∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {A : C}
  [inst_1 : HomotopicalAlgebra.CategoryWithWeakEquivalences C] (P : HomotopicalAlgebra.PathObject A)
  [inst_2 : CategoryTheory.Limits.HasBinaryProducts C] {Z : C} (h : A ⨯ A ⟶ Z),
  CategoryTheory.CategoryStruct.comp P.symm.p h =
    CategoryTheory.CategoryStruct.comp P.p
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.prod.braiding A A).hom h)