  Following the analysis of differentiable mappings of Y. Yomdin, M. Gromov has
stated a very elegant "Algebraic Lemma" which says that the "differentiable
size" of an algebraic subset may be bounded in terms only of its dimension,
degree and diameter. We give a complete and elementary proof of Gromov's result
using the ideas presented in his Bourbaki talk as well as other necessary
ingredients.
