Theorems · Theorem · real analysis

HasDerivWithinAt.clm_comp

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {E : Type w} [inst_3 : NormedAddCommGroup E] [inst_4 : NormedSpace 𝕜 E] {x : 𝕜} {s : Set 𝕜}
  {G : Type u_2} [inst_5 : NormedAddCommGroup G] [inst_6 : NormedSpace 𝕜 G] {c : 𝕜 → F →L[𝕜] G} {c' : F →L[𝕜] G}
  {d : 𝕜 → E →L[𝕜] F} {d' : E →L[𝕜] F},
  HasDerivWithinAt c c' s x →
    HasDerivWithinAt d d' s x → HasDerivWithinAt (fun y => c y ∘SL d y) (c' ∘SL d x + c x ∘SL d') s x

Defined in

Mathlib.Analysis.Calculus.Deriv.Mul

Cited by

2 results in Mathlib

Foundations

Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace