Theorems · Theorem · global analysis
DifferentiableOn.differentiableAt
∀ {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},
DifferentiableOn 𝕜 f s → s ∈ nhds x → DifferentiableAt 𝕜 f x- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Basic
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Filterstatement · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- DifferentiableAtstatement · cited by 617
- DifferentiableOnstatement and proof · cited by 419
- HasFDerivAt.differentiableAtproof · cited by 83
- DifferentiableOn.hasFDerivAtproof · cited by 4
Cited by26
Results whose statement or proof uses this declaration.
- DiffContOnCl.differentiableAtproof · cited by 7
- TendstoLocallyUniformlyOn.differentiableOnproof · cited by 7
- Real.hasDerivAt_mul_logproof · cited by 5
- Complex.differentiableOn_compl_singleton_and_continuousAt_iffproof · cited by 4
- Complex.differentiableOn_dslopeproof · cited by 3
- DifferentiableOn.eventually_differentiableAtproof · cited by 3
- Function.Periodic.differentiableAt_cuspFunction_zeroproof · cited by 3
- DifferentiableOn.iUnion_of_isOpenproof · cited by 2
- IsOpen.exists_eq_add_of_fderiv_eqproof · cited by 2
- ModularForm.differentiableAt_eta_tprodproof · cited by 2
- differentiableAt_iteratedDerivWithin_cexpproof · cited by 2
- AkraBazziRecurrence.isBigO_apply_r_sub_bproof · cited by 2