Theorems · Theorem · commutative algebra

HahnSeries.SummableFamily.smul_eq

∀ {Γ : Type u_1} {Γ' : Type u_2} {R : Type u_3} {V : Type u_4} {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'] {x : HahnSeries Γ R} {t : HahnSeries.SummableFamily Γ' V β},
  x • t = HahnSeries.SummableFamily.Equiv (Equiv.punitProd β) ((HahnSeries.SummableFamily.const Unit x).smul t)

Defined in

Mathlib.RingTheory.HahnSeries.Summable

Cited by

1 results in Mathlib

Foundations

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

Assumes

PartialOrderPartialOrderAddCommMonoidAddCommMonoidSMulWithZeroVAddIsOrderedCancelVAdd