∀ {n : ℕ} (S : Finset (Fin (n + 1))) (m : ℕ) (e : Fin (m + 1) ≃o ↥S) {j : SimplexCategory} (f : j ⟶ { len := m }),
  ∀
    x ∈
      Finset.image
        ⇑(SimplexCategory.Hom.toOrderHom
            (SSet.stdSimplex.objEquiv
              (SSet.stdSimplex.objMk
                ((OrderHom.Subtype.val fun x => x ∈ S).comp
                  (e.toOrderEmbedding.toOrderHom.comp (SimplexCategory.Hom.toOrderHom f))))))
        ⊤,
    x ∈ S