Theorems · Theorem · commutative algebra

HahnSeries.SummableFamily.coeff_smul

∀ {Γ : Type u_1} {Γ' : Type u_2} {α : Type u_5} {β : Type u_6} [inst : PartialOrder Γ] [inst_1 : PartialOrder Γ']
  [inst_2 : VAdd Γ Γ'] [inst_3 : IsOrderedCancelVAdd Γ Γ'] {R : Type u_7} {V : Type u_8} [inst_4 : Semiring R]
  [inst_5 : AddCommMonoid V] [inst_6 : Module R V] (s : HahnSeries.SummableFamily Γ R α)
  (t : HahnSeries.SummableFamily Γ' V β) (g : Γ'),
  (s.smul t).hsum.coeff g = ∑ gh ∈ Finset.VAddAntidiagonal g ⋯, s.hsum.coeff gh.1 • t.hsum.coeff gh.2

Defined in

Mathlib.RingTheory.HahnSeries.Summable

Cited by

2 results in Mathlib

Foundations

Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PartialOrderPartialOrderVAddIsOrderedCancelVAddSemiringAddCommMonoidModule