Theorems · Theorem · real analysis

fderivWithin_star

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] [inst_1 : StarRing 𝕜] {E : Type u_2} [inst_2 : NormedAddCommGroup E]
  [inst_3 : NormedSpace 𝕜 E] {F : Type u_3} [inst_4 : NormedAddCommGroup F] [inst_5 : StarAddMonoid F]
  [inst_6 : NormedSpace 𝕜 F] [inst_7 : StarModule 𝕜 F] [inst_8 : ContinuousStar F] {f : E → F} {x : E} {s : Set E}
  [inst_9 : TrivialStar 𝕜],
  UniqueDiffWithinAt 𝕜 s x → fderivWithin 𝕜 (fun y => star (f y)) s x = ↑(starL' 𝕜) ∘SL fderivWithin 𝕜 f s x

Defined in

Mathlib.Analysis.Calculus.FDeriv.Star

Cited by

1 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldStarRingNormedAddCommGroupNormedSpaceNormedAddCommGroupStarAddMonoidNormedSpaceStarModuleContinuousStarTrivialStar