\contentsline {factn}{{Fact}{1}{Szemerédi-Trotter '83}}{1}{factn.1}%
\contentsline {factn}{{Fact}{2}{Elekes-Szabó '12}}{1}{factn.2}%
\contentsline {factnb}{{Fact}{1}{Elekes-Szabó '12 ($m=3$), Raz-Sharir-de Zeeuw '18 ($m=4$), B-Breuillard '20}}{1}{factnb.1}%
\contentsline {remarkn}{{Remark}{1}{}}{1}{remarkn.1}%
\contentsline {definitionn}{{Definition}{1}{}}{1}{definitionn.1}%
\contentsline {factn}{{Fact}{3}{}}{1}{factn.3}%
\contentsline {examplen}{{Example}{1}{}}{1}{examplen.1}%
\contentsline {factn}{{Fact}{4}{Chernikov-Simon}}{1}{factn.4}%
\contentsline {factb}{{Fact}{1.{1}}{Chernikov-Galvin-Starchenko, Chernikov-Starchenko '20}}{1}{theorem.1.1}%
\contentsline {theoremn}{{Theorem}{1}{}}{1}{theoremn.1}%
\contentsline {corollaryn}{{Corollary}{1}{}}{1}{corollaryn.1}%
\contentsline {corollaryn}{{Corollary}{2}{}}{1}{corollaryn.2}%
\contentsline {examplen}{{Example}{2}{}}{1}{examplen.2}%
\contentsline {proposition}{{Proposition}{2.{1}}{}}{1}{theorem.2.1}%
\contentsline {lemman}{{Lemma}{1}{}}{1}{lemman.1}%
\contentsline {factn}{{Fact}{5}{Uniform Swiss Cheese Decomposition}}{1}{factn.5}%
\contentsline {lemman}{{Lemma}{2}{}}{1}{lemman.2}%
\contentsline {remarkn}{{Remark}{2}{}}{1}{remarkn.2}%
\contentsline {theoremn}{{Theorem}{2}{}}{1}{theoremn.2}%
\contentsline {theoremn}{{Theorem}{3}{}}{1}{theoremn.3}%