Theorems · Theorem · global analysis
uniqueMDiffWithinAt_iff_uniqueDiffWithinAt
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {s : Set E} {x : E}, UniqueMDiffAt[s] x ↔ UniqueDiffWithinAt 𝕜 s x- Defined in
- Mathlib.Geometry.Manifold.MFDeriv.FDeriv
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Set.preimageproof · cited by 4,946
- modelWithCornersSelfstatement · cited by 920
- PartialEquiv.toFunproof · cited by 821
- PartialEquiv.symmproof · cited by 453
- UniqueDiffWithinAtstatement and proof · cited by 252
- Set.inter_univproof · cited by 198
- UniqueMDiffWithinAtstatement · cited by 83
- PartialEquiv.reflproof · cited by 43
Cited by6
Results whose statement or proof uses this declaration.
- setOfPred_riemannianEDist_lt_subset_nhdsproof · cited by 2
- Manifold.pathELength_comp_of_monotoneOnproof · cited by 2
- UniqueDiffWithinAt.uniqueMDiffWithinAtproof · cited by 2
- Manifold.pathELength_comp_of_antitoneOnproof · cited by 1
- eventually_riemannianEDist_le_edist_extChartAtproof · cited by 1
- UniqueMDiffWithinAt.uniqueDiffWithinAtproof · cited by 0