  Let M be a compact symplectic manifold, and L be a closed Lagrangian
submanifold which can be lifted to a Legendrian submanifold in the
contactization of M. For any Legendrian deformation of L satisfying some given
conditions, we get a new Lagrangian submanifold L'. We prove that the number of
intersection of L and L' can be estimated from below by the sum of $Z_2$-Betti
numbers of L, provided they intersect transversally.
