theorem Th31: :: BVFUNC11:31

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
Ex (('not' (Ex (a,A,G))),B,G) '<' 'not' (All ((All (a,B,G)),A,G))