Theorems · Theorem · group theory

IsAddIndecomposable.pairwise_baseOf_sub_notMem

∀ {ι : Type u_1} {G : Type u_3} {S : Type u_4} [inst : AddCommGroup G] [inst_1 : LinearOrder S]
  [inst_2 : InvolutiveNeg ι] [inst_3 : AddCommGroup S] [IsOrderedAddMonoid S] (v : ι → G),
  (∀ (i : ι), v (-i) = -v i) →
    ∀ (f : G →+ S),
      (∀ (i : ι), f (v i) ≠ 0) → (IsAddIndecomposable.baseOf v f).Pairwise fun i j => v i - v j ∉ Set.range v

Defined in

Mathlib.Algebra.Group.Irreducible.Indecomposable

Cited by

1 results in Mathlib

Foundations

Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupLinearOrderInvolutiveNegAddCommGroupIsOrderedAddMonoid