Lemma 3.11 . [02KL]

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Lemma 3.11.

The collection $\Pi_{1}\cdot\Pi_{2}$ is a polyhedral complex. If $\Pi_{1}$ and $\Pi_{2}$ are complete, then

\operatorname{rec}(\Pi_{1}\cdot\Pi_{2})=\operatorname{rec}(\Pi_{1})\cdot\operatorname{rec}(\Pi_{2}).