Theorems · Theorem · real analysis

ContDiffWithinAt.pow

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type uE} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {s : Set E} {x : E} {n : WithTop ℕ∞} {𝔸 : Type u_3} [inst_3 : NormedRing 𝔸]
  [inst_4 : NormedAlgebra 𝕜 𝔸] {f : E → 𝔸},
  ContDiffWithinAt 𝕜 n f s x → ∀ (m : ℕ), ContDiffWithinAt 𝕜 n (fun y => f y ^ m) s x

Defined in

Mathlib.Analysis.Calculus.ContDiff.Operations

Cited by

4 results in Mathlib

Foundations

Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedRingNormedAlgebra