  In 1969 M. Gromov in his PhD thesis greatly generalized Smale-Hirsch-Phillips
immersion-submersion theory by proving what is now called the h-principle for
invariant open differential relations over open manifolds. Gromov extracted the
original geometric idea of Smale and put it to work in the maximal possible
generality. Gromov's thesis was brought to the West by A. Phillips and was
popularized in his talks. However, most western mathematicians first learned
about Gromov's theory from A. Haefliger's article. The current paper is devoted
to the same subject as the papers of Gromov and Haefliger. It seems to us that
we further purified Smale-Gromov's original idea by extracting from it a simple
but very general theorem about holonomic approximation of sections of
jet-bundles (see Theorem 1.2.1 below). We show below that Gromov's theorem as
well as some other results in the h-principle spirit are immediate corollaries
of Theorem 1.2.1.
