Theorems · Theorem · real analysis
ContDiffOn.continuousOn_derivWithin
∀ {𝕜 : Type u_1} {F : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {n : WithTop ℕ∞} {f : 𝕜 → F} {s : Set 𝕜},
ContDiffOn 𝕜 n f s → UniqueDiffOn 𝕜 s → 1 ≤ n → ContinuousOn (derivWithin f s) s- Defined in
- Mathlib.Analysis.Calculus.ContDiff.Deriv
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 198 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
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ENatstatement and proof · cited by 4,985
- WithTopstatement and proof · cited by 3,754
- ContinuousOnstatement · cited by 1,411
- ContDiffOnstatement and proof · cited by 294
- derivWithinstatement · cited by 258
- UniqueDiffOnstatement and proof · cited by 215
- ContDiffOn.of_leproof · cited by 25
- ContDiffOn.continuousOnproof · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- ContinuousOn.curveIntegrable_of_contDiffOnproof · cited by 0