Abstract. The Swing Lemma, due to G. Grätzer for slim semimodular lattices and extended by G. Czédli, G. Grätzer, and H. Lakser for all planar semimodular lattices, describes the congruence generated by a prime interval in an efficient way. Here we present a new, direct proof of this lemma, which is shorter than the earlier ones. Also, motivated by the Swing Lemma and mechanical pinball games with flippers, we construct an online game called Swing Lattice Game.

DOI: 10.14232/actasm-016-036-3

AMS Subject Classification (1991): 06C10

Keyword(s): Swing Lemma, Swing Lattice Game, semimodular lattice, planar lattice, lattice congruence

Received July 15, 2016, and in revised form March 14, 2017. (Registered under 36/2016.)