set F = { (Toler Y) where Y is Subset of X : verum } ;
{} c= X by XBOOLE_1:2;
then ( {} in Toler {} & Toler {} in { (Toler Y) where Y is Subset of X : verum } ) by Def19, TOLER_1:39;
hence not Toler_on_subsets X is empty by TARSKI:def 4; :: thesis: verum