General Mordell–Lang conjecture for function fields

Let $K/K_0$ be an extension of algebraically closed fields, let $A/K$ be an abelian variety, let $X\subseteq A$ be a subvariety, and let $\Lambda\subseteq A(K)$ be a subgroup of finite rank such that $\Lambda\cap X(K)$ is Zariski-dense in $X$. General Mordell–Lang conjecture for function fields. Then $X$ is $K/K_0$-special. This is the function-field form of the Mordell–Lang problem and is used as the main ingredient in the paper's one-dimensional result; the supplied text gives no evidence that this assertion has been resolved in the stated generality.