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Theorems · Theorem · real analysis

HasDerivWithinAt.iterate

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] (x : 𝕜) {s : Set 𝕜} {f : 𝕜 → 𝕜} {f' : 𝕜},
  HasDerivWithinAt f f' s x → f x = x → Set.MapsTo f s s → ∀ (n : ℕ), HasDerivWithinAt f^[n] (f' ^ n) s x
Defined in
Mathlib.Analysis.Calculus.Deriv.Comp
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0 results in Mathlib
Foundations
Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedField
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Set · cited by 53352SetRingHom.id · cited by 18349RingHom.idNontriviallyNormedField · cited by 8742NontriviallyNormedFieldContinuousLinearMap · cited by 5352ContinuousLinearMapNat.iterate · cited by 740Nat.iterateSet.MapsTo · cited by 732Set.MapsToHasFDerivWithinAt · cited by 356HasFDerivWithinAtHasDerivWithinAt · cited by 333HasDerivWithinAtContinuousLinearMap.toSpanSingleton · cited by 133ContinuousLinearMap.toSpa…ContinuousLinearMap.toSpanSingleton_pow · cited by 3ContinuousLinearMap.toSpa…HasFDerivWithinAt.iterate · cited by 2HasFDerivWithinAt.iterateHasDerivWithinAt.iterateCITED BYCITES

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