{C : Type u} →
  {P : Sort u_1} →
    {X Y Z : CategoryTheory.FreeMonoidalCategory C} →
      {f : X.Hom Y} →
        {g : Y.Hom Z} →
          {X' Y' Z' : CategoryTheory.FreeMonoidalCategory C} →
            {f' : X'.Hom Y'} →
              {g' : Y'.Hom Z'} →
                X = X' → Z = Z' → f.comp g ≍ f'.comp g' → (X ≍ X' → Y ≍ Y' → Z ≍ Z' → f ≍ f' → g ≍ g' → P) → P