Theorems · Theorem · real analysis
ContDiffOn.deriv_of_isOpen
∀ {𝕜 : Type u_1} {F : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {m n : WithTop ℕ∞} {f : 𝕜 → F} {s : Set 𝕜},
ContDiffOn 𝕜 n f s → IsOpen s → m + 1 ≤ n → ContDiffOn 𝕜 m (deriv f) s- Defined in
- Mathlib.Analysis.Calculus.ContDiff.Deriv
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- IsOpenstatement and proof · cited by 2,400
- derivstatement · cited by 676
- ContDiffOnstatement and proof · cited by 294
- IsOpen.uniqueDiffOnproof · cited by 15
- ContDiffOn.congrproof · cited by 13
- derivWithin_of_isOpenproof · cited by 7
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