  By explicitly computing wavefunction overlap via exact diagonalization in
finite systems, we provide evidence indicating that, in the limit of strong
coupling, i.e., $\Delta/t \to \infty$, the ground state of the
Gutzwiller-projected BCS Hamiltonian (accompanied by proper particle-number
projection) is identical to the exact ground state of the 2D antiferromagnetic
Heisenberg model on the square lattice. This identity is adiabatically
connected to a very high overlap between the ground states of the projected BCS
Hamiltonian and the t-J model at moderate doping.
