  The "quantum duality principle" states that the quantization of a Lie
bialgebra - via a quantum universal enveloping algebra (QUEA) - provides also a
quantization of the dual Lie bialgebra (through its associated formal Poisson
group) - via a quantum formal series Hopf algebra (QFSHA) - and, conversely, a
QFSHA associated to a Lie bialgebra (via its associated formal Poisson group)
yields a QUEA for the dual Lie bialgebra as well; more precisely, there exist
functors QUEA --> QFSHA and QFSHA --> QUEA, inverse of each other, such that in
either case the Lie bialgebra associated to the target object is the dual of
that of the source object. Such a result was claimed true by Drinfeld, but
seems to be unproved in literature: we give here a complete detailed proof of
it.
