Documentation Verification Report

Defs

πŸ“ Source: Mathlib/Geometry/Manifold/ContMDiff/Defs.lean

Statistics

MetricCount
DefinitionsContDiffWithinAtProp, ContMDiff, ContMDiffAt, ContMDiffOn, ContMDiffWithinAt
5
TheoremscontMDiffAt, contMDiffOn, continuous, of_le, of_succ, congr_of_eventuallyEq, contMDiffWithinAt, continuousAt, of_le, of_succ, congr_mono, contMDiffAt, continuousOn, mono, of_le, of_succ, congr', congr_of_eventuallyEq, congr_of_eventuallyEq_of_mem, congr_of_mem, congr_set, contMDiffAt, contMDiffOn, contMDiffOn', continuousWithinAt, insert, mono, mono_of_mem_nhdsWithin, of_insert, of_le, of_succ, contMDiffAt_iff, contMDiffWithinAt_iff, contDiffWithinAtProp_id, contDiffWithinAtProp_mono_of_mem_nhdsWithin, contDiffWithinAtProp_self, contDiffWithinAtProp_self_source, contDiffWithinAtProp_self_target, contDiffWithinAt_localInvariantProp, contDiffWithinAt_localInvariantProp_of_le, contMDiffAt_iff, contMDiffAt_iff_contMDiffAt_nhds, contMDiffAt_iff_contMDiffOn_nhds, contMDiffAt_iff_le_ne_infty, contMDiffAt_iff_nat, contMDiffAt_iff_of_mem_source, contMDiffAt_iff_source, contMDiffAt_iff_source_of_mem_source, contMDiffAt_iff_target, contMDiffAt_iff_target_of_mem_source, contMDiffAt_infty, contMDiffOn_congr, contMDiffOn_empty, contMDiffOn_iff, contMDiffOn_iff_of_mem_maximalAtlas, contMDiffOn_iff_of_mem_maximalAtlas', contMDiffOn_iff_of_subset_source, contMDiffOn_iff_of_subset_source', contMDiffOn_iff_source_of_mem_maximalAtlas, contMDiffOn_iff_target, contMDiffOn_infty, contMDiffOn_of_locally_contMDiffOn, contMDiffOn_univ, contMDiffOn_zero_iff, contMDiffWithinAt_congr, contMDiffWithinAt_congr_of_mem, contMDiffWithinAt_congr_set, contMDiffWithinAt_congr_set', contMDiffWithinAt_iff, contMDiffWithinAt_iff', contMDiffWithinAt_iff_contMDiffOn_nhds, contMDiffWithinAt_iff_contMDiffWithinAt_nhdsWithin, contMDiffWithinAt_iff_image, contMDiffWithinAt_iff_le_ne_infty, contMDiffWithinAt_iff_nat, contMDiffWithinAt_iff_of_mem_maximalAtlas, contMDiffWithinAt_iff_of_mem_source, contMDiffWithinAt_iff_of_mem_source', contMDiffWithinAt_iff_source, contMDiffWithinAt_iff_source_of_mem_maximalAtlas, contMDiffWithinAt_iff_source_of_mem_source, contMDiffWithinAt_iff_target, contMDiffWithinAt_iff_target_of_mem_source, contMDiffWithinAt_infty, contMDiffWithinAt_insert_self, contMDiffWithinAt_inter, contMDiffWithinAt_inter', contMDiffWithinAt_univ, contMDiff_congr, contMDiff_iff, contMDiff_iff_target, contMDiff_infty, contMDiff_of_locally_contMDiffOn, contMDiff_zero_iff
94
Total99

ContMDiff

Theorems

NameKindAssumesProvesValidatesDepends On
contMDiffAt πŸ“–mathematicalContMDiffContMDiffAtβ€”β€”
contMDiffOn πŸ“–mathematicalContMDiffContMDiffOnβ€”ContMDiffAt.contMDiffWithinAt
continuous πŸ“–mathematicalContMDiffContinuousβ€”continuous_iff_continuousAt
ContMDiffAt.continuousAt
of_le πŸ“–mathematicalContMDiff
WithTop
ENat
Preorder.toLE
WithTop.instPreorder
instPreorderENat
ContMDiffβ€”ContMDiffAt.of_le
of_succ πŸ“–mathematicalContMDiff
WithTop
ENat
WithTop.add
instAddENat
WithTop.one
AddMonoidWithOne.toOne
instAddMonoidWithOneENat
ContMDiffβ€”ContMDiffAt.of_succ

ContMDiffAt

Theorems

NameKindAssumesProvesValidatesDepends On
congr_of_eventuallyEq πŸ“–mathematicalContMDiffAt
Filter.EventuallyEq
nhds
ContMDiffAtβ€”StructureGroupoid.LocalInvariantProp.liftPropAt_congr_of_eventuallyEq
contDiffWithinAt_localInvariantProp
contMDiffWithinAt πŸ“–mathematicalContMDiffAtContMDiffWithinAtβ€”ContMDiffWithinAt.mono
Set.subset_univ
continuousAt πŸ“–mathematicalContMDiffAtContinuousAtβ€”continuousWithinAt_univ
ContMDiffWithinAt.continuousWithinAt
of_le πŸ“–mathematicalContMDiffAt
WithTop
ENat
Preorder.toLE
WithTop.instPreorder
instPreorderENat
ContMDiffAtβ€”ContMDiffWithinAt.of_le
of_succ πŸ“–mathematicalContMDiffAt
WithTop
ENat
WithTop.add
instAddENat
WithTop.one
AddMonoidWithOne.toOne
instAddMonoidWithOneENat
ContMDiffAtβ€”ContMDiffWithinAt.of_succ

ContMDiffOn

Theorems

NameKindAssumesProvesValidatesDepends On
congr_mono πŸ“–mathematicalContMDiffOn
Set
Set.instHasSubset
ContMDiffOnβ€”congr
mono
contMDiffAt πŸ“–mathematicalContMDiffOn
Set
Filter
Filter.instMembership
nhds
ContMDiffAtβ€”ContMDiffWithinAt.contMDiffAt
mem_of_mem_nhds
continuousOn πŸ“–mathematicalContMDiffOnContinuousOnβ€”ContMDiffWithinAt.continuousWithinAt
mono πŸ“–mathematicalContMDiffOn
Set
Set.instHasSubset
ContMDiffOnβ€”ContMDiffWithinAt.mono
of_le πŸ“–mathematicalContMDiffOn
WithTop
ENat
Preorder.toLE
WithTop.instPreorder
instPreorderENat
ContMDiffOnβ€”ContMDiffWithinAt.of_le
of_succ πŸ“–mathematicalContMDiffOn
WithTop
ENat
WithTop.add
instAddENat
WithTop.one
AddMonoidWithOne.toOne
instAddMonoidWithOneENat
ContMDiffOnβ€”ContMDiffWithinAt.of_succ

ContMDiffWithinAt

Theorems

NameKindAssumesProvesValidatesDepends On
congr' πŸ“–mathematicalContMDiffWithinAt
Set
Set.instHasSubset
Set.instMembership
ContMDiffWithinAtβ€”congr
congr_of_eventuallyEq πŸ“–mathematicalContMDiffWithinAt
Filter.EventuallyEq
nhdsWithin
ContMDiffWithinAtβ€”StructureGroupoid.LocalInvariantProp.liftPropWithinAt_congr_of_eventuallyEq
contDiffWithinAt_localInvariantProp
congr_of_eventuallyEq_of_mem πŸ“–mathematicalContMDiffWithinAt
Filter.EventuallyEq
nhdsWithin
Set
Set.instMembership
ContMDiffWithinAtβ€”StructureGroupoid.LocalInvariantProp.liftPropWithinAt_congr_of_eventuallyEq_of_mem
contDiffWithinAt_localInvariantProp
congr_of_mem πŸ“–mathematicalContMDiffWithinAt
Set
Set.instMembership
ContMDiffWithinAtβ€”StructureGroupoid.LocalInvariantProp.liftPropWithinAt_congr_of_mem
contDiffWithinAt_localInvariantProp
congr_set πŸ“–mathematicalContMDiffWithinAt
Filter.EventuallyEq
nhds
ContMDiffWithinAtβ€”contMDiffWithinAt_congr_set
contMDiffAt πŸ“–mathematicalContMDiffWithinAt
Set
Filter
Filter.instMembership
nhds
ContMDiffAtβ€”StructureGroupoid.LocalInvariantProp.liftPropAt_of_liftPropWithinAt
contDiffWithinAt_localInvariantProp
contMDiffOn πŸ“–mathematicalWithTop
ENat
Preorder.toLE
WithTop.instPreorder
instPreorderENat
Top.top
WithTop.top
ContMDiffWithinAt
Set
Filter
Filter.instMembership
nhdsWithin
Set.instInsert
Set.instHasSubset
ContMDiffOn
β€”contMDiffOn'
inter_mem_nhdsWithin
IsOpen.mem_nhds
Set.inter_subset_left
contMDiffOn' πŸ“–mathematicalWithTop
ENat
Preorder.toLE
WithTop.instPreorder
instPreorderENat
Top.top
WithTop.top
ContMDiffWithinAt
Set
IsOpen
Set.instMembership
ContMDiffOn
Set.instInter
Set.instInsert
β€”IsManifold.of_le
contMDiffWithinAt_iff_contMDiffOn_nhds
of_le
mem_nhdsWithin
ContMDiffOn.mono
Set.inter_comm
ContMDiffOn.of_le
continuousWithinAt πŸ“–mathematicalContMDiffWithinAtContinuousWithinAtβ€”ChartedSpace.LiftPropWithinAt.continuousWithinAt
insert πŸ“–mathematicalContMDiffWithinAtContMDiffWithinAt
Set
Set.instInsert
β€”contMDiffWithinAt_insert_self
mono πŸ“–mathematicalContMDiffWithinAt
Set
Set.instHasSubset
ContMDiffWithinAtβ€”mono_of_mem_nhdsWithin
Filter.mem_of_superset
self_mem_nhdsWithin
mono_of_mem_nhdsWithin πŸ“–mathematicalContMDiffWithinAt
Set
Filter
Filter.instMembership
nhdsWithin
ContMDiffWithinAtβ€”StructureGroupoid.LocalInvariantProp.liftPropWithinAt_mono_of_mem_nhdsWithin
contDiffWithinAtProp_mono_of_mem_nhdsWithin
of_insert πŸ“–mathematicalContMDiffWithinAt
Set
Set.instInsert
ContMDiffWithinAtβ€”contMDiffWithinAt_insert_self
of_le πŸ“–mathematicalContMDiffWithinAt
WithTop
ENat
Preorder.toLE
WithTop.instPreorder
instPreorderENat
ContMDiffWithinAtβ€”ChartedSpace.LiftPropWithinAt.continuousWithinAt
ContDiffWithinAt.of_le
ChartedSpace.LiftPropWithinAt.prop
of_succ πŸ“–mathematicalContMDiffWithinAt
WithTop
ENat
WithTop.add
instAddENat
WithTop.one
AddMonoidWithOne.toOne
instAddMonoidWithOneENat
ContMDiffWithinAtβ€”of_le
le_self_add
WithTop.canonicallyOrderedAdd

Filter.EventuallyEq

Theorems

NameKindAssumesProvesValidatesDepends On
contMDiffAt_iff πŸ“–mathematicalFilter.EventuallyEq
nhds
ContMDiffAtβ€”StructureGroupoid.LocalInvariantProp.liftPropAt_congr_iff_of_eventuallyEq
contDiffWithinAt_localInvariantProp
contMDiffWithinAt_iff πŸ“–mathematicalFilter.EventuallyEq
nhdsWithin
ContMDiffWithinAtβ€”StructureGroupoid.LocalInvariantProp.liftPropWithinAt_congr_iff_of_eventuallyEq
contDiffWithinAt_localInvariantProp

(root)

Definitions

NameCategoryTheorems
ContDiffWithinAtProp πŸ“–MathDef
11 mathmath: contDiffWithinAtProp_self, smoothSheafCommRing.eval_germ, contDiffWithinAtProp_id, smoothSheafCommRing.evalHom_germ, contDiffWithinAtProp_self_source, contDiffWithinAt_localInvariantProp, contDiffWithinAt_localInvariantProp_of_le, contDiffWithinAtProp_mono_of_mem_nhdsWithin, contDiffWithinAtProp_self_target, smoothSheaf.eval_germ, smoothSheaf.contMDiff_section
ContMDiff πŸ“–MathDef
181 mathmath: contMDiff_prod_assoc, contMDiff_congr, Bundle.ContMDiffRiemannianMetric.contMDiff, ContMDiff.divβ‚€, ContMDiff.comp, contMDiff_finprod, ContMDiff.of_comp_isOpenEmbedding, contMDiff_finset_prod', contMDiff_addInvariantVectorField, contMDiff_neg_sphere, ContMDiff.sub_const, SmoothBumpCovering.exists_immersion_euclidean, IsOpen.exists_msmooth_support_eq, ContMDiffMul.contMDiff_mul, ContMDiff.of_succ, ContMDiff.clm_apply, contMDiff_mul, contMDiff_mulInvariantVectorField, ContMDiff.along_snd, contMDiff_sum_map, contMDiff_equivTangentBundleProd_symm, contMDiff_finprod_cond, contMDiff_add_right, contMDiff_inclusion, ContinuousLinearMap.contMDiff, contMDiff_finset_prod, contMDiff_mul_right, contMDiff_infty, ContMDiffMonoidMorphism.contMDiff_toFun, ContMDiff.coordChange, contMDiff_pow, ContMDiffAdd.contMDiff_add, contMDiff_of_contMDiff_inl, ContMDiff.smul, Diffeomorph.contMDiff_comp_diffeomorph_iff, ContMDiff.inr, Diffeomorph.contMDiff_toFun, contMDiff_mul_left, ContMDiff.sum_section_of_locallyFinite, ContMDiff.contMDiff_tangentMap, ContMDiff.piecewise_Iic, UpperHalfPlane.contMDiff_coe, contMDiff_coe_sphere, IsOpen.exists_contMDiff_support_eq_aux, ContMDiff.inv, contMDiff_isOpenEmbedding, contMDiff_model, ContMDiff.mul, UpperHalfPlane.contMDiff_inv_denom, ContMDiff.sumMap, contMDiff_of_discreteTopology, ContMDiff.nsmul, BumpCovering.contMDiff_toPartitionOfUnity, contMDiff_zero_iff, ContMDiff.inl, ContMDiff.congr, contMDiff_vectorSpace_iff_contDiff, ContDiff.comp_contMDiff, IsLocalDiffeomorph.contMDiff, ContMDiff.div, IsContMDiffRiemannianBundle.exists_contMDiff, contMDiff_snd, contMDiff_subtype_coe_Icc, contMDiff_const, contMDiff_iff_contDiff, contMDiff_iff_target, ContMDiff.fst, UpperHalfPlane.contMDiff_num, ContMDiffMap.contMDiff, ContMDiff.swap, ContMDiff.pow, contMDiff_of_tsupport, IsOpen.exists_contMDiff_support_eq, contMDiff_finsum_cond, contMDiff_smul, contMDiff_of_contMDiffOn_union_of_isOpen, contMDiff_neg, contMDiff_of_mulTSupport, ContMDiffOn.comp_contMDiff, ContMDiff.add, exists_msmooth_support_eq_eq_one_iff, LieGroup.contMDiff_inv, exists_msmooth_zero_iff_one_iff_of_isClosed, ContMDiff.extend_zero, ContMDiffRing.contMDiff_mul, contMDiff_prod_iff, ContDiff.contMDiff, contMDiff_of_contMDiff_inr, ContMDiff.finsum_section_of_locallyFinite, Manifold.riemannianEDist_def, contMDiff_one, ContMDiff.sub, UpperHalfPlane.contMDiff_denom_zpow, ContMDiff.clm_bundle_apply, ContMDiff.invβ‚€, ContMDiff.clm_bundle_applyβ‚‚, IsOpen.exists_msmooth_support_eq_aux, exists_contMDiff_zero_iff_one_iff_of_isClosed, SmoothBumpFunction.contMDiff_smul, Bundle.contMDiff_proj, Diffeomorph.contMDiff_invFun, LieAddGroup.contMDiff_neg, contMDiff_inv, ContinuousLinearEquiv.contMDiff_transContinuousLinearEquiv_right, contMDiff_iff, ContMDiff.sumElim, ContMDiff.neg_section, ContMDiffAddMonoidMorphism.contMDiff_toFun, contMDiff_finsum, Bundle.Trivialization.contMDiff_iff, contMDiff_of_contMDiffOn_iUnion_of_isOpen, Bundle.contMDiff_zeroSection, ContDiff.mlieBracket_vectorField, contMDiff_prod_module_iff, contMDiffOn_univ, ContMDiff.clm_postcomp, ContMDiff.inner_bundle, contMDiff_id, ContMDiff.clm_prodMap, exists_contMDiff_support_eq_eq_one_iff, ContMDiffSection.contMDiff, contMDiff_equivTangentBundleProd, ContMDiff.piecewise, SmoothPartitionOfUnity.contMDiff_finsum_smul, contMDiff_zero, contMDiff_finset_sum, ContMDiff.iterate, ContMDiff.of_le, contMDiffOn_comp_projIcc_iff, SmoothBumpFunction.contMDiff, smoothSheaf.contMDiff_section, contMDiff_add, contMDiff_of_locally_contMDiffOn, exists_embedding_euclidean_of_compact, ContinuousLinearEquiv.contMDiff_transContinuousLinearEquiv_left, ContMDiff.sub_section, Units.contMDiff_val, contMDiff_tangentBundleModelSpaceHomeomorph, ContMDiffOn.smul_section_of_tsupport, ContMDiff.div_const, contMDiff_pi_space, contMDiff_nsmul, Diffeomorph.contMDiff_diffeomorph_comp_iff, ContMDiff.extend_one, ContMDiff.clm_comp, contMDiff_tangentBundleModelSpaceHomeomorph_symm, ContMDiff.snd, contMDiff_of_subsingleton, ContMDiff.clm_precomp, ContMDiff.add_section, Diffeomorph.contMDiff, ContMDiff.codRestrict_sphere, ContMDiff.curry_right, SmoothPartitionOfUnity.contMDiff_smul, ContMDiffMap.coeFn_mk, ContMDiff.prodMk_space, ContMDiff.prod, ContMDiff.const_smul_section, UpperHalfPlane.contMDiff_smul, UpperHalfPlane.contMDiff_denom, ContMDiffSection.contMDiff_toFun, SmoothPartitionOfUnity.IsSubordinate.contMDiff_finsum_smul, ContMDiff.neg, contMDiff_finset_sum', contMDiff_fst, Manifold.exists_lt_locally_constant_of_riemannianEDist_lt, ContMDiff.sum_section, ContMDiff.prodMap, contMDiff_snd_tangentBundle_modelSpace, ContMDiff.sum, contMDiff_subtype_val, ContMDiff.cle_arrowCongr, ContMDiff.mpullback_vectorField, ContMDiff.coordChangeL, SmoothPartitionOfUnity.contMDiff_sum, contMDiff_add_left, ContMDiff.smul_section, contMDiff_circleExp, ContMDiff.along_fst, ContMDiff.curry_left, ContMDiff.prodMk
ContMDiffAt πŸ“–MathDef
138 mathmath: ContMDiffAt.coordChangeL, contMDiffAt_add_right, ContMDiffAt.inv, ContMDiffAt.compβ‚‚, contMDiffAt_extend, ContinuousLinearEquiv.contMDiffAt_transContinuousLinearEquiv_right, contMDiffAt_iff_of_mem_source, contMDiffAt_finset_prod, ContDiffAt.contMDiffAt, contMDiffAt_iff_source, SmoothPartitionOfUnity.contMDiffAt_finsum, contMDiffAt_iff_le_ne_infty, ContMDiffAt.finsum_section_of_locallyFinite, IsLocalFrameOn.contMDiffAt_of_coeff, ContMDiffAt.div_const, ContMDiffAt.clm_postcomp, ContMDiffAt.add_section, ContMDiffAt.mfderiv_apply, ContMDiffAt.divβ‚€, Bundle.contMDiffAt_zeroSection, contMDiffAt_mulInvariantVectorField, contMDiffAt_add_left, contMDiffAt_const, ContMDiffAt.smul, ContinuousLinearEquiv.contMDiffAt_transContinuousLinearEquiv_left, ContMDiffAt.prodMap, contMDiffAt_iff_source_of_mem_source, ContMDiffAt.curry_left, ContMDiffAt.const_smul_section, ContMDiffWithinAt.contMDiffAt, ContMDiffAt.mfderiv_const, ContMDiffAt.clm_apply_of_inCoordinates, contMDiffAt_iff_contMDiffOn_nhds, ContMDiffAt.compβ‚‚_of_eq, SmoothBumpFunction.contMDiffAt, contMDiffAt_finprod, ContMDiffAt.clm_bundle_apply, contMDiffAt_prod_iff, contMDiffAt_coordChangeL, ContMDiffAt.of_succ, ContMDiffAt.prodMk_space, ContMDiffInvβ‚€.contMDiffAt_invβ‚€, ContMDiffAt.snd, ContMDiffAt.prod, Diffeomorph.contMDiffAt_diffeomorph_comp_iff, contMDiffAt_iff, ContMDiffAt.neg, ContDiffAt.comp_contMDiffAt, ContMDiffAt.pow, ContMDiffAt.div, contMDiffAt_of_notMem, ContMDiffAt.of_le, ContMDiffAt.along_fst, ContMDiffAt.along_snd, contMDiffAt_iff_contMDiffAt_nhds, IsLocalFrameOn.contMDiffAt, contMDiffAt_hom_bundle, ContMDiffAt.invβ‚€, ContMDiffAt.mlieBracket_vectorField, ContMDiffAt.clm_precomp, contMDiffAt_id, contMDiffAt_localFrame_coeff, contMDiffAt_finset_sum, contMDiffAt_one, Bundle.contMDiffAt_totalSpace, ContMDiffAt.comp_of_eq, ContMDiffAt.congr_of_eventuallyEq, Diffeomorph.contMDiffAt_comp_diffeomorph_iff, contMDiffWithinAt_comp_projIcc_iff, contMDiffAt_iff_nat, Filter.EventuallyEq.contMDiffAt_iff, FiberBundle.contMDiffAt_extend', ContMDiffAt.nsmul, contMDiffAt_iff_target_of_mem_source, IsLocalDiffeomorphAt.localInverse_contMDiffAt, contMDiffAt_vectorSpace_iff_contDiffAt, ContMDiffAt.clm_prodMap, ContMDiffAt.curry_right, contMDiffAt_extChartAt, ContMDiffOn.contMDiffAt, contMDiffAt_symm_of_mem_maximalAtlas, ContMDiffAt.sum, contMDiffAt_localFrame_of_mem, Bundle.Trivialization.contMDiffAt_section_iff, Diffeomorph.contMDiffAt, ContMDiffAt.sub_section, ContMDiffAt.inner_bundle, contMDiffAt_subtype_iff, Bundle.Trivialization.contMDiffAt_iff, Bundle.contMDiffAt_section, ContMDiffAt.fst, ContMDiffAt.clm_bundle_applyβ‚‚, contMDiffAt_iff_localFrame_coeff, contMDiffAt_prod_module_iff, contMDiffWithinAt_univ, ContMDiffAt.prodMap', UpperHalfPlane.contMDiffAt_ofComplex, ContMDiffAt.sum_section_of_locallyFinite, ContMDiffAt.mfderiv, UpperHalfPlane.contMDiffAt_iff, contMDiffAt_of_mem_maximalAtlas, ContMDiffAt.prodMk, Bundle.contMDiffAt_proj, contMDiffAt_addInvariantVectorField, ContMDiffAt.sub, ContMDiffAt.mpullback_vectorField_preimage, contMDiffAt_extChartAt', ContMDiffAt.clm_apply, contMDiffAt_infty, ContMDiff.contMDiffAt, contMDiffAt_mul_right, contMDiffAt_of_subsingleton, ContMDiffAt.coordChange, contMDiffAt_mul_left, contMDiffAt_finsum, contMDiffAt_fst, contMDiffAt_finset_prod', contMDiffAt_invβ‚€, ContMDiffAt.sum_section, ContMDiffAt.sub_const, ContMDiffAt.comp, contMDiffAt_pi_space, contMDiffAt_iff_target, ContMDiffAt.smul_section, contMDiffAt_finset_sum', ContMDiffAt.clm_comp, IsLocalDiffeomorphAt.contMDiffAt, ContMDiffAt.neg_section, IsLocalFrameOn.contMDiffAt_of_coeff_aux, ContMDiffAt.cle_arrowCongr, ContinuousLinearMap.contMDiffAt, contMDiffAt_iff_contDiffAt, ContMDiffAt.add, contMDiffAt_snd, ContDiff.comp_contMDiffAt, ContMDiffAt.mul, contMDiffAt_zero, contMDiffAt_of_notMem_mulTSupport
ContMDiffOn πŸ“–MathDef
151 mathmath: contMDiffOn_of_subsingleton, Bundle.contMDiffOn_zeroSection, contMDiffOn_finsum, Diffeomorph.contMDiffOn_comp_diffeomorph_iff, ContMDiffOn.prodMk, ContMDiffOn.mlieBracketWithin_vectorField, PartialDiffeomorph.contMDiffOn, ContMDiffOn.of_succ, contMDiffOn_chart, Bundle.Trivialization.contMDiffOn_section_baseSet_iff, ContMDiffOn.clm_postcomp, Bundle.Trivialization.contMDiffOn, contMDiffOn_of_locally_contMDiffOn, contMDiffOn_localFrame_coeff, OpenPartialHomeomorph.contMDiffOn_writtenInExtend_iff, VectorBundleCore.contMDiffOn_coordChange, contMDiffOn_chart_symm, contMDiffOn_baseSet_iff_localFrame_coeff, PartialDiffeomorph.contMDiffOn_toFun, contMDiffOn_isOpenEmbedding_symm, contMDiffOn_finset_prod, contMDiffOn_invβ‚€, ContMDiffOn.of_le, contMDiffOn_iff_contDiffOn, contMDiffOn_finset_sum, ContDiffOn.contMDiffOn, ContMDiffFiberwiseLinear.locality_auxβ‚‚, ContMDiffOn.finsum_section_of_locallyFinite, ContMDiffOn.clm_precomp, ContMDiffOn.coordChangeL, IsLocalDiffeomorphAt.localInverse_contMDiffOn, contMDiffOn_pi_space, ContMDiffOn.mul, ContMDiffOn.mpullbackWithin_vectorField_inter, contMDiffAt_iff_contMDiffOn_nhds, FiberBundle.exists_contMDiffOn_extend, ContMDiffOn.cle_arrowCongr, Bundle.Trivialization.contMDiffOn_localFrame_baseSet, contMDiffOn_zero, ContMDiffOn.along_snd, ContMDiffOn.curry_right, contMDiff_iff_target, ContMDiffOn.clm_comp, contMDiffOn_extChartAt, ContMDiff.contMDiffOn, contMDiffOn_baseSet_localFrame_coeff, contMDiffOn_finset_prod', ContMDiffOn.div, contMDiffOn_iff_of_mem_maximalAtlas', contMDiffOn_continuousLinearMapCoordChange, contMDiffOn_extChartAt_symm, IsLocalFrameOn.contMDiffOn, IsLocalDiffeomorphAt.contmdiffOn_localInverse, IsLocalDiffeomorphOn.contMDiffOn, contMDiffOn_iff_of_subset_source', ContMDiffOn.prodMk_space, isLocalStructomorphOn_contDiffGroupoid_iff, contMDiffWithinAt_iff_contMDiffOn_nhds, contMDiffOn_iUnion_iff_of_isOpen, contMDiffOn_of_mem_contDiffGroupoid, contMDiffOn_symm_coordChangeL, ContMDiffOn.prodMap, ContMDiffOn.add_section, ContMDiffOn.inner_bundle, ContMDiff.comp_contMDiffOn, ContMDiffOn.clm_apply, contMDiffOn_finset_sum', ContMDiffOn.curry_left, Diffeomorph.contMDiffOn_diffeomorph_comp_iff, ContMDiffOn.iterate, ContMDiffOn.sub_const, ContMDiffOn.mono, Bundle.contMDiffOn_proj, contMDiffOn_fst, contMDiffOn_prod_iff, contMDiffOn_iff, contMDiffOn_iff_source_of_mem_maximalAtlas, ContMDiffWithinAt.contMDiffOn', ContMDiffOn.comp', contMDiffOn_finprod, ContMDiffVectorBundle.contMDiffOn_coordChangeL, VectorBundleCore.IsContMDiff.contMDiffOn_coordChange, ContMDiffOn.congr, contMDiffOn_univ, contMDiffOn_iff_of_mem_maximalAtlas, ContMDiffOn.const_smul_section, contMDiffOn_iff_of_subset_source, Bundle.Trivialization.contMDiffOn_symm, ContMDiffOn.nsmul, ContMDiffOn.sum_section_of_locallyFinite, contMDiffOn_of_mem_maximalAtlas, ContMDiffCovariantDerivativeOn.contMDiff, contMDiffOn_comp_projIcc_iff, ContMDiffOn.contMDiffOn_tangentMapWithin, contMDiffOn_const, ContMDiffOn.sub, ContMDiffFiberwiseLinear.locality_aux₁, PartialDiffeomorph.contMDiffOn_invFun, ContMDiffOn.mpullback_vectorField_preimage, IsLocalFrameOn.contMDiffOn_of_coeff, ContMDiffOn.iUnion_of_isOpen, ContMDiffOn.div_const, contMDiffOn_extend_symm, VectorPrebundle.contMDiffOn_contMDiffCoordChange, ContMDiffOn.along_fst, ContMDiffOn.coordChange, ContMDiffOn.congr_mono, isLocalStructomorphOn_contDiffGroupoid_iff_aux, VectorPrebundle.IsContMDiff.exists_contMDiffCoordChange, ContinuousLinearMap.contMDiffOn, contMDiffOn_coordChangeL, contMDiffOn_model_symm, ContinuousLinearEquiv.contMDiffOn_transContinuousLinearEquiv_left, ContMDiffOn.inv, ContMDiffOn.sub_section, ContMDiffOn.clm_prodMap, ContMDiffOn.sum_section, ContMDiffOn.neg_section, ContMDiffWithinAt.contMDiffOn, Bundle.Trivialization.contMDiffOn_iff, ContMDiffOn.smul, contMDiffOn_extend, contMDiffOn_one, contMDiffOn_empty, contMDiffOn_union_iff_of_isOpen, contMDiffOn_iff_target, contMDiffOn_symm_of_mem_maximalAtlas, contMDiffOn_vectorSpace_iff_contDiffOn, ContMDiffOn.neg, ContMDiffOn.clm_bundle_apply, Manifold.exists_lt_of_riemannianEDist_lt, Bundle.Trivialization.contMDiffOn_section_iff, contMDiffOn_zero_iff, ContMDiffOn.union_of_isOpen, contMDiffOn_snd, ContMDiffOn.add, contMDiffOn_prod_module_iff, contMDiffOn_congr, Bundle.Trivialization.contMDiffOn_symm_trans, mem_contMDiffFiberwiseLinear_iff, contMDiffOn_id, ContMDiffOn.divβ‚€, contMDiffOn_infty, ContMDiffOn.clm_bundle_applyβ‚‚, ContinuousLinearEquiv.contMDiffOn_transContinuousLinearEquiv_right, ContMDiffOn.comp, contMDiffOn_projIcc, ContMDiffOn.pow, ContMDiffOn.invβ‚€, ContMDiffOn.smul_section, contMDiffOn_iff_localFrame_coeff
ContMDiffWithinAt πŸ“–MathDef
155 mathmath: ContMDiffWithinAt.sub, contMDiffWithinAt_insert_self, Diffeomorph.contMDiffWithinAt, contMDiffWithinAt_iff_target, contMDiffWithinAt_congr_set', ContMDiffWithinAt.comp_of_eq, ContDiffWithinAt.contMDiffWithinAt, contMDiffWithinAt_vectorSpace_iff_contDiffWithinAt, ContMDiffWithinAt.mono, ContMDiffWithinAt.mlieBracketWithin_vectorField, contMDiffWithinAt_congr_of_mem, contMDiffWithinAt_iff_contMDiffWithinAt_nhdsWithin, contMDiffAt_iff_source, ContMDiffAt.contMDiffWithinAt, contMDiffWithinAt_inter', ContMDiffWithinAt.sub_section, ContMDiffWithinAt.mfderivWithin_const, Bundle.contMDiffWithinAt_zeroSection, contMDiffWithinAt_iff_image, contMDiffWithinAt_snd, contMDiffWithinAt_prod_iff, ContMDiffWithinAt.clm_postcomp, ContMDiffWithinAt.nsmul, ContMDiffWithinAt.coordChange, ContMDiffWithinAt.snd, ContMDiffWithinAt.add_section, contMDiffWithinAt_congr_set, contMDiffWithinAt_prod_module_iff, ContMDiffWithinAt.pow, ContMDiffWithinAt.sum_section, ContDiffAt.comp_contMDiffWithinAt, contMDiffWithinAt_finset_prod, contMDiffWithinAt_pi_space, ContMDiffWithinAt.congr', contMDiffAt_iff_source_of_mem_source, ContMDiffWithinAt.neg_section, ContMDiffWithinAt.mpullbackWithin_vectorField_inter, ContMDiffWithinAt.inv, ContMDiffWithinAt.fst, ContMDiffWithinAt.change_section_trivialization, ContMDiffWithinAt.prodMk_space, contMDiffWithinAt_finset_sum, ContMDiffAt.comp_contMDiffWithinAt_of_eq, contMDiffWithinAt_const, ContMDiffWithinAt.mpullback_vectorField_of_mem_nhdsWithin_of_eq, contMDiffWithinAt_zero, ContMDiffWithinAt.mpullback_vectorField_preimage, contMDiffWithinAt_iff_of_mem_source', ContMDiffWithinAt.comp', ContDiff.comp_contMDiffWithinAt, ContMDiffWithinAt.compβ‚‚, ContMDiffWithinAt.mpullback_vectorField_preimage_of_eq, ContMDiffWithinAt.congr_of_mem, contMDiffWithinAt_finprod, ContMDiffWithinAt.prod, contMDiffWithinAt_extChartAt_symm_range_self, contMDiffWithinAt_iff_target_of_mem_source, ContMDiffWithinAt.finsum_section_of_locallyFinite, Bundle.contMDiffWithinAt_totalSpace, contMDiffWithinAt_iff_source_of_mem_maximalAtlas, ContMDiffWithinAt.smul, ContMDiffWithinAt.curry_right, Bundle.Trivialization.contMDiffWithinAt_iff, ContMDiffWithinAt.add, ContMDiffWithinAt.mpullbackWithin_vectorField', contMDiffWithinAt_one, contMDiffWithinAt_iff_contMDiffOn_nhds, contMDiffWithinAt_iff_le_ne_infty, ContMDiffWithinAt.clm_bundle_applyβ‚‚, contMDiffWithinAt_iff, ContMDiffWithinAt.mono_of_mem_nhdsWithin, contMDiffWithinAt_of_subsingleton, ContMDiffWithinAt.congr_of_eventuallyEq_of_mem, Bundle.contMDiffWithinAt_proj, contMDiffWithinAt_id, ContMDiffWithinAt.clm_bundle_apply, ContinuousLinearEquiv.contMDiffWithinAt_transContinuousLinearEquiv_right, contMDiffWithinAt_comp_projIcc_iff, ContMDiffWithinAt.div, ContMDiffWithinAt.along_fst, ContMDiffWithinAt.mfderivWithin, ContMDiffWithinAt.of_insert, contMDiffWithinAt_fst, ContMDiffWithinAt.prodMk, contMDiffWithinAt_iff', ContMDiffWithinAt.mpullbackWithin_vectorField_of_mem_of_eq, Diffeomorph.contMDiffWithinAt_comp_diffeomorph_iff, contMDiffWithinAt_extChartAt_symm_target_self, contMDiffWithinAt_inter, ContMDiffWithinAt.invβ‚€, ContMDiffWithinAt.compβ‚‚_of_eq, contMDiffWithinAt_iff_contDiffWithinAt, contMDiffWithinAt_finset_sum', ContMDiffWithinAt.mfderivWithin_apply, ContMDiffWithinAt.congr, VectorField.contMDiffWithinAt_mpullbackWithin_extChartAt_symm, ContMDiffWithinAt.sum_section_of_locallyFinite, ContinuousLinearEquiv.contMDiffWithinAt_transContinuousLinearEquiv_left, contMDiffWithinAt_extChartAt_symm_target, ContMDiffWithinAt.of_le, ContMDiffWithinAt.of_succ, ContMDiffWithinAt.clm_apply_of_inCoordinates, contMDiffWithinAt_iff_source, Bundle.Trivialization.contMDiffWithinAt_section, ContMDiffWithinAt.congr_set, contMDiffWithinAt_iff_source_of_mem_source, ContMDiffWithinAt.mpullbackWithin_vectorField_inter_of_eq, ContMDiffWithinAt.along_snd, contMDiffWithinAt_iff_of_mem_maximalAtlas, contMDiffWithinAt_univ, ContMDiffWithinAt.sub_const, ContMDiffWithinAt.clm_apply, contMDiffWithinAt_infty, ContMDiffWithinAt.sum, contMDiffWithinAt_extChartAt_symm_range, ContMDiffWithinAt.coordChangeL, ContMDiffWithinAt.div_const, ContMDiffWithinAt.const_smul_section, ContMDiffWithinAt.prodMap', Diffeomorph.contMDiffWithinAt_diffeomorph_comp_iff, ContinuousLinearMap.contMDiffWithinAt, ContMDiffWithinAt.mpullbackWithin_vectorField, ContMDiffWithinAt.congr_of_eventuallyEq, ContMDiffWithinAt.clm_prodMap, ContMDiffWithinAt.mul, contMDiffWithinAt_finsum, OpenPartialHomeomorph.contMDiffWithinAt_writtenInExtend_iff, ContMDiffWithinAt.smul_section, Bundle.contMDiffWithinAt_section, ContMDiffWithinAt.divβ‚€, ContMDiffWithinAt.clm_precomp, contMDiffWithinAt_of_notMem_mulTSupport, ContMDiffWithinAt.mpullbackWithin_vectorField_of_eq, ContMDiffWithinAt.neg, ContMDiffWithinAt.clm_comp, ContMDiffAt.comp_contMDiffWithinAt, ContMDiffWithinAt.prodMap, ContMDiffWithinAt.mpullbackWithin_vectorField_of_mem, VectorField.eventually_contMDiffWithinAt_mpullbackWithin_extChartAt_symm, Bundle.Trivialization.contMDiffWithinAt_snd_comp_iffβ‚‚, ContMDiffWithinAt.cle_arrowCongr, contMDiffWithinAt_of_notMem, contMDiffWithinAt_iff_nat, contMDiffWithinAt_congr, ContMDiffWithinAt.inner_bundle, contMDiffWithinAt_finset_prod', Filter.EventuallyEq.contMDiffWithinAt_iff, ContMDiffWithinAt.curry_left, ContMDiffWithinAt.mpullbackWithin_vectorField_of_eq', contMDiffWithinAt_hom_bundle, ContDiffWithinAt.comp_contMDiffWithinAt, contMDiffWithinAt_iff_of_mem_source, ContMDiffWithinAt.insert, ContMDiffWithinAt.comp, ContMDiffWithinAt.mpullback_vectorField_of_mem_nhdsWithin

Theorems

NameKindAssumesProvesValidatesDepends On
contDiffWithinAtProp_id πŸ“–mathematicalβ€”ContDiffWithinAtProp
Set.univ
β€”Set.univ_inter
ContDiffAt.contDiffWithinAt
ContDiff.contDiffAt
contDiff_id
ContDiffWithinAt.congr
ModelWithCorners.right_inv
ModelWithCorners.left_inv
contDiffWithinAtProp_mono_of_mem_nhdsWithin πŸ“–mathematicalSet
Filter
Filter.instMembership
nhdsWithin
ContDiffWithinAtProp
ContDiffWithinAtPropβ€”ContDiffWithinAt.mono_of_mem_nhdsWithin
Filter.inter_mem
Filter.mem_map
ModelWithCorners.image_eq
ModelWithCorners.symm_map_nhdsWithin_image
Filter.mem_of_superset
self_mem_nhdsWithin
Set.inter_subset_right
contDiffWithinAtProp_self πŸ“–mathematicalβ€”ContDiffWithinAtProp
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
NormedAddCommGroup.toSeminormedAddCommGroup
modelWithCornersSelf
ContDiffWithinAt
β€”contDiffWithinAtProp_self_source
contDiffWithinAtProp_self_source πŸ“–mathematicalβ€”ContDiffWithinAtProp
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
NormedAddCommGroup.toSeminormedAddCommGroup
modelWithCornersSelf
ContDiffWithinAt
ModelWithCorners.toFun'
β€”Set.range_id
Set.inter_univ
CompTriple.comp_eq
CompTriple.instComp_id
CompTriple.instIsIdId
contDiffWithinAtProp_self_target πŸ“–mathematicalβ€”ContDiffWithinAtProp
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
NormedAddCommGroup.toSeminormedAddCommGroup
modelWithCornersSelf
ContDiffWithinAt
PartialEquiv.toFun
ModelWithCorners.symm
Set
Set.instInter
Set.preimage
Set.range
ModelWithCorners.toFun'
β€”β€”
contDiffWithinAt_localInvariantProp πŸ“–mathematicalβ€”StructureGroupoid.LocalInvariantProp
contDiffGroupoid
ContDiffWithinAtProp
β€”contDiffWithinAt_localInvariantProp_of_le
le_rfl
contDiffWithinAt_localInvariantProp_of_le πŸ“–mathematicalWithTop
ENat
Preorder.toLE
WithTop.instPreorder
instPreorderENat
StructureGroupoid.LocalInvariantProp
contDiffGroupoid
ContDiffWithinAtProp
β€”Set.inter_right_comm
ContDiffWithinAtProp.eq_1
contDiffWithinAt_inter
ModelWithCorners.left_inv
IsOpen.mem_nhds
ContinuousAt.preimage_mem_nhds
Continuous.continuousAt
ModelWithCorners.continuous_symm
OpenPartialHomeomorph.left_inv
ContDiffOn.contDiffWithinAt
mem_groupoid_of_pregroupoid
ContDiffWithinAt.mono_of_mem_nhdsWithin
ContDiffWithinAt.comp_inter
ContDiffWithinAt.of_le
mem_nhdsWithin
IsOpen.preimage
OpenPartialHomeomorph.open_target
OpenPartialHomeomorph.mapsTo
ContDiffWithinAt.congr
ContDiffWithinAt.comp
contMDiffAt_iff πŸ“–mathematicalβ€”ContMDiffAt
ContinuousAt
ContDiffWithinAt
PartialEquiv.toFun
extChartAt
PartialEquiv.symm
Set.range
ModelWithCorners.toFun'
β€”ChartedSpace.liftPropAt_iff
ContDiffWithinAtProp.eq_1
Set.preimage_univ
Set.univ_inter
contMDiffAt_iff_contMDiffAt_nhds πŸ“–mathematicalβ€”ContMDiffAt
Filter.Eventually
nhds
β€”contMDiffAt_iff_contMDiffOn_nhds
Filter.Eventually.mono
eventually_mem_nhds_iff
ContMDiffWithinAt.contMDiffAt
mem_of_mem_nhds
Filter.Eventually.self_of_nhds
contMDiffAt_iff_contMDiffOn_nhds πŸ“–mathematicalβ€”ContMDiffAt
Set
Filter
Filter.instMembership
nhds
ContMDiffOn
β€”contMDiffWithinAt_iff_contMDiffOn_nhds
Set.insert_eq_of_mem
nhdsWithin_univ
contMDiffAt_iff_le_ne_infty πŸ“–mathematicalβ€”ContMDiffAtβ€”contMDiffWithinAt_iff_le_ne_infty
contMDiffAt_iff_nat πŸ“–mathematicalβ€”ContMDiffAt
WithTop.some
ENat
WithTop
WithTop.natCast
ENat.instNatCast
β€”β€”
contMDiffAt_iff_of_mem_source πŸ“–mathematicalSet
Set.instMembership
PartialEquiv.source
OpenPartialHomeomorph.toPartialEquiv
chartAt
ContMDiffAt
ContinuousAt
ContDiffWithinAt
PartialEquiv.toFun
extChartAt
PartialEquiv.symm
Set.range
ModelWithCorners.toFun'
β€”contMDiffWithinAt_iff_of_mem_source
continuousWithinAt_univ
Set.preimage_univ
Set.univ_inter
contMDiffAt_iff_source πŸ“–mathematicalβ€”ContMDiffAt
ContMDiffWithinAt
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
NormedAddCommGroup.toSeminormedAddCommGroup
modelWithCornersSelf
chartedSpaceSelf
PartialEquiv.toFun
PartialEquiv.symm
extChartAt
Set.range
ModelWithCorners.toFun'
β€”contMDiffWithinAt_univ
contMDiffWithinAt_iff_source
Set.univ_inter
contMDiffAt_iff_source_of_mem_source πŸ“–mathematicalSet
Set.instMembership
PartialEquiv.source
OpenPartialHomeomorph.toPartialEquiv
chartAt
ContMDiffAt
ContMDiffWithinAt
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
NormedAddCommGroup.toSeminormedAddCommGroup
modelWithCornersSelf
chartedSpaceSelf
PartialEquiv.toFun
PartialEquiv.symm
extChartAt
Set.range
ModelWithCorners.toFun'
β€”contMDiffWithinAt_iff_source_of_mem_source
Set.univ_inter
contMDiffAt_iff_target πŸ“–mathematicalβ€”ContMDiffAt
ContinuousAt
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
NormedAddCommGroup.toSeminormedAddCommGroup
modelWithCornersSelf
chartedSpaceSelf
PartialEquiv.toFun
extChartAt
β€”ContMDiffAt.eq_1
contMDiffWithinAt_iff_target
continuousWithinAt_univ
contMDiffAt_iff_target_of_mem_source πŸ“–mathematicalSet
Set.instMembership
PartialEquiv.source
OpenPartialHomeomorph.toPartialEquiv
chartAt
ContMDiffAt
ContinuousAt
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
NormedAddCommGroup.toSeminormedAddCommGroup
modelWithCornersSelf
chartedSpaceSelf
PartialEquiv.toFun
extChartAt
β€”ContMDiffAt.eq_1
contMDiffWithinAt_iff_target_of_mem_source
continuousWithinAt_univ
contMDiffAt_infty πŸ“–mathematicalβ€”ContMDiffAt
WithTop.some
ENat
Top.top
instTopENat
WithTop
WithTop.natCast
ENat.instNatCast
β€”contMDiffWithinAt_infty
contMDiffOn_congr πŸ“–mathematicalβ€”ContMDiffOnβ€”StructureGroupoid.LocalInvariantProp.liftPropOn_congr_iff
contDiffWithinAt_localInvariantProp
contMDiffOn_empty πŸ“–mathematicalβ€”ContMDiffOn
Set
Set.instEmptyCollection
β€”β€”
contMDiffOn_iff πŸ“–mathematicalβ€”ContMDiffOn
ContinuousOn
ContDiffOn
PartialEquiv.toFun
extChartAt
PartialEquiv.symm
Set
Set.instInter
PartialEquiv.target
Set.preimage
PartialEquiv.source
β€”ChartedSpace.LiftPropWithinAt.continuousWithinAt
ModelWithCorners.target_eq
ModelWithCorners.source_eq
Set.inter_univ
OpenPartialHomeomorph.right_inv
ModelWithCorners.right_inv
ContDiffWithinAt.mono
contMDiffWithinAt_iff_of_mem_source
StructureGroupoid.LocalInvariantProp.liftPropWithinAt_iff
contDiffWithinAt_localInvariantProp
Set.ext
ModelWithCorners.left_inv
OpenPartialHomeomorph.left_inv
contMDiffOn_iff_of_mem_maximalAtlas πŸ“–mathematicalOpenPartialHomeomorph
Set
Set.instMembership
IsManifold.maximalAtlas
Set.instHasSubset
PartialEquiv.source
OpenPartialHomeomorph.toPartialEquiv
Set.MapsTo
ContMDiffOn
ContinuousOn
ContDiffOn
PartialEquiv.toFun
OpenPartialHomeomorph.extend
PartialEquiv.symm
Set.image
β€”contMDiffWithinAt_iff_image
contMDiffOn_iff_of_mem_maximalAtlas' πŸ“–mathematicalOpenPartialHomeomorph
Set
Set.instMembership
IsManifold.maximalAtlas
Set.instHasSubset
PartialEquiv.source
OpenPartialHomeomorph.toPartialEquiv
Set.MapsTo
ContMDiffOn
ContDiffOn
PartialEquiv.toFun
OpenPartialHomeomorph.extend
PartialEquiv.symm
Set.image
β€”contMDiffOn_iff_of_mem_maximalAtlas
OpenPartialHomeomorph.continuousOn_writtenInExtend_iff
ContDiffOn.continuousOn
contMDiffOn_iff_of_subset_source πŸ“–mathematicalSet
Set.instHasSubset
PartialEquiv.source
OpenPartialHomeomorph.toPartialEquiv
chartAt
Set.MapsTo
ContMDiffOn
ContinuousOn
ContDiffOn
PartialEquiv.toFun
extChartAt
PartialEquiv.symm
Set.image
β€”contMDiffOn_iff_of_mem_maximalAtlas
IsManifold.chart_mem_maximalAtlas
contMDiffOn_iff_of_subset_source' πŸ“–mathematicalSet
Set.instHasSubset
PartialEquiv.source
extChartAt
Set.MapsTo
ContMDiffOn
ContDiffOn
PartialEquiv.toFun
extChartAt
PartialEquiv.symm
Set.image
β€”contMDiffOn_iff_of_mem_maximalAtlas'
IsManifold.chart_mem_maximalAtlas
extChartAt_source
contMDiffOn_iff_source_of_mem_maximalAtlas πŸ“–mathematicalOpenPartialHomeomorph
Set
Set.instMembership
IsManifold.maximalAtlas
Set.instHasSubset
PartialEquiv.source
OpenPartialHomeomorph.toPartialEquiv
ContMDiffOn
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
NormedAddCommGroup.toSeminormedAddCommGroup
modelWithCornersSelf
chartedSpaceSelf
PartialEquiv.toFun
PartialEquiv.symm
OpenPartialHomeomorph.extend
Set.image
β€”contMDiffWithinAt_iff_source_of_mem_maximalAtlas
contMDiffWithinAt_congr_set
OpenPartialHomeomorph.extend_symm_preimage_inter_range_eventuallyEq
contMDiffOn_iff_target πŸ“–mathematicalβ€”ContMDiffOn
ContinuousOn
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
NormedAddCommGroup.toSeminormedAddCommGroup
modelWithCornersSelf
chartedSpaceSelf
PartialEquiv.toFun
extChartAt
Set
Set.instInter
Set.preimage
PartialEquiv.source
β€”IsManifold.instOfTopWithTopENat
instIsManifoldModelSpace
PartialEquiv.refl_trans
ModelWithCorners.source_eq
Set.inter_univ
Continuous.continuousOn
ModelWithCorners.continuous
ContinuousOn.comp_inter
OpenPartialHomeomorph.continuousOn_toFun
contMDiffOn_infty πŸ“–mathematicalβ€”ContMDiffOn
WithTop.some
ENat
Top.top
instTopENat
WithTop
WithTop.natCast
ENat.instNatCast
β€”ContMDiffOn.of_le
le_top
contMDiffWithinAt_infty
contMDiffOn_of_locally_contMDiffOn πŸ“–mathematicalSet
IsOpen
Set.instMembership
ContMDiffOn
Set.instInter
ContMDiffOnβ€”StructureGroupoid.LocalInvariantProp.liftPropOn_of_locally_liftPropOn
contDiffWithinAt_localInvariantProp
contMDiffOn_univ πŸ“–mathematicalβ€”ContMDiffOn
Set.univ
ContMDiff
β€”β€”
contMDiffOn_zero_iff πŸ“–mathematicalβ€”ContMDiffOn
WithTop
ENat
WithTop.zero
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringENat
ContinuousOn
β€”contMDiffOn_iff
IsManifold.instOfNatWithTopENat
contDiffOn_zero
ContinuousOn.comp
continuousOn_extChartAt
ContinuousOn.mono
continuousOn_extChartAt_symm
Set.inter_subset_left
contMDiffWithinAt_congr πŸ“–mathematicalβ€”ContMDiffWithinAtβ€”StructureGroupoid.LocalInvariantProp.liftPropWithinAt_congr_iff
contDiffWithinAt_localInvariantProp
contMDiffWithinAt_congr_of_mem πŸ“–mathematicalSet
Set.instMembership
ContMDiffWithinAtβ€”StructureGroupoid.LocalInvariantProp.liftPropWithinAt_congr_iff_of_mem
contDiffWithinAt_localInvariantProp
contMDiffWithinAt_congr_set πŸ“–mathematicalFilter.EventuallyEq
nhds
ContMDiffWithinAtβ€”StructureGroupoid.LocalInvariantProp.liftPropWithinAt_congr_set
contDiffWithinAt_localInvariantProp
contMDiffWithinAt_congr_set' πŸ“–mathematicalFilter.EventuallyEq
nhdsWithin
Compl.compl
Set
Set.instCompl
Set.instSingletonSet
ContMDiffWithinAtβ€”ModelWithCorners.t1Space
contMDiffWithinAt_insert_self
contMDiffWithinAt_congr_set
eventuallyEq_insert
contMDiffWithinAt_iff πŸ“–mathematicalβ€”ContMDiffWithinAt
ContinuousWithinAt
ContDiffWithinAt
PartialEquiv.toFun
extChartAt
PartialEquiv.symm
Set
Set.instInter
Set.preimage
Set.range
ModelWithCorners.toFun'
β€”β€”
contMDiffWithinAt_iff' πŸ“–mathematicalβ€”ContMDiffWithinAt
ContinuousWithinAt
ContDiffWithinAt
PartialEquiv.toFun
extChartAt
PartialEquiv.symm
Set
Set.instInter
PartialEquiv.target
Set.preimage
PartialEquiv.source
β€”contDiffWithinAt_congr_set
ContinuousWithinAt.extChartAt_symm_preimage_inter_range_eventuallyEq
contMDiffWithinAt_iff_contMDiffOn_nhds πŸ“–mathematicalβ€”ContMDiffWithinAt
Set
Filter
Filter.instMembership
nhdsWithin
Set.instInsert
ContMDiffOn
β€”Set.insert_eq_of_mem
ContDiffWithinAt.contDiffOn
le_rfl
instIsEmptyFalse
contMDiffWithinAt_iff'
PartialEquiv.map_source
mem_extChartAt_source
extChartAt_to_inv
map_extChartAt_symm_nhdsWithin
ContinuousWithinAt.nhdsWithin_extChartAt_symm_preimage_inter_range
ChartedSpace.LiftPropWithinAt.continuousWithinAt
Filter.image_mem_map
Set.image_subset_iff
PartialEquiv.map_target
contMDiffOn_iff_of_subset_source'
PartialEquiv.image_symm_image_of_subset_target
HasSubset.Subset.trans
Set.instIsTransSubset
Set.inter_subset_left
ContMDiffWithinAt.mono_of_mem_nhdsWithin
mem_of_mem_nhdsWithin
contMDiffWithinAt_insert_self
Set.mem_insert
Set.insert_idem
contMDiffWithinAt_iff_contMDiffWithinAt_nhdsWithin πŸ“–mathematicalβ€”ContMDiffWithinAt
Filter.Eventually
nhdsWithin
Set
Set.instInsert
β€”contMDiffWithinAt_iff_contMDiffOn_nhds
Filter.mp_mem
eventually_mem_nhdsWithin_iff
Filter.univ_mem'
ContMDiffWithinAt.mono_of_mem_nhdsWithin
nhdsWithin_mono
Set.subset_insert
mem_of_mem_nhdsWithin
Set.mem_insert
contMDiffWithinAt_iff_image πŸ“–mathematicalOpenPartialHomeomorph
Set
Set.instMembership
IsManifold.maximalAtlas
Set.instHasSubset
PartialEquiv.source
OpenPartialHomeomorph.toPartialEquiv
ContMDiffWithinAt
ContinuousWithinAt
ContDiffWithinAt
PartialEquiv.toFun
OpenPartialHomeomorph.extend
PartialEquiv.symm
Set.image
β€”contMDiffWithinAt_iff_of_mem_maximalAtlas
contDiffWithinAt_congr_set
OpenPartialHomeomorph.extend_symm_preimage_inter_range_eventuallyEq
contMDiffWithinAt_iff_le_ne_infty πŸ“–mathematicalβ€”ContMDiffWithinAtβ€”ContMDiffWithinAt.of_le
le_rfl
contMDiffWithinAt_iff_nat
contMDiffWithinAt_iff_nat πŸ“–mathematicalβ€”ContMDiffWithinAt
WithTop.some
ENat
WithTop
WithTop.natCast
ENat.instNatCast
β€”ContMDiffWithinAt.of_le
contMDiffWithinAt_infty
le_top
le_rfl
contMDiffWithinAt_iff_of_mem_maximalAtlas πŸ“–mathematicalOpenPartialHomeomorph
Set
Set.instMembership
IsManifold.maximalAtlas
PartialEquiv.source
OpenPartialHomeomorph.toPartialEquiv
ContMDiffWithinAt
ContinuousWithinAt
ContDiffWithinAt
PartialEquiv.toFun
OpenPartialHomeomorph.extend
PartialEquiv.symm
Set
Set.instInter
Set.preimage
Set.range
ModelWithCorners.toFun'
β€”StructureGroupoid.LocalInvariantProp.liftPropWithinAt_indep_chart
contDiffWithinAt_localInvariantProp
IsManifold.toHasGroupoid
contMDiffWithinAt_iff_of_mem_source πŸ“–mathematicalSet
Set.instMembership
PartialEquiv.source
OpenPartialHomeomorph.toPartialEquiv
chartAt
ContMDiffWithinAt
ContinuousWithinAt
ContDiffWithinAt
PartialEquiv.toFun
extChartAt
PartialEquiv.symm
Set
Set.instInter
Set.preimage
Set.range
ModelWithCorners.toFun'
β€”contMDiffWithinAt_iff_of_mem_maximalAtlas
IsManifold.chart_mem_maximalAtlas
contMDiffWithinAt_iff_of_mem_source' πŸ“–mathematicalSet
Set.instMembership
PartialEquiv.source
OpenPartialHomeomorph.toPartialEquiv
chartAt
ContMDiffWithinAt
ContinuousWithinAt
ContDiffWithinAt
PartialEquiv.toFun
extChartAt
PartialEquiv.symm
Set
Set.instInter
PartialEquiv.target
Set.preimage
PartialEquiv.source
β€”contMDiffWithinAt_iff_of_mem_source
contDiffWithinAt_congr_set
nhdsWithin_eq_iff_eventuallyEq
PartialEquiv.image_source_inter_eq'
map_extChartAt_nhdsWithin_eq_image'
extChartAt_source
map_extChartAt_nhdsWithin'
Set.inter_comm
nhdsWithin_inter_of_mem
extChartAt_source_mem_nhds'
contMDiffWithinAt_iff_source πŸ“–mathematicalβ€”ContMDiffWithinAt
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
NormedAddCommGroup.toSeminormedAddCommGroup
modelWithCornersSelf
chartedSpaceSelf
PartialEquiv.toFun
PartialEquiv.symm
extChartAt
Set
Set.instInter
Set.preimage
Set.range
ModelWithCorners.toFun'
β€”ContinuousWithinAt.comp_of_eq
ContinuousAt.continuousWithinAt
continuousAt_extChartAt_symm
Set.MapsTo.mono_left
Set.mapsTo_preimage
Set.inter_subset_left
extChartAt_to_inv
continuousWithinAt_inter
extChartAt_source_mem_nhds
ContinuousWithinAt.comp
continuousAt_extChartAt
OpenPartialHomeomorph.left_inv
ModelWithCorners.source_eq
Set.inter_univ
ModelWithCorners.left_inv
ContinuousWithinAt.congr
Set.range_id
contMDiffWithinAt_iff_source_of_mem_maximalAtlas πŸ“–mathematicalOpenPartialHomeomorph
Set
Set.instMembership
IsManifold.maximalAtlas
PartialEquiv.source
OpenPartialHomeomorph.toPartialEquiv
ContMDiffWithinAt
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
NormedAddCommGroup.toSeminormedAddCommGroup
modelWithCornersSelf
chartedSpaceSelf
PartialEquiv.toFun
PartialEquiv.symm
OpenPartialHomeomorph.extend
Set
Set.instInter
Set.preimage
Set.range
ModelWithCorners.toFun'
β€”StructureGroupoid.LocalInvariantProp.liftPropWithinAt_indep_chart_source
contDiffWithinAt_localInvariantProp
IsManifold.toHasGroupoid
OpenPartialHomeomorph.extend_symm_continuousWithinAt_comp_right_iff
OpenPartialHomeomorph.left_inv
PartialEquiv.left_inv
OpenPartialHomeomorph.extend_source
contMDiffWithinAt_iff_source_of_mem_source πŸ“–mathematicalSet
Set.instMembership
PartialEquiv.source
OpenPartialHomeomorph.toPartialEquiv
chartAt
ContMDiffWithinAt
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
NormedAddCommGroup.toSeminormedAddCommGroup
modelWithCornersSelf
chartedSpaceSelf
PartialEquiv.toFun
PartialEquiv.symm
extChartAt
Set
Set.instInter
Set.preimage
Set.range
ModelWithCorners.toFun'
β€”contMDiffWithinAt_iff_source_of_mem_maximalAtlas
IsManifold.chart_mem_maximalAtlas
contMDiffWithinAt_iff_target πŸ“–mathematicalβ€”ContMDiffWithinAt
ContinuousWithinAt
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
NormedAddCommGroup.toSeminormedAddCommGroup
modelWithCornersSelf
chartedSpaceSelf
PartialEquiv.toFun
extChartAt
β€”ContinuousAt.comp_continuousWithinAt
continuousAt_extChartAt
contMDiffWithinAt_iff_target_of_mem_source πŸ“–mathematicalSet
Set.instMembership
PartialEquiv.source
OpenPartialHomeomorph.toPartialEquiv
chartAt
ContMDiffWithinAt
ContinuousWithinAt
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
NormedAddCommGroup.toSeminormedAddCommGroup
modelWithCornersSelf
chartedSpaceSelf
PartialEquiv.toFun
extChartAt
β€”StructureGroupoid.LocalInvariantProp.liftPropWithinAt_indep_chart_target
contDiffWithinAt_localInvariantProp
IsManifold.toHasGroupoid
IsManifold.chart_mem_maximalAtlas
ContinuousAt.comp_continuousWithinAt
OpenPartialHomeomorph.continuousAt
continuousAt_extChartAt'
extChartAt_source
contMDiffWithinAt_infty πŸ“–mathematicalβ€”ContMDiffWithinAt
WithTop.some
ENat
Top.top
instTopENat
WithTop
WithTop.natCast
ENat.instNatCast
β€”ChartedSpace.LiftPropWithinAt.continuousWithinAt
contDiffWithinAt_infty
ChartedSpace.LiftPropWithinAt.prop
contMDiffWithinAt_insert_self πŸ“–mathematicalβ€”ContMDiffWithinAt
Set
Set.instInsert
β€”Iff.and
contDiffWithinAt_congr_set
nhdsWithin_insert
Filter.map_sup
contDiffWithinAt_insert_self
contMDiffWithinAt_inter πŸ“–mathematicalSet
Filter
Filter.instMembership
nhds
ContMDiffWithinAt
Set
Set.instInter
β€”StructureGroupoid.LocalInvariantProp.liftPropWithinAt_inter
contDiffWithinAt_localInvariantProp
contMDiffWithinAt_inter' πŸ“–mathematicalSet
Filter
Filter.instMembership
nhdsWithin
ContMDiffWithinAt
Set
Set.instInter
β€”StructureGroupoid.LocalInvariantProp.liftPropWithinAt_inter'
contDiffWithinAt_localInvariantProp
contMDiffWithinAt_univ πŸ“–mathematicalβ€”ContMDiffWithinAt
Set.univ
ContMDiffAt
β€”β€”
contMDiff_congr πŸ“–mathematicalβ€”ContMDiffβ€”contMDiffOn_congr
contMDiff_iff πŸ“–mathematicalβ€”ContMDiff
Continuous
ContDiffOn
PartialEquiv.toFun
extChartAt
PartialEquiv.symm
Set
Set.instInter
PartialEquiv.target
Set.preimage
PartialEquiv.source
β€”ModelWithCorners.target_eq
ModelWithCorners.source_eq
Set.inter_univ
Set.univ_inter
contMDiff_iff_target πŸ“–mathematicalβ€”ContMDiff
Continuous
ContMDiffOn
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
SeminormedAddCommGroup.toPseudoMetricSpace
NormedAddCommGroup.toSeminormedAddCommGroup
modelWithCornersSelf
chartedSpaceSelf
PartialEquiv.toFun
extChartAt
Set.preimage
PartialEquiv.source
β€”contMDiffOn_univ
contMDiffOn_iff_target
ModelWithCorners.source_eq
Set.inter_univ
Set.univ_inter
contMDiff_infty πŸ“–mathematicalβ€”ContMDiff
WithTop.some
ENat
Top.top
instTopENat
WithTop
WithTop.natCast
ENat.instNatCast
β€”ContMDiff.of_le
le_top
contMDiffWithinAt_infty
contMDiff_of_locally_contMDiffOn πŸ“–mathematicalSet
IsOpen
Set.instMembership
ContMDiffOn
ContMDiffβ€”StructureGroupoid.LocalInvariantProp.liftProp_of_locally_liftPropOn
contDiffWithinAt_localInvariantProp
contMDiff_zero_iff πŸ“–mathematicalβ€”ContMDiff
WithTop
ENat
WithTop.zero
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringENat
Continuous
β€”contMDiffOn_univ
continuousOn_univ
contMDiffOn_zero_iff

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