Let's have waves with their carried power proportional to the square of their amplitude(s). The waves obey the principle of superposition. Before superposition, we can calculate the power output based on the amplitudes. After superposition, there will be new values for the amplitudes, but the power output is expected to remain the same, by the Law of CoE. I'm looking for a mathematical proof which shows that the superposition of such waves is consistent the Law of CoE.