Instantiating the universal property where h := \langle f, g \rangle \circ h, f := f \circ h, and g := g \circ h: \pi _0 \circ \langle f, g \rangle \circ h = f \circ h \land \pi _1 \circ \langle f, g \rangle \circ h = g \circ h\ \text {iff}\ \langle f, g \rangle \circ h = \langle f \circ h , g \circ h \rangle Simplifying using the pictorial properties in § [dt-0027] (shown equivalent to the universal property in Exercise [dt-0028]): f \circ h = f \circ h \land g \circ h = g \circ h\ \text {iff}\ \langle f, g \rangle \circ h = \langle f \circ h , g \circ h \rangle By logical simplifications, we arrive at \langle f, g \rangle \circ h = \langle f \circ h , g \circ h \rangle as required.