17
Proof 2
•Remark: if  L1 ºk L2 then the duplicator has a winning strategy where it responds with min(L2) to min(L1), and with max(L2) to max(L1), and vice versa.  [why ?]
•
•Lemma If L1· a ºk L2 · b and L1¸ a ºk L2 ¸ b 
then (L1 ,a) ºk (L2 ,b)
•
•[how does this help us prove the theorem ?]