Mordell–Lang conjecture for Shimura varieties

Let $S$ be a Shimura variety. For a subset $obreak\boldsymbol{\Xi} obreak\to S$, let $obreak\boldsymbol{\bar{\Xi}} obreak$ be the union in $S$ of the generalised Hecke orbits of the points of $obreak\boldsymbol{\Xi}$. A \subset $obreak\boldsymbol{\Sigma} obreak\to S$ is a structure of finite rank if $obreak\boldsymbol{\Sigma=\bar{\Xi}} obreak$ for some $obreak\boldsymbol{\Xi} obreak$ containing only finitely many non-special points; a weakly special subvariety is $obreak\boldsymbol{\Sigma} obreak$-special if it contains a point of $obreak\boldsymbol{\Sigma} obreak$. Mordell–Lang conjecture for $S$. Any subvariety $V$ of $S$ contains only finitely many maximal $obreak\boldsymbol{\Sigma} obreak$-special subvarieties. This is the Shimura-variety analogue of Mordell–Lang and is stated alongside an equivalent formulation in terms of Zariski closures of subsets of $obreak\boldsymbol{\Sigma} obreak$; no resolution is supplied in the source.