  In 1987, Yomdin proved a lemma on smooth parametrizations of semialgebraic
sets as part of his solution of Shub's entropy conjecture for $C^\infty$ maps.
The statement was further refined by Gromov, producing what is now known as the
Yomdin-Gromov algebraic lemma. Several complete proofs based on Gromov's sketch
have appeared in the literature, but these have been considerably more
complicated than Gromov's original presentation due to some technical issues.
  In this note we give a proof that closely follows Gromov's original
presentation. We prove a somewhat stronger statement, where the parameterizing
maps are guaranteed to be \emph{cellular}. It turns out that this additional
restriction, along with some elementary lemmas on differentiable functions in
o-minimal structures, allows the induction to be carried out without technical
difficulties.
