Theorems · Theorem · global analysis
DifferentiableWithinAt.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},
DifferentiableWithinAt 𝕜 f s x → s ∈ nhds x → DifferentiableAt 𝕜 f x- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Basic
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- RingHom.idproof · cited by 18,349
- 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
- ContinuousLinearMapproof · cited by 5,352
- DifferentiableAtstatement · cited by 617
- DifferentiableWithinAtstatement and proof · cited by 453
- HasFDerivWithinAtproof · cited by 356
Cited by21
Results whose statement or proof uses this declaration.
- exists_deriv_eq_slopeproof · cited by 6
- intervalIntegral.integral_deriv_of_contDiffOn_Iccproof · cited by 4
- DifferentiableOn.hasFDerivAtproof · cited by 4
- UpperHalfPlane.mdifferentiable_iffproof · cited by 3
- DifferentiableOn.union_of_isOpenproof · cited by 2
- hasFDerivWithinAt_closure_of_tendsto_fderivproof · cited by 2
- DiffContOnCl.circleAverage_smul_divproof · cited by 2
- HurwitzZeta.differentiableAt_update_of_residueproof · cited by 2
- logDeriv_tprod_eq_tsumproof · cited by 1
- hasDerivAt_of_tendsto_locally_uniformly_on'proof · cited by 1
- MDifferentiableAt.isInteriorPoint_of_surjective_mfderivproof · cited by 1
- Real.differentiableAt_negMulLog_iffproof · cited by 1