let Y be non empty set ; :: thesis: for a being Element of Funcs Y,BOOLEAN
for G being Subset of (PARTITIONS Y)
for PA, PB being a_partition of Y holds All a,PA,G '<' Ex a,PB,G
let a be Element of Funcs Y,BOOLEAN ; :: thesis: for G being Subset of (PARTITIONS Y)
for PA, PB being a_partition of Y holds All a,PA,G '<' Ex a,PB,G
let G be Subset of (PARTITIONS Y); :: thesis: for PA, PB being a_partition of Y holds All a,PA,G '<' Ex a,PB,G
let PA, PB be a_partition of Y; :: thesis: All a,PA,G '<' Ex a,PB,G
A1: All a,PA,G '<' a by BVFUNC_2:11;
a '<' Ex a,PB,G by BVFUNC_2:12;
hence All a,PA,G '<' Ex a,PB,G by A1, BVFUNC_1:18; :: thesis: verum