•Lemma. Assume (2X, µ) ºk (2Y, µ). Then the duplicator has a winning strategy where he responds to ; with ;, to Y with X, to X with Y.
•[Why ?]
•Lemma. Assume X1 Å X2 = ;, Y1 Å Y2 = ; and that (2X1, µ) ºk (2Y1, µ), (2X2, µ) ºk (2Y2, µ). Then:
(2X1 [ X2, X1, X2, µ) ºk (2Y1 [ Y2, Y1, Y2, µ)
•[Why ?]
•[How do prove the
proposition ?]