Theorems · Theorem · real analysis
ContDiffAt.continuousAt_fderiv
∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F} {x : E}
{n : WithTop ℕ∞}, ContDiffAt 𝕜 n f x → n ≠ 0 → ContinuousAt (fderiv 𝕜 f) x- Defined in
- Mathlib.Analysis.Calculus.ContDiff.Comp
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 207 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.
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ContinuousLinearMapstatement · cited by 5,352
- ENatstatement and proof · cited by 4,985
- WithTopstatement and proof · cited by 3,754
- zero_addproof · cited by 2,366
- ContinuousAtstatement · cited by 697
- fderivstatement · cited by 398
- ContDiffAtstatement and proof · cited by 262
- ContDiffAt.continuousAtproof · cited by 9
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