Theorems · Theorem · group theory

AddSubgroup.closure_image_isAddIndecomposable_baseOf

∀ {ι : Type u_1} {G : Type u_3} {S : Type u_4} [inst : AddCommGroup G] [inst_1 : LinearOrder S] [Finite ι]
  [inst_3 : InvolutiveNeg ι] [inst_4 : AddCommGroup S] [IsOrderedAddMonoid S] (v : ι → G),
  (∀ (i : ι), v (-i) = -v i) →
    ∀ (f : G →+ S),
      (∀ (i : ι), f (v i) ≠ 0) →
        AddSubgroup.closure (v '' IsAddIndecomposable.baseOf v f) = AddSubgroup.closure (Set.range v)

Defined in

Mathlib.Algebra.Group.Irreducible.Indecomposable

Cited by

1 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupLinearOrderFiniteInvolutiveNegAddCommGroupIsOrderedAddMonoid