environ vocabulary FUNCT_2, MARGREL1, PARTIT1, EQREL_1, BVFUNC_2, ZF_LANG; notation XBOOLE_0, SUBSET_1, FRAENKEL, MARGREL1, VALUAT_1, EQREL_1, BVFUNC_1, BVFUNC_2; constructors BVFUNC_2, BVFUNC_1; clusters MARGREL1, XBOOLE_0; begin reserve Y for non empty set, a for Element of Funcs(Y,BOOLEAN), G for Subset of PARTITIONS(Y), A,B for a_partition of Y; canceled 5; theorem :: BVFUNC19:6 G is independent implies All('not' Ex(a,A,G),B,G) '<' All(All('not' a,B,G),A,G);