  We provide a Rademacher theorem for intrinsically Lipschitz functions
$\phi:U\subseteq \mathbb W\to \mathbb L$, where $U$ is a Borel set, $\mathbb W$
and $\mathbb L$ are complementary subgroups of a Carnot group, where we require
that $\mathbb L$ is a normal subgroup. Our hypotheses are satisfied for example
when $\mathbb W$ is a horizontal subgroup. Moreover, we provide an area formula
for this class of intrinsically Lipschitz functions.
