Theorems · Theorem · real analysis
contDiffOn_infty_iff_derivWithin
∀ {𝕜 : Type u_1} {F : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {s : Set 𝕜},
UniqueDiffOn 𝕜 s → (ContDiffOn 𝕜 (↑⊤) f s ↔ DifferentiableOn 𝕜 f s ∧ ContDiffOn 𝕜 (↑⊤) (derivWithin f s) s)- Defined in
- Mathlib.Analysis.Calculus.ContDiff.Deriv
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites14
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
- Top.topstatement and proof · cited by 9,680
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ENatstatement and proof · cited by 4,985
- WithTopproof · cited by 3,754
- WithTop.somestatement and proof · cited by 1,128
- DifferentiableOnstatement and proof · cited by 419
- ContDiffOnstatement and proof · cited by 294
- derivWithinstatement and proof · cited by 258
- UniqueDiffOnstatement and proof · cited by 215
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