.logDeriv_exp`, `ModularForm.logDeriv_one_sub_mul_cexp_comp`, `logDeriv_apply`, `logDeriv_id`, `ModularForm.logDeriv_eta_eq_E2`, `MeromorphicOn.logDeriv`, `ModularForm.logDeriv_one_sub_cexp`, `logDeriv_eq_zero_of_not_differentiableAt`, `logDeriv_id'`, `Real.logDeriv_exp`, `Complex.digamma_def`, `ModularForm.summable_logDeriv_one_sub_eta_q`, `logDeriv_inv`, `Complex.LogDeriv_exp`, `logDeriv_prod`, `Meromorphic.logDeriv`, `logDeriv_prod_sineTerm_eq_sum_cotTerm`, `Real.logDeriv_sin`, `logDeriv_const_mul`, `logDeriv_fun_zpow`, `Complex.logDeriv_cos`, `logDeriv_mul_const`, `ModularForm.logDeriv_qParam`, `Real.logDeriv_cos`, `Real.logDeriv_cosh`, `Real.deriv_log_comp_eq_logDeriv`, `logDeriv_sineTerm_eq_cotTerm`, `logDeriv_pow`, `logDeriv_zpow`, `Complex.deriv_log_comp_eq_logDeriv`, `Complex.logDeriv_cosh`

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`logDeriv_apply` 📖	mathematical	—	`logDeriv` `DivInvMonoid.toDiv` `DivisionRing.toDivInvMonoid` `NormedDivisionRing.toDivisionRing` `NormedField.toNormedDivisionRing` `NontriviallyNormedField.toNormedField` `deriv` `NormedAddCommGroup.toAddCommGroup` `NonUnitalNormedRing.toNormedAddCommGroup` `NonUnitalNormedCommRing.toNonUnitalNormedRing` `NormedCommRing.toNonUnitalNormedCommRing` `NormedField.toNormedCommRing` `NormedSpace.toModule` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing` `SeminormedCommRing.toNonUnitalSeminormedCommRing` `NormedCommRing.toSeminormedCommRing` `NormedAlgebra.toNormedSpace` `SeminormedCommRing.toSeminormedRing` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedRing.toPseudoMetricSpace`	—	—
`logDeriv_comp` 📖	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` `NormedAlgebra.toNormedSpace`	`logDeriv` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `NormedCommRing.toNonUnitalNormedCommRing` `NormedField.toNormedCommRing` `NontriviallyNormedField.toNormedField` `NormedAlgebra.id` `deriv` `NormedAddCommGroup.toAddCommGroup` `NonUnitalNormedRing.toNormedAddCommGroup` `NonUnitalNormedCommRing.toNonUnitalNormedRing` `NormedSpace.toModule` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing` `SeminormedCommRing.toNonUnitalSeminormedCommRing` `NormedCommRing.toSeminormedCommRing` `NormedAlgebra.toNormedSpace` `SeminormedCommRing.toSeminormedRing` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedRing.toPseudoMetricSpace`	—	`deriv_comp` `Mathlib.Tactic.Ring.of_eq` `Mathlib.Tactic.Ring.div_congr` `Mathlib.Tactic.Ring.mul_congr` `Mathlib.Tactic.Ring.atom_pf` `Mathlib.Tactic.Ring.add_mul` `Mathlib.Tactic.Ring.mul_add` `Mathlib.Tactic.Ring.mul_pf_left` `Mathlib.Tactic.Ring.mul_pf_right` `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.div_pf` `Mathlib.Tactic.Ring.inv_single` `Mathlib.Tactic.Ring.inv_mul` `Mathlib.Meta.NormNum.IsNat.to_raw_eq` `Mathlib.Meta.NormNum.isNat_inv_one` `Mathlib.Meta.NormNum.IsNat.of_raw`
`logDeriv_const` 📖	mathematical	—	`logDeriv` `Pi.instZero` `MulZeroClass.toZero` `NonUnitalNonAssocSemiring.toMulZeroClass` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `NormedCommRing.toNonUnitalNormedCommRing` `NormedField.toNormedCommRing` `NontriviallyNormedField.toNormedField`	—	`deriv_const'` `zero_div`
`logDeriv_const_mul` 📖	mathematical	—	`logDeriv` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `NormedCommRing.toNonUnitalNormedCommRing` `NormedField.toNormedCommRing` `NontriviallyNormedField.toNormedField`	—	`deriv_const_mul_field` `mul_div_mul_left`
`logDeriv_div` 📖	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` `NormedAlgebra.toNormedSpace`	`logDeriv` `DivInvMonoid.toDiv` `DivisionRing.toDivInvMonoid` `NormedDivisionRing.toDivisionRing` `NormedField.toNormedDivisionRing` `NontriviallyNormedField.toNormedField` `SubNegMonoid.toSub` `AddGroup.toSubNegMonoid` `NormedAddGroup.toAddGroup` `NormedAddCommGroup.toNormedAddGroup` `NonUnitalNormedRing.toNormedAddCommGroup` `NonUnitalNormedCommRing.toNonUnitalNormedRing` `NormedCommRing.toNonUnitalNormedCommRing` `NormedField.toNormedCommRing`	—	`deriv_fun_div` `Mathlib.Tactic.FieldSimp.eq_eq_cancel_eq` `IsCancelMulZero.toIsLeftCancelMulZero` `instIsCancelMulZero` `Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul` `Mathlib.Tactic.FieldSimp.NF.div_eq_eval` `Mathlib.Tactic.FieldSimp.subst_sub` `Mathlib.Tactic.FieldSimp.NF.mul_eq_eval` `Mathlib.Tactic.FieldSimp.NF.atom_eq_eval` `Mathlib.Tactic.FieldSimp.NF.mul_eq_eval₃` `mul_one` `Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons` `one_mul` `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.pow_eq_eval` `Mathlib.Tactic.FieldSimp.NF.div_eq_eval₁` `Mathlib.Tactic.FieldSimp.NF.one_div_eq_eval` `Mathlib.Tactic.FieldSimp.NF.div_eq_eval₃` `Mathlib.Tactic.FieldSimp.NF.div_eq_eval₂` `Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval` `Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval_cons_neg` `Mathlib.Tactic.FieldSimp.NF.cons_ne_zero` `one_ne_zero` `NeZero.one` `GroupWithZero.toNontrivial`
`logDeriv_eqOn_iff` 📖	mathematical	`DifferentiableOn` `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` `NormedAlgebra.toNormedSpace` `IsOpen` `IsPreconnected`	`Set.EqOn` `logDeriv` `Function.hasSMul` `Algebra.toSMul` `Semifield.toCommSemiring` `Field.toSemifield` `NormedField.toField` `NontriviallyNormedField.toNormedField` `CommSemiring.toSemiring` `Algebra.id`	—	`Set.eq_empty_or_nonempty` `one_ne_zero` `NeZero.one` `IsSimpleRing.instNontrivial` `DivisionRing.isSimpleRing` `deriv_mul` `DifferentiableOn.differentiableAt` `IsOpen.mem_nhds` `DifferentiableAt.inv` `deriv_comp` `differentiableAt_inv` `deriv_inv` `neg_mul` `mul_neg` `Mathlib.Tactic.Ring.of_eq` `Mathlib.Tactic.Ring.add_congr` `Mathlib.Tactic.Ring.mul_congr` `Mathlib.Tactic.Ring.atom_pf` `Mathlib.Tactic.Ring.inv_congr` `Mathlib.Tactic.Ring.inv_single` `Mathlib.Tactic.Ring.inv_mul` `Mathlib.Meta.NormNum.IsNat.to_raw_eq` `Mathlib.Meta.NormNum.isNat_inv_one` `Mathlib.Meta.NormNum.IsNat.of_raw` `Mathlib.Tactic.Ring.mul_pf_right` `Mathlib.Tactic.Ring.one_mul` `Mathlib.Tactic.Ring.add_mul` `Mathlib.Tactic.Ring.mul_add` `Mathlib.Tactic.Ring.mul_pf_left` `Mathlib.Tactic.Ring.mul_zero` `Mathlib.Tactic.Ring.add_pf_add_zero` `Mathlib.Tactic.Ring.zero_mul` `Mathlib.Tactic.Ring.neg_congr` `Mathlib.Tactic.Ring.pow_congr` `Mathlib.Tactic.Ring.cast_pos` `Mathlib.Meta.NormNum.isNat_ofNat` `Mathlib.Tactic.Ring.pow_add` `Mathlib.Tactic.Ring.single_pow` `Mathlib.Tactic.Ring.mul_pow` `Mathlib.Tactic.Ring.one_pow` `Mathlib.Tactic.Ring.pow_zero` `Mathlib.Tactic.Ring.neg_add` `Mathlib.Tactic.Ring.neg_mul` `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.Tactic.Ring.neg_zero` `Mathlib.Tactic.Ring.add_pf_add_lt` `Mathlib.Tactic.Ring.add_pf_zero_add` `Mathlib.Tactic.Ring.sub_congr` `Mathlib.Tactic.Ring.div_congr` `Mathlib.Tactic.Ring.div_pf` `Mathlib.Tactic.Ring.sub_pf` `Set.EqOn.trans` `IsOpen.exists_is_const_of_deriv_eq_zero` `DifferentiableOn.mul` `DifferentiableOn.inv` `Set.EqOn.deriv` `deriv_const_smul` `Algebra.to_smulCommClass` `SeparatelyContinuousMul.to_continuousSMul` `IsSemitopologicalSemiring.toSeparatelyContinuousMul` `IsSemitopologicalRing.toIsSemitopologicalSemiring` `IsTopologicalRing.toIsSemitopologicalRing` `IsTopologicalDivisionRing.toIsTopologicalRing` `NormedDivisionRing.to_isTopologicalDivisionRing` `mul_div_mul_left`
`logDeriv_eq_zero_of_not_differentiableAt` 📖	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` `NormedAlgebra.toNormedSpace`	`logDeriv` `MulZeroClass.toZero` `NonUnitalNonAssocSemiring.toMulZeroClass` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `NormedCommRing.toNonUnitalNormedCommRing` `NormedField.toNormedCommRing` `NontriviallyNormedField.toNormedField`	—	`deriv_zero_of_not_differentiableAt` `zero_div`
`logDeriv_fun_pow` 📖	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` `NormedAlgebra.toNormedSpace`	`logDeriv` `Monoid.toPow` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `NontriviallyNormedField.toNormedField` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `NormedCommRing.toNonUnitalNormedCommRing` `NormedField.toNormedCommRing` `AddMonoidWithOne.toNatCast` `AddGroupWithOne.toAddMonoidWithOne` `Ring.toAddGroupWithOne` `NormedRing.toRing` `NormedCommRing.toNormedRing`	—	`zpow_natCast` `Int.cast_natCast` `logDeriv_fun_zpow`
`logDeriv_fun_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` `NormedAlgebra.toNormedSpace`	`logDeriv` `DivInvMonoid.toZPow` `DivisionRing.toDivInvMonoid` `NormedDivisionRing.toDivisionRing` `NormedField.toNormedDivisionRing` `NontriviallyNormedField.toNormedField` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `NormedCommRing.toNonUnitalNormedCommRing` `NormedField.toNormedCommRing` `AddGroupWithOne.toIntCast` `Ring.toAddGroupWithOne` `NormedRing.toRing` `NormedCommRing.toNormedRing`	—	`eq_or_ne` `zpow_zero` `logDeriv_const` `Int.cast_zero` `MulZeroClass.zero_mul` `zero_zpow` `div_zero` `MulZeroClass.mul_zero` `logDeriv_apply` `deriv_comp` `differentiableAt_zpow` `deriv_zpow` `zpow_sub_one₀` `Mathlib.Tactic.FieldSimp.eq_eq_cancel_eq` `IsCancelMulZero.toIsLeftCancelMulZero` `instIsCancelMulZero` `Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul` `Mathlib.Tactic.FieldSimp.NF.div_eq_eval` `Mathlib.Tactic.FieldSimp.NF.mul_eq_eval` `Mathlib.Tactic.FieldSimp.NF.atom_eq_eval` `Mathlib.Tactic.FieldSimp.NF.inv_eq_eval` `Mathlib.Tactic.FieldSimp.NF.mul_eq_eval₃` `mul_one` `Mathlib.Tactic.FieldSimp.NF.div_eq_eval₁` `Mathlib.Tactic.FieldSimp.NF.div_eq_eval₂` `div_one` `Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons` `Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval` `Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons_zero` `one_mul` `Mathlib.Tactic.FieldSimp.NF.eval_cons_of_pow_eq_zero` `Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst` `Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div` `Mathlib.Tactic.FieldSimp.NF.eval_cons` `Mathlib.Tactic.FieldSimp.zpow'_one` `Mathlib.Tactic.FieldSimp.NF.one_div_eq_eval` `Mathlib.Tactic.FieldSimp.NF.cons_ne_zero` `one_ne_zero` `NeZero.one` `GroupWithZero.toNontrivial`
`logDeriv_id` 📖	mathematical	—	`logDeriv` `NormedAlgebra.id` `NontriviallyNormedField.toNormedField` `DivInvMonoid.toDiv` `DivisionRing.toDivInvMonoid` `NormedDivisionRing.toDivisionRing` `NormedField.toNormedDivisionRing` `AddMonoidWithOne.toOne` `AddGroupWithOne.toAddMonoidWithOne` `Ring.toAddGroupWithOne` `NormedRing.toRing` `NormedCommRing.toNormedRing` `NormedField.toNormedCommRing`	—	`deriv_id'` `one_div`
`logDeriv_id'` 📖	mathematical	—	`logDeriv` `NormedAlgebra.id` `NontriviallyNormedField.toNormedField` `DivInvMonoid.toDiv` `DivisionRing.toDivInvMonoid` `NormedDivisionRing.toDivisionRing` `NormedField.toNormedDivisionRing` `AddMonoidWithOne.toOne` `AddGroupWithOne.toAddMonoidWithOne` `Ring.toAddGroupWithOne` `NormedRing.toRing` `NormedCommRing.toNormedRing` `NormedField.toNormedCommRing`	—	`logDeriv_id`
`logDeriv_inv` 📖	mathematical	—	`logDeriv` `NormedAlgebra.id` `NontriviallyNormedField.toNormedField` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `DivisionCommMonoid.toDivisionMonoid` `CommGroupWithZero.toDivisionCommMonoid` `Semifield.toCommGroupWithZero` `Field.toSemifield` `NormedField.toField` `DivInvMonoid.toDiv` `DivisionRing.toDivInvMonoid` `NormedDivisionRing.toDivisionRing` `NormedField.toNormedDivisionRing` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `AddCommGroup.toDivisionAddCommMonoid` `NormedAddCommGroup.toAddCommGroup` `NonUnitalNormedRing.toNormedAddCommGroup` `NonUnitalNormedCommRing.toNonUnitalNormedRing` `NormedCommRing.toNonUnitalNormedCommRing` `NormedField.toNormedCommRing` `AddMonoidWithOne.toOne` `AddGroupWithOne.toAddMonoidWithOne` `Ring.toAddGroupWithOne` `NormedRing.toRing` `NormedCommRing.toNormedRing`	—	`zpow_neg` `zpow_one` `Int.cast_neg` `Int.cast_one` `logDeriv_zpow`
`logDeriv_mul` 📖	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` `NormedAlgebra.toNormedSpace`	`logDeriv` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `NormedCommRing.toNonUnitalNormedCommRing` `NormedField.toNormedCommRing` `NontriviallyNormedField.toNormedField` `Distrib.toAdd`	—	`deriv_fun_mul` `Mathlib.Tactic.FieldSimp.eq_eq_cancel_eq` `IsCancelMulZero.toIsLeftCancelMulZero` `instIsCancelMulZero` `Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul` `Mathlib.Tactic.FieldSimp.NF.div_eq_eval` `Mathlib.Tactic.FieldSimp.subst_add` `Mathlib.Tactic.FieldSimp.NF.mul_eq_eval` `Mathlib.Tactic.FieldSimp.NF.atom_eq_eval` `Mathlib.Tactic.FieldSimp.NF.mul_eq_eval₃` `mul_one` `Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons` `one_mul` `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.mul_eq_eval₁` `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.div_eq_eval₃` `Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval_cons_neg` `Mathlib.Tactic.FieldSimp.NF.cons_ne_zero` `one_ne_zero` `NeZero.one` `GroupWithZero.toNontrivial`
`logDeriv_mul_const` 📖	mathematical	—	`logDeriv` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `NormedCommRing.toNonUnitalNormedCommRing` `NormedField.toNormedCommRing` `NontriviallyNormedField.toNormedField`	—	`deriv_mul_const_field` `mul_div_mul_right`
`logDeriv_pow` 📖	mathematical	—	`logDeriv` `NormedAlgebra.id` `NontriviallyNormedField.toNormedField` `Monoid.toPow` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `DivInvMonoid.toDiv` `DivisionRing.toDivInvMonoid` `NormedDivisionRing.toDivisionRing` `NormedField.toNormedDivisionRing` `AddMonoidWithOne.toNatCast` `AddGroupWithOne.toAddMonoidWithOne` `Ring.toAddGroupWithOne` `NormedRing.toRing` `NormedCommRing.toNormedRing` `NormedField.toNormedCommRing`	—	`zpow_natCast` `Int.cast_natCast` `logDeriv_zpow`
`logDeriv_prod` 📖	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` `NormedAlgebra.toNormedSpace`	`logDeriv` `Finset.prod` `CommRing.toCommMonoid` `Field.toCommRing` `NormedField.toField` `NontriviallyNormedField.toNormedField` `Finset.sum` `ESeminormedAddCommMonoid.toAddCommMonoid` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedRing.toPseudoMetricSpace` `SeminormedCommRing.toSeminormedRing` `NormedCommRing.toSeminormedCommRing` `NormedField.toNormedCommRing` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `NonUnitalNormedRing.toNormedAddCommGroup` `NonUnitalNormedCommRing.toNonUnitalNormedRing` `NormedCommRing.toNonUnitalNormedCommRing`	—	`Finset.cons_induction` `logDeriv_const` `Finset.prod_cons` `Finset.sum_cons` `logDeriv_mul` `Finset.forall_mem_cons` `IsSimpleRing.instNontrivial` `DivisionRing.isSimpleRing` `NormMulClass.toNoZeroDivisors` `NormedDivisionRing.toNormMulClass` `DifferentiableAt.fun_finset_prod`
`logDeriv_zpow` 📖	mathematical	—	`logDeriv` `NormedAlgebra.id` `NontriviallyNormedField.toNormedField` `DivInvMonoid.toZPow` `DivisionRing.toDivInvMonoid` `NormedDivisionRing.toDivisionRing` `NormedField.toNormedDivisionRing` `DivInvMonoid.toDiv` `AddGroupWithOne.toIntCast` `Ring.toAddGroupWithOne` `NormedRing.toRing` `NormedCommRing.toNormedRing` `NormedField.toNormedCommRing`	—	`logDeriv_fun_zpow` `differentiableAt_id` `logDeriv_id'` `mul_one_div`

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