Theorems · Theorem · real analysis
HasDerivWithinAt.tendsto_nhdsWithin_nhdsNE
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {f' : F} {s : Set 𝕜} {x : 𝕜},
HasDerivWithinAt f f' s x → f' ≠ 0 → Filter.Tendsto f (nhdsWithin x (s \ {x})) (nhdsWithin (f x) {f x}ᶜ)- Defined in
- Mathlib.Analysis.Calculus.Deriv.Inverse
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
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
- Realproof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Norm.normproof · cited by 5,413
- mul_oneproof · cited by 3,885
- Filter.Tendstostatement · cited by 3,814
- Compl.complstatement · cited by 2,925
- one_mulproof · cited by 2,841
- le_reflproof · cited by 2,061
- nhdsWithinstatement · cited by 1,912
Cited by1
Results whose statement or proof uses this declaration.
- HasDerivAt.tendsto_nhdsNEproof · cited by 5