∀ (Γ : Type u_1) (R : Type u_2) [inst : LinearOrder Γ] [inst_1 : LinearOrder R] [inst_2 : AddCommGroup R]
  [inst_3 : IsOrderedAddMonoid R],
  (↑(HahnSeries.finiteArchimedeanClassOrderHomLex Γ R)).comp ↑(HahnSeries.finiteArchimedeanClassOrderHomInvLex Γ R) =
    OrderHom.id