Mathlib Map

Theorems · Theorem · global analysis

uniqueDiffWithinAt_univ

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : DivisionSemiring 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
  [inst_3 : TopologicalSpace E] [inst_4 : TopologicalSpace 𝕜] [(nhdsWithin 0 {0}ᶜ).NeBot] [ContinuousSMul 𝕜 E] {x : E},
  UniqueDiffWithinAt 𝕜 Set.univ x
Defined in
Mathlib.Analysis.Calculus.TangentCone.Basic
Cited by
16 results in Mathlib
Foundations
Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DivisionSemiringAddCommGroupModuleTopologicalSpaceTopologicalSpaceFilter.NeBotContinuousSMul

Around this declaration

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

uniqueDiffOn_univ · cited by 66uniqueDiffOn_univHasFDerivAt.unique · cited by 9HasFDerivAt.uniqueContinuousLinearEquiv.comp_fderiv · cited by 3ContinuousLinearEquiv.com…fderiv_comp_smul · cited by 2fderiv_comp_smuluniqueDiffWithinAt_of_mem_nhds · cited by 2uniqueDiffWithinAt_of_mem…differentiableAt_iff_restrictScalars · cited by 2differentiableAt_iff_rest…TangentBundle.coordChange_model_space · cited by 2TangentBundle.coordChange…ContinuousLinearEquiv.comp_right_fderiv · cited by 1ContinuousLinearEquiv.com…fderiv_const_smul_field · cited by 1fderiv_const_smul_fieldVectorField.lieBracket_smul_right · cited by 1VectorField.lieBracket_sm…fderiv_fun_neg · cited by 1fderiv_fun_negnorm_iteratedFDeriv_one · cited by 0norm_iteratedFDeriv_onefderiv_const_sub · cited by 0fderiv_const_subfderiv_const_smul_of_invertible · cited by 0fderiv_const_smul_of_inve…VectorField.lieBracket_const_smul_right · cited by 0VectorField.lieBracket_co…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceModule · cited by 20661ModuleAddCommGroup · cited by 12871AddCommGroupSetLike.coe · cited by 8199SetLike.coeSet.univ · cited by 3945Set.univCompl.compl · cited by 2925Compl.complnhdsWithin · cited by 1912nhdsWithinSubmodule.span · cited by 1504Submodule.spanclosure · cited by 1254closureContinuousSMul · cited by 1016ContinuousSMulFilter.NeBot · cited by 853Filter.NeBotDense · cited by 359DenseUniqueDiffWithinAt · cited by 252UniqueDiffWithinAtDivisionSemiring · cited by 216DivisionSemiringuniqueDiffWithinAt_univCITED BYCITES

Cites19

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by16

Results whose statement or proof uses this declaration.