theorem :: BVFUNC11:32

for Y being non empty set
for a being Function of Y,BOOLEAN
for G being Subset of (PARTITIONS Y)
for A, B being a_partition of Y st G is independent holds
'not' (All ((Ex (a,A,G)),B,G)) '<' 'not' (Ex ((All (a,B,G)),A,G)) by PARTIT_2:11, PARTIT_2:17;