Theorems · Theorem · several complex variables

FormalMultilinearSeries.comp_assoc

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} {G : Type u_4} {H : Type u_5} [inst : NontriviallyNormedField 𝕜]
  [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F]
  [inst_5 : NormedAddCommGroup G] [inst_6 : NormedSpace 𝕜 G] [inst_7 : NormedAddCommGroup H] [inst_8 : NormedSpace 𝕜 H]
  (r : FormalMultilinearSeries 𝕜 G H) (q : FormalMultilinearSeries 𝕜 F G) (p : FormalMultilinearSeries 𝕜 E F),
  (r.comp q).comp p = r.comp (q.comp p)

Defined in

Mathlib.Analysis.Analytic.Composition

Cited by

1 results in Mathlib

Foundations

Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace