Question: Proof. Define verifier V(((M), z),H: (a) Run M on input z for up to k steps. If (M), E) E LHALT, then M must halt

"Proof". Define verifier V(((M), z),H: (a) Run M on input z

"Proof". Define verifier V(((M), z),H: (a) Run M on input z for up to k steps. If (M), E) E LHALT, then M must halt on z after some finite number of steps k, which means that V(((M), z), k) will accept. And if M), z) LH ALT, then V will reject no matter what certificate k is provided. Therefore, V is an efficient verifier for LHALI, so LHALT E NP

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