 Let $a,b,c\in V\cup W$ with $a\neq b$, and let $p^{ab}, p^{bc}, p^{ac}$ be geodesics in $\Gamma$ from $a$ to $b$, from $b$ to $c$, and from $a$ to $c$, respectively. Let $\ell=|a,b|_S$ and let $0\leq i \leq \ell