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By a) and Lemma 6.1, ?t ? µ\{y}, label k (t) ? label k (y) So ?(k) = y, which completes the proof. c) We assume for contradiction that ?t ? µ \ {y}, ? ?1 (t) < ? ?1 (y) and ?t ? µ \ {y} | N um i (t) ? N um i (y) By Lemma 6.2 ?t 1 ? µ \ {y} | ?t ? µ[t 1 , y] \ {t 1 }, N um i (t) ? N um i (t 1 ), pp.1-1 ,