  We demonstrate that the physical reason for the nontrivial topological
properties of Dirac semimetals $A_3 Bi$ (A=Na,K,Rb) is connected with a
discrete symmetry of the low-energy effective Hamiltonian. By making use of
this discrete symmetry, we argue that all electron states can be split into two
separate sectors of the theory. Each sector describes a Weyl semimetal with a
pair of Weyl nodes and broken time-reversal symmetry. The latter symmetry is
not broken in the complete theory because the time-reversal transformation
interchanges states from different sectors. Our findings are supported by
explicit calculations of the Berry curvature. In each sector, the field lines
of the curvature reveal a pair of monopoles of the Berry flux at the positions
of Weyl nodes. The $Z_2$ Weyl semimetal nature is also confirmed by the
existence of pairs of surface Fermi arcs, which originate from different
sectors of the theory.
