Theorems · Theorem · real analysis

HasDerivAtFilter.star

∀ {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] {f : 𝕜 → F} {f' : F}
  [TrivialStar 𝕜] {L : Filter (𝕜 × 𝕜)}, HasDerivAtFilter f f' L → HasDerivAtFilter (fun x => star (f x)) (star f') L

Defined in

Mathlib.Analysis.Calculus.Deriv.Star

Cited by

3 results in Mathlib

Foundations

Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldStarRingNormedAddCommGroupNormedSpaceStarAddMonoidStarModuleContinuousStarTrivialStar