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 (Ex ('not' a),A,G),B,G '<' Ex (Ex ('not' 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 (Ex ('not' a),A,G),B,G '<' Ex (Ex ('not' a),B,G),A,G
let G be Subset of (PARTITIONS Y); :: thesis: for A, B being a_partition of Y holds All (Ex ('not' a),A,G),B,G '<' Ex (Ex ('not' a),B,G),A,G
let A, B be a_partition of Y; :: thesis: All (Ex ('not' a),A,G),B,G '<' Ex (Ex ('not' a),B,G),A,G
'not' (Ex (All a,A,G),B,G) = All (Ex ('not' a),A,G),B,G by BVFUNC11:22;
hence All (Ex ('not' a),A,G),B,G '<' Ex (Ex ('not' a),B,G),A,G by BVFUNC11:15; :: thesis: verum