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Theorems · Theorem · global analysis

DifferentiableWithinAt.iterate

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {x : E} {s : Set E} {f : E → E},
  DifferentiableWithinAt 𝕜 f s x → f x = x → Set.MapsTo f s s → ∀ (n : ℕ), DifferentiableWithinAt 𝕜 f^[n] s x
Defined in
Mathlib.Analysis.Calculus.FDeriv.Comp
Cited by
0 results in Mathlib
Foundations
Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpace
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Set · cited by 53352SetNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldNat.iterate · cited by 740Nat.iterateSet.MapsTo · cited by 732Set.MapsToDifferentiableWithinAt · cited by 453DifferentiableWithinAtDifferentiableWithinAt.hasFDerivWithinAt · cited by 132DifferentiableWithinAt.ha…HasFDerivWithinAt.differentiableWithinAt · cited by 65HasFDerivWithinAt.differe…HasFDerivWithinAt.iterate · cited by 2HasFDerivWithinAt.iterateDifferentiableWithinAt.iterateCITED BYCITES

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