Theorems · Theorem · real analysis

HasDerivAtFilter.tendsto_nhds

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {f' : F} {x : 𝕜} {L : Filter 𝕜},
  L ≤ nhds x → HasDerivAtFilter f f' (L ×ˢ pure x) → Filter.Tendsto f L (nhds (f x))

Defined in

Mathlib.Analysis.Calculus.Deriv.Basic

Cited by

2 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace