  We establish a full $h-$principle ($C^0-$close, relative, parametric) for the
simplification of singularities of Lagrangian and Legendrian fronts. More
precisely, we prove that if there is no homotopy theoretic obstruction to
simplifying the singularities of tangency of a Lagrangian or Legendrian
submanifold with respect to an ambient foliation by Lagrangian or Legendrian
leaves, then the simplification can be achieved by means of a Hamiltonian
isotopy.
