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Theorems · Theorem · global analysis

AnalyticAt.differentiableWithinAt

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type v} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F} {x : E}
  {s : Set E}, AnalyticAt 𝕜 f x → DifferentiableWithinAt 𝕜 f s x
Defined in
Mathlib.Analysis.Calculus.FDeriv.Analytic
Cited by
5 results in Mathlib
Foundations
Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace
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Around this declaration

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InnerProductSpace.HarmonicOnNhd.circleAverage_eq · cited by 5HarmonicOnNhd.circleAvera…AnalyticOnNhd.differentiableOn · cited by 3AnalyticOnNhd.differentia…InnerProductSpace.HarmonicOnNhd.circleAverage_re_herglotzRieszKernel_smul · cited by 2HarmonicOnNhd.circleAvera…HasFPowerSeriesOnBall.differentiableOn · cited by 1HasFPowerSeriesOnBall.dif…HasFiniteFPowerSeriesOnBall.differentiableOn · cited by 0HasFiniteFPowerSeriesOnBa…Set · cited by 53352SetNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldDifferentiableWithinAt · cited by 453DifferentiableWithinAtAnalyticAt · cited by 321AnalyticAtDifferentiableAt.differentiableWithinAt · cited by 96DifferentiableAt.differen…AnalyticAt.differentiableAt · cited by 18AnalyticAt.differentiable…AnalyticAt.differentiableWith…CITED BYCITES

Cites8

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Cited by5

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