theorem :: BVFUNC_2:31

for Y being non empty set
for G being Subset of (PARTITIONS Y)
for a, u being Function of Y,BOOLEAN
for PA being a_partition of Y st u is_independent_of PA,G holds
All ((a 'eqv' u),PA,G) '<' (All (a,PA,G)) 'eqv' u by Th30;