Strong Zilber–Pink conjecture II for optimal subvarieties

Let $S$ be a Shimura variety and let $V$ be an irreducible subvariety of $S$. An irreducible subvariety $W$ of $V$ is called optimal if, for every irreducible subvariety $Y$ of $V$ strictly containing $W$, one has $\delta(Y)>\delta(W)$. Write $\operatorname{Opt}(V)$ for the set of optimal subvarieties of $V$. Strong Zilber–Pink II. The set $\operatorname{Opt}(V)$ is finite. This is another formulation of Zilber–Pink, equivalent to the atypical-subvariety formulation according to the cited work; the survey also notes that the formulation is equivalent to Zilber–Pink when quantified over all Shimura varieties.