Theorems · Theorem · real analysis
HasStrictDerivAt.map_nhds_eq
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] [CompleteSpace 𝕜] {f : 𝕜 → 𝕜} {f' a : 𝕜},
HasStrictDerivAt f f' a → f' ≠ 0 → Filter.map f (nhds a) = nhds (f a)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 186 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Filterstatement · cited by 8,121
- nhdsstatement · cited by 5,554
- CompleteSpacestatement and proof · cited by 2,532
- Filter.mapstatement · cited by 819
- HasStrictDerivAtstatement and proof · cited by 163
- HasStrictDerivAt.hasStrictFDerivAt_equivproof · cited by 10
- HasStrictFDerivAt.map_nhds_eq_of_equivproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- isOpenMap_of_hasStrictDerivAtproof · cited by 1