Fix a bug in the proof: i \in Overlap(x, Acquired) should be acquired[i] \in Overlap(x, Acquired).
Fix a bug in the proof: i \in Overlap(x, Acquired) should be
acquired[i] \in Overlap(x, Acquired).

eaburns/pbnf,eaburns/pbnf,eaburns/pbnf,eaburns/pbnf