IntegrationByParts

📁 Source: Mathlib/Analysis/Calculus/LineDeriv/IntegrationByParts.lean

Statistics

Metric	Count
Definitions	0
Theorems integral_bilinear_fderiv_right_eq_neg_left_of_integrable, integral_bilinear_hasFDerivAt_right_eq_neg_left_of_integrable, integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable, integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable_aux1, integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable_aux2, integral_mul_fderiv_eq_neg_fderiv_mul_of_integrable, integral_smul_fderiv_eq_neg_fderiv_smul_of_integrable	7
Total	7

(root)

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
integral_bilinear_fderiv_right_eq_neg_left_of_integrable 📖	mathematical	MeasureTheory.Integrable UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup SeminormedAddGroup.toContinuousENorm SeminormedAddCommGroup.toSeminormedAddGroup DFunLike.coe ContinuousLinearMap Real Real.semiring RingHom.id Semiring.toNonAssocSemiring ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule Real.normedField ContinuousLinearMap.funLike ContinuousLinearMap.topologicalSpace SeminormedAddCommGroup.toAddCommGroup SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousLinearMap.addCommMonoid IsTopologicalAddGroup.toContinuousAdd NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup ContinuousLinearMap.module smulCommClass_self Real.instCommMonoid DistribMulAction.toMulAction CommMonoid.toMonoid AddCommMonoid.toAddMonoid Module.toDistribMulAction Ring.toSemiring CommRing.toRing Real.commRing UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero IsBoundedSMul.toUniformContinuousConstSMul Real.pseudoMetricSpace Real.instZero NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedAddCommGroup.toAddCommGroup NormedSpace.toIsBoundedSMul DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField DenselyNormedField.toNontriviallyNormedField Real.denselyNormedField AddCommGroup.toAddCommMonoid fderiv Differentiable	MeasureTheory.integral NegZeroClass.toNeg	—	SeminormedAddCommGroup.toIsTopologicalAddGroup IsTopologicalAddGroup.toContinuousAdd smulCommClass_self UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul integral_bilinear_hasFDerivAt_right_eq_neg_left_of_integrable DifferentiableAt.hasFDerivAt
integral_bilinear_hasFDerivAt_right_eq_neg_left_of_integrable 📖	mathematical	MeasureTheory.Integrable UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup SeminormedAddGroup.toContinuousENorm SeminormedAddCommGroup.toSeminormedAddGroup DFunLike.coe ContinuousLinearMap Real Real.semiring RingHom.id Semiring.toNonAssocSemiring ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule Real.normedField ContinuousLinearMap.funLike ContinuousLinearMap.topologicalSpace SeminormedAddCommGroup.toAddCommGroup SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousLinearMap.addCommMonoid IsTopologicalAddGroup.toContinuousAdd NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup ContinuousLinearMap.module smulCommClass_self Real.instCommMonoid DistribMulAction.toMulAction CommMonoid.toMonoid AddCommMonoid.toAddMonoid Module.toDistribMulAction Ring.toSemiring CommRing.toRing Real.commRing UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero IsBoundedSMul.toUniformContinuousConstSMul Real.pseudoMetricSpace Real.instZero NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedAddCommGroup.toAddCommGroup NormedSpace.toIsBoundedSMul HasFDerivAt DenselyNormedField.toNontriviallyNormedField Real.denselyNormedField	MeasureTheory.integral NegZeroClass.toNeg	—	SeminormedAddCommGroup.toIsTopologicalAddGroup IsTopologicalAddGroup.toContinuousAdd smulCommClass_self UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable HasFDerivAt.hasLineDerivAt
integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable 📖	mathematical	MeasureTheory.Integrable UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup SeminormedAddGroup.toContinuousENorm SeminormedAddCommGroup.toSeminormedAddGroup DFunLike.coe ContinuousLinearMap Real Real.semiring RingHom.id Semiring.toNonAssocSemiring ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule Real.normedField ContinuousLinearMap.funLike ContinuousLinearMap.topologicalSpace SeminormedAddCommGroup.toAddCommGroup SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousLinearMap.addCommMonoid IsTopologicalAddGroup.toContinuousAdd NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup ContinuousLinearMap.module smulCommClass_self Real.instCommMonoid DistribMulAction.toMulAction CommMonoid.toMonoid AddCommMonoid.toAddMonoid Module.toDistribMulAction Ring.toSemiring CommRing.toRing Real.commRing UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero IsBoundedSMul.toUniformContinuousConstSMul Real.pseudoMetricSpace Real.instZero NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedAddCommGroup.toAddCommGroup NormedSpace.toIsBoundedSMul HasLineDerivAt DenselyNormedField.toNontriviallyNormedField Real.denselyNormedField	MeasureTheory.integral NegZeroClass.toNeg	—	SeminormedAddCommGroup.toIsTopologicalAddGroup IsTopologicalAddGroup.toContinuousAdd smulCommClass_self UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul eq_or_ne HasLineDerivAt.lineDeriv hasLineDerivAt_zero map_zero AddMonoidHomClass.toZeroHomClass DistribMulActionSemiHomClass.toAddMonoidHomClass SemilinearMapClass.distribMulActionSemiHomClass ContinuousSemilinearMapClass.toSemilinearMapClass ContinuousLinearMap.continuousSemilinearMapClass MeasureTheory.integral_zero neg_zero nontrivial_iff RingHomInvPair.ids Module.finrank_prod commRing_strongRankCondition Real.instNontrivial Module.Free.function Finite.of_fintype Module.Free.self FiniteDimensional.finiteDimensional_pi' FiniteDimensional.rclike_to_real Module.finrank_fintype_fun_eq_card Fintype.card_fin Module.finrank_self zero_add Module.finrank_pos Real.instIsDomain instIsTorsionFreeOfIsDomainOfNoZeroSMulDivisors GroupWithZero.toNoZeroSMulDivisors Prod.instIsTopologicalAddGroup Pi.topologicalAddGroup instIsTopologicalAddGroupReal Prod.continuousSMul instContinuousSMulForall IsModuleTopology.toContinuousSMul IsTopologicalSemiring.toIsModuleTopology IsTopologicalRing.toIsTopologicalSemiring instIsTopologicalRingReal IsBoundedSMul.continuousSMul Real.instCompleteSpace Prod.t2Space Pi.t2Space TopologicalSpace.t2Space_of_metrizableSpace EMetricSpace.metrizableSpace Module.instFiniteDimensionalOfIsReflexive Prod.instModuleIsReflexive Module.instIsReflexiveOfFiniteOfProjective Module.Projective.of_free SeparatingDual.exists_continuousLinearEquiv_apply_eq instSeparatingDualRealOfIsTopologicalAddGroupOfContinuousSMulOfLocallyConvexSpaceOfT1Space NormedSpace.toLocallyConvexSpace instT1SpaceProd instT1SpaceForall T5Space.toT1Space T6Space.toT5Space instT6SpaceOfMetrizableSpace EquivLike.toEmbeddingLike ContinuousSemilinearEquivClass.continuousSemilinearMapClass ContinuousLinearEquiv.continuousSemilinearEquivClass NeZero.charZero_one RCLike.charZero_rclike RingHomCompTriple.ids Homeomorph.measurableEmbedding Prod.borelSpace Pi.borelSpace instCountableFin instSecondCountableTopologyReal Real.borelSpace secondCountableTopologyEither_of_right integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable_aux2 ContinuousLinearEquiv.isAddHaarMeasure_map MeasurableEmbedding.integrable_map_iff ContinuousLinearEquiv.symm_apply_apply ContinuousLinearEquiv.apply_symm_apply HasLineDerivAt.of_comp MeasureTheory.Measure.map_map Continuous.measurable Prod.opensMeasurableSpace Pi.opensMeasurableSpace BorelSpace.opensMeasurable ContinuousLinearEquiv.continuous ContinuousLinearEquiv.symm_comp_self MeasureTheory.Measure.map_id Homeomorph.isClosedEmbedding Topology.IsClosedEmbedding.integral_map MeasureTheory.integral_def
integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable_aux1 📖	mathematical	MeasureTheory.Integrable UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup SeminormedAddGroup.toContinuousENorm SeminormedAddCommGroup.toSeminormedAddGroup Real Prod.instMeasurableSpace MeasureTheory.MeasureSpace.toMeasurableSpace Real.measureSpace DFunLike.coe ContinuousLinearMap Real.semiring RingHom.id Semiring.toNonAssocSemiring ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule Real.normedField ContinuousLinearMap.funLike ContinuousLinearMap.topologicalSpace SeminormedAddCommGroup.toAddCommGroup SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousLinearMap.addCommMonoid IsTopologicalAddGroup.toContinuousAdd NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup ContinuousLinearMap.module smulCommClass_self Real.instCommMonoid DistribMulAction.toMulAction CommMonoid.toMonoid AddCommMonoid.toAddMonoid Module.toDistribMulAction Ring.toSemiring CommRing.toRing Real.commRing UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero IsBoundedSMul.toUniformContinuousConstSMul Real.pseudoMetricSpace Real.instZero NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedAddCommGroup.toAddCommGroup NormedSpace.toIsBoundedSMul MeasureTheory.Measure.prod MeasureTheory.MeasureSpace.volume HasLineDerivAt DenselyNormedField.toNontriviallyNormedField Real.denselyNormedField Prod.instAddCommGroup Real.instAddCommGroup Prod.instModule DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField Real.instAddCommMonoid NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing Real.normedCommRing InnerProductSpace.toNormedSpace Real.instRCLike RCLike.toInnerProductSpaceReal Real.instOne	MeasureTheory.integral NegZeroClass.toNeg	—	SeminormedAddCommGroup.toIsTopologicalAddGroup IsTopologicalAddGroup.toContinuousAdd smulCommClass_self UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul MeasureTheory.integral_prod MeasureTheory.instSFiniteOfSigmaFinite MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite instIsAddHaarMeasureVolume FiniteDimensional.rclike_to_real Real.borelSpace SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace instIsTopologicalAddGroupReal TopologicalSpace.SecondCountableTopology.to_separableSpace instSecondCountableTopologyReal instWeaklyLocallyCompactSpaceOfLocallyCompactSpace locallyCompact_of_proper instProperSpaceReal MeasureTheory.integral_congr_ae Filter.mp_mem MeasureTheory.Measure.instOuterMeasureClass MeasureTheory.Integrable.prod_right_ae Filter.univ_mem' MeasureTheory.integral_bilinear_hasDerivAt_right_eq_neg_left_of_integrable IsBoundedSMul.continuousSMul smul_zero mul_one add_zero add_neg_cancel_comm_assoc one_smul HasDerivAt.scomp_of_eq IsScalarTower.left HasDerivAt.add hasDerivAt_id hasDerivAt_const add_neg_cancel MeasureTheory.integral_neg
integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable_aux2 📖	mathematical	MeasureTheory.Integrable UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup SeminormedAddGroup.toContinuousENorm SeminormedAddCommGroup.toSeminormedAddGroup Real Prod.instMeasurableSpace Real.measurableSpace DFunLike.coe ContinuousLinearMap Real.semiring RingHom.id Semiring.toNonAssocSemiring ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule Real.normedField ContinuousLinearMap.funLike ContinuousLinearMap.topologicalSpace SeminormedAddCommGroup.toAddCommGroup SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousLinearMap.addCommMonoid IsTopologicalAddGroup.toContinuousAdd NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup ContinuousLinearMap.module smulCommClass_self Real.instCommMonoid DistribMulAction.toMulAction CommMonoid.toMonoid AddCommMonoid.toAddMonoid Module.toDistribMulAction Ring.toSemiring CommRing.toRing Real.commRing UniformContinuousConstSMul.to_continuousConstSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero IsBoundedSMul.toUniformContinuousConstSMul Real.pseudoMetricSpace Real.instZero NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedAddCommGroup.toAddCommGroup NormedSpace.toIsBoundedSMul HasLineDerivAt DenselyNormedField.toNontriviallyNormedField Real.denselyNormedField Prod.instAddCommGroup Real.instAddCommGroup Prod.instModule DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField Real.instAddCommMonoid NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing Real.normedCommRing InnerProductSpace.toNormedSpace Real.instRCLike RCLike.toInnerProductSpaceReal Real.instOne	MeasureTheory.integral NegZeroClass.toNeg	—	SeminormedAddCommGroup.toIsTopologicalAddGroup IsTopologicalAddGroup.toContinuousAdd smulCommClass_self UniformContinuousConstSMul.to_continuousConstSMul IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul locallyCompact_of_proper FiniteDimensional.proper_real IsScalarTower.right Prod.instIsTopologicalAddGroup instIsTopologicalAddGroupReal Prod.borelSpace Real.borelSpace secondCountableTopologyEither_of_right instSecondCountableTopologyReal MeasureTheory.Measure.prod.instIsFiniteMeasureOnCompacts MeasureTheory.Measure.IsAddHaarMeasure.toIsFiniteMeasureOnCompacts MeasureTheory.Measure.isAddHaarMeasure_addHaarMeasure instIsAddHaarMeasureVolume FiniteDimensional.rclike_to_real MeasureTheory.Measure.prod.instIsAddLeftInvariant ContinuousAdd.measurableAdd MeasureTheory.Measure.isAddLeftInvariant_addHaarMeasure MeasureTheory.instSFiniteOfSigmaFinite MeasureTheory.Measure.sigmaFinite_addHaarMeasure secondCountable_of_proper IsTopologicalSemiring.toContinuousAdd IsTopologicalRing.toIsTopologicalSemiring instIsTopologicalRingReal MeasureTheory.Measure.IsAddHaarMeasure.toIsAddLeftInvariant MeasureTheory.Measure.IsAddHaarMeasure.sigmaFinite SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace TopologicalSpace.SecondCountableTopology.to_separableSpace instWeaklyLocallyCompactSpaceOfLocallyCompactSpace instProperSpaceReal MeasureTheory.Measure.isAddLeftInvariant_eq_smul Prod.locallyCompactSpace TopologicalSpace.instSecondCountableTopologyProd MeasureTheory.Integrable.smul_measure_nnreal MeasureTheory.Measure.prod.instIsAddHaarMeasure MeasureTheory.integral_smul_nnreal_measure integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable_aux1 smul_neg
integral_mul_fderiv_eq_neg_fderiv_mul_of_integrable 📖	mathematical	MeasureTheory.Integrable UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing SeminormedAddGroup.toContinuousENorm SeminormedAddCommGroup.toSeminormedAddGroup NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing DFunLike.coe ContinuousLinearMap Real DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField DenselyNormedField.toNontriviallyNormedField Real.denselyNormedField RingHom.id Semiring.toNonAssocSemiring SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup AddCommGroup.toAddCommMonoid NormedAddCommGroup.toAddCommGroup NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedSpace.toModule Real.normedField NormedAlgebra.toNormedSpace ContinuousLinearMap.funLike fderiv Differentiable	MeasureTheory.integral NegZeroClass.toNeg SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid	—	integral_bilinear_fderiv_right_eq_neg_left_of_integrable IsScalarTower.right Algebra.to_smulCommClass
integral_smul_fderiv_eq_neg_fderiv_smul_of_integrable 📖	mathematical	MeasureTheory.Integrable UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup SeminormedAddGroup.toContinuousENorm SeminormedAddCommGroup.toSeminormedAddGroup SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass ESeminormedAddMonoid.toAddMonoid ESeminormedAddCommMonoid.toESeminormedAddMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField Module.toDistribMulAction ESeminormedAddCommMonoid.toAddCommMonoid NormedSpace.toModule DFunLike.coe ContinuousLinearMap Real NontriviallyNormedField.toNormedField DenselyNormedField.toNontriviallyNormedField Real.denselyNormedField RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid NormedAddCommGroup.toAddCommGroup SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedCommRing.toSeminormedCommRing NormedField.toNormedCommRing NonUnitalNormedRing.toNormedAddCommGroup NonUnitalNormedCommRing.toNonUnitalNormedRing NormedCommRing.toNonUnitalNormedCommRing Real.normedField NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedAlgebra.toNormedSpace ContinuousLinearMap.funLike fderiv Differentiable	MeasureTheory.integral NegZeroClass.toNeg SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid	—	integral_bilinear_fderiv_right_eq_neg_left_of_integrable NormedSpace.toIsBoundedSMul

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