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
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.