  It is shown that the single $0^+$ THSR (Tohsaki-Horiuchi-Schuck-R\"{o}pke)
wave function which is extended to include 2$\alpha$ correlation is almost
completely equivalent to the 3$\alpha$ wave function obtained as the full
solution of 3$\alpha$ cluster model. Their squared overlap is as high as 98\%
while it is 93\% if the 2$\alpha$ correlation is not included. This result
implies that, by incorporating the 2$\alpha$ correlation in the 3$\alpha$
model, the ground state of $^{12}$C is describable in the container picture
which is valid for the Hoyle state for which the 2$\alpha$ correlation is weak
and a single $0^+$ THSR wave function without 2$\alpha$ correlation is almost
completely equivalent to the full solution of 3$\alpha$ cluster model.
