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