let Y be non empty set ; :: thesis: for a being Function of 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 Function of 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_1:15; :: thesis: verum