Theorems · Theorem · real analysis

HasDerivWithinAt.hasFDerivWithinAt

∀ {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} {x : 𝕜} {s : Set 𝕜} [inst_4 : ContinuousSMul 𝕜 F] {f' : F},
  HasDerivWithinAt f f' s x → HasFDerivWithinAt f (ContinuousLinearMap.toSpanSingleton 𝕜 f') s x

Alias of the forward direction of hasDerivWithinAt_iff_hasFDerivWithinAt. Expressing HasDerivWithinAt f f' s x in terms of HasFDerivWithinAt

Defined in

Mathlib.Analysis.Calculus.Deriv.Basic

Cited by

26 results in Mathlib

Foundations

Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldAddCommGroupModuleTopologicalSpaceContinuousSMul