Mul

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

Statistics

Metric	Count
Definitions	0
Theorems `const_mul`, `fun_inv`, `fun_mul`, `fun_smul`, `inv`, `inverse`, `mul`, `mul_const`, `smul`, `smul_const`, `const_mul`, `fun_inv`, `fun_mul`, `fun_smul`, `inv`, `inverse`, `mul`, `mul_const`, `smul`, `smul_const`, `const_mul`, `fun_inv`, `fun_mul`, `fun_smul`, `inv`, `inverse`, `mul`, `mul_const`, `smul`, `smul_const`, `const_mul`, `fun_inv`, `fun_mul`, `fun_smul`, `inv`, `inverse`, `mul`, `mul_const`, `smul`, `smul_const`, `const_mul`, `finset_prod`, `fun_mul`, `fun_mul'`, `fun_smul`, `list_prod'`, `mul`, `mul'`, `mul_const`, `mul_const'`, `multiset_prod`, `smul`, `smul_const`, `const_mul`, `finset_prod`, `fun_mul`, `fun_mul'`, `fun_smul`, `list_prod'`, `mul`, `mul'`, `mul_const`, `mul_const'`, `multiset_prod`, `smul`, `smul_const`, `const_mul`, `finset_prod`, `fun_mul`, `fun_mul'`, `fun_smul`, `list_prod'`, `mul`, `mul'`, `mul_const`, `mul_const'`, `multiset_prod`, `smul`, `smul_const`, `differentiableAt_inv`, `differentiableAt_inverse`, `differentiableOn_inv`, `differentiableOn_inverse`, `differentiableWithinAt_inv`, `differentiableWithinAt_inverse`, `fderivWithin_const_mul`, `fderivWithin_finset_prod`, `fderivWithin_fun_mul`, `fderivWithin_fun_mul'`, `fderivWithin_fun_smul`, `fderivWithin_inv'`, `fderivWithin_list_prod'`, `fderivWithin_mul`, `fderivWithin_mul'`, `fderivWithin_mul_const`, `fderivWithin_mul_const'`, `fderivWithin_multiset_prod`, `fderivWithin_smul`, `fderivWithin_smul_const`, `fderiv_const_mul`, `fderiv_finset_prod`, `fderiv_fun_mul`, `fderiv_fun_mul'`, `fderiv_fun_smul`, `fderiv_inv'`, `fderiv_inverse`, `fderiv_list_prod'`, `fderiv_mul`, `fderiv_mul'`, `fderiv_mul_const`, `fderiv_mul_const'`, `fderiv_multiset_prod`, `fderiv_smul`, `fderiv_smul_const`, `hasFDerivAt_finset_prod`, `hasFDerivAt_inv'`, `hasFDerivAt_list_prod'`, `hasFDerivAt_list_prod_attach'`, `hasFDerivAt_list_prod_finRange'`, `hasFDerivAt_multiset_prod`, `hasFDerivAt_ringInverse`, `hasStrictFDerivAt_finset_prod`, `hasStrictFDerivAt_inv'`, `hasStrictFDerivAt_list_prod`, `hasStrictFDerivAt_list_prod'`, `hasStrictFDerivAt_list_prod_attach'`, `hasStrictFDerivAt_list_prod_finRange'`, `hasStrictFDerivAt_multiset_prod`, `hasStrictFDerivAt_ringInverse`	129
Total	129

Differentiable

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`const_mul` 📖	mathematical	`Differentiable` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing`	—	`DifferentiableAt.const_mul`
`fun_inv` 📖	mathematical	`Differentiable` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NormedDivisionRing.toNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `GroupWithZero.toDivisionMonoid` `DivisionSemiring.toGroupWithZero` `DivisionRing.toDivisionSemiring` `NormedDivisionRing.toDivisionRing`	—	`inv`
`fun_mul` 📖	mathematical	`Differentiable` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing`	—	`mul`
`fun_smul` 📖	mathematical	`Differentiable` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `ESeminormedAddMonoid.toAddMonoid` `ESeminormedAddCommMonoid.toESeminormedAddMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `DistribSMul.toSMulZeroClass` `DistribMulAction.toDistribSMul` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing` `Module.toDistribMulAction` `ESeminormedAddCommMonoid.toAddCommMonoid`	—	`smul`
`inv` 📖	mathematical	`Differentiable` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NormedDivisionRing.toNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Pi.instInv` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `GroupWithZero.toDivisionMonoid` `DivisionSemiring.toGroupWithZero` `DivisionRing.toDivisionSemiring` `NormedDivisionRing.toDivisionRing`	—	`DifferentiableAt.inv`
`inverse` 📖	mathematical	`Differentiable` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace` `IsUnit` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing`	`Ring.inverse`	—	`DifferentiableAt.inverse`
`mul` 📖	mathematical	`Differentiable` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Pi.instMul` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing`	—	`DifferentiableAt.mul`
`mul_const` 📖	mathematical	`Differentiable` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing`	—	`DifferentiableAt.mul_const`
`smul` 📖	mathematical	`Differentiable` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Pi.smul'` `SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `ESeminormedAddMonoid.toAddMonoid` `ESeminormedAddCommMonoid.toESeminormedAddMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `DistribSMul.toSMulZeroClass` `DistribMulAction.toDistribSMul` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing` `Module.toDistribMulAction` `ESeminormedAddCommMonoid.toAddCommMonoid`	—	`DifferentiableAt.smul`
`smul_const` 📖	mathematical	`Differentiable` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `ESeminormedAddMonoid.toAddMonoid` `ESeminormedAddCommMonoid.toESeminormedAddMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `DistribSMul.toSMulZeroClass` `DistribMulAction.toDistribSMul` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing` `Module.toDistribMulAction` `ESeminormedAddCommMonoid.toAddCommMonoid`	—	`DifferentiableAt.smul_const`

DifferentiableAt

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`const_mul` 📖	mathematical	`DifferentiableAt` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing`	—	`HasFDerivAt.differentiableAt` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `HasFDerivAt.const_mul` `hasFDerivAt`
`fun_inv` 📖	mathematical	`DifferentiableAt` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NormedDivisionRing.toNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `GroupWithZero.toDivisionMonoid` `DivisionSemiring.toGroupWithZero` `DivisionRing.toDivisionSemiring` `NormedDivisionRing.toDivisionRing`	—	`inv`
`fun_mul` 📖	mathematical	`DifferentiableAt` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing`	—	`mul`
`fun_smul` 📖	mathematical	`DifferentiableAt` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `ESeminormedAddMonoid.toAddMonoid` `ESeminormedAddCommMonoid.toESeminormedAddMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `DistribSMul.toSMulZeroClass` `DistribMulAction.toDistribSMul` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing` `Module.toDistribMulAction` `ESeminormedAddCommMonoid.toAddCommMonoid`	—	`smul`
`inv` 📖	mathematical	`DifferentiableAt` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NormedDivisionRing.toNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Pi.instInv` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `GroupWithZero.toDivisionMonoid` `DivisionSemiring.toGroupWithZero` `DivisionRing.toDivisionSemiring` `NormedDivisionRing.toDivisionRing`	—	`comp` `differentiableAt_inv`
`inverse` 📖	mathematical	`DifferentiableAt` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace` `IsUnit` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing`	`Ring.inverse`	—	`comp` `differentiableAt_inverse`
`mul` 📖	mathematical	`DifferentiableAt` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Pi.instMul` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing`	—	`HasFDerivAt.differentiableAt` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `SMulCommClass.opposite_mid` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `HasFDerivAt.mul'` `hasFDerivAt`
`mul_const` 📖	mathematical	`DifferentiableAt` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing`	—	`HasFDerivAt.differentiableAt` `SMulCommClass.opposite_mid` `IsScalarTower.right` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul_op` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `HasFDerivAt.mul_const'` `hasFDerivAt`
`smul` 📖	mathematical	`DifferentiableAt` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Pi.smul'` `SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `ESeminormedAddMonoid.toAddMonoid` `ESeminormedAddCommMonoid.toESeminormedAddMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `DistribSMul.toSMulZeroClass` `DistribMulAction.toDistribSMul` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing` `Module.toDistribMulAction` `ESeminormedAddCommMonoid.toAddCommMonoid`	—	`HasFDerivAt.differentiableAt` `IsTopologicalAddGroup.toContinuousAdd` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsScalarTower.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `IsBoundedSMul.continuousSMul` `HasFDerivAt.smul` `hasFDerivAt`
`smul_const` 📖	mathematical	`DifferentiableAt` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `ESeminormedAddMonoid.toAddMonoid` `ESeminormedAddCommMonoid.toESeminormedAddMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `DistribSMul.toSMulZeroClass` `DistribMulAction.toDistribSMul` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing` `Module.toDistribMulAction` `ESeminormedAddCommMonoid.toAddCommMonoid`	—	`HasFDerivAt.differentiableAt` `IsBoundedSMul.continuousSMul` `HasFDerivAt.smul_const` `hasFDerivAt`

DifferentiableOn

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`const_mul` 📖	mathematical	`DifferentiableOn` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing`	—	`DifferentiableWithinAt.const_mul`
`fun_inv` 📖	mathematical	`DifferentiableOn` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NormedDivisionRing.toNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `GroupWithZero.toDivisionMonoid` `DivisionSemiring.toGroupWithZero` `DivisionRing.toDivisionSemiring` `NormedDivisionRing.toDivisionRing`	—	`inv`
`fun_mul` 📖	mathematical	`DifferentiableOn` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing`	—	`mul`
`fun_smul` 📖	mathematical	`DifferentiableOn` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `ESeminormedAddMonoid.toAddMonoid` `ESeminormedAddCommMonoid.toESeminormedAddMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `DistribSMul.toSMulZeroClass` `DistribMulAction.toDistribSMul` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing` `Module.toDistribMulAction` `ESeminormedAddCommMonoid.toAddCommMonoid`	—	`smul`
`inv` 📖	mathematical	`DifferentiableOn` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NormedDivisionRing.toNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Pi.instInv` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `GroupWithZero.toDivisionMonoid` `DivisionSemiring.toGroupWithZero` `DivisionRing.toDivisionSemiring` `NormedDivisionRing.toDivisionRing`	—	`DifferentiableWithinAt.inv`
`inverse` 📖	mathematical	`DifferentiableOn` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace` `IsUnit` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing`	`Ring.inverse`	—	`DifferentiableWithinAt.inverse`
`mul` 📖	mathematical	`DifferentiableOn` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Pi.instMul` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing`	—	`DifferentiableWithinAt.mul`
`mul_const` 📖	mathematical	`DifferentiableOn` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing`	—	`DifferentiableWithinAt.mul_const`
`smul` 📖	mathematical	`DifferentiableOn` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Pi.smul'` `SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `ESeminormedAddMonoid.toAddMonoid` `ESeminormedAddCommMonoid.toESeminormedAddMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `DistribSMul.toSMulZeroClass` `DistribMulAction.toDistribSMul` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing` `Module.toDistribMulAction` `ESeminormedAddCommMonoid.toAddCommMonoid`	—	`DifferentiableWithinAt.smul`
`smul_const` 📖	mathematical	`DifferentiableOn` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `ESeminormedAddMonoid.toAddMonoid` `ESeminormedAddCommMonoid.toESeminormedAddMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `DistribSMul.toSMulZeroClass` `DistribMulAction.toDistribSMul` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing` `Module.toDistribMulAction` `ESeminormedAddCommMonoid.toAddCommMonoid`	—	`DifferentiableWithinAt.smul_const`

DifferentiableWithinAt

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`const_mul` 📖	mathematical	`DifferentiableWithinAt` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing`	—	`HasFDerivWithinAt.differentiableWithinAt` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `HasFDerivWithinAt.const_mul` `hasFDerivWithinAt`
`fun_inv` 📖	mathematical	`DifferentiableWithinAt` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NormedDivisionRing.toNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `GroupWithZero.toDivisionMonoid` `DivisionSemiring.toGroupWithZero` `DivisionRing.toDivisionSemiring` `NormedDivisionRing.toDivisionRing`	—	`inv`
`fun_mul` 📖	mathematical	`DifferentiableWithinAt` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing`	—	`mul`
`fun_smul` 📖	mathematical	`DifferentiableWithinAt` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `ESeminormedAddMonoid.toAddMonoid` `ESeminormedAddCommMonoid.toESeminormedAddMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `DistribSMul.toSMulZeroClass` `DistribMulAction.toDistribSMul` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing` `Module.toDistribMulAction` `ESeminormedAddCommMonoid.toAddCommMonoid`	—	`smul`
`inv` 📖	mathematical	`DifferentiableWithinAt` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NormedDivisionRing.toNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Pi.instInv` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `GroupWithZero.toDivisionMonoid` `DivisionSemiring.toGroupWithZero` `DivisionRing.toDivisionSemiring` `NormedDivisionRing.toDivisionRing`	—	`DifferentiableAt.comp_differentiableWithinAt` `differentiableAt_inv`
`inverse` 📖	mathematical	`DifferentiableWithinAt` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace` `IsUnit` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing`	`Ring.inverse`	—	`DifferentiableAt.comp_differentiableWithinAt` `differentiableAt_inverse`
`mul` 📖	mathematical	`DifferentiableWithinAt` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Pi.instMul` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing`	—	`HasFDerivWithinAt.differentiableWithinAt` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `SMulCommClass.opposite_mid` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `HasFDerivWithinAt.mul'` `hasFDerivWithinAt`
`mul_const` 📖	mathematical	`DifferentiableWithinAt` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing`	—	`HasFDerivWithinAt.differentiableWithinAt` `SMulCommClass.opposite_mid` `IsScalarTower.right` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul_op` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `HasFDerivWithinAt.mul_const'` `hasFDerivWithinAt`
`smul` 📖	mathematical	`DifferentiableWithinAt` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Pi.smul'` `SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `ESeminormedAddMonoid.toAddMonoid` `ESeminormedAddCommMonoid.toESeminormedAddMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `DistribSMul.toSMulZeroClass` `DistribMulAction.toDistribSMul` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing` `Module.toDistribMulAction` `ESeminormedAddCommMonoid.toAddCommMonoid`	—	`HasFDerivWithinAt.differentiableWithinAt` `IsTopologicalAddGroup.toContinuousAdd` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsScalarTower.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `IsBoundedSMul.continuousSMul` `HasFDerivWithinAt.smul` `hasFDerivWithinAt`
`smul_const` 📖	mathematical	`DifferentiableWithinAt` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `ESeminormedAddMonoid.toAddMonoid` `ESeminormedAddCommMonoid.toESeminormedAddMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `DistribSMul.toSMulZeroClass` `DistribMulAction.toDistribSMul` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing` `Module.toDistribMulAction` `ESeminormedAddCommMonoid.toAddCommMonoid`	—	`HasFDerivWithinAt.differentiableWithinAt` `IsBoundedSMul.continuousSMul` `HasFDerivWithinAt.smul_const` `hasFDerivWithinAt`

HasFDerivAt

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`const_mul` 📖	mathematical	`HasFDerivAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedRing.toNonUnitalNormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `NonUnitalNormedRing.toNormedAddCommGroup` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing`	—	`comp` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `smulCommClass_self` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `NormedSpace.toIsBoundedSMul` `IsScalarTower.right` `Algebra.to_smulCommClass` `ContinuousLinearMap.hasFDerivAt`
`finset_prod` 📖	mathematical	`HasFDerivAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing` `SeminormedCommRing.toNonUnitalSeminormedCommRing` `NormedCommRing.toSeminormedCommRing` `NormedAlgebra.toNormedSpace` `SeminormedCommRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Finset.prod` `CommRing.toCommMonoid` `NormedCommRing.toCommRing` `Finset.sum` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.addCommMonoid` `IsTopologicalSemiring.toContinuousAdd` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `NormedCommRing.toNonUnitalNormedCommRing` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `NonUnitalNormedRing.toNormedAddCommGroup` `NonUnitalNormedCommRing.toNonUnitalNormedRing` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `NormedRing.toRing` `NormedCommRing.toNormedRing` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `Finset.erase`	—	`IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `Finset.prod_attach` `congr_fderiv` `RingHomCompTriple.ids` `comp` `hasFDerivAt_finset_prod` `Finite.of_fintype` `hasFDerivAt_pi` `Subtype.prop` `ContinuousLinearMap.ext` `ContinuousLinearMap.comp.congr_simp` `Finset.sum_congr` `Finset.prod_erase_attach` `ContinuousLinearMap.coe_sum'` `Finset.sum_apply` `Finset.sum_attach`
`fun_mul` 📖	mathematical	`HasFDerivAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing` `SeminormedCommRing.toNonUnitalSeminormedCommRing` `NormedCommRing.toSeminormedCommRing` `NormedAlgebra.toNormedSpace` `SeminormedCommRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `NormedCommRing.toNonUnitalNormedCommRing` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `NonUnitalNormedRing.toNormedAddCommGroup` `NonUnitalNormedCommRing.toNonUnitalNormedRing` `ContinuousLinearMap.add` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `NormedRing.toRing` `NormedCommRing.toNormedRing` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing`	—	`IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `mul`
`fun_mul'` 📖	mathematical	`HasFDerivAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedRing.toNonUnitalNormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `NonUnitalNormedRing.toNormedAddCommGroup` `ContinuousLinearMap.add` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `MulOpposite` `DistribMulAction.toDistribSMul` `MulOpposite.instMonoid` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Module.toDistribMulAction` `MulOpposite.instSemiring` `Semiring.toOppositeModule` `SMulCommClass.opposite_mid` `MulZeroClass.toMul` `MulZeroOneClass.toMulZeroClass` `MonoidWithZero.toMulZeroOneClass` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `MulOpposite.op`	—	`IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `SMulCommClass.opposite_mid` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `mul'`
`fun_smul` 📖	mathematical	`HasFDerivAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedRing.toNonUnitalNormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `ESeminormedAddMonoid.toAddMonoid` `ESeminormedAddCommMonoid.toESeminormedAddMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `DistribSMul.toSMulZeroClass` `DistribMulAction.toDistribSMul` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing` `Module.toDistribMulAction` `ESeminormedAddCommMonoid.toAddCommMonoid` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `ContinuousLinearMap.add` `IsTopologicalAddGroup.toContinuousAdd` `NormedAddGroup.toAddGroup` `NormedAddCommGroup.toNormedAddGroup` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `ContinuousLinearMap.instSMul` `AddCommMonoid.toAddMonoid` `IsScalarTower.to_smulCommClass` `Semifield.toCommSemiring` `NormedAlgebra.toAlgebra` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `MulZeroClass.toZero` `NonUnitalNonAssocSemiring.toMulZeroClass` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `AddCommGroup.toDivisionAddCommMonoid` `NormedAddCommGroup.toAddCommGroup` `ContinuousLinearMap.smulRight` `IsBoundedSMul.continuousSMul`	—	`IsTopologicalAddGroup.toContinuousAdd` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsScalarTower.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `IsBoundedSMul.continuousSMul` `smul`
`list_prod'` 📖	mathematical	`HasFDerivAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedRing.toNonUnitalNormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing` `AddMonoidWithOne.toOne` `AddGroupWithOne.toAddMonoidWithOne` `Ring.toAddGroupWithOne` `Finset.sum` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.addCommMonoid` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Finset.univ` `Fin.fintype` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `NonUnitalNormedRing.toNormedAddCommGroup` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `MulOpposite` `DistribMulAction.toDistribSMul` `MulOpposite.instMonoid` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Module.toDistribMulAction` `MulOpposite.instSemiring` `Semiring.toOppositeModule` `SMulCommClass.opposite_mid` `MulZeroClass.toMul` `MulZeroOneClass.toMulZeroClass` `MonoidWithZero.toMulZeroOneClass` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `MulOpposite.op`	—	`IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `SMulCommClass.opposite_mid` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `Finset.sum_congr` `congr_fderiv` `RingHomCompTriple.ids` `comp` `hasFDerivAt_list_prod_finRange'` `hasFDerivAt_pi` `Finite.of_fintype` `ContinuousLinearMap.ext` `ContinuousLinearMap.comp.congr_simp` `ContinuousLinearMap.sum_apply`
`mul` 📖	mathematical	`HasFDerivAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing` `SeminormedCommRing.toNonUnitalSeminormedCommRing` `NormedCommRing.toSeminormedCommRing` `NormedAlgebra.toNormedSpace` `SeminormedCommRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Pi.instMul` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `NormedCommRing.toNonUnitalNormedCommRing` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `NonUnitalNormedRing.toNormedAddCommGroup` `NonUnitalNormedCommRing.toNonUnitalNormedRing` `ContinuousLinearMap.add` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `NormedRing.toRing` `NormedCommRing.toNormedRing` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing`	—	`IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `SMulCommClass.opposite_mid` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `ContinuousLinearMap.ext` `mul_comm` `mul'`
`mul'` 📖	mathematical	`HasFDerivAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedRing.toNonUnitalNormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Pi.instMul` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `NonUnitalNormedRing.toNormedAddCommGroup` `ContinuousLinearMap.add` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `MulOpposite` `DistribMulAction.toDistribSMul` `MulOpposite.instMonoid` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Module.toDistribMulAction` `MulOpposite.instSemiring` `Semiring.toOppositeModule` `SMulCommClass.opposite_mid` `MulZeroClass.toMul` `MulZeroOneClass.toMulZeroClass` `MonoidWithZero.toMulZeroOneClass` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `MulOpposite.op`	—	`comp` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsTopologicalAddGroup.toContinuousAdd` `smulCommClass_self` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `NormedSpace.toIsBoundedSMul` `IsScalarTower.right` `Algebra.to_smulCommClass` `ContinuousLinearMap.isBoundedBilinearMap` `IsBoundedBilinearMap.hasFDerivAt` `prodMk`
`mul_const` 📖	mathematical	`HasFDerivAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing` `SeminormedCommRing.toNonUnitalSeminormedCommRing` `NormedCommRing.toSeminormedCommRing` `NormedAlgebra.toNormedSpace` `SeminormedCommRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `NormedCommRing.toNonUnitalNormedCommRing` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `NonUnitalNormedRing.toNormedAddCommGroup` `NonUnitalNormedCommRing.toNonUnitalNormedRing` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `NormedRing.toRing` `NormedCommRing.toNormedRing` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing`	—	`Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `SMulCommClass.opposite_mid` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `ContinuousLinearMap.ext` `mul_comm` `mul_const'`
`mul_const'` 📖	mathematical	`HasFDerivAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedRing.toNonUnitalNormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing` `MulOpposite` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `NonUnitalNormedRing.toNormedAddCommGroup` `ContinuousLinearMap.instSMul` `DistribMulAction.toDistribSMul` `MulOpposite.instMonoid` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `AddCommMonoid.toAddMonoid` `Module.toDistribMulAction` `MulOpposite.instSemiring` `Semiring.toOppositeModule` `SMulCommClass.opposite_mid` `MulZeroClass.toMul` `MulZeroOneClass.toMulZeroClass` `MonoidWithZero.toMulZeroOneClass` `SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `DistribSMul.toSMulZeroClass` `IsScalarTower.right` `Semifield.toCommSemiring` `SeminormedRing.toRing` `NormedAlgebra.toAlgebra` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul_op` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `MulOpposite.op`	—	`comp` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsTopologicalAddGroup.toContinuousAdd` `smulCommClass_self` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `NormedSpace.toIsBoundedSMul` `RingHomIsometric.ids` `IsScalarTower.right` `Algebra.to_smulCommClass` `ContinuousLinearMap.hasFDerivAt`
`multiset_prod` 📖	mathematical	`HasFDerivAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing` `SeminormedCommRing.toNonUnitalSeminormedCommRing` `NormedCommRing.toSeminormedCommRing` `NormedAlgebra.toNormedSpace` `SeminormedCommRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Multiset.prod` `CommRing.toCommMonoid` `NormedCommRing.toCommRing` `Multiset.map` `Multiset.sum` `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.addCommMonoid` `IsTopologicalSemiring.toContinuousAdd` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `NormedRing.toRing` `NormedCommRing.toNormedRing` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `Multiset.erase`	—	`IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `Multiset.map_congr` `Multiset.attach_map_val` `Multiset.map_map` `congr_fderiv` `RingHomCompTriple.ids` `comp` `hasFDerivAt_multiset_prod` `Finite.of_fintype` `hasFDerivAt_pi` `Subtype.prop` `ContinuousLinearMap.ext` `ContinuousLinearMap.comp.congr_simp` `Multiset.erase_attach_map` `Finset.sum_multiset_map_count` `Finset.sum_congr` `Multiset.count_attach` `ContinuousLinearMap.coe_sum'` `nsmul_eq_mul` `Algebra.mul_smul_comm` `Finset.sum_apply`
`smul` 📖	mathematical	`HasFDerivAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedRing.toNonUnitalNormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Pi.smul'` `SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `ESeminormedAddMonoid.toAddMonoid` `ESeminormedAddCommMonoid.toESeminormedAddMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `DistribSMul.toSMulZeroClass` `DistribMulAction.toDistribSMul` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing` `Module.toDistribMulAction` `ESeminormedAddCommMonoid.toAddCommMonoid` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `ContinuousLinearMap.add` `IsTopologicalAddGroup.toContinuousAdd` `NormedAddGroup.toAddGroup` `NormedAddCommGroup.toNormedAddGroup` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `ContinuousLinearMap.instSMul` `AddCommMonoid.toAddMonoid` `IsScalarTower.to_smulCommClass` `Semifield.toCommSemiring` `NormedAlgebra.toAlgebra` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `MulZeroClass.toZero` `NonUnitalNonAssocSemiring.toMulZeroClass` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `AddCommGroup.toDivisionAddCommMonoid` `NormedAddCommGroup.toAddCommGroup` `ContinuousLinearMap.smulRight` `IsBoundedSMul.continuousSMul`	—	`comp` `isBoundedBilinearMap_smul` `IsBoundedBilinearMap.hasFDerivAt` `prodMk`
`smul_const` 📖	mathematical	`HasFDerivAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedRing.toNonUnitalNormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`NormedAddCommGroup.toAddCommGroup` `SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `ESeminormedAddMonoid.toAddMonoid` `ESeminormedAddCommMonoid.toESeminormedAddMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `DistribSMul.toSMulZeroClass` `DistribMulAction.toDistribSMul` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing` `Module.toDistribMulAction` `ESeminormedAddCommMonoid.toAddCommMonoid` `ContinuousLinearMap.smulRight` `AddCommGroup.toAddCommMonoid` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `IsBoundedSMul.continuousSMul` `MulZeroClass.toZero` `NonUnitalNonAssocSemiring.toMulZeroClass` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `AddCommGroup.toDivisionAddCommMonoid` `AddCommMonoid.toAddMonoid`	—	`IsTopologicalAddGroup.toContinuousAdd` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsScalarTower.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `IsBoundedSMul.continuousSMul` `smul_zero` `RingHomIsometric.ids` `zero_add` `smul` `hasFDerivAt_const`

HasFDerivWithinAt

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`const_mul` 📖	mathematical	`HasFDerivWithinAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedRing.toNonUnitalNormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `NonUnitalNormedRing.toNormedAddCommGroup` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing`	—	`HasFDerivAt.comp_hasFDerivWithinAt` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `smulCommClass_self` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `NormedSpace.toIsBoundedSMul` `IsScalarTower.right` `Algebra.to_smulCommClass` `ContinuousLinearMap.hasFDerivAt`
`finset_prod` 📖	mathematical	`HasFDerivWithinAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing` `SeminormedCommRing.toNonUnitalSeminormedCommRing` `NormedCommRing.toSeminormedCommRing` `NormedAlgebra.toNormedSpace` `SeminormedCommRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Finset.prod` `CommRing.toCommMonoid` `NormedCommRing.toCommRing` `Finset.sum` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.addCommMonoid` `IsTopologicalSemiring.toContinuousAdd` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `NormedCommRing.toNonUnitalNormedCommRing` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `NonUnitalNormedRing.toNormedAddCommGroup` `NonUnitalNormedCommRing.toNonUnitalNormedRing` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `NormedRing.toRing` `NormedCommRing.toNormedRing` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `Finset.erase`	—	`IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `Finset.prod_attach` `congr_fderiv` `RingHomCompTriple.ids` `HasFDerivAt.comp_hasFDerivWithinAt` `hasFDerivAt_finset_prod` `Finite.of_fintype` `hasFDerivWithinAt_pi` `Subtype.prop` `ContinuousLinearMap.ext` `ContinuousLinearMap.comp.congr_simp` `Finset.sum_congr` `Finset.prod_erase_attach` `ContinuousLinearMap.coe_sum'` `Finset.sum_apply` `Finset.sum_attach`
`fun_mul` 📖	mathematical	`HasFDerivWithinAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing` `SeminormedCommRing.toNonUnitalSeminormedCommRing` `NormedCommRing.toSeminormedCommRing` `NormedAlgebra.toNormedSpace` `SeminormedCommRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `NormedCommRing.toNonUnitalNormedCommRing` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `NonUnitalNormedRing.toNormedAddCommGroup` `NonUnitalNormedCommRing.toNonUnitalNormedRing` `ContinuousLinearMap.add` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `NormedRing.toRing` `NormedCommRing.toNormedRing` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing`	—	`IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `mul`
`fun_mul'` 📖	mathematical	`HasFDerivWithinAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedRing.toNonUnitalNormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `NonUnitalNormedRing.toNormedAddCommGroup` `ContinuousLinearMap.add` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `MulOpposite` `DistribMulAction.toDistribSMul` `MulOpposite.instMonoid` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Module.toDistribMulAction` `MulOpposite.instSemiring` `Semiring.toOppositeModule` `SMulCommClass.opposite_mid` `MulZeroClass.toMul` `MulZeroOneClass.toMulZeroClass` `MonoidWithZero.toMulZeroOneClass` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `MulOpposite.op`	—	`IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `SMulCommClass.opposite_mid` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `mul'`
`fun_smul` 📖	mathematical	`HasFDerivWithinAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedRing.toNonUnitalNormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `ESeminormedAddMonoid.toAddMonoid` `ESeminormedAddCommMonoid.toESeminormedAddMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `DistribSMul.toSMulZeroClass` `DistribMulAction.toDistribSMul` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing` `Module.toDistribMulAction` `ESeminormedAddCommMonoid.toAddCommMonoid` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `ContinuousLinearMap.add` `IsTopologicalAddGroup.toContinuousAdd` `NormedAddGroup.toAddGroup` `NormedAddCommGroup.toNormedAddGroup` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `ContinuousLinearMap.instSMul` `AddCommMonoid.toAddMonoid` `IsScalarTower.to_smulCommClass` `Semifield.toCommSemiring` `NormedAlgebra.toAlgebra` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `MulZeroClass.toZero` `NonUnitalNonAssocSemiring.toMulZeroClass` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `AddCommGroup.toDivisionAddCommMonoid` `NormedAddCommGroup.toAddCommGroup` `ContinuousLinearMap.smulRight` `IsBoundedSMul.continuousSMul`	—	`IsTopologicalAddGroup.toContinuousAdd` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsScalarTower.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `IsBoundedSMul.continuousSMul` `smul`
`list_prod'` 📖	mathematical	`HasFDerivWithinAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedRing.toNonUnitalNormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing` `AddMonoidWithOne.toOne` `AddGroupWithOne.toAddMonoidWithOne` `Ring.toAddGroupWithOne` `Finset.sum` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.addCommMonoid` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Finset.univ` `Fin.fintype` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `NonUnitalNormedRing.toNormedAddCommGroup` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `MulOpposite` `DistribMulAction.toDistribSMul` `MulOpposite.instMonoid` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Module.toDistribMulAction` `MulOpposite.instSemiring` `Semiring.toOppositeModule` `SMulCommClass.opposite_mid` `MulZeroClass.toMul` `MulZeroOneClass.toMulZeroClass` `MonoidWithZero.toMulZeroOneClass` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `MulOpposite.op`	—	`IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `SMulCommClass.opposite_mid` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `Finset.sum_congr` `congr_fderiv` `RingHomCompTriple.ids` `HasFDerivAt.comp_hasFDerivWithinAt` `hasFDerivAt_list_prod_finRange'` `hasFDerivWithinAt_pi` `Finite.of_fintype` `ContinuousLinearMap.ext` `ContinuousLinearMap.comp.congr_simp` `ContinuousLinearMap.sum_apply`
`mul` 📖	mathematical	`HasFDerivWithinAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing` `SeminormedCommRing.toNonUnitalSeminormedCommRing` `NormedCommRing.toSeminormedCommRing` `NormedAlgebra.toNormedSpace` `SeminormedCommRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Pi.instMul` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `NormedCommRing.toNonUnitalNormedCommRing` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `NonUnitalNormedRing.toNormedAddCommGroup` `NonUnitalNormedCommRing.toNonUnitalNormedRing` `ContinuousLinearMap.add` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `NormedRing.toRing` `NormedCommRing.toNormedRing` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing`	—	`IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `SMulCommClass.opposite_mid` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `ContinuousLinearMap.ext` `mul_comm` `mul'`
`mul'` 📖	mathematical	`HasFDerivWithinAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedRing.toNonUnitalNormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Pi.instMul` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `NonUnitalNormedRing.toNormedAddCommGroup` `ContinuousLinearMap.add` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `MulOpposite` `DistribMulAction.toDistribSMul` `MulOpposite.instMonoid` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Module.toDistribMulAction` `MulOpposite.instSemiring` `Semiring.toOppositeModule` `SMulCommClass.opposite_mid` `MulZeroClass.toMul` `MulZeroOneClass.toMulZeroClass` `MonoidWithZero.toMulZeroOneClass` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `MulOpposite.op`	—	`HasFDerivAt.comp_hasFDerivWithinAt` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsTopologicalAddGroup.toContinuousAdd` `smulCommClass_self` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `NormedSpace.toIsBoundedSMul` `IsScalarTower.right` `Algebra.to_smulCommClass` `ContinuousLinearMap.isBoundedBilinearMap` `IsBoundedBilinearMap.hasFDerivAt` `prodMk`
`mul_const` 📖	mathematical	`HasFDerivWithinAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing` `SeminormedCommRing.toNonUnitalSeminormedCommRing` `NormedCommRing.toSeminormedCommRing` `NormedAlgebra.toNormedSpace` `SeminormedCommRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `NormedCommRing.toNonUnitalNormedCommRing` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `NonUnitalNormedRing.toNormedAddCommGroup` `NonUnitalNormedCommRing.toNonUnitalNormedRing` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `NormedRing.toRing` `NormedCommRing.toNormedRing` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing`	—	`Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `SMulCommClass.opposite_mid` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `ContinuousLinearMap.ext` `mul_comm` `mul_const'`
`mul_const'` 📖	mathematical	`HasFDerivWithinAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedRing.toNonUnitalNormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing` `MulOpposite` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `NonUnitalNormedRing.toNormedAddCommGroup` `ContinuousLinearMap.instSMul` `DistribMulAction.toDistribSMul` `MulOpposite.instMonoid` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `AddCommMonoid.toAddMonoid` `Module.toDistribMulAction` `MulOpposite.instSemiring` `Semiring.toOppositeModule` `SMulCommClass.opposite_mid` `MulZeroClass.toMul` `MulZeroOneClass.toMulZeroClass` `MonoidWithZero.toMulZeroOneClass` `SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `DistribSMul.toSMulZeroClass` `IsScalarTower.right` `Semifield.toCommSemiring` `SeminormedRing.toRing` `NormedAlgebra.toAlgebra` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul_op` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `MulOpposite.op`	—	`HasFDerivAt.comp_hasFDerivWithinAt` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsTopologicalAddGroup.toContinuousAdd` `smulCommClass_self` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `NormedSpace.toIsBoundedSMul` `RingHomIsometric.ids` `IsScalarTower.right` `Algebra.to_smulCommClass` `ContinuousLinearMap.hasFDerivAt`
`multiset_prod` 📖	mathematical	`HasFDerivWithinAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing` `SeminormedCommRing.toNonUnitalSeminormedCommRing` `NormedCommRing.toSeminormedCommRing` `NormedAlgebra.toNormedSpace` `SeminormedCommRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Multiset.prod` `CommRing.toCommMonoid` `NormedCommRing.toCommRing` `Multiset.map` `Multiset.sum` `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.addCommMonoid` `IsTopologicalSemiring.toContinuousAdd` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `NormedRing.toRing` `NormedCommRing.toNormedRing` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `Multiset.erase`	—	`IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `Multiset.map_congr` `Multiset.attach_map_val` `Multiset.map_map` `congr_fderiv` `RingHomCompTriple.ids` `HasFDerivAt.comp_hasFDerivWithinAt` `hasFDerivAt_multiset_prod` `Finite.of_fintype` `hasFDerivWithinAt_pi` `Subtype.prop` `ContinuousLinearMap.ext` `ContinuousLinearMap.comp.congr_simp` `Multiset.erase_attach_map` `Finset.sum_multiset_map_count` `Finset.sum_congr` `Multiset.count_attach` `ContinuousLinearMap.coe_sum'` `nsmul_eq_mul` `Algebra.mul_smul_comm` `Finset.sum_apply`
`smul` 📖	mathematical	`HasFDerivWithinAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedRing.toNonUnitalNormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Pi.smul'` `SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `ESeminormedAddMonoid.toAddMonoid` `ESeminormedAddCommMonoid.toESeminormedAddMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `DistribSMul.toSMulZeroClass` `DistribMulAction.toDistribSMul` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing` `Module.toDistribMulAction` `ESeminormedAddCommMonoid.toAddCommMonoid` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `ContinuousLinearMap.add` `IsTopologicalAddGroup.toContinuousAdd` `NormedAddGroup.toAddGroup` `NormedAddCommGroup.toNormedAddGroup` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `ContinuousLinearMap.instSMul` `AddCommMonoid.toAddMonoid` `IsScalarTower.to_smulCommClass` `Semifield.toCommSemiring` `NormedAlgebra.toAlgebra` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `MulZeroClass.toZero` `NonUnitalNonAssocSemiring.toMulZeroClass` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `AddCommGroup.toDivisionAddCommMonoid` `NormedAddCommGroup.toAddCommGroup` `ContinuousLinearMap.smulRight` `IsBoundedSMul.continuousSMul`	—	`HasFDerivAt.comp_hasFDerivWithinAt` `isBoundedBilinearMap_smul` `IsBoundedBilinearMap.hasFDerivAt` `prodMk`
`smul_const` 📖	mathematical	`HasFDerivWithinAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedRing.toNonUnitalNormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`NormedAddCommGroup.toAddCommGroup` `SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `ESeminormedAddMonoid.toAddMonoid` `ESeminormedAddCommMonoid.toESeminormedAddMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `DistribSMul.toSMulZeroClass` `DistribMulAction.toDistribSMul` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing` `Module.toDistribMulAction` `ESeminormedAddCommMonoid.toAddCommMonoid` `ContinuousLinearMap.smulRight` `AddCommGroup.toAddCommMonoid` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `IsBoundedSMul.continuousSMul` `MulZeroClass.toZero` `NonUnitalNonAssocSemiring.toMulZeroClass` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `AddCommGroup.toDivisionAddCommMonoid` `AddCommMonoid.toAddMonoid`	—	`IsTopologicalAddGroup.toContinuousAdd` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsScalarTower.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `IsBoundedSMul.continuousSMul` `smul_zero` `RingHomIsometric.ids` `zero_add` `smul` `hasFDerivWithinAt_const`

HasStrictFDerivAt

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`const_mul` 📖	mathematical	`HasStrictFDerivAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedRing.toNonUnitalNormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `NonUnitalNormedRing.toNormedAddCommGroup` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing`	—	`comp` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `smulCommClass_self` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `NormedSpace.toIsBoundedSMul` `IsScalarTower.right` `Algebra.to_smulCommClass` `ContinuousLinearMap.hasStrictFDerivAt`
`finset_prod` 📖	mathematical	`HasStrictFDerivAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing` `SeminormedCommRing.toNonUnitalSeminormedCommRing` `NormedCommRing.toSeminormedCommRing` `NormedAlgebra.toNormedSpace` `SeminormedCommRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Finset.prod` `CommRing.toCommMonoid` `NormedCommRing.toCommRing` `Finset.sum` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.addCommMonoid` `IsTopologicalSemiring.toContinuousAdd` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `NormedCommRing.toNonUnitalNormedCommRing` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `NonUnitalNormedRing.toNormedAddCommGroup` `NonUnitalNormedCommRing.toNonUnitalNormedRing` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `NormedRing.toRing` `NormedCommRing.toNormedRing` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `Finset.erase`	—	`IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `Finset.prod_attach` `congr_fderiv` `RingHomCompTriple.ids` `comp` `hasStrictFDerivAt_finset_prod` `Finite.of_fintype` `hasStrictFDerivAt_pi` `Subtype.prop` `ContinuousLinearMap.ext` `ContinuousLinearMap.comp.congr_simp` `Finset.sum_congr` `Finset.prod_erase_attach` `ContinuousLinearMap.coe_sum'` `Finset.sum_apply` `Finset.sum_attach`
`fun_mul` 📖	mathematical	`HasStrictFDerivAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing` `SeminormedCommRing.toNonUnitalSeminormedCommRing` `NormedCommRing.toSeminormedCommRing` `NormedAlgebra.toNormedSpace` `SeminormedCommRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `NormedCommRing.toNonUnitalNormedCommRing` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `NonUnitalNormedRing.toNormedAddCommGroup` `NonUnitalNormedCommRing.toNonUnitalNormedRing` `ContinuousLinearMap.add` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `NormedRing.toRing` `NormedCommRing.toNormedRing` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing`	—	`IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `mul`
`fun_mul'` 📖	mathematical	`HasStrictFDerivAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedRing.toNonUnitalNormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `NonUnitalNormedRing.toNormedAddCommGroup` `ContinuousLinearMap.add` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `MulOpposite` `DistribMulAction.toDistribSMul` `MulOpposite.instMonoid` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Module.toDistribMulAction` `MulOpposite.instSemiring` `Semiring.toOppositeModule` `SMulCommClass.opposite_mid` `MulZeroClass.toMul` `MulZeroOneClass.toMulZeroClass` `MonoidWithZero.toMulZeroOneClass` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `MulOpposite.op`	—	`IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `SMulCommClass.opposite_mid` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `mul'`
`fun_smul` 📖	mathematical	`HasStrictFDerivAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedRing.toNonUnitalNormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `ESeminormedAddMonoid.toAddMonoid` `ESeminormedAddCommMonoid.toESeminormedAddMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `DistribSMul.toSMulZeroClass` `DistribMulAction.toDistribSMul` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing` `Module.toDistribMulAction` `ESeminormedAddCommMonoid.toAddCommMonoid` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `ContinuousLinearMap.add` `IsTopologicalAddGroup.toContinuousAdd` `NormedAddGroup.toAddGroup` `NormedAddCommGroup.toNormedAddGroup` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `ContinuousLinearMap.instSMul` `AddCommMonoid.toAddMonoid` `IsScalarTower.to_smulCommClass` `Semifield.toCommSemiring` `NormedAlgebra.toAlgebra` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `MulZeroClass.toZero` `NonUnitalNonAssocSemiring.toMulZeroClass` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `AddCommGroup.toDivisionAddCommMonoid` `NormedAddCommGroup.toAddCommGroup` `ContinuousLinearMap.smulRight` `IsBoundedSMul.continuousSMul`	—	`IsTopologicalAddGroup.toContinuousAdd` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsScalarTower.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `IsBoundedSMul.continuousSMul` `smul`
`list_prod'` 📖	mathematical	`HasStrictFDerivAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedRing.toNonUnitalNormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing` `AddMonoidWithOne.toOne` `AddGroupWithOne.toAddMonoidWithOne` `Ring.toAddGroupWithOne` `Finset.sum` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.addCommMonoid` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Finset.univ` `Fin.fintype` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `NonUnitalNormedRing.toNormedAddCommGroup` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `MulOpposite` `DistribMulAction.toDistribSMul` `MulOpposite.instMonoid` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Module.toDistribMulAction` `MulOpposite.instSemiring` `Semiring.toOppositeModule` `SMulCommClass.opposite_mid` `MulZeroClass.toMul` `MulZeroOneClass.toMulZeroClass` `MonoidWithZero.toMulZeroOneClass` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `MulOpposite.op`	—	`IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `SMulCommClass.opposite_mid` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `Finset.sum_congr` `congr_fderiv` `RingHomCompTriple.ids` `comp` `hasStrictFDerivAt_list_prod_finRange'` `hasStrictFDerivAt_pi` `Finite.of_fintype` `ContinuousLinearMap.ext` `ContinuousLinearMap.comp.congr_simp` `ContinuousLinearMap.sum_apply`
`mul` 📖	mathematical	`HasStrictFDerivAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing` `SeminormedCommRing.toNonUnitalSeminormedCommRing` `NormedCommRing.toSeminormedCommRing` `NormedAlgebra.toNormedSpace` `SeminormedCommRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Pi.instMul` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `NormedCommRing.toNonUnitalNormedCommRing` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `NonUnitalNormedRing.toNormedAddCommGroup` `NonUnitalNormedCommRing.toNonUnitalNormedRing` `ContinuousLinearMap.add` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `NormedRing.toRing` `NormedCommRing.toNormedRing` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing`	—	`IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `SMulCommClass.opposite_mid` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `ContinuousLinearMap.ext` `mul_comm` `mul'`
`mul'` 📖	mathematical	`HasStrictFDerivAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedRing.toNonUnitalNormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Pi.instMul` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `NonUnitalNormedRing.toNormedAddCommGroup` `ContinuousLinearMap.add` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `MulOpposite` `DistribMulAction.toDistribSMul` `MulOpposite.instMonoid` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Module.toDistribMulAction` `MulOpposite.instSemiring` `Semiring.toOppositeModule` `SMulCommClass.opposite_mid` `MulZeroClass.toMul` `MulZeroOneClass.toMulZeroClass` `MonoidWithZero.toMulZeroOneClass` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `MulOpposite.op`	—	`comp` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsTopologicalAddGroup.toContinuousAdd` `smulCommClass_self` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `NormedSpace.toIsBoundedSMul` `IsScalarTower.right` `Algebra.to_smulCommClass` `ContinuousLinearMap.isBoundedBilinearMap` `IsBoundedBilinearMap.hasStrictFDerivAt` `prodMk`
`mul_const` 📖	mathematical	`HasStrictFDerivAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing` `SeminormedCommRing.toNonUnitalSeminormedCommRing` `NormedCommRing.toSeminormedCommRing` `NormedAlgebra.toNormedSpace` `SeminormedCommRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `NormedCommRing.toNonUnitalNormedCommRing` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `NonUnitalNormedRing.toNormedAddCommGroup` `NonUnitalNormedCommRing.toNonUnitalNormedRing` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `NormedRing.toRing` `NormedCommRing.toNormedRing` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing`	—	`Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `SMulCommClass.opposite_mid` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `ContinuousLinearMap.ext` `mul_comm` `mul_const'`
`mul_const'` 📖	mathematical	`HasStrictFDerivAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedRing.toNonUnitalNormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing` `MulOpposite` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `NonUnitalNormedRing.toNormedAddCommGroup` `ContinuousLinearMap.instSMul` `DistribMulAction.toDistribSMul` `MulOpposite.instMonoid` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `AddCommMonoid.toAddMonoid` `Module.toDistribMulAction` `MulOpposite.instSemiring` `Semiring.toOppositeModule` `SMulCommClass.opposite_mid` `MulZeroClass.toMul` `MulZeroOneClass.toMulZeroClass` `MonoidWithZero.toMulZeroOneClass` `SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `DistribSMul.toSMulZeroClass` `IsScalarTower.right` `Semifield.toCommSemiring` `SeminormedRing.toRing` `NormedAlgebra.toAlgebra` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul_op` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `MulOpposite.op`	—	`comp` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsTopologicalAddGroup.toContinuousAdd` `smulCommClass_self` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `NormedSpace.toIsBoundedSMul` `RingHomIsometric.ids` `IsScalarTower.right` `Algebra.to_smulCommClass` `ContinuousLinearMap.hasStrictFDerivAt`
`multiset_prod` 📖	mathematical	`HasStrictFDerivAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing` `SeminormedCommRing.toNonUnitalSeminormedCommRing` `NormedCommRing.toSeminormedCommRing` `NormedAlgebra.toNormedSpace` `SeminormedCommRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Multiset.prod` `CommRing.toCommMonoid` `NormedCommRing.toCommRing` `Multiset.map` `Multiset.sum` `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.addCommMonoid` `IsTopologicalSemiring.toContinuousAdd` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `NormedRing.toRing` `NormedCommRing.toNormedRing` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `Multiset.erase`	—	`IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `Multiset.map_congr` `Multiset.attach_map_val` `Multiset.map_map` `congr_fderiv` `RingHomCompTriple.ids` `comp` `hasStrictFDerivAt_multiset_prod` `Finite.of_fintype` `hasStrictFDerivAt_pi` `Subtype.prop` `ContinuousLinearMap.ext` `ContinuousLinearMap.comp.congr_simp` `Multiset.erase_attach_map` `Finset.sum_multiset_map_count` `Finset.sum_congr` `Multiset.count_attach` `ContinuousLinearMap.coe_sum'` `nsmul_eq_mul` `Algebra.mul_smul_comm` `Finset.sum_apply`
`smul` 📖	mathematical	`HasStrictFDerivAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedRing.toNonUnitalNormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`Pi.smul'` `SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `ESeminormedAddMonoid.toAddMonoid` `ESeminormedAddCommMonoid.toESeminormedAddMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `DistribSMul.toSMulZeroClass` `DistribMulAction.toDistribSMul` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing` `Module.toDistribMulAction` `ESeminormedAddCommMonoid.toAddCommMonoid` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `ContinuousLinearMap.add` `IsTopologicalAddGroup.toContinuousAdd` `NormedAddGroup.toAddGroup` `NormedAddCommGroup.toNormedAddGroup` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `ContinuousLinearMap.instSMul` `AddCommMonoid.toAddMonoid` `IsScalarTower.to_smulCommClass` `Semifield.toCommSemiring` `NormedAlgebra.toAlgebra` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `MulZeroClass.toZero` `NonUnitalNonAssocSemiring.toMulZeroClass` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `AddCommGroup.toDivisionAddCommMonoid` `NormedAddCommGroup.toAddCommGroup` `ContinuousLinearMap.smulRight` `IsBoundedSMul.continuousSMul`	—	`comp` `isBoundedBilinearMap_smul` `IsBoundedBilinearMap.hasStrictFDerivAt` `prodMk`
`smul_const` 📖	mathematical	`HasStrictFDerivAt` `SeminormedAddCommGroup.toAddCommGroup` `NormedAddCommGroup.toSeminormedAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedRing.toNonUnitalNormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`NormedAddCommGroup.toAddCommGroup` `SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `ESeminormedAddMonoid.toAddMonoid` `ESeminormedAddCommMonoid.toESeminormedAddMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `DistribSMul.toSMulZeroClass` `DistribMulAction.toDistribSMul` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing` `Module.toDistribMulAction` `ESeminormedAddCommMonoid.toAddCommMonoid` `ContinuousLinearMap.smulRight` `AddCommGroup.toAddCommMonoid` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `IsBoundedSMul.continuousSMul` `MulZeroClass.toZero` `NonUnitalNonAssocSemiring.toMulZeroClass` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `AddCommGroup.toDivisionAddCommMonoid` `AddCommMonoid.toAddMonoid`	—	`IsTopologicalAddGroup.toContinuousAdd` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsScalarTower.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `IsBoundedSMul.continuousSMul` `smul_zero` `RingHomIsometric.ids` `zero_add` `smul` `hasStrictFDerivAt_const`

(root)

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`differentiableAt_inv` 📖	mathematical	—	`DifferentiableAt` `NormedAddCommGroup.toAddCommGroup` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NormedDivisionRing.toNormedRing` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedRing.toPseudoMetricSpace` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `GroupWithZero.toDivisionMonoid` `DivisionSemiring.toGroupWithZero` `DivisionRing.toDivisionSemiring` `NormedDivisionRing.toDivisionRing`	—	`HasFDerivAt.differentiableAt` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `smulCommClass_self` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `NormedSpace.toIsBoundedSMul` `ContinuousLinearMap.topologicalAddGroup` `ContinuousLinearMap.smulCommClass` `ContinuousLinearMap.continuousConstSMul` `IsScalarTower.right` `Algebra.to_smulCommClass` `hasFDerivAt_inv'`
`differentiableAt_inverse` 📖	mathematical	`IsUnit` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing`	`DifferentiableAt` `NormedAddCommGroup.toAddCommGroup` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedRing.toPseudoMetricSpace` `Ring.inverse`	—	`HasFDerivAt.differentiableAt` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `smulCommClass_self` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `NormedSpace.toIsBoundedSMul` `ContinuousLinearMap.topologicalAddGroup` `ContinuousLinearMap.smulCommClass` `ContinuousLinearMap.continuousConstSMul` `IsScalarTower.right` `Algebra.to_smulCommClass` `hasFDerivAt_ringInverse`
`differentiableOn_inv` 📖	mathematical	—	`DifferentiableOn` `NormedAddCommGroup.toAddCommGroup` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NormedDivisionRing.toNormedRing` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedRing.toPseudoMetricSpace` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `GroupWithZero.toDivisionMonoid` `DivisionSemiring.toGroupWithZero` `DivisionRing.toDivisionSemiring` `NormedDivisionRing.toDivisionRing` `setOf` `MulZeroClass.toZero` `NonUnitalNonAssocSemiring.toMulZeroClass` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing`	—	`differentiableWithinAt_inv`
`differentiableOn_inverse` 📖	mathematical	—	`DifferentiableOn` `NormedAddCommGroup.toAddCommGroup` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedRing.toPseudoMetricSpace` `Ring.inverse` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing` `setOf` `IsUnit` `MonoidWithZero.toMonoid`	—	`differentiableWithinAt_inverse`
`differentiableWithinAt_inv` 📖	mathematical	—	`DifferentiableWithinAt` `NormedAddCommGroup.toAddCommGroup` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NormedDivisionRing.toNormedRing` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedRing.toPseudoMetricSpace` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `GroupWithZero.toDivisionMonoid` `DivisionSemiring.toGroupWithZero` `DivisionRing.toDivisionSemiring` `NormedDivisionRing.toDivisionRing`	—	`DifferentiableAt.differentiableWithinAt` `differentiableAt_inv`
`differentiableWithinAt_inverse` 📖	mathematical	`IsUnit` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing`	`DifferentiableWithinAt` `NormedAddCommGroup.toAddCommGroup` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedRing.toPseudoMetricSpace` `Ring.inverse`	—	`DifferentiableAt.differentiableWithinAt` `differentiableAt_inverse`
`fderivWithin_const_mul` 📖	mathematical	`UniqueDiffWithinAt` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `DifferentiableWithinAt` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`fderivWithin` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing` `ContinuousLinearMap` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing`	—	`HasFDerivWithinAt.fderivWithin` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `IsTopologicalAddGroup.toContinuousAdd` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsBoundedSMul.continuousSMul` `NormedSpace.toIsBoundedSMul` `IsTopologicalSemiring.toContinuousAdd` `TopologicalSpace.t2Space_of_metrizableSpace` `EMetricSpace.metrizableSpace` `HasFDerivWithinAt.const_mul` `DifferentiableWithinAt.hasFDerivWithinAt`
`fderivWithin_finset_prod` 📖	mathematical	`UniqueDiffWithinAt` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `DifferentiableWithinAt` `NonUnitalNormedRing.toNormedAddCommGroup` `NonUnitalNormedCommRing.toNonUnitalNormedRing` `NormedCommRing.toNonUnitalNormedCommRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing` `SeminormedCommRing.toNonUnitalSeminormedCommRing` `NormedCommRing.toSeminormedCommRing` `NormedAlgebra.toNormedSpace` `SeminormedCommRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`fderivWithin` `Finset.prod` `CommRing.toCommMonoid` `NormedCommRing.toCommRing` `Finset.sum` `ContinuousLinearMap` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.addCommMonoid` `IsTopologicalSemiring.toContinuousAdd` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `NormedRing.toRing` `NormedCommRing.toNormedRing` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `Finset.erase`	—	`HasFDerivWithinAt.fderivWithin` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `IsTopologicalAddGroup.toContinuousAdd` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsBoundedSMul.continuousSMul` `NormedSpace.toIsBoundedSMul` `TopologicalSpace.t2Space_of_metrizableSpace` `EMetricSpace.metrizableSpace` `HasFDerivWithinAt.finset_prod` `DifferentiableWithinAt.hasFDerivWithinAt`
`fderivWithin_fun_mul` 📖	mathematical	`UniqueDiffWithinAt` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `DifferentiableWithinAt` `NonUnitalNormedRing.toNormedAddCommGroup` `NonUnitalNormedCommRing.toNonUnitalNormedRing` `NormedCommRing.toNonUnitalNormedCommRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing` `SeminormedCommRing.toNonUnitalSeminormedCommRing` `NormedCommRing.toSeminormedCommRing` `NormedAlgebra.toNormedSpace` `SeminormedCommRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`fderivWithin` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `ContinuousLinearMap` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.add` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `NormedRing.toRing` `NormedCommRing.toNormedRing` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing`	—	`HasFDerivWithinAt.fderivWithin` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `IsTopologicalAddGroup.toContinuousAdd` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsBoundedSMul.continuousSMul` `NormedSpace.toIsBoundedSMul` `TopologicalSpace.t2Space_of_metrizableSpace` `EMetricSpace.metrizableSpace` `HasFDerivWithinAt.mul` `DifferentiableWithinAt.hasFDerivWithinAt`
`fderivWithin_fun_mul'` 📖	mathematical	`UniqueDiffWithinAt` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `DifferentiableWithinAt` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`fderivWithin` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing` `ContinuousLinearMap` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.add` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `MulOpposite` `DistribMulAction.toDistribSMul` `MulOpposite.instMonoid` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Module.toDistribMulAction` `MulOpposite.instSemiring` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `Semiring.toOppositeModule` `SMulCommClass.opposite_mid` `MulZeroClass.toMul` `MulZeroOneClass.toMulZeroClass` `MonoidWithZero.toMulZeroOneClass` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `MulOpposite.op`	—	`HasFDerivWithinAt.fderivWithin` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `SMulCommClass.opposite_mid` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `IsTopologicalAddGroup.toContinuousAdd` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsBoundedSMul.continuousSMul` `NormedSpace.toIsBoundedSMul` `TopologicalSpace.t2Space_of_metrizableSpace` `EMetricSpace.metrizableSpace` `HasFDerivWithinAt.mul'` `DifferentiableWithinAt.hasFDerivWithinAt`
`fderivWithin_fun_smul` 📖	mathematical	`UniqueDiffWithinAt` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `DifferentiableWithinAt` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`fderivWithin` `SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `ESeminormedAddMonoid.toAddMonoid` `ESeminormedAddCommMonoid.toESeminormedAddMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `DistribSMul.toSMulZeroClass` `DistribMulAction.toDistribSMul` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing` `Module.toDistribMulAction` `ESeminormedAddCommMonoid.toAddCommMonoid` `ContinuousLinearMap` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.add` `IsTopologicalAddGroup.toContinuousAdd` `NormedAddGroup.toAddGroup` `NormedAddCommGroup.toNormedAddGroup` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `ContinuousLinearMap.instSMul` `AddCommMonoid.toAddMonoid` `IsScalarTower.to_smulCommClass` `Semifield.toCommSemiring` `NormedAlgebra.toAlgebra` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `MulZeroClass.toZero` `NonUnitalNonAssocSemiring.toMulZeroClass` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `AddCommGroup.toDivisionAddCommMonoid` `ContinuousLinearMap.smulRight` `IsBoundedSMul.continuousSMul`	—	`HasFDerivWithinAt.fderivWithin` `IsTopologicalAddGroup.toContinuousAdd` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsScalarTower.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `IsBoundedSMul.continuousSMul` `NormedSpace.toIsBoundedSMul` `TopologicalSpace.t2Space_of_metrizableSpace` `EMetricSpace.metrizableSpace` `HasFDerivWithinAt.smul` `DifferentiableWithinAt.hasFDerivWithinAt`
`fderivWithin_inv'` 📖	mathematical	`UniqueDiffWithinAt` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toAddCommGroup` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NormedDivisionRing.toNormedRing` `NormedSpace.toModule` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedRing.toPseudoMetricSpace`	`fderivWithin` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `GroupWithZero.toDivisionMonoid` `DivisionSemiring.toGroupWithZero` `DivisionRing.toDivisionSemiring` `NormedDivisionRing.toDivisionRing` `ContinuousLinearMap` `RingHom.id` `Semiring.toNonAssocSemiring` `NonUnitalSeminormedRing.toPseudoMetricSpace` `NonUnitalNonAssocSemiring.toAddCommMonoid` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalRing.toNonUnitalNonAssocRing` `NonUnitalSeminormedRing.toNonUnitalRing` `ContinuousLinearMap.neg` `NormedRing.toRing` `NormedCommRing.toNormedRing` `NormedField.toNormedCommRing` `SeminormedAddCommGroup.toAddCommGroup` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `DFunLike.coe` `ContinuousLinearMap.topologicalSpace` `ContinuousLinearMap.addCommMonoid` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ContinuousLinearMap.module` `smulCommClass_self` `CommRing.toCommMonoid` `Field.toCommRing` `DistribMulAction.toMulAction` `CommMonoid.toMonoid` `AddCommMonoid.toAddMonoid` `Module.toDistribMulAction` `Ring.toSemiring` `CommRing.toRing` `UniformContinuousConstSMul.to_continuousConstSMul` `SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `DistribSMul.toSMulZeroClass` `DistribMulAction.toDistribSMul` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `IsBoundedSMul.toUniformContinuousConstSMul` `SeminormedCommRing.toSeminormedRing` `NormedCommRing.toSeminormedCommRing` `MulZeroClass.toZero` `NonUnitalNonAssocSemiring.toMulZeroClass` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `NormedCommRing.toNonUnitalNormedCommRing` `NormedSpace.toIsBoundedSMul` `ContinuousLinearMap.funLike` `ContinuousLinearMap.addCommGroup` `ContinuousLinearMap.topologicalAddGroup` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `ContinuousLinearMap.ring` `SeminormedRing.toNonUnitalSeminormedRing` `ContinuousLinearMap.toSeminormedRing` `ContinuousLinearMap.smulCommClass` `ContinuousLinearMap.continuousConstSMul` `ContinuousLinearMap.mulLeftRight` `IsScalarTower.right` `Semifield.toCommSemiring` `SeminormedRing.toRing` `NormedAlgebra.toAlgebra` `Algebra.to_smulCommClass`	—	`SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `smulCommClass_self` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `NormedSpace.toIsBoundedSMul` `ContinuousLinearMap.topologicalAddGroup` `ContinuousLinearMap.smulCommClass` `ContinuousLinearMap.continuousConstSMul` `IsScalarTower.right` `Algebra.to_smulCommClass` `DifferentiableAt.fderivWithin` `IsTopologicalDivisionRing.toIsTopologicalRing` `NormedDivisionRing.to_isTopologicalDivisionRing` `IsBoundedSMul.continuousSMul` `TopologicalSpace.t2Space_of_metrizableSpace` `EMetricSpace.metrizableSpace` `differentiableAt_inv` `fderiv_inv'`
`fderivWithin_list_prod'` 📖	mathematical	`UniqueDiffWithinAt` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `DifferentiableWithinAt` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`fderivWithin` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing` `AddMonoidWithOne.toOne` `AddGroupWithOne.toAddMonoidWithOne` `Ring.toAddGroupWithOne` `Finset.sum` `ContinuousLinearMap` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.addCommMonoid` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Finset.univ` `Fin.fintype` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `MulOpposite` `DistribMulAction.toDistribSMul` `MulOpposite.instMonoid` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Module.toDistribMulAction` `MulOpposite.instSemiring` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `Semiring.toOppositeModule` `SMulCommClass.opposite_mid` `MulZeroClass.toMul` `MulZeroOneClass.toMulZeroClass` `MonoidWithZero.toMulZeroOneClass` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `MulOpposite.op`	—	`HasFDerivWithinAt.fderivWithin` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `SMulCommClass.opposite_mid` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `IsTopologicalAddGroup.toContinuousAdd` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsBoundedSMul.continuousSMul` `NormedSpace.toIsBoundedSMul` `TopologicalSpace.t2Space_of_metrizableSpace` `EMetricSpace.metrizableSpace` `HasFDerivWithinAt.list_prod'` `DifferentiableWithinAt.hasFDerivWithinAt`
`fderivWithin_mul` 📖	mathematical	`UniqueDiffWithinAt` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `DifferentiableWithinAt` `NonUnitalNormedRing.toNormedAddCommGroup` `NonUnitalNormedCommRing.toNonUnitalNormedRing` `NormedCommRing.toNonUnitalNormedCommRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing` `SeminormedCommRing.toNonUnitalSeminormedCommRing` `NormedCommRing.toSeminormedCommRing` `NormedAlgebra.toNormedSpace` `SeminormedCommRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`fderivWithin` `Pi.instMul` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `ContinuousLinearMap` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.add` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `NormedRing.toRing` `NormedCommRing.toNormedRing` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing`	—	`HasFDerivWithinAt.fderivWithin` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `IsTopologicalAddGroup.toContinuousAdd` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsBoundedSMul.continuousSMul` `NormedSpace.toIsBoundedSMul` `TopologicalSpace.t2Space_of_metrizableSpace` `EMetricSpace.metrizableSpace` `HasFDerivWithinAt.mul` `DifferentiableWithinAt.hasFDerivWithinAt`
`fderivWithin_mul'` 📖	mathematical	`UniqueDiffWithinAt` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `DifferentiableWithinAt` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`fderivWithin` `Pi.instMul` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing` `ContinuousLinearMap` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.add` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `MulOpposite` `DistribMulAction.toDistribSMul` `MulOpposite.instMonoid` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Module.toDistribMulAction` `MulOpposite.instSemiring` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `Semiring.toOppositeModule` `SMulCommClass.opposite_mid` `MulZeroClass.toMul` `MulZeroOneClass.toMulZeroClass` `MonoidWithZero.toMulZeroOneClass` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `MulOpposite.op`	—	`HasFDerivWithinAt.fderivWithin` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `SMulCommClass.opposite_mid` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `IsTopologicalAddGroup.toContinuousAdd` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsBoundedSMul.continuousSMul` `NormedSpace.toIsBoundedSMul` `TopologicalSpace.t2Space_of_metrizableSpace` `EMetricSpace.metrizableSpace` `HasFDerivWithinAt.mul'` `DifferentiableWithinAt.hasFDerivWithinAt`
`fderivWithin_mul_const` 📖	mathematical	`UniqueDiffWithinAt` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `DifferentiableWithinAt` `NonUnitalNormedRing.toNormedAddCommGroup` `NonUnitalNormedCommRing.toNonUnitalNormedRing` `NormedCommRing.toNonUnitalNormedCommRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing` `SeminormedCommRing.toNonUnitalSeminormedCommRing` `NormedCommRing.toSeminormedCommRing` `NormedAlgebra.toNormedSpace` `SeminormedCommRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`fderivWithin` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `ContinuousLinearMap` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `NormedRing.toRing` `NormedCommRing.toNormedRing` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing`	—	`HasFDerivWithinAt.fderivWithin` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `IsTopologicalAddGroup.toContinuousAdd` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsBoundedSMul.continuousSMul` `NormedSpace.toIsBoundedSMul` `IsTopologicalSemiring.toContinuousAdd` `TopologicalSpace.t2Space_of_metrizableSpace` `EMetricSpace.metrizableSpace` `HasFDerivWithinAt.mul_const` `DifferentiableWithinAt.hasFDerivWithinAt`
`fderivWithin_mul_const'` 📖	mathematical	`UniqueDiffWithinAt` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `DifferentiableWithinAt` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`fderivWithin` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing` `MulOpposite` `ContinuousLinearMap` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.instSMul` `DistribMulAction.toDistribSMul` `MulOpposite.instMonoid` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `AddCommMonoid.toAddMonoid` `Module.toDistribMulAction` `MulOpposite.instSemiring` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `Semiring.toOppositeModule` `SMulCommClass.opposite_mid` `MulZeroClass.toMul` `MulZeroOneClass.toMulZeroClass` `MonoidWithZero.toMulZeroOneClass` `SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `DistribSMul.toSMulZeroClass` `IsScalarTower.right` `Semifield.toCommSemiring` `SeminormedRing.toRing` `NormedAlgebra.toAlgebra` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul_op` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `MulOpposite.op`	—	`HasFDerivWithinAt.fderivWithin` `SMulCommClass.opposite_mid` `IsScalarTower.right` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul_op` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `IsTopologicalAddGroup.toContinuousAdd` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsBoundedSMul.continuousSMul` `NormedSpace.toIsBoundedSMul` `IsTopologicalSemiring.toContinuousAdd` `TopologicalSpace.t2Space_of_metrizableSpace` `EMetricSpace.metrizableSpace` `HasFDerivWithinAt.mul_const'` `DifferentiableWithinAt.hasFDerivWithinAt`
`fderivWithin_multiset_prod` 📖	mathematical	`UniqueDiffWithinAt` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `DifferentiableWithinAt` `NonUnitalNormedRing.toNormedAddCommGroup` `NonUnitalNormedCommRing.toNonUnitalNormedRing` `NormedCommRing.toNonUnitalNormedCommRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing` `SeminormedCommRing.toNonUnitalSeminormedCommRing` `NormedCommRing.toSeminormedCommRing` `NormedAlgebra.toNormedSpace` `SeminormedCommRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`fderivWithin` `Multiset.prod` `CommRing.toCommMonoid` `NormedCommRing.toCommRing` `Multiset.map` `Multiset.sum` `ContinuousLinearMap` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.addCommMonoid` `IsTopologicalSemiring.toContinuousAdd` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `NormedRing.toRing` `NormedCommRing.toNormedRing` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `Multiset.erase`	—	`HasFDerivWithinAt.fderivWithin` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `IsTopologicalAddGroup.toContinuousAdd` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsBoundedSMul.continuousSMul` `NormedSpace.toIsBoundedSMul` `TopologicalSpace.t2Space_of_metrizableSpace` `EMetricSpace.metrizableSpace` `HasFDerivWithinAt.multiset_prod` `DifferentiableWithinAt.hasFDerivWithinAt`
`fderivWithin_smul` 📖	mathematical	`UniqueDiffWithinAt` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `DifferentiableWithinAt` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`fderivWithin` `Pi.smul'` `SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `ESeminormedAddMonoid.toAddMonoid` `ESeminormedAddCommMonoid.toESeminormedAddMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `DistribSMul.toSMulZeroClass` `DistribMulAction.toDistribSMul` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing` `Module.toDistribMulAction` `ESeminormedAddCommMonoid.toAddCommMonoid` `ContinuousLinearMap` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.add` `IsTopologicalAddGroup.toContinuousAdd` `NormedAddGroup.toAddGroup` `NormedAddCommGroup.toNormedAddGroup` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `ContinuousLinearMap.instSMul` `AddCommMonoid.toAddMonoid` `IsScalarTower.to_smulCommClass` `Semifield.toCommSemiring` `NormedAlgebra.toAlgebra` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `MulZeroClass.toZero` `NonUnitalNonAssocSemiring.toMulZeroClass` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `AddCommGroup.toDivisionAddCommMonoid` `ContinuousLinearMap.smulRight` `IsBoundedSMul.continuousSMul`	—	`HasFDerivWithinAt.fderivWithin` `IsTopologicalAddGroup.toContinuousAdd` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsScalarTower.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `IsBoundedSMul.continuousSMul` `NormedSpace.toIsBoundedSMul` `TopologicalSpace.t2Space_of_metrizableSpace` `EMetricSpace.metrizableSpace` `HasFDerivWithinAt.smul` `DifferentiableWithinAt.hasFDerivWithinAt`
`fderivWithin_smul_const` 📖	mathematical	`UniqueDiffWithinAt` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `DifferentiableWithinAt` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`fderivWithin` `SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `ESeminormedAddMonoid.toAddMonoid` `ESeminormedAddCommMonoid.toESeminormedAddMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `DistribSMul.toSMulZeroClass` `DistribMulAction.toDistribSMul` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing` `Module.toDistribMulAction` `ESeminormedAddCommMonoid.toAddCommMonoid` `ContinuousLinearMap.smulRight` `AddCommGroup.toAddCommMonoid` `IsBoundedSMul.continuousSMul` `MulZeroClass.toZero` `NonUnitalNonAssocSemiring.toMulZeroClass` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `AddCommGroup.toDivisionAddCommMonoid` `AddCommMonoid.toAddMonoid`	—	`HasFDerivWithinAt.fderivWithin` `IsBoundedSMul.continuousSMul` `IsTopologicalAddGroup.toContinuousAdd` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `NormedSpace.toIsBoundedSMul` `TopologicalSpace.t2Space_of_metrizableSpace` `EMetricSpace.metrizableSpace` `HasFDerivWithinAt.smul_const` `DifferentiableWithinAt.hasFDerivWithinAt`
`fderiv_const_mul` 📖	mathematical	`DifferentiableAt` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`fderiv` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing`	—	`HasFDerivAt.fderiv` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `IsTopologicalAddGroup.toContinuousAdd` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsBoundedSMul.continuousSMul` `NormedSpace.toIsBoundedSMul` `IsTopologicalSemiring.toContinuousAdd` `TopologicalSpace.t2Space_of_metrizableSpace` `EMetricSpace.metrizableSpace` `HasFDerivAt.const_mul` `DifferentiableAt.hasFDerivAt`
`fderiv_finset_prod` 📖	mathematical	`DifferentiableAt` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NonUnitalNormedCommRing.toNonUnitalNormedRing` `NormedCommRing.toNonUnitalNormedCommRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing` `SeminormedCommRing.toNonUnitalSeminormedCommRing` `NormedCommRing.toSeminormedCommRing` `NormedAlgebra.toNormedSpace` `SeminormedCommRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`fderiv` `Finset.prod` `CommRing.toCommMonoid` `NormedCommRing.toCommRing` `Finset.sum` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.addCommMonoid` `IsTopologicalSemiring.toContinuousAdd` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `NormedRing.toRing` `NormedCommRing.toNormedRing` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `Finset.erase`	—	`HasFDerivAt.fderiv` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `IsTopologicalAddGroup.toContinuousAdd` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsBoundedSMul.continuousSMul` `NormedSpace.toIsBoundedSMul` `TopologicalSpace.t2Space_of_metrizableSpace` `EMetricSpace.metrizableSpace` `HasFDerivAt.finset_prod` `DifferentiableAt.hasFDerivAt`
`fderiv_fun_mul` 📖	mathematical	`DifferentiableAt` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NonUnitalNormedCommRing.toNonUnitalNormedRing` `NormedCommRing.toNonUnitalNormedCommRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing` `SeminormedCommRing.toNonUnitalSeminormedCommRing` `NormedCommRing.toSeminormedCommRing` `NormedAlgebra.toNormedSpace` `SeminormedCommRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`fderiv` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.add` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `NormedRing.toRing` `NormedCommRing.toNormedRing` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing`	—	`HasFDerivAt.fderiv` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `IsTopologicalAddGroup.toContinuousAdd` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsBoundedSMul.continuousSMul` `NormedSpace.toIsBoundedSMul` `TopologicalSpace.t2Space_of_metrizableSpace` `EMetricSpace.metrizableSpace` `HasFDerivAt.mul` `DifferentiableAt.hasFDerivAt`
`fderiv_fun_mul'` 📖	mathematical	`DifferentiableAt` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`fderiv` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.add` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `MulOpposite` `DistribMulAction.toDistribSMul` `MulOpposite.instMonoid` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Module.toDistribMulAction` `MulOpposite.instSemiring` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `Semiring.toOppositeModule` `SMulCommClass.opposite_mid` `MulZeroClass.toMul` `MulZeroOneClass.toMulZeroClass` `MonoidWithZero.toMulZeroOneClass` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `MulOpposite.op`	—	`HasFDerivAt.fderiv` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `SMulCommClass.opposite_mid` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `IsTopologicalAddGroup.toContinuousAdd` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsBoundedSMul.continuousSMul` `NormedSpace.toIsBoundedSMul` `TopologicalSpace.t2Space_of_metrizableSpace` `EMetricSpace.metrizableSpace` `HasFDerivAt.mul'` `DifferentiableAt.hasFDerivAt`
`fderiv_fun_smul` 📖	mathematical	`DifferentiableAt` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`fderiv` `SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `ESeminormedAddMonoid.toAddMonoid` `ESeminormedAddCommMonoid.toESeminormedAddMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `DistribSMul.toSMulZeroClass` `DistribMulAction.toDistribSMul` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing` `Module.toDistribMulAction` `ESeminormedAddCommMonoid.toAddCommMonoid` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.add` `IsTopologicalAddGroup.toContinuousAdd` `NormedAddGroup.toAddGroup` `NormedAddCommGroup.toNormedAddGroup` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `ContinuousLinearMap.instSMul` `AddCommMonoid.toAddMonoid` `IsScalarTower.to_smulCommClass` `Semifield.toCommSemiring` `NormedAlgebra.toAlgebra` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `MulZeroClass.toZero` `NonUnitalNonAssocSemiring.toMulZeroClass` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `AddCommGroup.toDivisionAddCommMonoid` `ContinuousLinearMap.smulRight` `IsBoundedSMul.continuousSMul`	—	`HasFDerivAt.fderiv` `IsTopologicalAddGroup.toContinuousAdd` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsScalarTower.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `IsBoundedSMul.continuousSMul` `NormedSpace.toIsBoundedSMul` `TopologicalSpace.t2Space_of_metrizableSpace` `EMetricSpace.metrizableSpace` `HasFDerivAt.smul` `DifferentiableAt.hasFDerivAt`
`fderiv_inv'` 📖	mathematical	—	`fderiv` `NormedAddCommGroup.toAddCommGroup` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NormedDivisionRing.toNormedRing` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedRing.toPseudoMetricSpace` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `GroupWithZero.toDivisionMonoid` `DivisionSemiring.toGroupWithZero` `DivisionRing.toDivisionSemiring` `NormedDivisionRing.toDivisionRing` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `NonUnitalSeminormedRing.toPseudoMetricSpace` `NonUnitalNonAssocSemiring.toAddCommMonoid` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalRing.toNonUnitalNonAssocRing` `NonUnitalSeminormedRing.toNonUnitalRing` `ContinuousLinearMap.neg` `NormedRing.toRing` `NormedCommRing.toNormedRing` `NormedField.toNormedCommRing` `SeminormedAddCommGroup.toAddCommGroup` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `DFunLike.coe` `ContinuousLinearMap.topologicalSpace` `ContinuousLinearMap.addCommMonoid` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ContinuousLinearMap.module` `smulCommClass_self` `CommRing.toCommMonoid` `Field.toCommRing` `DistribMulAction.toMulAction` `CommMonoid.toMonoid` `AddCommMonoid.toAddMonoid` `Module.toDistribMulAction` `Ring.toSemiring` `CommRing.toRing` `UniformContinuousConstSMul.to_continuousConstSMul` `SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `DistribSMul.toSMulZeroClass` `DistribMulAction.toDistribSMul` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `IsBoundedSMul.toUniformContinuousConstSMul` `SeminormedCommRing.toSeminormedRing` `NormedCommRing.toSeminormedCommRing` `MulZeroClass.toZero` `NonUnitalNonAssocSemiring.toMulZeroClass` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `NormedCommRing.toNonUnitalNormedCommRing` `NormedSpace.toIsBoundedSMul` `ContinuousLinearMap.funLike` `ContinuousLinearMap.addCommGroup` `ContinuousLinearMap.topologicalAddGroup` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `ContinuousLinearMap.ring` `SeminormedRing.toNonUnitalSeminormedRing` `ContinuousLinearMap.toSeminormedRing` `ContinuousLinearMap.smulCommClass` `ContinuousLinearMap.continuousConstSMul` `ContinuousLinearMap.mulLeftRight` `IsScalarTower.right` `Semifield.toCommSemiring` `SeminormedRing.toRing` `NormedAlgebra.toAlgebra` `Algebra.to_smulCommClass`	—	`HasFDerivAt.fderiv` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `smulCommClass_self` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `NormedSpace.toIsBoundedSMul` `ContinuousLinearMap.topologicalAddGroup` `ContinuousLinearMap.smulCommClass` `ContinuousLinearMap.continuousConstSMul` `IsScalarTower.right` `Algebra.to_smulCommClass` `IsTopologicalDivisionRing.toIsTopologicalRing` `NormedDivisionRing.to_isTopologicalDivisionRing` `IsBoundedSMul.continuousSMul` `TopologicalSpace.t2Space_of_metrizableSpace` `EMetricSpace.metrizableSpace` `hasFDerivAt_inv'`
`fderiv_inverse` 📖	mathematical	—	`fderiv` `NormedAddCommGroup.toAddCommGroup` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedRing.toPseudoMetricSpace` `Ring.inverse` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing` `Units.val` `MonoidWithZero.toMonoid` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `NonUnitalSeminormedRing.toPseudoMetricSpace` `NonUnitalNonAssocSemiring.toAddCommMonoid` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalRing.toNonUnitalNonAssocRing` `NonUnitalSeminormedRing.toNonUnitalRing` `ContinuousLinearMap.neg` `NormedCommRing.toNormedRing` `NormedField.toNormedCommRing` `SeminormedAddCommGroup.toAddCommGroup` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `DFunLike.coe` `ContinuousLinearMap.topologicalSpace` `ContinuousLinearMap.addCommMonoid` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ContinuousLinearMap.module` `smulCommClass_self` `CommRing.toCommMonoid` `Field.toCommRing` `DistribMulAction.toMulAction` `CommMonoid.toMonoid` `AddCommMonoid.toAddMonoid` `Module.toDistribMulAction` `CommRing.toRing` `UniformContinuousConstSMul.to_continuousConstSMul` `SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `DistribSMul.toSMulZeroClass` `DistribMulAction.toDistribSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `SeminormedCommRing.toSeminormedRing` `NormedCommRing.toSeminormedCommRing` `MulZeroClass.toZero` `NonUnitalNonAssocSemiring.toMulZeroClass` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `NormedCommRing.toNonUnitalNormedCommRing` `NormedSpace.toIsBoundedSMul` `ContinuousLinearMap.funLike` `ContinuousLinearMap.addCommGroup` `ContinuousLinearMap.topologicalAddGroup` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `ContinuousLinearMap.ring` `SeminormedRing.toNonUnitalSeminormedRing` `ContinuousLinearMap.toSeminormedRing` `ContinuousLinearMap.smulCommClass` `ContinuousLinearMap.continuousConstSMul` `ContinuousLinearMap.mulLeftRight` `IsScalarTower.right` `Semifield.toCommSemiring` `SeminormedRing.toRing` `NormedAlgebra.toAlgebra` `Algebra.to_smulCommClass` `Units` `Units.instInv`	—	`HasFDerivAt.fderiv` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `smulCommClass_self` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `NormedSpace.toIsBoundedSMul` `ContinuousLinearMap.topologicalAddGroup` `ContinuousLinearMap.smulCommClass` `ContinuousLinearMap.continuousConstSMul` `IsScalarTower.right` `Algebra.to_smulCommClass` `IsBoundedSMul.continuousSMul` `TopologicalSpace.t2Space_of_metrizableSpace` `EMetricSpace.metrizableSpace` `hasFDerivAt_ringInverse`
`fderiv_list_prod'` 📖	mathematical	`DifferentiableAt` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`fderiv` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing` `AddMonoidWithOne.toOne` `AddGroupWithOne.toAddMonoidWithOne` `Ring.toAddGroupWithOne` `Finset.sum` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.addCommMonoid` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Finset.univ` `Fin.fintype` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `MulOpposite` `DistribMulAction.toDistribSMul` `MulOpposite.instMonoid` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Module.toDistribMulAction` `MulOpposite.instSemiring` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `Semiring.toOppositeModule` `SMulCommClass.opposite_mid` `MulZeroClass.toMul` `MulZeroOneClass.toMulZeroClass` `MonoidWithZero.toMulZeroOneClass` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `MulOpposite.op`	—	`HasFDerivAt.fderiv` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `SMulCommClass.opposite_mid` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `IsTopologicalAddGroup.toContinuousAdd` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsBoundedSMul.continuousSMul` `NormedSpace.toIsBoundedSMul` `TopologicalSpace.t2Space_of_metrizableSpace` `EMetricSpace.metrizableSpace` `HasFDerivAt.list_prod'` `DifferentiableAt.hasFDerivAt`
`fderiv_mul` 📖	mathematical	`DifferentiableAt` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NonUnitalNormedCommRing.toNonUnitalNormedRing` `NormedCommRing.toNonUnitalNormedCommRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing` `SeminormedCommRing.toNonUnitalSeminormedCommRing` `NormedCommRing.toSeminormedCommRing` `NormedAlgebra.toNormedSpace` `SeminormedCommRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`fderiv` `Pi.instMul` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.add` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `NormedRing.toRing` `NormedCommRing.toNormedRing` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing`	—	`HasFDerivAt.fderiv` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `IsTopologicalAddGroup.toContinuousAdd` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsBoundedSMul.continuousSMul` `NormedSpace.toIsBoundedSMul` `TopologicalSpace.t2Space_of_metrizableSpace` `EMetricSpace.metrizableSpace` `HasFDerivAt.mul` `DifferentiableAt.hasFDerivAt`
`fderiv_mul'` 📖	mathematical	`DifferentiableAt` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`fderiv` `Pi.instMul` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.add` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `MulOpposite` `DistribMulAction.toDistribSMul` `MulOpposite.instMonoid` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Module.toDistribMulAction` `MulOpposite.instSemiring` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `Semiring.toOppositeModule` `SMulCommClass.opposite_mid` `MulZeroClass.toMul` `MulZeroOneClass.toMulZeroClass` `MonoidWithZero.toMulZeroOneClass` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `MulOpposite.op`	—	`HasFDerivAt.fderiv` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `SMulCommClass.opposite_mid` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `IsTopologicalAddGroup.toContinuousAdd` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsBoundedSMul.continuousSMul` `NormedSpace.toIsBoundedSMul` `TopologicalSpace.t2Space_of_metrizableSpace` `EMetricSpace.metrizableSpace` `HasFDerivAt.mul'` `DifferentiableAt.hasFDerivAt`
`fderiv_mul_const` 📖	mathematical	`DifferentiableAt` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NonUnitalNormedCommRing.toNonUnitalNormedRing` `NormedCommRing.toNonUnitalNormedCommRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing` `SeminormedCommRing.toNonUnitalSeminormedCommRing` `NormedCommRing.toSeminormedCommRing` `NormedAlgebra.toNormedSpace` `SeminormedCommRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`fderiv` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `NormedRing.toRing` `NormedCommRing.toNormedRing` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing`	—	`HasFDerivAt.fderiv` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `IsTopologicalAddGroup.toContinuousAdd` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsBoundedSMul.continuousSMul` `NormedSpace.toIsBoundedSMul` `IsTopologicalSemiring.toContinuousAdd` `TopologicalSpace.t2Space_of_metrizableSpace` `EMetricSpace.metrizableSpace` `HasFDerivAt.mul_const` `DifferentiableAt.hasFDerivAt`
`fderiv_mul_const'` 📖	mathematical	`DifferentiableAt` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`fderiv` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NormedRing.toRing` `MulOpposite` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.instSMul` `DistribMulAction.toDistribSMul` `MulOpposite.instMonoid` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `AddCommMonoid.toAddMonoid` `Module.toDistribMulAction` `MulOpposite.instSemiring` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `Semiring.toOppositeModule` `SMulCommClass.opposite_mid` `MulZeroClass.toMul` `MulZeroOneClass.toMulZeroClass` `MonoidWithZero.toMulZeroOneClass` `SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `DistribSMul.toSMulZeroClass` `IsScalarTower.right` `Semifield.toCommSemiring` `SeminormedRing.toRing` `NormedAlgebra.toAlgebra` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul_op` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `MulOpposite.op`	—	`HasFDerivAt.fderiv` `SMulCommClass.opposite_mid` `IsScalarTower.right` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul_op` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `IsTopologicalAddGroup.toContinuousAdd` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsBoundedSMul.continuousSMul` `NormedSpace.toIsBoundedSMul` `IsTopologicalSemiring.toContinuousAdd` `TopologicalSpace.t2Space_of_metrizableSpace` `EMetricSpace.metrizableSpace` `HasFDerivAt.mul_const'` `DifferentiableAt.hasFDerivAt`
`fderiv_multiset_prod` 📖	mathematical	`DifferentiableAt` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NonUnitalNormedCommRing.toNonUnitalNormedRing` `NormedCommRing.toNonUnitalNormedCommRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing` `SeminormedCommRing.toNonUnitalSeminormedCommRing` `NormedCommRing.toSeminormedCommRing` `NormedAlgebra.toNormedSpace` `SeminormedCommRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`fderiv` `Multiset.prod` `CommRing.toCommMonoid` `NormedCommRing.toCommRing` `Multiset.map` `Multiset.sum` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.addCommMonoid` `IsTopologicalSemiring.toContinuousAdd` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `NormedRing.toRing` `NormedCommRing.toNormedRing` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `Multiset.erase`	—	`HasFDerivAt.fderiv` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `IsTopologicalAddGroup.toContinuousAdd` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsBoundedSMul.continuousSMul` `NormedSpace.toIsBoundedSMul` `TopologicalSpace.t2Space_of_metrizableSpace` `EMetricSpace.metrizableSpace` `HasFDerivAt.multiset_prod` `DifferentiableAt.hasFDerivAt`
`fderiv_smul` 📖	mathematical	`DifferentiableAt` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`fderiv` `Pi.smul'` `SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `ESeminormedAddMonoid.toAddMonoid` `ESeminormedAddCommMonoid.toESeminormedAddMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `DistribSMul.toSMulZeroClass` `DistribMulAction.toDistribSMul` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing` `Module.toDistribMulAction` `ESeminormedAddCommMonoid.toAddCommMonoid` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.add` `IsTopologicalAddGroup.toContinuousAdd` `NormedAddGroup.toAddGroup` `NormedAddCommGroup.toNormedAddGroup` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `ContinuousLinearMap.instSMul` `AddCommMonoid.toAddMonoid` `IsScalarTower.to_smulCommClass` `Semifield.toCommSemiring` `NormedAlgebra.toAlgebra` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `MulZeroClass.toZero` `NonUnitalNonAssocSemiring.toMulZeroClass` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `AddCommGroup.toDivisionAddCommMonoid` `ContinuousLinearMap.smulRight` `IsBoundedSMul.continuousSMul`	—	`HasFDerivAt.fderiv` `IsTopologicalAddGroup.toContinuousAdd` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsScalarTower.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `IsBoundedSMul.continuousSMul` `NormedSpace.toIsBoundedSMul` `TopologicalSpace.t2Space_of_metrizableSpace` `EMetricSpace.metrizableSpace` `HasFDerivAt.smul` `DifferentiableAt.hasFDerivAt`
`fderiv_smul_const` 📖	mathematical	`DifferentiableAt` `NormedAddCommGroup.toAddCommGroup` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAddCommGroup.toSeminormedAddCommGroup` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedAddCommGroup.toPseudoMetricSpace` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `SeminormedRing.toPseudoMetricSpace`	`fderiv` `SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `ESeminormedAddMonoid.toAddMonoid` `ESeminormedAddCommMonoid.toESeminormedAddMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `DistribSMul.toSMulZeroClass` `DistribMulAction.toDistribSMul` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing` `Module.toDistribMulAction` `ESeminormedAddCommMonoid.toAddCommMonoid` `ContinuousLinearMap.smulRight` `AddCommGroup.toAddCommMonoid` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `IsBoundedSMul.continuousSMul` `MulZeroClass.toZero` `NonUnitalNonAssocSemiring.toMulZeroClass` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `AddCommGroup.toDivisionAddCommMonoid` `AddCommMonoid.toAddMonoid`	—	`HasFDerivAt.fderiv` `IsBoundedSMul.continuousSMul` `IsTopologicalAddGroup.toContinuousAdd` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `NormedSpace.toIsBoundedSMul` `TopologicalSpace.t2Space_of_metrizableSpace` `EMetricSpace.metrizableSpace` `HasFDerivAt.smul_const` `DifferentiableAt.hasFDerivAt`
`hasFDerivAt_finset_prod` 📖	mathematical	—	`HasFDerivAt` `Pi.addCommGroup` `NormedAddCommGroup.toAddCommGroup` `NonUnitalNormedRing.toNormedAddCommGroup` `NonUnitalNormedCommRing.toNonUnitalNormedRing` `NormedCommRing.toNonUnitalNormedCommRing` `Pi.Function.module` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `NontriviallyNormedField.toNormedField` `NonUnitalNonAssocSemiring.toAddCommMonoid` `NonUnitalSemiring.toNonUnitalNonAssocSemiring` `Semiring.toNonUnitalSemiring` `Ring.toSemiring` `NormedRing.toRing` `NormedCommRing.toNormedRing` `NormedSpace.toModule` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing` `SeminormedCommRing.toNonUnitalSeminormedCommRing` `NormedCommRing.toSeminormedCommRing` `NormedAlgebra.toNormedSpace` `SeminormedCommRing.toSeminormedRing` `Pi.topologicalSpace` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedRing.toPseudoMetricSpace` `Finset.prod` `CommRing.toCommMonoid` `NormedCommRing.toCommRing` `Finset.sum` `ContinuousLinearMap` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.addCommMonoid` `IsTopologicalSemiring.toContinuousAdd` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Pi.addCommMonoid` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `Pi.module` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `Finset.erase` `ContinuousLinearMap.proj`	—	`HasStrictFDerivAt.hasFDerivAt` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `hasStrictFDerivAt_finset_prod`
`hasFDerivAt_inv'` 📖	mathematical	—	`HasFDerivAt` `SeminormedAddCommGroup.toAddCommGroup` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedRing.toNonUnitalNormedRing` `NormedDivisionRing.toNormedRing` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `NonUnitalSeminormedRing.toPseudoMetricSpace` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `GroupWithZero.toDivisionMonoid` `DivisionSemiring.toGroupWithZero` `DivisionRing.toDivisionSemiring` `NormedDivisionRing.toDivisionRing` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `NonUnitalNonAssocSemiring.toAddCommMonoid` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalRing.toNonUnitalNonAssocRing` `NonUnitalSeminormedRing.toNonUnitalRing` `ContinuousLinearMap.neg` `NormedRing.toRing` `NormedCommRing.toNormedRing` `NormedField.toNormedCommRing` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `DFunLike.coe` `ContinuousLinearMap.topologicalSpace` `ContinuousLinearMap.addCommMonoid` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ContinuousLinearMap.module` `smulCommClass_self` `CommRing.toCommMonoid` `Field.toCommRing` `DistribMulAction.toMulAction` `CommMonoid.toMonoid` `AddCommMonoid.toAddMonoid` `Module.toDistribMulAction` `Ring.toSemiring` `CommRing.toRing` `UniformContinuousConstSMul.to_continuousConstSMul` `SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `DistribSMul.toSMulZeroClass` `DistribMulAction.toDistribSMul` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `IsBoundedSMul.toUniformContinuousConstSMul` `SeminormedRing.toPseudoMetricSpace` `SeminormedCommRing.toSeminormedRing` `NormedCommRing.toSeminormedCommRing` `MulZeroClass.toZero` `NonUnitalNonAssocSemiring.toMulZeroClass` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `NormedCommRing.toNonUnitalNormedCommRing` `NormedSpace.toIsBoundedSMul` `ContinuousLinearMap.funLike` `ContinuousLinearMap.addCommGroup` `ContinuousLinearMap.topologicalAddGroup` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `ContinuousLinearMap.ring` `SeminormedRing.toNonUnitalSeminormedRing` `ContinuousLinearMap.toSeminormedRing` `ContinuousLinearMap.smulCommClass` `ContinuousLinearMap.continuousConstSMul` `ContinuousLinearMap.mulLeftRight` `IsScalarTower.right` `Semifield.toCommSemiring` `SeminormedRing.toRing` `NormedAlgebra.toAlgebra` `Algebra.to_smulCommClass`	—	`SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `smulCommClass_self` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `NormedSpace.toIsBoundedSMul` `ContinuousLinearMap.topologicalAddGroup` `ContinuousLinearMap.smulCommClass` `ContinuousLinearMap.continuousConstSMul` `IsScalarTower.right` `Algebra.to_smulCommClass` `Ring.inverse_eq_inv'` `Units.val_inv_eq_inv_val` `hasFDerivAt_ringInverse` `instHasSummableGeomSeries`
`hasFDerivAt_list_prod'` 📖	mathematical	—	`HasFDerivAt` `Pi.addCommGroup` `NormedAddCommGroup.toAddCommGroup` `NonUnitalNormedRing.toNormedAddCommGroup` `NonUnitalNormedCommRing.toNonUnitalNormedRing` `NormedCommRing.toNonUnitalNormedCommRing` `Pi.Function.module` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `NontriviallyNormedField.toNormedField` `NonUnitalNonAssocSemiring.toAddCommMonoid` `NonUnitalSemiring.toNonUnitalNonAssocSemiring` `Semiring.toNonUnitalSemiring` `Ring.toSemiring` `NormedRing.toRing` `NormedCommRing.toNormedRing` `NormedSpace.toModule` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing` `SeminormedCommRing.toNonUnitalSeminormedCommRing` `NormedCommRing.toSeminormedCommRing` `NormedAlgebra.toNormedSpace` `SeminormedCommRing.toSeminormedRing` `Pi.topologicalSpace` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedRing.toPseudoMetricSpace` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `AddMonoidWithOne.toOne` `AddGroupWithOne.toAddMonoidWithOne` `Ring.toAddGroupWithOne` `Finset.sum` `ContinuousLinearMap` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.addCommMonoid` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Finset.univ` `Fin.fintype` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `MulOpposite` `Pi.addCommMonoid` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `Pi.module` `DistribMulAction.toDistribSMul` `MulOpposite.instMonoid` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `CommSemiring.toSemiring` `CommRing.toCommSemiring` `NormedCommRing.toCommRing` `Module.toDistribMulAction` `MulOpposite.instSemiring` `Semiring.toOppositeModule` `SMulCommClass.opposite_mid` `MulZeroClass.toMul` `MulZeroOneClass.toMulZeroClass` `MonoidWithZero.toMulZeroOneClass` `IsScalarTower.right` `ContinuousConstSMul.op` `Algebra.toSMul` `Algebra.id` `CommSemigroup.isCentralScalar` `NonUnitalCommSemiring.toCommSemigroup` `NonUnitalCommRing.toNonUnitalCommSemiring` `MulOpposite.op` `ContinuousLinearMap.proj`	—	`HasStrictFDerivAt.hasFDerivAt` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `SMulCommClass.opposite_mid` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `hasStrictFDerivAt_list_prod'`
`hasFDerivAt_list_prod_attach'` 📖	mathematical	—	`HasFDerivAt` `Pi.addCommGroup` `NormedAddCommGroup.toAddCommGroup` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `Pi.Function.module` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `NontriviallyNormedField.toNormedField` `NonUnitalNonAssocSemiring.toAddCommMonoid` `NonUnitalSemiring.toNonUnitalNonAssocSemiring` `Semiring.toNonUnitalSemiring` `Ring.toSemiring` `NormedRing.toRing` `NormedSpace.toModule` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `Pi.topologicalSpace` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedRing.toPseudoMetricSpace` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `AddMonoidWithOne.toOne` `AddGroupWithOne.toAddMonoidWithOne` `Ring.toAddGroupWithOne` `Finset.sum` `ContinuousLinearMap` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.addCommMonoid` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Finset.univ` `Fin.fintype` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `MulOpposite` `Pi.addCommMonoid` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `Pi.module` `DistribMulAction.toDistribSMul` `MulOpposite.instMonoid` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Module.toDistribMulAction` `MulOpposite.instSemiring` `Semiring.toOppositeModule` `SMulCommClass.opposite_mid` `MulZeroClass.toMul` `MulZeroOneClass.toMulZeroClass` `MonoidWithZero.toMulZeroOneClass` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `MulOpposite.op` `ContinuousLinearMap.proj`	—	`HasStrictFDerivAt.hasFDerivAt` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `SMulCommClass.opposite_mid` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `hasStrictFDerivAt_list_prod_attach'`
`hasFDerivAt_list_prod_finRange'` 📖	mathematical	—	`HasFDerivAt` `Pi.addCommGroup` `NormedAddCommGroup.toAddCommGroup` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `Pi.Function.module` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `NontriviallyNormedField.toNormedField` `NonUnitalNonAssocSemiring.toAddCommMonoid` `NonUnitalSemiring.toNonUnitalNonAssocSemiring` `Semiring.toNonUnitalSemiring` `Ring.toSemiring` `NormedRing.toRing` `NormedSpace.toModule` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `Pi.topologicalSpace` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedRing.toPseudoMetricSpace` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `AddMonoidWithOne.toOne` `AddGroupWithOne.toAddMonoidWithOne` `Ring.toAddGroupWithOne` `Finset.sum` `ContinuousLinearMap` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.addCommMonoid` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Finset.univ` `Fin.fintype` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `MulOpposite` `Pi.addCommMonoid` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `Pi.module` `DistribMulAction.toDistribSMul` `MulOpposite.instMonoid` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Module.toDistribMulAction` `MulOpposite.instSemiring` `Semiring.toOppositeModule` `SMulCommClass.opposite_mid` `MulZeroClass.toMul` `MulZeroOneClass.toMulZeroClass` `MonoidWithZero.toMulZeroOneClass` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `MulOpposite.op` `ContinuousLinearMap.proj`	—	`HasStrictFDerivAt.hasFDerivAt` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `SMulCommClass.opposite_mid` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `hasStrictFDerivAt_list_prod_finRange'`
`hasFDerivAt_multiset_prod` 📖	mathematical	—	`HasFDerivAt` `Pi.addCommGroup` `NormedAddCommGroup.toAddCommGroup` `NonUnitalNormedRing.toNormedAddCommGroup` `NonUnitalNormedCommRing.toNonUnitalNormedRing` `NormedCommRing.toNonUnitalNormedCommRing` `Pi.Function.module` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `NontriviallyNormedField.toNormedField` `NonUnitalNonAssocSemiring.toAddCommMonoid` `NonUnitalSemiring.toNonUnitalNonAssocSemiring` `Semiring.toNonUnitalSemiring` `Ring.toSemiring` `NormedRing.toRing` `NormedCommRing.toNormedRing` `NormedSpace.toModule` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing` `SeminormedCommRing.toNonUnitalSeminormedCommRing` `NormedCommRing.toSeminormedCommRing` `NormedAlgebra.toNormedSpace` `SeminormedCommRing.toSeminormedRing` `Pi.topologicalSpace` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedRing.toPseudoMetricSpace` `Multiset.prod` `CommRing.toCommMonoid` `NormedCommRing.toCommRing` `Multiset.map` `Multiset.sum` `ContinuousLinearMap` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.addCommMonoid` `IsTopologicalSemiring.toContinuousAdd` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Pi.addCommMonoid` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `Pi.module` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `Multiset.erase` `ContinuousLinearMap.proj`	—	`HasStrictFDerivAt.hasFDerivAt` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `hasStrictFDerivAt_multiset_prod`
`hasFDerivAt_ringInverse` 📖	mathematical	—	`HasFDerivAt` `SeminormedAddCommGroup.toAddCommGroup` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedRing.toNonUnitalNormedRing` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `NonUnitalSeminormedRing.toPseudoMetricSpace` `Ring.inverse` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `NonUnitalNonAssocSemiring.toAddCommMonoid` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalRing.toNonUnitalNonAssocRing` `NonUnitalSeminormedRing.toNonUnitalRing` `ContinuousLinearMap.neg` `NormedCommRing.toNormedRing` `NormedField.toNormedCommRing` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `DFunLike.coe` `ContinuousLinearMap.topologicalSpace` `ContinuousLinearMap.addCommMonoid` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ContinuousLinearMap.module` `smulCommClass_self` `CommRing.toCommMonoid` `Field.toCommRing` `DistribMulAction.toMulAction` `CommMonoid.toMonoid` `AddCommMonoid.toAddMonoid` `Module.toDistribMulAction` `CommRing.toRing` `UniformContinuousConstSMul.to_continuousConstSMul` `SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `DistribSMul.toSMulZeroClass` `DistribMulAction.toDistribSMul` `MonoidWithZero.toMonoid` `IsBoundedSMul.toUniformContinuousConstSMul` `SeminormedRing.toPseudoMetricSpace` `SeminormedCommRing.toSeminormedRing` `NormedCommRing.toSeminormedCommRing` `MulZeroClass.toZero` `NonUnitalNonAssocSemiring.toMulZeroClass` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `NormedCommRing.toNonUnitalNormedCommRing` `NormedSpace.toIsBoundedSMul` `ContinuousLinearMap.funLike` `ContinuousLinearMap.addCommGroup` `ContinuousLinearMap.topologicalAddGroup` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `ContinuousLinearMap.ring` `SeminormedRing.toNonUnitalSeminormedRing` `ContinuousLinearMap.toSeminormedRing` `ContinuousLinearMap.smulCommClass` `ContinuousLinearMap.continuousConstSMul` `ContinuousLinearMap.mulLeftRight` `IsScalarTower.right` `Semifield.toCommSemiring` `SeminormedRing.toRing` `NormedAlgebra.toAlgebra` `Algebra.to_smulCommClass` `Units.val` `Units` `Units.instInv`	—	`Asymptotics.IsBigO.trans_isLittleO` `NormedRing.inverse_add_norm_diff_second_order` `Asymptotics.isLittleO_norm_pow_id` `one_lt_two` `Nat.instZeroLEOneClass` `IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono` `AddLeftCancelSemigroup.toIsLeftCancelAdd` `IsOrderedAddMonoid.toAddLeftMono` `Nat.instIsOrderedAddMonoid` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `smulCommClass_self` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `NormedSpace.toIsBoundedSMul` `ContinuousLinearMap.topologicalAddGroup` `ContinuousLinearMap.smulCommClass` `ContinuousLinearMap.continuousConstSMul` `IsScalarTower.right` `Algebra.to_smulCommClass` `Ring.inverse_invertible` `invOf_units` `sub_neg_eq_add`
`hasStrictFDerivAt_finset_prod` 📖	mathematical	—	`HasStrictFDerivAt` `Pi.addCommGroup` `NormedAddCommGroup.toAddCommGroup` `NonUnitalNormedRing.toNormedAddCommGroup` `NonUnitalNormedCommRing.toNonUnitalNormedRing` `NormedCommRing.toNonUnitalNormedCommRing` `Pi.Function.module` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `NontriviallyNormedField.toNormedField` `NonUnitalNonAssocSemiring.toAddCommMonoid` `NonUnitalSemiring.toNonUnitalNonAssocSemiring` `Semiring.toNonUnitalSemiring` `Ring.toSemiring` `NormedRing.toRing` `NormedCommRing.toNormedRing` `NormedSpace.toModule` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing` `SeminormedCommRing.toNonUnitalSeminormedCommRing` `NormedCommRing.toSeminormedCommRing` `NormedAlgebra.toNormedSpace` `SeminormedCommRing.toSeminormedRing` `Pi.topologicalSpace` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedRing.toPseudoMetricSpace` `Finset.prod` `CommRing.toCommMonoid` `NormedCommRing.toCommRing` `Finset.sum` `ContinuousLinearMap` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.addCommMonoid` `IsTopologicalSemiring.toContinuousAdd` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Pi.addCommMonoid` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `Pi.module` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `Finset.erase` `ContinuousLinearMap.proj`	—	`IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `Finset.sum_congr` `hasStrictFDerivAt_multiset_prod`
`hasStrictFDerivAt_inv'` 📖	mathematical	—	`HasStrictFDerivAt` `SeminormedAddCommGroup.toAddCommGroup` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedRing.toNonUnitalNormedRing` `NormedDivisionRing.toNormedRing` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `NonUnitalSeminormedRing.toPseudoMetricSpace` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `GroupWithZero.toDivisionMonoid` `DivisionSemiring.toGroupWithZero` `DivisionRing.toDivisionSemiring` `NormedDivisionRing.toDivisionRing` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `NonUnitalNonAssocSemiring.toAddCommMonoid` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalRing.toNonUnitalNonAssocRing` `NonUnitalSeminormedRing.toNonUnitalRing` `ContinuousLinearMap.neg` `NormedRing.toRing` `NormedCommRing.toNormedRing` `NormedField.toNormedCommRing` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `DFunLike.coe` `ContinuousLinearMap.topologicalSpace` `ContinuousLinearMap.addCommMonoid` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ContinuousLinearMap.module` `smulCommClass_self` `CommRing.toCommMonoid` `Field.toCommRing` `DistribMulAction.toMulAction` `CommMonoid.toMonoid` `AddCommMonoid.toAddMonoid` `Module.toDistribMulAction` `Ring.toSemiring` `CommRing.toRing` `UniformContinuousConstSMul.to_continuousConstSMul` `SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `DistribSMul.toSMulZeroClass` `DistribMulAction.toDistribSMul` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `IsBoundedSMul.toUniformContinuousConstSMul` `SeminormedRing.toPseudoMetricSpace` `SeminormedCommRing.toSeminormedRing` `NormedCommRing.toSeminormedCommRing` `MulZeroClass.toZero` `NonUnitalNonAssocSemiring.toMulZeroClass` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `NormedCommRing.toNonUnitalNormedCommRing` `NormedSpace.toIsBoundedSMul` `ContinuousLinearMap.funLike` `ContinuousLinearMap.addCommGroup` `ContinuousLinearMap.topologicalAddGroup` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `ContinuousLinearMap.ring` `SeminormedRing.toNonUnitalSeminormedRing` `ContinuousLinearMap.toSeminormedRing` `ContinuousLinearMap.smulCommClass` `ContinuousLinearMap.continuousConstSMul` `ContinuousLinearMap.mulLeftRight` `IsScalarTower.right` `Semifield.toCommSemiring` `SeminormedRing.toRing` `NormedAlgebra.toAlgebra` `Algebra.to_smulCommClass`	—	`SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `smulCommClass_self` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `NormedSpace.toIsBoundedSMul` `ContinuousLinearMap.topologicalAddGroup` `ContinuousLinearMap.smulCommClass` `ContinuousLinearMap.continuousConstSMul` `IsScalarTower.right` `Algebra.to_smulCommClass` `Ring.inverse_eq_inv'` `Units.val_inv_eq_inv_val` `hasStrictFDerivAt_ringInverse` `instHasSummableGeomSeries`
`hasStrictFDerivAt_list_prod` 📖	mathematical	—	`HasStrictFDerivAt` `Pi.addCommGroup` `NormedAddCommGroup.toAddCommGroup` `NonUnitalNormedRing.toNormedAddCommGroup` `NonUnitalNormedCommRing.toNonUnitalNormedRing` `NormedCommRing.toNonUnitalNormedCommRing` `Pi.Function.module` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `NontriviallyNormedField.toNormedField` `NonUnitalNonAssocSemiring.toAddCommMonoid` `NonUnitalSemiring.toNonUnitalNonAssocSemiring` `Semiring.toNonUnitalSemiring` `Ring.toSemiring` `NormedRing.toRing` `NormedCommRing.toNormedRing` `NormedSpace.toModule` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing` `SeminormedCommRing.toNonUnitalSeminormedCommRing` `NormedCommRing.toSeminormedCommRing` `NormedAlgebra.toNormedSpace` `SeminormedCommRing.toSeminormedRing` `Pi.topologicalSpace` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedRing.toPseudoMetricSpace` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `AddMonoidWithOne.toOne` `AddGroupWithOne.toAddMonoidWithOne` `Ring.toAddGroupWithOne` `ContinuousLinearMap` `RingHom.id` `Semiring.toNonAssocSemiring` `Pi.addCommMonoid` `AddCommGroup.toAddCommMonoid` `Pi.module` `ContinuousLinearMap.add` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ContinuousLinearMap.zero` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `ContinuousLinearMap.proj`	—	`HasStrictFDerivAt.congr_fderiv` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `SMulCommClass.opposite_mid` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `hasStrictFDerivAt_list_prod'` `Finset.sum_congr` `List.Perm.prod_eq` `List.erase_getElem` `Semigroup.to_isLawfulIdentity` `Semigroup.to_isAssociative` `List.sum_toFinset` `List.toFinset_finRange` `ContinuousLinearMap.ext` `IsCentralScalar.op_smul_eq_smul` `ContinuousLinearMap.isCentralScalar` `CommSemigroup.isCentralScalar` `Mathlib.Tactic.Ring.of_eq` `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`
`hasStrictFDerivAt_list_prod'` 📖	mathematical	—	`HasStrictFDerivAt` `Pi.addCommGroup` `NormedAddCommGroup.toAddCommGroup` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `Pi.Function.module` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `NontriviallyNormedField.toNormedField` `NonUnitalNonAssocSemiring.toAddCommMonoid` `NonUnitalSemiring.toNonUnitalNonAssocSemiring` `Semiring.toNonUnitalSemiring` `Ring.toSemiring` `NormedRing.toRing` `NormedSpace.toModule` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `Pi.topologicalSpace` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedRing.toPseudoMetricSpace` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `AddMonoidWithOne.toOne` `AddGroupWithOne.toAddMonoidWithOne` `Ring.toAddGroupWithOne` `Finset.sum` `ContinuousLinearMap` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.addCommMonoid` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Finset.univ` `Fin.fintype` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `MulOpposite` `Pi.addCommMonoid` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `Pi.module` `DistribMulAction.toDistribSMul` `MulOpposite.instMonoid` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Module.toDistribMulAction` `MulOpposite.instSemiring` `Semiring.toOppositeModule` `SMulCommClass.opposite_mid` `MulZeroClass.toMul` `MulZeroOneClass.toMulZeroClass` `MonoidWithZero.toMulZeroOneClass` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `MulOpposite.op` `ContinuousLinearMap.proj`	—	`IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `SMulCommClass.opposite_mid` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `Finset.sum_congr` `Finset.univ_eq_empty` `Fin.isEmpty'` `one_smul` `HasStrictFDerivAt.congr_fderiv` `HasStrictFDerivAt.mul'` `ContinuousLinearMap.hasStrictFDerivAt` `ContinuousLinearMap.ext` `add_comm` `ContinuousLinearMap.coe_sum'` `Finset.sum_apply` `Finset.mul_sum` `Fin.sum_univ_succ` `mul_assoc`
`hasStrictFDerivAt_list_prod_attach'` 📖	mathematical	—	`HasStrictFDerivAt` `Pi.addCommGroup` `NormedAddCommGroup.toAddCommGroup` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `Pi.Function.module` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `NontriviallyNormedField.toNormedField` `NonUnitalNonAssocSemiring.toAddCommMonoid` `NonUnitalSemiring.toNonUnitalNonAssocSemiring` `Semiring.toNonUnitalSemiring` `Ring.toSemiring` `NormedRing.toRing` `NormedSpace.toModule` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `Pi.topologicalSpace` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedRing.toPseudoMetricSpace` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `AddMonoidWithOne.toOne` `AddGroupWithOne.toAddMonoidWithOne` `Ring.toAddGroupWithOne` `Finset.sum` `ContinuousLinearMap` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.addCommMonoid` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Finset.univ` `Fin.fintype` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `MulOpposite` `Pi.addCommMonoid` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `Pi.module` `DistribMulAction.toDistribSMul` `MulOpposite.instMonoid` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Module.toDistribMulAction` `MulOpposite.instSemiring` `Semiring.toOppositeModule` `SMulCommClass.opposite_mid` `MulZeroClass.toMul` `MulZeroOneClass.toMulZeroClass` `MonoidWithZero.toMulZeroOneClass` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `MulOpposite.op` `ContinuousLinearMap.proj`	—	`HasStrictFDerivAt.congr_fderiv` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `SMulCommClass.opposite_mid` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `hasStrictFDerivAt_list_prod'` `Finite.of_fintype` `Finset.sum_equiv`
`hasStrictFDerivAt_list_prod_finRange'` 📖	mathematical	—	`HasStrictFDerivAt` `Pi.addCommGroup` `NormedAddCommGroup.toAddCommGroup` `NonUnitalNormedRing.toNormedAddCommGroup` `NormedRing.toNonUnitalNormedRing` `Pi.Function.module` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `NontriviallyNormedField.toNormedField` `NonUnitalNonAssocSemiring.toAddCommMonoid` `NonUnitalSemiring.toNonUnitalNonAssocSemiring` `Semiring.toNonUnitalSemiring` `Ring.toSemiring` `NormedRing.toRing` `NormedSpace.toModule` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `Pi.topologicalSpace` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedRing.toPseudoMetricSpace` `Distrib.toMul` `NonUnitalNonAssocSemiring.toDistrib` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `AddMonoidWithOne.toOne` `AddGroupWithOne.toAddMonoidWithOne` `Ring.toAddGroupWithOne` `Finset.sum` `ContinuousLinearMap` `RingHom.id` `Semiring.toNonAssocSemiring` `AddCommGroup.toAddCommMonoid` `ContinuousLinearMap.addCommMonoid` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Finset.univ` `Fin.fintype` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `MulOpposite` `Pi.addCommMonoid` `ESeminormedAddCommMonoid.toAddCommMonoid` `ENormedAddCommMonoid.toESeminormedAddCommMonoid` `NormedAddCommGroup.toENormedAddCommMonoid` `Pi.module` `DistribMulAction.toDistribSMul` `MulOpposite.instMonoid` `MonoidWithZero.toMonoid` `Semiring.toMonoidWithZero` `Module.toDistribMulAction` `MulOpposite.instSemiring` `Semiring.toOppositeModule` `SMulCommClass.opposite_mid` `MulZeroClass.toMul` `MulZeroOneClass.toMulZeroClass` `MonoidWithZero.toMulZeroOneClass` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `MulOpposite.op` `ContinuousLinearMap.proj`	—	`HasStrictFDerivAt.congr_fderiv` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `SMulCommClass.opposite_mid` `IsScalarTower.right` `Ring.uniformContinuousConstSMul_op` `hasStrictFDerivAt_list_prod'` `Finite.of_fintype` `Finset.sum_equiv`
`hasStrictFDerivAt_multiset_prod` 📖	mathematical	—	`HasStrictFDerivAt` `Pi.addCommGroup` `NormedAddCommGroup.toAddCommGroup` `NonUnitalNormedRing.toNormedAddCommGroup` `NonUnitalNormedCommRing.toNonUnitalNormedRing` `NormedCommRing.toNonUnitalNormedCommRing` `Pi.Function.module` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `NontriviallyNormedField.toNormedField` `NonUnitalNonAssocSemiring.toAddCommMonoid` `NonUnitalSemiring.toNonUnitalNonAssocSemiring` `Semiring.toNonUnitalSemiring` `Ring.toSemiring` `NormedRing.toRing` `NormedCommRing.toNormedRing` `NormedSpace.toModule` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing` `SeminormedCommRing.toNonUnitalSeminormedCommRing` `NormedCommRing.toSeminormedCommRing` `NormedAlgebra.toNormedSpace` `SeminormedCommRing.toSeminormedRing` `Pi.topologicalSpace` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `SeminormedRing.toPseudoMetricSpace` `Multiset.prod` `CommRing.toCommMonoid` `NormedCommRing.toCommRing` `Multiset.map` `Multiset.sum` `ContinuousLinearMap` `RingHom.id` `Semiring.toNonAssocSemiring` `Pi.addCommMonoid` `AddCommGroup.toAddCommMonoid` `Pi.module` `ContinuousLinearMap.addCommMonoid` `IsTopologicalSemiring.toContinuousAdd` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ContinuousLinearMap.instSMul` `NonUnitalNonAssocSemiring.toDistribSMul` `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` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `Multiset.erase` `ContinuousLinearMap.proj`	—	`IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `Algebra.to_smulCommClass` `UniformContinuousConstSMul.to_continuousConstSMul` `Ring.uniformContinuousConstSMul` `SeminormedAddCommGroup.to_isUniformAddGroup` `IsTopologicalSemiring.toContinuousMul` `Multiset.map_congr` `hasStrictFDerivAt_list_prod`
`hasStrictFDerivAt_ringInverse` 📖	mathematical	—	`HasStrictFDerivAt` `SeminormedAddCommGroup.toAddCommGroup` `NonUnitalSeminormedRing.toSeminormedAddCommGroup` `NonUnitalNormedRing.toNonUnitalSeminormedRing` `NormedRing.toNonUnitalNormedRing` `NormedSpace.toModule` `NontriviallyNormedField.toNormedField` `NormedAlgebra.toNormedSpace` `NormedRing.toSeminormedRing` `UniformSpace.toTopologicalSpace` `PseudoMetricSpace.toUniformSpace` `NonUnitalSeminormedRing.toPseudoMetricSpace` `Ring.inverse` `Semiring.toMonoidWithZero` `Ring.toSemiring` `NormedRing.toRing` `ContinuousLinearMap` `DivisionSemiring.toSemiring` `Semifield.toDivisionSemiring` `Field.toSemifield` `NormedField.toField` `RingHom.id` `Semiring.toNonAssocSemiring` `NonUnitalNonAssocSemiring.toAddCommMonoid` `NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring` `NonUnitalRing.toNonUnitalNonAssocRing` `NonUnitalSeminormedRing.toNonUnitalRing` `ContinuousLinearMap.neg` `NormedCommRing.toNormedRing` `NormedField.toNormedCommRing` `SeminormedAddCommGroup.toIsTopologicalAddGroup` `DFunLike.coe` `ContinuousLinearMap.topologicalSpace` `ContinuousLinearMap.addCommMonoid` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `ContinuousLinearMap.module` `smulCommClass_self` `CommRing.toCommMonoid` `Field.toCommRing` `DistribMulAction.toMulAction` `CommMonoid.toMonoid` `AddCommMonoid.toAddMonoid` `Module.toDistribMulAction` `CommRing.toRing` `UniformContinuousConstSMul.to_continuousConstSMul` `SMulZeroClass.toSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `DistribSMul.toSMulZeroClass` `DistribMulAction.toDistribSMul` `MonoidWithZero.toMonoid` `IsBoundedSMul.toUniformContinuousConstSMul` `SeminormedRing.toPseudoMetricSpace` `SeminormedCommRing.toSeminormedRing` `NormedCommRing.toSeminormedCommRing` `MulZeroClass.toZero` `NonUnitalNonAssocSemiring.toMulZeroClass` `NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing` `NonUnitalCommRing.toNonUnitalNonAssocCommRing` `NonUnitalNormedCommRing.toNonUnitalCommRing` `NormedCommRing.toNonUnitalNormedCommRing` `NormedSpace.toIsBoundedSMul` `ContinuousLinearMap.funLike` `ContinuousLinearMap.addCommGroup` `ContinuousLinearMap.topologicalAddGroup` `NonAssocRing.toNonUnitalNonAssocRing` `Ring.toNonAssocRing` `ContinuousLinearMap.ring` `SeminormedRing.toNonUnitalSeminormedRing` `ContinuousLinearMap.toSeminormedRing` `ContinuousLinearMap.smulCommClass` `ContinuousLinearMap.continuousConstSMul` `ContinuousLinearMap.mulLeftRight` `IsScalarTower.right` `Semifield.toCommSemiring` `SeminormedRing.toRing` `NormedAlgebra.toAlgebra` `Algebra.to_smulCommClass` `Units.val` `Units` `Units.instInv`	—	`SeminormedAddCommGroup.toIsTopologicalAddGroup` `IsTopologicalSemiring.toContinuousAdd` `IsTopologicalRing.toIsTopologicalSemiring` `NonUnitalSeminormedRing.toIsTopologicalRing` `smulCommClass_self` `UniformContinuousConstSMul.to_continuousConstSMul` `IsBoundedSMul.toUniformContinuousConstSMul` `NormedSpace.toIsBoundedSMul` `ContinuousLinearMap.topologicalAddGroup` `ContinuousLinearMap.smulCommClass` `ContinuousLinearMap.continuousConstSMul` `IsScalarTower.right` `Algebra.to_smulCommClass` `fderiv_inverse` `AnalyticAt.hasStrictFDerivAt` `analyticAt_inverse`

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