∀ {K : Type u_1} [inst : DivisionRing K] [inst_1 : LinearOrder K] [inst_2 : IsOrderedRing K] [inst_3 : Archimedean K]
  {M : Type u_2} [inst_4 : AddCommGroup M] [inst_5 : LinearOrder M] [inst_6 : IsOrderedAddMonoid M]
  [inst_7 : Module K M] [inst_8 : IsOrderedModule K M] {R : Type u_3} [inst_9 : AddCommGroup R]
  [inst_10 : LinearOrder R] [inst_11 : Module K R] [IsOrderedAddMonoid R] [Archimedean R]
  [h : Nonempty (HahnEmbedding.Seed K M R)],
  ∃ f,
    StrictMono ⇑f ∧ ∀ (a : M), ArchimedeanClass.mk a = (FiniteArchimedeanClass.withTopOrderIso M) (ofLex (f a)).orderTop