If the program fails, it only proves that the chosen defeatEpsilon proof does not work. In order to prove that that their is no defeatEpsilon, you would need to

If the program fails, it only proves that the chosen defeatEpsilon proof does not work. In order to prove that that their is no defeatEpsilon, you would need to run you program against every function of the Real->Real. If your delta epsilon did work, you would need to test in for every delta>0.