TangentCone

📁 Source: Mathlib/Analysis/RCLike/TangentCone.lean

Statistics

Metric	Count
Definitions	0
Theorems of_real, of_real, tangentConeAt_real_subset_isRCLikeNormedField, uniqueDiffOn_convex_of_isRCLikeNormedField, uniqueDiffWithinAt_convex_of_isRCLikeNormedField	5
Total	5

UniqueDiffOn

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
of_real 📖	mathematical	UniqueDiffOn Real Real.semiring NormedAddCommGroup.toAddCommGroup NormedSpace.toModule Real.normedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace	DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField	—	UniqueDiffWithinAt.of_real

UniqueDiffWithinAt

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
of_real 📖	mathematical	UniqueDiffWithinAt Real Real.semiring NormedAddCommGroup.toAddCommGroup NormedSpace.toModule Real.normedField NormedAddCommGroup.toSeminormedAddCommGroup UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace	DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField	—	mono_field Real.isScalarTower IsBoundedSMul.continuousSMul NormedSpace.toIsBoundedSMul TopologicalSpace.t2Space_of_metrizableSpace EMetricSpace.metrizableSpace

(root)

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
tangentConeAt_real_subset_isRCLikeNormedField 📖	mathematical	—	Set Set.instHasSubset tangentConeAt Real NormedAddCommGroup.toAddCommGroup SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass ESeminormedAddMonoid.toAddMonoid UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ESeminormedAddCommMonoid.toESeminormedAddMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul Real.instMonoid Module.toDistribMulAction Real.semiring ESeminormedAddCommMonoid.toAddCommMonoid NormedSpace.toModule Real.normedField MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField	—	tangentConeAt_mono_field Real.isScalarTower IsBoundedSMul.continuousSMul NormedSpace.toIsBoundedSMul TopologicalSpace.t2Space_of_metrizableSpace EMetricSpace.metrizableSpace
uniqueDiffOn_convex_of_isRCLikeNormedField 📖	mathematical	Convex Real Real.semiring Real.partialOrder ESeminormedAddCommMonoid.toAddCommMonoid UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass ESeminormedAddMonoid.toAddMonoid ESeminormedAddCommMonoid.toESeminormedAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul Real.instMonoid Module.toDistribMulAction NormedSpace.toModule Real.normedField Set.Nonempty interior	UniqueDiffOn DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField NormedAddCommGroup.toAddCommGroup	—	UniqueDiffOn.of_real uniqueDiffOn_convex IsBoundedSMul.continuousSMul NormedSpace.toIsBoundedSMul SeminormedAddCommGroup.toIsTopologicalAddGroup
uniqueDiffWithinAt_convex_of_isRCLikeNormedField 📖	mathematical	Convex Real Real.semiring Real.partialOrder ESeminormedAddCommMonoid.toAddCommMonoid UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass ESeminormedAddMonoid.toAddMonoid ESeminormedAddCommMonoid.toESeminormedAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul Real.instMonoid Module.toDistribMulAction NormedSpace.toModule Real.normedField Set.Nonempty interior Set Set.instMembership closure	UniqueDiffWithinAt DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield NormedField.toField NontriviallyNormedField.toNormedField NormedAddCommGroup.toAddCommGroup	—	UniqueDiffWithinAt.of_real uniqueDiffWithinAt_convex IsBoundedSMul.continuousSMul NormedSpace.toIsBoundedSMul SeminormedAddCommGroup.toIsTopologicalAddGroup

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