Congruence structure of planar semimodular lattices: the General Swing Lemma

The Swing Lemma, proved by G. Grätzer in 2015, describes how a congruence spreads from a prime interval to another in a slim (having no M3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {M}_{3}$$\end{document} sublattice), planar, semimodular lattice. We generalize the Swing Lemma to planar semimodular lattices.