set D = {{} ,1};
reconsider a = {} as Element of {{} ,1} by TARSKI:def 2;
set Y = STS {{} ,1},a;
take STS {{} ,1},a ; :: thesis: ( not STS {{} ,1},a is almost_discrete & STS {{} ,1},a is strict & not STS {{} ,1},a is empty )
reconsider A = {a} as non empty Subset of (STS {{} ,1},a) ;
( 1 in {{} ,1} & not 1 in A ) by TARSKI:def 1, TARSKI:def 2;
then not {{} ,1} \ A is empty by XBOOLE_0:def 5;
hence ( not STS {{} ,1},a is almost_discrete & STS {{} ,1},a is strict & not STS {{} ,1},a is empty ) by Th39; :: thesis: verum