Theorems · Theorem · functional analysis

fderiv_continuousLinearEquiv_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] {G' : Type u_5} [inst_7 : NormedAddCommGroup G']
  [inst_8 : NormedSpace 𝕜 G'] (L : G ≃L[𝕜] G') (f : E → F →L[𝕜] G) (x : E),
  fderiv 𝕜 (fun x => ↑L ∘SL f x) x = ↑((ContinuousLinearEquiv.refl 𝕜 F).arrowCongr L) ∘SL fderiv 𝕜 f x

Defined in

Mathlib.Analysis.Calculus.FDeriv.Equiv

Cited by

1 results in Mathlib

Foundations

Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace