  We prove in a large number of cases, that a Zariski dense discrete subgroup
of a simple real algebraic group $G$ which contains a higher rank lattice is a
lattice in the group $G$. For example, we show that a Zariski dense subgroup of
$SL_n({\mathbb R})$ which contains $SL_3({\mathbb Z})$ in the top left hand
corner, is conjugate to $SL_n({\mathbb Z})$ .
