{α : Type u_1} →
  {β : Type u_2} →
    [inst : LinearOrder α] →
      [inst_1 : LinearOrder β] →
        [inst_2 : DenselyOrdered β] →
          [inst_3 : NoMinOrder β] →
            [inst_4 : NoMaxOrder β] →
              [inst_5 : Nonempty β] →
                (a : α) →
                  (I : Order.Ideal (Order.PartialIso α β)) →
                    (∃ f ∈ Order.PartialIso.definedAtLeft β a, f ∈ I) → { b // ∃ f ∈ I, (a, b) ∈ ↑f }