let Y be non empty set ; :: thesis: for a being Element of Funcs Y,BOOLEAN
for G being Subset of (PARTITIONS Y)
for A, B being a_partition of Y holds All (All a,A,G),B,G '<' Ex (Ex a,B,G),A,G
let a be Element of Funcs Y,BOOLEAN ; :: thesis: for G being Subset of (PARTITIONS Y)
for A, B being a_partition of Y holds All (All a,A,G),B,G '<' Ex (Ex a,B,G),A,G
let G be Subset of (PARTITIONS Y); :: thesis: for A, B being a_partition of Y holds All (All a,A,G),B,G '<' Ex (Ex a,B,G),A,G
let A, B be a_partition of Y; :: thesis: All (All a,A,G),B,G '<' Ex (Ex a,B,G),A,G
A1: All (All a,A,G),B,G '<' All a,A,G by BVFUNC_2:11;
All a,A,G '<' Ex (Ex a,B,G),A,G by Th8, BVFUNC_2:12;
hence All (All a,A,G),B,G '<' Ex (Ex a,B,G),A,G by A1, BVFUNC_1:18; :: thesis: verum