Theorems · Theorem · commutative algebra

HahnSeries.SummableFamily.sum_vAddAntidiagonal_eq

∀ {Γ : Type u_1} {Γ' : Type u_2} {R : Type u_3} {V : Type u_4} {α : Type u_5} {β : Type u_6} [inst : PartialOrder Γ]
  [inst_1 : PartialOrder Γ'] [inst_2 : AddCommMonoid V] [inst_3 : AddCommMonoid R] [inst_4 : SMulWithZero R V]
  [inst_5 : VAdd Γ Γ'] [inst_6 : IsOrderedCancelVAdd Γ Γ'] (s : HahnSeries.SummableFamily Γ R α)
  (t : HahnSeries.SummableFamily Γ' V β) (g : Γ') (a : α × β),
  ∑ x ∈ Finset.VAddAntidiagonal g ⋯, (s a.1).coeff x.1 • (t a.2).coeff x.2 =
    ∑ x ∈ Finset.VAddAntidiagonal g ⋯, (s a.1).coeff x.1 • (t a.2).coeff x.2

Defined in

Mathlib.RingTheory.HahnSeries.Summable

Cited by

1 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PartialOrderPartialOrderAddCommMonoidAddCommMonoidSMulWithZeroVAddIsOrderedCancelVAdd