∀ {G : Type u_1} {G' : Type u_2} [inst : CommGroup G] [inst_1 : LinearOrder G] [IsOrderedMonoid G]
  [inst_3 : CommGroup G'] [inst_4 : LinearOrder G'] [IsOrderedMonoid G'] (x : G) (y : G'),
  1 < max x x⁻¹ →
    1 < max y y⁻¹ →
      ∀ (hxc : Subgroup.closure {x} = Subgroup.closure {max x x⁻¹})
        (hyc : Subgroup.closure {y} = Subgroup.closure {max y y⁻¹}),
        Function.LeftInverse (fun a => ⟨max x x⁻¹ ^ ⋯.choose, ⋯⟩) fun a => ⟨max y y⁻¹ ^ ⋯.choose, ⋯⟩