Theorems · Theorem · global analysis
differentiableWithinAt_univ
∀ {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}, DifferentiableWithinAt 𝕜 f Set.univ x ↔ DifferentiableAt 𝕜 f x- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Basic
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 66 from the axioms · 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.
- 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
- ContinuousLinearMapproof · cited by 5,352
- Set.univstatement · cited by 3,945
- DifferentiableAtstatement · cited by 617
- DifferentiableWithinAtstatement · cited by 453
- HasFDerivAtproof · cited by 350
Cited by14
Results whose statement or proof uses this declaration.
- DifferentiableAt.hasFDerivAtproof · cited by 134
- DifferentiableAt.differentiableWithinAtproof · cited by 96
- fderiv_zero_of_not_differentiableAtproof · cited by 9
- ContDiffAt.differentiableAt_iteratedFDerivproof · cited by 4
- DifferentiableAt.powproof · cited by 3
- ContinuousLinearEquiv.comp_differentiableAt_iffproof · cited by 3
- differentiableAt_iff_restrictScalarsproof · cited by 2
- LocallyBoundedVariationOn.ae_differentiableAtproof · cited by 1
- DifferentiableAt.inversionproof · cited by 1
- Complex.norm_eventually_eq_of_mdifferentiableAt_of_isLocalMaxproof · cited by 1
- DifferentiableAt.of_dslopeproof · cited by 0
- Complex.deriv_const_cpowproof · cited by 0