Theorems · Theorem · commutative algebra

HahnModule.coeff_single_smul_vadd

∀ {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 : MulZeroClass R]
  [inst_6 : SMulWithZero R V] {r : R} {x : HahnModule Γ' R V} {a : Γ'} {b : Γ},
  ((HahnModule.of R).symm ((HahnSeries.single b) r • x)).coeff (b +ᵥ a) = r • ((HahnModule.of R).symm x).coeff a

Defined in

Mathlib.RingTheory.HahnSeries.Multiplication

Cited by

2 results in Mathlib

Foundations

Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PartialOrderPartialOrderVAddIsOrderedCancelVAddAddCommMonoidMulZeroClassSMulWithZero