  We study the behavior of Lipschitz functions on intrinsic $C^1$ submanifolds
of Heisenberg groups: our main result is their almost everywhere tangential
Pansu differentiability. We also provide two applications: a Lusin-type
approximation of Lipschitz functions on $\HH$-rectifiable sets, and a coarea
formula on $\HH$-rectifiable sets that completes the program started
in~\cite{JNGV}.
