We also know that the symbol X cannot be removed from the stack once P has entered this configuration.

Therefore for some , if we consider the strings uZ and vZ, then we must have

                             

                            

So, either both uZ and vZ are accepted or both are rejected by P. But since u and v are distinct, for some z one may be in L while other is not. This leads to a contradiction. (Since P should have accepted only one of these two, which is in L and the other should have been rejected.)

Hence our assumption that P accepts L must be false.