Theorems · Theorem · commutative algebra

HahnSeries.SummableFamily.hsum_smulFamily

∀ {Γ : Type u_1} {R : Type u_3} {V : Type u_4} {α : Type u_5} [inst : PartialOrder Γ] [inst_1 : AddCommMonoid R]
  [inst_2 : AddCommMonoid V] [inst_3 : SMulWithZero R V] (f : α → R) (s : HahnSeries.SummableFamily Γ V α) (g : Γ),
  (HahnSeries.SummableFamily.smulFamily f s).hsum.coeff g = ∑ᶠ (i : α), f i • (s i).coeff g

Defined in

Mathlib.RingTheory.HahnSeries.Summable

Cited by

0 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PartialOrderAddCommMonoidAddCommMonoidSMulWithZero