Theorems · Theorem · real analysis

HasDerivAtFilter.comp_hasFDerivAtFilter_of_eq

Deprecated since 2026-02-17Use HasDerivAtFilter.comp_hasFDerivAtFilter instead.

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {E : Type w} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {𝕜' : Type u_1} [inst_3 : NontriviallyNormedField 𝕜'] [inst_4 : NormedAlgebra 𝕜 𝕜']
  {h₂ : 𝕜' → 𝕜'} {h₂' y : 𝕜'} {f : E → 𝕜'} {f' : E →L[𝕜] 𝕜'} (x : E) {L' : Filter 𝕜'} {L'' : Filter E},
  HasDerivAtFilter h₂ h₂' (L' ×ˢ pure y) →
    HasFDerivAtFilter f f' (L'' ×ˢ pure x) →
      Filter.Tendsto f L'' L' → y = f x → HasFDerivAtFilter (h₂ ∘ f) (h₂' • f') (L'' ×ˢ pure x)

Defined in

Mathlib.Analysis.Calculus.Deriv.Comp

Cited by

0 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNontriviallyNormedFieldNormedAlgebra