Associativity conjecture for fusion of one-dimensional domain walls

Let $\CC$ be a modular tensor category, let $A$ be a condensable algebra, and let $B_1,B_2$ be condensable algebras defining walls in $\CC_A$.

Wall-fusion associativity conjecture. Fusion through $\CC$ satisfies

$${}_{B_1}(\CC_A)_{B_1}\boxtimes_{\CC}{}_{B_2}(\CC_A)_{B_2}\simeq{}_{B_1\ot B_2}(\CC_A)_{B_1\ot B_2}.$$

The claim expresses compatibility of different fusion procedures for domain walls. The source gives no proof or resolution.