Theorems · Theorem · group theory

IsMulIndecomposable.image_baseOf_inv_comp_eq

∀ {ι : Type u_1} {G : Type u_3} {S : Type u_4} [inst : CommGroup G] [inst_1 : LinearOrder S] [inst_2 : InvolutiveInv ι]
  [inst_3 : CommGroup S] [IsOrderedMonoid S] (v : ι → G),
  (∀ (i : ι), v i⁻¹ = (v i)⁻¹) →
    ∀ (f : G →* S),
      v '' IsMulIndecomposable.baseOf v (invMonoidHom.comp f) = ⇑invMonoidHom ∘ v '' IsMulIndecomposable.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

CommGroupLinearOrderInvolutiveInvCommGroupIsOrderedMonoid