  We introduce novel equations, in the spirit of rough path theory, that
parametrize level sets of intrinsically regular maps on the Heisenberg group
with values in $\mathbb{R}^2$. These equations can be seen as a sub-Riemannian
counterpart to classical ODEs arising from the implicit function theorem. We
show that they enjoy all the natural well-posedness properties, thus allowing
for a "good calculus" on nonsmooth level sets. We apply these results to prove
an area formula for the intrinsic measure of level sets, along with the
corresponding coarea formula.
