Theorems · Theorem · real analysis

HasDerivAtFilter.isEquivalent_sub

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {f' : F} {L : Filter (𝕜 × 𝕜)},
  HasDerivAtFilter f f' L → f' ≠ 0 → Asymptotics.IsEquivalent L (fun p => f p.1 - f p.2) fun p => (p.1 - p.2) • f'

Defined in

Mathlib.Analysis.Calculus.Deriv.Basic

Cited by

0 results in Mathlib

Foundations

Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace