•So let spoiler choose U µ A.
–|U| · 2k-1. Pick any V µ B s.t. |V| = |U|
–|A-U| · 2k-1. Pick
any V µ B s.t. |V| = |U|
–|U| > 2k-1 and |A-U| > 2k-1.
We pick a V
s.t. |V| > 2k-1 and |A-V| > 2k-1.
•By induction duplicator has two winning strategies:
–on U, V
–on A-U, A-V
•Combine the strategy to get a winning strategy on A, B. [ how ? ]