Theorems · Theorem · real analysis

differentiableAt_star_conj_iff

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] [inst_1 : StarRing 𝕜] {F : Type v} [inst_2 : NormedAddCommGroup F]
  [inst_3 : NormedSpace 𝕜 F] [inst_4 : StarAddMonoid F] [StarModule 𝕜 F] [ContinuousStar F] {x : 𝕜} [NormedStarGroup 𝕜]
  {f : 𝕜 → F}, DifferentiableAt 𝕜 (star ∘ f ∘ ⇑(starRingEnd 𝕜)) x ↔ DifferentiableAt 𝕜 f ((starRingEnd 𝕜) x)

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

Defined in

Mathlib.Analysis.Calculus.Deriv.Star

Cited by

2 results in Mathlib

Foundations

Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldStarRingNormedAddCommGroupNormedSpaceStarAddMonoidStarModuleContinuousStarNormedStarGroup