= Quasiconvexity from no missing shells
{title2=$C=L/2$}
Let $X$ be a finite combinatorial <2-complex> satisfying $C'(1/6)$, and let $Y$ be a connected <CW subcomplex> of its <universal cover> with no missing shells. If the largest cell perimeter is $L$, then $Y^{(1)}$ is $(L/2)$-quasiconvex in the universal cover's unit-edge <1-skeleton>. Bound an ambient <metric geodesic> and an intrinsic <metric geodesic> of $Y^{(1)}$ by a <reduced disc diagram>. A shell on the ambient side would shorten a <metric geodesic>. A shell on the intrinsic side belongs to $Y$ and would shorten its intrinsic <metric geodesic>. Spurs are likewise excluded from side interiors. The <Greendlinger ladder theorem> forces a ladder between the two marked corners. Each cell gives a path of length at most half its perimeter from either side to the other.
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