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Theorems · Theorem · real analysis

differentiableAt_apply

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {ι : Type u_6} {F' : ι → Type u_7}
  [inst_1 : (i : ι) → NormedAddCommGroup (F' i)] [inst_2 : (i : ι) → NormedSpace 𝕜 (F' i)] (i : ι) (f : (i : ι) → F' i),
  DifferentiableAt 𝕜 (fun f => f i) f
Defined in
Mathlib.Analysis.Calculus.FDeriv.Prod
Cited by
1 results in Mathlib
Foundations
Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpace
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Around this declaration

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

differentiable_apply · cited by 1differentiable_applyNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldDifferentiableAt · cited by 617DifferentiableAtContinuousLinearMap.proj · cited by 77ContinuousLinearMap.projhasFDerivAt_apply · cited by 4hasFDerivAt_applydifferentiableAt_applyCITED BYCITES

Cites6

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Cited by1

Results whose statement or proof uses this declaration.