  In this paper we extend the discussion on Homological Mirror Symmetry for
Fano toric varieties presented by Hori and Vafa to more general case of
monotone symplectic manifolds with real polarizations. We claim that the Hori
-- Vafa prediction, proven by Cho and Oh for toric Fano varieties, can be
checked in much more wider context. Then the notion of Bohr - Sommerfeld with
respect to the canonical class lagrangian submanifold appears and plays an
important role. The discussion presents a bridge between Geometric Quantization
and Homological Mirror Symmetry programmes both applied to the projective plane
in terms of its lagrangian geometry. Due to this relation one could exploit
some standard facts known in GQ to produce results in HMS.
