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Theorems · Theorem · real analysis

HasDerivAtFilter.iterate

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {L : Filter (𝕜 × 𝕜)} {f : 𝕜 → 𝕜} {f' : 𝕜},
  HasDerivAtFilter f f' L → Filter.Tendsto (Prod.map f f) L L → ∀ (n : ℕ), HasDerivAtFilter f^[n] (f' ^ n) L
Defined in
Mathlib.Analysis.Calculus.Deriv.Comp
Cited by
1 results in Mathlib
Foundations
Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedField
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Around this declaration

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HasDerivAt.iterate · cited by 0HasDerivAt.iterateRingHom.id · cited by 18349RingHom.idNontriviallyNormedField · cited by 8742NontriviallyNormedFieldFilter · cited by 8121FilterContinuousLinearMap · cited by 5352ContinuousLinearMapFilter.Tendsto · cited by 3814Filter.TendstoNat.iterate · cited by 740Nat.iterateContinuousLinearMap.toSpanSingleton · cited by 133ContinuousLinearMap.toSpa…HasFDerivAtFilter · cited by 81HasFDerivAtFilterHasDerivAtFilter · cited by 63HasDerivAtFilterHasDerivAtFilter.hasFDerivAtFilter · cited by 5HasDerivAtFilter.hasFDeri…HasFDerivAtFilter.iterate · cited by 4HasFDerivAtFilter.iterateContinuousLinearMap.toSpanSingleton_pow · cited by 3ContinuousLinearMap.toSpa…HasDerivAtFilter.iterateCITED BYCITES

Cites12

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