Theorems · Theorem · real analysis

hasStrictDerivAt_iff_hasStrictFDerivAt

∀ {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} {x : 𝕜} [inst_4 : ContinuousSMul 𝕜 F],
  HasStrictDerivAt f f' x ↔ HasStrictFDerivAt f (ContinuousLinearMap.toSpanSingleton 𝕜 f') x

Defined in

Mathlib.Analysis.Calculus.Deriv.Basic

Cited by

1 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldAddCommGroupModuleTopologicalSpaceContinuousSMul