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Complete the proof of theorem $7.27$ by showing that

$(q_{P},w,Z_{0})\vdash(q,\in,\gamma)$ if and only if $(q_{P},q_{A},w,Z_{0}) \vdash((q,p),\in,\gamma),$  where $p =\hat{\delta}(p_{A},w).$

in Theory of Computation by Veteran (58.8k points)
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