let f, g, f1, g1 be complex-valued Function; :: thesis: (f / g) / (f1 / g1) = (f (#) (g1 | (dom (g1 ^)))) / (g (#) f1)
thus (f / g) / (f1 / g1) = (f / g) (#) ((f1 / g1) ^) by Th47
.= (f / g) (#) ((g1 | (dom (g1 ^))) / f1) by Th51
.= (f (#) (g1 | (dom (g1 ^)))) / (g (#) f1) by Th50 ; :: thesis: verum