{X : SSet} →
  {A : X.Subcomplex} →
    {P : A.Pairing} →
      {α : Type v} →
        {inst : PartialOrder α} →
          {P_1 : Sort u_1} →
            {rank : ↑P.II → α} →
              {lt : ∀ {x y : ↑P.II}, P.AncestralRel x y → rank x < rank y} →
                {rank' : ↑P.II → α} →
                  {lt' : ∀ {x y : ↑P.II}, P.AncestralRel x y → rank' x < rank' y} →
                    { rank := rank, lt := lt } = { rank := rank', lt := lt' } → (rank ≍ rank' → P_1) → P_1