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Theorems · Theorem · global analysis

HasFPowerSeriesWithinAt.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]
  {p : FormalMultilinearSeries 𝕜 E F} {f : E → F} {x : E} {s : Set E},
  HasFPowerSeriesWithinAt f p s x → DifferentiableWithinAt 𝕜 f (insert x s) x
Defined in
Mathlib.Analysis.Calculus.FDeriv.Analytic
Cited by
1 results in Mathlib
Foundations
Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AnalyticWithinAt.differentiableWithinAt · cited by 3AnalyticWithinAt.differen…Set · cited by 53352SetNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldFormalMultilinearSeries · cited by 615FormalMultilinearSeriesDifferentiableWithinAt · cited by 453DifferentiableWithinAtHasFDerivWithinAt.differentiableWithinAt · cited by 65HasFDerivWithinAt.differe…HasFPowerSeriesWithinAt · cited by 53HasFPowerSeriesWithinAtHasFPowerSeriesWithinAt.hasFDerivWithinAt · cited by 3HasFPowerSeriesWithinAt.h…HasFPowerSeriesWithinAt.diffe…CITED BYCITES

Cites9

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Cited by1

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