  The Chekanov theorem generalizes the classic Lyusternik-Shnirel'man and Morse
theorems concerning critical points of a smooth function on a closed manifold.
A Legendrian submanifold \Lambda of space of 1-jets of the functions on a
manifold M defines a multi-valued function whose graph is the projection of
\Lambda in J^0 M = M x R. The Chekanov theorem asserts that if \Lambda is
homotopic to the 1-jet of a smooth function in the class of embedded Legendrian
manifolds, then such a graph of a multi-valued function must have a lot of
points (their number is determined by the topology of M) at which the tangent
plane to the graph is parallel to M \times 0.
  In the present paper a similar estimate is proved for a wider class of
Legendrian manifolds. We consider Legendrian manifolds homotopic (in the class
of embedded Legendrian manifolds) to Legendrian manifolds specified by
generating families.
