fig-mirror-proof.tex

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\begin{document}\begin{tikzpicture}

\node[box,text width=10.5cm] (hyp) at (6,6.3) {\textbf{Suppose a longer proper even suffix exists: $V=yY$}\\The overlap lemma turns $yY=Yy^R$ into a $c$-preceded suffix inside $Y$.};
\node[box,text width=4.9cm] (direct) at (2.6,3.9) {\textbf{Direct case}\\$y$ is a suffix of $Zc$\\$|y|\le |Z|+1$};
\node[box,text width=5.3cm] (reset) at (9.3,3.9) {\textbf{Reset case}\\$y$ is a suffix of $Ycc$\\$|y|\le |Y|+2$};
\node[warmbox,text width=4.9cm] (d) at (2.6,1.5) {Maximality of $D_c(Y)$ gives\\$|y|\ge |Z|+1$.\\Thus $V=F$, not proper.};
\node[warmbox,text width=5.3cm] (r) at (9.3,1.5) {If $|y|\le|Y|$: $D_c(Y)$ would exist.\\Otherwise parity gives\\$|y|=|Y|+2$, so $V=F$.};
\node[box,text width=10.5cm] (c) at (6,-.7) {No longer proper suffix remains. Therefore $\lambda(F)=Y$.};
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