  A detailed derivation of the master equation of the cavity radiation of a
coherently prepared $Y$-shaped four-level correlated emission laser is
presented. The outline of the procedures that can be employed in analytically
solving the stochastic differential equations and the rate equations of various
correlations are also provided. It is shown that coherently preparing the atoms
in the upper two energy levels and the lower, initially, can lead to a genuine
continuous variable tripartite entanglement. Moreover, preparing the atoms in
the coherent superposition, other than the possible maximum or minimum, of the
upper two energy levels, leaving the lower unpopulated, may lead to a similar
observation. With the possibility of the atom at the intermediate energy level
to take three different transition roots guided by the induced coherence, this
system in general is found to encompass versatile options for practical
utilization. In particular, coupling at least one of the dipole forbidden
transitions by an external radiation is expected to enhance the degree of
detectable entanglement.
