theorem Th38: :: BVFUNC_2:38

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
u 'xor' (Ex (a,PA,G)) '<' Ex ((u 'xor' a),PA,G)