{X : SSet} →
  {A : X.Subcomplex} →
    {P : A.Pairing} →
      {α : Type v} →
        [inst : PartialOrder α] →
          (rank : ↑P.II → α) →
            (∀ {x y : ↑P.II}, P.AncestralRel x y → (↑x).dim = (↑y).dim → rank x < rank y) → P.WeakRankFunction α