Theorems · Theorem · several complex variables

FormalMultilinearSeries.comp_rightInv_aux1

∀ {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] {n : ℕ},
  0 < n →
    ∀ (p : FormalMultilinearSeries 𝕜 E F) (q : FormalMultilinearSeries 𝕜 F E) (v : Fin n → F),
      (p.comp q n) v = ∑ c ∈ {c | 1 < c.length}.toFinset, (p c.length) (q.applyComposition c v) + (p 1) fun x => (q n) v

Defined in

Mathlib.Analysis.Analytic.Inverse

Cited by

2 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace