Theorems · Theorem · group theory

IsAddIndecomposable.image_baseOf_neg_comp_eq

∀ {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),
      v '' IsAddIndecomposable.baseOf v (negAddMonoidHom.comp f) =
        ⇑negAddMonoidHom ∘ v '' IsAddIndecomposable.baseOf v f

Defined in

Mathlib.Algebra.Group.Irreducible.Indecomposable

Cited by

1 results in Mathlib

Foundations

Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupLinearOrderInvolutiveNegAddCommGroupIsOrderedAddMonoid