∀ {R : Type u_1} [inst : LinearOrder R] [inst_1 : CommRing R] [inst_2 : IsStrictOrderedRing R] {S : Type u_3}
  [inst_3 : LinearOrder S] [inst_4 : CommRing S] [inst_5 : IsStrictOrderedRing S] (f : S →+o R),
  (ArchimedeanClass.orderHom f) 0 = ArchimedeanClass.mk (f 1)