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I'm reviewing max flow min cut for an upcoming exam and one of the proofs relies on the fact that for any flow $f$ on graph $G$ and residual graph $G_f$, $$\mathrm{maxflow}(G) = \mathrm{val}(f) + \mathrm{maxflow}(G_f).$$

This seems to be intuitively true, but I can't seem to prove it. Any help would be appreciated!

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