Theorems · Theorem · real analysis

HasDerivAt.star_conj

∀ {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} {f' : F}, HasDerivAt f f' x → HasDerivAt (star ∘ f ∘ ⇑(starRingEnd 𝕜)) (star f') ((starRingEnd 𝕜) x)

If f has derivative f' at z, then star ∘ f ∘ conj has derivative star f' at conj z.

Defined in

Mathlib.Analysis.Calculus.Deriv.Star

Cited by

3 results in Mathlib

Foundations

Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldStarRingNormedAddCommGroupNormedSpaceStarAddMonoidStarModuleContinuousStarNormedStarGroup