  We give a simpler proof as well as a generalization of the main result of an
article of Shestakov and Umirbaev. This latter article being the first of two
that solve a long-standing conjecture about the non-tameness, or "wildness", of
Nagata's automorphism. As corollaries we get interesting informations about the
leading terms of polynomials forming an automorphism in any dimension and
reprove the tameness of automorphisms in dimension two.
