Theorems · Theorem · global analysis

HasFDerivWithinAt.comp

∀ {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] {G : Type u_4}
  [inst_5 : NormedAddCommGroup G] [inst_6 : NormedSpace 𝕜 G] {f : E → F} {f' : E →L[𝕜] F} (x : E) {s : Set E}
  {g : F → G} {g' : F →L[𝕜] G} {t : Set F},
  HasFDerivWithinAt g g' t (f x) →
    HasFDerivWithinAt f f' s x → Set.MapsTo f s t → HasFDerivWithinAt (g ∘ f) (g' ∘SL f') s x

Defined in

Mathlib.Analysis.Calculus.FDeriv.Comp

Cited by

11 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace