∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] {X Y : C} {f g : X ⟶ Y} {X' Y' : C} {f' g' : X' ⟶ Y'}
  (e₀ : X ≅ X') (e₁ : Y ≅ Y'),
  CategoryTheory.CategoryStruct.comp e₀.hom f' = CategoryTheory.CategoryStruct.comp f e₁.hom →
    CategoryTheory.CategoryStruct.comp
        ((CategoryTheory.Limits.parallelPair f g).map CategoryTheory.Limits.WalkingParallelPairHom.left) e₁.hom =
      CategoryTheory.CategoryStruct.comp e₀.hom
        ((CategoryTheory.Limits.parallelPair f' g').map CategoryTheory.Limits.WalkingParallelPairHom.left)