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safe edge theorem proof clarification

Although correct, that statement, "$w(T') = w(T) - w(x,y) + w(u,v) \le w(T)$" alone is indeed confusing, since it leaves the impression that $w(T')$ might be smaller than $w(T)$. Well, the ...
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Recursively deleting spanning forest from graph, how many iterations maximum to get to the empty graph?

This was an irrelevant answer that I had to replace manually (since I cannot delete from my current device)
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