  We prove that the Lie algebra of primitive elements of a graded and connected
bialgebra, free as an associative algebra, over a eld of characteristic zero,
is a free Lie algebra. The main tool is a ltration, which allows to embed the
associated graded Lie algebra into the Lie algebra of a free and cocommutative
bialgebra. The result is then a consequence of Cartier-Quillen-Milnor-Moore's
Shirshov-Witt's theorems.
