Swing lattice game and a short proof of the swing lemma for planar semimodular lattices

The swing lemma, due to G. Gr"atzer for slim semimodular lattices and extended by G. Cz'edli and G. Gr"atzer for all planar semimodular lattices, describes the congruence generated by a prime interval in an efficient way. Here we present a new proof for this lemma, which is shorter than the earlier two. Also, motivated by the swing lemma and mechanical pinball games with flippers, we construct an online game called Swing lattice game. A computer program realizing this game is available from the authors’ websites.