∀ {α : Type u_2} {β : Type u_3} [inst : Field α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α] [inst_3 : Field β]
  [inst_4 : ConditionallyCompleteLinearOrder β] [IsStrictOrderedRing β] [Archimedean α] {a : α},
  0 < a →
    ∀ b ∈ LinearOrderedField.cutMap β (a * a),
      b ≤
        ConditionallyCompleteLinearOrderedField.inducedMap α β a *
          ConditionallyCompleteLinearOrderedField.inducedMap α β a