Theorems · Theorem · global analysis

HasStrictFDerivAt.clm_apply

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {G : Type u_4} [inst_3 : NormedAddCommGroup G] [inst_4 : NormedSpace 𝕜 G] {x : E}
  {H : Type u_5} [inst_5 : NormedAddCommGroup H] [inst_6 : NormedSpace 𝕜 H] {c : E → G →L[𝕜] H} {c' : E →L[𝕜] G →L[𝕜] H}
  {u : E → G} {u' : E →L[𝕜] G},
  HasStrictFDerivAt c c' x →
    HasStrictFDerivAt u u' x → HasStrictFDerivAt (fun y => (c y) (u y)) (c x ∘SL u' + c'.flip (u x)) x

Defined in

Mathlib.Analysis.Calculus.FDeriv.CompCLM

Cited by

2 results in Mathlib

Foundations

Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace