theorem :: BVFUNC14:41

for Y being non empty set
for G being Subset of (PARTITIONS Y)
for A, B, C, D, E, F being a_partition of Y
for z, u being Element of Y
for h being Function st G is independent & G = {A,B,C,D,E,F} & A <> B & A <> C & A <> D & A <> E & A <> F & B <> C & B <> D & B <> E & B <> F & C <> D & C <> E & C <> F & D <> E & D <> F & E <> F & EqClass (z,(((C '/\' D) '/\' E) '/\' F)) = EqClass (u,(((C '/\' D) '/\' E) '/\' F)) holds
EqClass (u,(CompF (A,G))) meets EqClass (z,(CompF (B,G)))