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Let ? be a flow network, and let ? be a flow for ?. Prove that...

Let ? be a flow network, and let ? be a flow for ?. Prove that for any cut, x, of ?, the value of ? is equal to the flow across cut x, that is, |?| = ?(x). Use an induction proof on the number of vertices in set ? of the cut. That is, the base case would be |?| = 1, where ? = {?}.

Please use induction to prove it.

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