∀ {X : SSet} {A : X.Subcomplex} {P : A.Pairing} {α : Type v} [inst : PartialOrder α] (rank : ↑P.II → α)
  (lt : ∀ {x y : ↑P.II}, P.AncestralRel x y → (↑x).dim = (↑y).dim → rank x < rank y) (rank_1 : ↑P.II → α)
  (lt_1 : ∀ {x y : ↑P.II}, P.AncestralRel x y → (↑x).dim = (↑y).dim → rank_1 x < rank_1 y),
  ({ rank := rank, lt := lt } = { rank := rank_1, lt := lt_1 }) = (rank = rank_1)