{P : Type u_2} →
  [inst : LE P] →
    {motive : Order.Ideal P → Sort u} →
      (t : Order.Ideal P) →
        ((toLowerSet : LowerSet P) →
            (nonempty' : toLowerSet.carrier.Nonempty) →
              (directed' : DirectedOn (fun x1 x2 => x1 ≤ x2) toLowerSet.carrier) →
                motive { toLowerSet := toLowerSet, nonempty' := nonempty', directed' := directed' }) →
          motive t