Theorems · Theorem · real analysis

HasDerivAtFilter.hasFDerivAtFilter

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : AddCommGroup F] [inst_2 : Module 𝕜 F]
  [inst_3 : TopologicalSpace F] {f : 𝕜 → F} {f' : F} {L : Filter (𝕜 × 𝕜)} [inst_4 : ContinuousSMul 𝕜 F],
  HasDerivAtFilter f f' L → HasFDerivAtFilter f (ContinuousLinearMap.toSpanSingleton 𝕜 f') L

Alias of the forward direction of hasDerivAtFilter_iff_hasFDerivAtFilter.

Defined in

Mathlib.Analysis.Calculus.Deriv.Basic

Cited by

5 results in Mathlib

Foundations

Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldAddCommGroupModuleTopologicalSpaceContinuousSMul