Toward a contradiction assume there exists a Turing machine H which when given as input the encoding for an arbitrary Turing machine, M, and an arbitrary input string, x, can decide if M will halt, (ie., accept or reject), on input x or Loop. Then it would be possible to build a Turing machine IMP which could take its input string, x, using the H machine coding as a subroutine determine if a M_x, with control encoding x, would Halt or x and then do the opposite. Show that machine IMP cannot possibly exist. What does this prove