Theorems · Theorem · real analysis
differentiableWithinAt_Ioi_iff_Ici
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {x : 𝕜} [inst_3 : PartialOrder 𝕜],
DifferentiableWithinAt 𝕜 f (Set.Ioi x) x ↔ DifferentiableWithinAt 𝕜 f (Set.Ici x) x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 172 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.
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- PartialOrderstatement and proof · cited by 6,410
- Set.Ioistatement and proof · cited by 1,463
- Set.Icistatement and proof · cited by 1,070
- DifferentiableWithinAtstatement and proof · cited by 453
- DifferentiableWithinAt.hasDerivWithinAtproof · cited by 85
- HasDerivWithinAt.differentiableWithinAtproof · cited by 19
- HasDerivWithinAt.Ioi_of_Iciproof · cited by 5
- HasDerivWithinAt.Ici_of_Ioiproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- derivWithin_Ioi_eq_Iciproof · cited by 2