Intrinsically Lipschitz functions with normal target in Carnot groups

We provide a Rademacher theorem for intrinsically Lipschitz functions $\varphi :U\subseteq \mathbb{W}\to \mathbb{L}$, 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.