  Certain quantization problems are equivalent to the construction of morphisms
from "quantum" to "classical" props. Once such a morphism is constructed,
Hensel's lemma shows that it is in fact an isomorphism. This gives a new,
simple proof that any Etingof-Kazhdan quantization functor is an equivalence of
categories between quantized universal enveloping (QUE) algebras and Lie
bialgebras over a formal series ring (dequantization). We apply the same
argument to construct dequantizations of formal solutions of the quantum
Yang-Baxter equation and of quasitriangular QUE algebras. We also give
structure results for the props involved in quantization of Lie bialgebras,
which yield an associator-independent proof that the prop of QUE algebras is a
flat deformation of the prop of co-Poisson universal enveloping algebras.
