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Theorems · Theorem · global analysis

uniqueMDiffWithinAt_univ

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {H : Type u_3} [inst_3 : TopologicalSpace H] (I : ModelWithCorners 𝕜 E H) {M : Type u_4}
  [inst_4 : TopologicalSpace M] [inst_5 : ChartedSpace H M] {x : M}, UniqueMDiffAt[Set.univ] x
Defined in
Mathlib.Geometry.Manifold.MFDeriv.Basic
Cited by
14 results in Mathlib
Foundations
Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpace

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IsOpen.uniqueMDiffWithinAt · cited by 2IsOpen.uniqueMDiffWithinAtmfderiv_neg · cited by 1mfderiv_negmfderiv_prodMk · cited by 1mfderiv_prodMkhasMFDerivAt_unique · cited by 1hasMFDerivAt_uniquemfderiv_prodMap · cited by 0mfderiv_prodMapVectorField.mlieBracket_add_left · cited by 0VectorField.mlieBracket_a…VectorField.mlieBracket_add_right · cited by 0VectorField.mlieBracket_a…VectorField.mlieBracket_const_smul_left · cited by 0VectorField.mlieBracket_c…VectorField.mlieBracket_const_smul_right · cited by 0VectorField.mlieBracket_c…VectorField.mlieBracket_smul_left · cited by 0VectorField.mlieBracket_s…VectorField.mlieBracket_smul_right · cited by 0VectorField.mlieBracket_s…mfderiv_sumInl · cited by 0mfderiv_sumInlmfderiv_sumInr · cited by 0mfderiv_sumInrmfderiv_sumSwap · cited by 0mfderiv_sumSwapTopologicalSpace · cited by 24529TopologicalSpaceNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldSet.range · cited by 4705Set.rangeSet.univ · cited by 3945Set.univModelWithCorners · cited by 2462ModelWithCornersChartedSpace · cited by 2397ChartedSpacePartialEquiv.source · cited by 964PartialEquiv.sourcePartialHomeomorph.toPartialEquiv · cited by 917PartialHomeomorph.toParti…OpenPartialHomeomorph.toPartialHomeomorph · cited by 851OpenPartialHomeomorph.toP…PartialEquiv.toFun · cited by 821PartialEquiv.toFunPartialEquiv.symm · cited by 453PartialEquiv.symmModelWithCorners.toFun' · cited by 373ModelWithCorners.toFun'Set.mem_range_self · cited by 328Set.mem_range_selfuniqueMDiffWithinAt_univCITED BYCITES

Cites23

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Cited by14

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