  Whereas the t-J model has gained wide popularity among physicists as a model
for high-T_C superconductivity, its physical origin is not at all clear. In
this communication we show that the Hubbard model with occupation-dependent
hopping (t_1-t_2-t_3-U model), recently proposed to account for the relaxation
of doubly-occupied orbitals, reduces, in a physically relevant parameter
region, to an effective t-J-t' model with no upper bound on the J/t ratio.
Results of exact diagonalization studies on finite size systems demonstrate the
equivalence between the t_1-t_2-t_3-U model with intermediate/large U and the
t-J-t' model even for very large J/t ratio (up to 16). On the contrary, t-U and
t-J models turn out to be equivalent to t-J-t' model only for very small J
values (J much smaller than t). Implications of the results on high-T_C
superconductivity are briefly discussed.
