  Crystallization of supercooled liquids is mainly determined by two competing
processes associated with the transition of particles (atoms) from liquid phase
to crystalline one and, vice versa, with the return of particles from
crystalline phase to liquid one. The quantitative characteristics of these
processes are the so-called attachment rate $g^{+}$ and the detachment rate
$g^{-}$, which determine how particles change their belonging from one phase to
another. In the present study, a {\it correspondence rule} between the rates
$g^{+}$ and $g^{-}$ as functions of the size $N$ of growing crystalline nuclei
is defined for the first time. In contrast to the well-known detailed balance
condition, which relates $g^{+}(N)$ and $g^{-}(N)$ at $N=n_c$ (where $n_c$ is
the critical nucleus size) and is satisfied only at the beginning of the
nucleation regime, the found {\it correspondence rule} is fulfilled at all the
main stages of crystallization kinetics (crystal nucleation, growth and
coalescence). On the example of crystallizing supercooled Lennard-Jones liquid,
the rate $g^{-}$ was calculated for the first time at different supercooling
levels and for the wide range of nucleus sizes $N\in[n_c;\,40\,n_c]$. It was
found that for the whole range of nucleus sizes, the detachment rate $g^{-}$ is
only $\approx2$\% less than the attachment rate $g^{+}$. This is direct
evidence that the role of the processes that counteract crystallization remains
significant at all the stages of crystallization. Based on the obtained
results, a kinetic equation was formulated for the time-dependent distribution
function of the nucleus sizes, that is an alternative to the well-known kinetic
Becker-D\"{o}ring-Zeldovich-Frenkel equation.
