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 st G is independent holds
All ((All (('not' a),A,G)),B,G) = All (('not' (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 st G is independent holds
All ((All (('not' a),A,G)),B,G) = All (('not' (Ex (a,B,G))),A,G)
let G be Subset of (PARTITIONS Y); :: thesis: for A, B being a_partition of Y st G is independent holds
All ((All (('not' a),A,G)),B,G) = All (('not' (Ex (a,B,G))),A,G)
let A, B be a_partition of Y; :: thesis: ( G is independent implies All ((All (('not' a),A,G)),B,G) = All (('not' (Ex (a,B,G))),A,G) )
assume G is independent ; :: thesis: All ((All (('not' a),A,G)),B,G) = All (('not' (Ex (a,B,G))),A,G)
then All ((All (('not' a),A,G)),B,G) = All ((All (('not' a),B,G)),A,G) by PARTIT_2:15;
hence All ((All (('not' a),A,G)),B,G) = All (('not' (Ex (a,B,G))),A,G) by BVFUNC_2:19; :: thesis: verum