Rolle

📁 Source: Mathlib/Analysis/Calculus/LocalExtr/Rolle.lean

Statistics

Metric	Count
Definitions	0
Theorems exists_deriv_eq_zero, exists_deriv_eq_zero', exists_hasDerivAt_eq_zero, exists_hasDerivAt_eq_zero'	4
Total	4

(root)

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
exists_deriv_eq_zero 📖	mathematical	Real Real.instLT ContinuousOn UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real.pseudoMetricSpace Set.Icc Real.instPreorder	Set Set.instMembership Set.Ioo deriv DenselyNormedField.toNontriviallyNormedField Real.denselyNormedField Real.instAddCommGroup NormedSpace.toModule Real.normedField NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing Real.normedCommRing NormedField.toNormedSpace Real.instZero	—	exists_isLocalExtr_Ioo LinearOrderedSemiField.toDenselyOrdered PosMulReflectLE.toPosMulReflectLT PosMulStrictMono.toPosMulReflectLE IsStrictOrderedRing.toPosMulStrictMono Real.instIsStrictOrderedRing instOrderTopologyReal IsLocalExtr.deriv_eq_zero
exists_deriv_eq_zero' 📖	mathematical	Real Real.instLT Filter.Tendsto nhdsWithin UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real.pseudoMetricSpace Set.Ioi Real.instPreorder nhds Set.Iio	Set Set.instMembership Set.Ioo deriv DenselyNormedField.toNontriviallyNormedField Real.denselyNormedField Real.instAddCommGroup NormedSpace.toModule Real.normedField NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing Real.normedCommRing NormedField.toNormedSpace Real.instZero	—	exists_hasDerivAt_eq_zero' DifferentiableAt.hasDerivAt Mathlib.Tactic.Push.not_forall_eq deriv_zero_of_not_differentiableAt
exists_hasDerivAt_eq_zero 📖	mathematical	Real Real.instLT ContinuousOn UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real.pseudoMetricSpace Set.Icc Real.instPreorder HasDerivAt DenselyNormedField.toNontriviallyNormedField Real.denselyNormedField Real.instAddCommGroup NormedSpace.toModule Real.normedField NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing Real.normedCommRing NormedField.toNormedSpace ContinuousMul.to_continuousSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedField.toNormedCommRing NontriviallyNormedField.toNormedField MulZeroClass.toMul MulZeroOneClass.toMulZeroClass MonoidWithZero.toMulZeroOneClass Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField IsTopologicalSemiring.toContinuousMul NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring IsTopologicalRing.toIsTopologicalSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing instIsTopologicalRingReal	Set Set.instMembership Set.Ioo Real.instZero	—	ContinuousMul.to_continuousSMul IsTopologicalSemiring.toContinuousMul IsTopologicalRing.toIsTopologicalSemiring instIsTopologicalRingReal exists_isLocalExtr_Ioo LinearOrderedSemiField.toDenselyOrdered PosMulReflectLE.toPosMulReflectLT PosMulStrictMono.toPosMulReflectLE IsStrictOrderedRing.toPosMulStrictMono Real.instIsStrictOrderedRing instOrderTopologyReal IsLocalExtr.hasDerivAt_eq_zero
exists_hasDerivAt_eq_zero' 📖	mathematical	Real Real.instLT Filter.Tendsto nhdsWithin UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real.pseudoMetricSpace Set.Ioi Real.instPreorder nhds Set.Iio HasDerivAt DenselyNormedField.toNontriviallyNormedField Real.denselyNormedField Real.instAddCommGroup NormedSpace.toModule Real.normedField NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing Real.normedCommRing NormedField.toNormedSpace ContinuousMul.to_continuousSMul SeminormedRing.toPseudoMetricSpace SeminormedCommRing.toSeminormedRing NormedField.toNormedCommRing NontriviallyNormedField.toNormedField MulZeroClass.toMul MulZeroOneClass.toMulZeroClass MonoidWithZero.toMulZeroOneClass Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField IsTopologicalSemiring.toContinuousMul NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring IsTopologicalRing.toIsTopologicalSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing instIsTopologicalRingReal	Set Set.instMembership Set.Ioo Real.instZero	—	ContinuousMul.to_continuousSMul IsTopologicalSemiring.toContinuousMul IsTopologicalRing.toIsTopologicalSemiring instIsTopologicalRingReal exists_isLocalExtr_Ioo_of_tendsto LinearOrderedSemiField.toDenselyOrdered PosMulReflectLE.toPosMulReflectLT PosMulStrictMono.toPosMulReflectLE IsStrictOrderedRing.toPosMulStrictMono Real.instIsStrictOrderedRing instOrderTopologyReal ContinuousAt.continuousWithinAt HasDerivAt.continuousAt IsLocalExtr.hasDerivAt_eq_zero

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