Theorems · Theorem · commutative algebra

HahnModule.add_smul

∀ {Γ : Type u_1} {Γ' : Type u_2} {R : Type u_3} {V : Type u_5} [inst : PartialOrder Γ] [inst_1 : PartialOrder Γ']
  [inst_2 : VAdd Γ Γ'] [inst_3 : IsOrderedCancelVAdd Γ Γ'] [inst_4 : AddCommMonoid V] [inst_5 : AddCommMonoid R]
  [inst_6 : SMulWithZero R V] {x y : HahnSeries Γ R} {z : HahnModule Γ' R V},
  (∀ (r s : R) (u : V), (r + s) • u = r • u + s • u) → (x + y) • z = x • z + y • z

Defined in

Mathlib.RingTheory.HahnSeries.Multiplication

Cited by

0 results in Mathlib

Foundations

Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PartialOrderPartialOrderVAddIsOrderedCancelVAddAddCommMonoidAddCommMonoidSMulWithZero