Lemma: between any two consecutive saturations of (v,w), both d(v) and d(w) increase by at least 2.

In first saturation, increasing flow along augmenting path, and

d(v)= d(w)+1.

Before edge can be saturated again, must send flow back from w to v. => d’(w)= d’(v)+1.

In next saturation, again have d’’(v)=d’’(w)+ 1.

=> d’’(v)= d’’(w)+1 >= d’(w)+1 >= d’(v)+2 >= d(v)+2.

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