We introduce novel equations, in the spirit of Young-Rough Path theory, that parametrize level sets of intrinsically regular maps on the Heisenberg group with values in the plane. 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, e.g., measuring their length. Examples and recent progress towards the higher co-dimension case will be discussed. Joint work with V. Magnani and E. Stepanov.