Theorems · Theorem · global analysis
DifferentiableAt.differentiableWithinAt
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
[inst_3 : TopologicalSpace E] {F : Type u_3} [inst_4 : AddCommGroup F] [inst_5 : Module 𝕜 F]
[inst_6 : TopologicalSpace F] {f : E → F} {x : E} {s : Set E}, DifferentiableAt 𝕜 f x → DifferentiableWithinAt 𝕜 f s x- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Basic
- Cited by
- 96 results in Mathlib
- Foundations
- Depth 164 from the axioms, rests on 3,721 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- DifferentiableAtstatement and proof · cited by 617
- DifferentiableWithinAtstatement · cited by 453
- Set.subset_univproof · cited by 228
- DifferentiableWithinAt.monoproof · cited by 15
- differentiableWithinAt_univproof · cited by 14
Cited by96
Results whose statement or proof uses this declaration.
- DifferentiableAt.comp_differentiableWithinAtproof · cited by 14
- strictMonoOn_of_deriv_posproof · cited by 9
- differentiableWithinAt_constproof · cited by 7
- differentiableWithinAt_idproof · cited by 7
- TendstoLocallyUniformlyOn.differentiableOnproof · cited by 7
- fderivWithin_eq_fderivproof · cited by 6
- AnalyticAt.differentiableWithinAtproof · cited by 5
- strictAntiOn_of_deriv_negproof · cited by 5
- InnerProductSpace.HarmonicOnNhd.exists_analyticOnNhd_ball_re_eqproof · cited by 4
- Real.differentiableAt_arcsinproof · cited by 4
- Complex.differentiableOn_compl_singleton_and_continuousAt_iffproof · cited by 4
- strictConcaveOn_of_deriv2_negproof · cited by 4