Lemma 22.1.93.9434BE558E6A Let $\Gamma $ be a piecewise linear curve in $\mathrm{PSH}(X,\theta )$. Then $\Gamma ^{\mathrm{An}}\in \mathrm{PSH}(L^{\mathrm{An}})$.
Lemma 22.1.939434BE558E6A
Proof. The result follows from (22.1.87), proposition 22.1.73 and 22.1.92. $\square$
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