  The generalized Mordell-Lang conjecture (GML) is the statement that the
irreducible components of the Zariski closure of a subset of a group of finite
rank inside a semi-abelian variety are translates of closed algebraic
subgroups. M. McQuillan gave a proof of this statement. We revisit his proof,
indicating some simplifications. This text contains a complete elementary proof
of the fact that (GML) for groups of torsion points (= generalized
Manin-Mumford conjecture), together with (GML) for finitely generated groups
imply the full generalized Mordell-Lang conjecture.
