Theorems · Theorem · real analysis

differentiableAt_conj_conj_iff

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] [inst_1 : StarRing 𝕜] {x : 𝕜} [NormedStarGroup 𝕜] {f : 𝕜 → 𝕜},
  DifferentiableAt 𝕜 (⇑(starRingEnd 𝕜) ∘ f ∘ ⇑(starRingEnd 𝕜)) x ↔ DifferentiableAt 𝕜 f ((starRingEnd 𝕜) x)

A function f is differentiable at conj z iff conj ∘ f ∘ conj is differentiable at z.

Defined in

Mathlib.Analysis.Calculus.Deriv.Star

Cited by

1 results in Mathlib

Foundations

Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldStarRingNormedStarGroup