∀ {α : Type u_1} [inst : Field α] [inst_1 : LinearOrder α] [inst_2 : IsStrictOrderedRing α] {β : Type u_2}
  [inst_3 : Ring β] {abv : β → α} [inst_4 : IsAbsoluteValue abv] {f g : CauSeq β abv},
  CauSeq.Completion.mk f = CauSeq.Completion.mk g ↔ (f - g).LimZero