Theorems · Theorem · global analysis

HasFDerivAt.isEquivalent_sub

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
  [inst_3 : TopologicalSpace E] {F : Type u_3} [inst_4 : NormedAddCommGroup F] [inst_5 : NormedSpace 𝕜 F] {f : E → F}
  {f' : E →L[𝕜] F} {x : E},
  HasFDerivAt f f' x →
    Topology.IsInducing ⇑f' → Asymptotics.IsEquivalent (nhds x) (fun x_1 => f x_1 - f x) fun x_1 => f' (x_1 - x)

Defined in

Mathlib.Analysis.Calculus.FDeriv.Basic

Cited by

0 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldAddCommGroupModuleTopologicalSpaceNormedAddCommGroupNormedSpace