∀ {p q n : ℕ}
  (x :
    (CategoryTheory.MonoidalCategoryStruct.tensorObj (SSet.stdSimplex.obj (SimplexCategory.mk p))
          (SSet.stdSimplex.obj (SimplexCategory.mk q))).obj
      (Opposite.op (SimplexCategory.mk n)))
  {m : ℕ} (hm : p + q = m) (i j : Fin (n + 1)),
  i ≤ j → (fun i => ⟨↑(x.1 i) + ↑(x.2 i), ⋯⟩) i ≤ (fun i => ⟨↑(x.1 i) + ↑(x.2 i), ⋯⟩) j