Theorems · Theorem · global analysis

DifferentiableAt.isBigO_sub

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F}
  {x₀ : E}, DifferentiableAt 𝕜 f x₀ → (fun x => f x - f x₀) =O[nhds x₀] fun x => x - x₀

Defined in

Mathlib.Analysis.Calculus.FDeriv.Basic

Cited by

7 results in Mathlib

Foundations

Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace