Proposition 17.10.37.9335B48D7458 Let $\varphi _1,\varphi _0\in \mathcal{E}^{\infty }(X,\theta ;\phi )$. Let $(\varphi _ t)_{t\in (0,1)}$ be the geodesic from $\varphi _0$ to $\varphi _1$. Then
\[ t\inf _{\{ \phi \neq -\infty \} }(\varphi _1-\varphi _0)=\inf _{\{ \phi \neq -\infty \} }(\varphi _ t-\varphi _0) \]
for all $t\in (0,1]$.
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