Theorems · Theorem · group theory

IsAddIndecomposable.mem_or_neg_mem_closure_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) (f : G →+ S) (i : ι),
  f (v i) ≠ 0 →
    v (-i) = -v i →
      v i ∈ AddSubmonoid.closure (v '' IsAddIndecomposable.baseOf v f) ∨
        -v i ∈ AddSubmonoid.closure (v '' IsAddIndecomposable.baseOf v f)

Defined in

Mathlib.Algebra.Group.Irreducible.Indecomposable

Cited by

5 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupLinearOrderFiniteInvolutiveNegAddCommGroupIsOrderedAddMonoid