∀ {X : SSet} {d : ℕ} (x : X.obj (Opposite.op (SimplexCategory.mk d)))
  (y : X.obj (Opposite.op (SimplexCategory.mk (d + 1)))),
  { dim := d, simplex := x }.IsUniquelyCodimOneFace { dim := d + 1, simplex := y } ↔
    ∃! i, CategoryTheory.SimplicialObject.δ X i y = x