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)) ;
A1: not 1 in A by TARSKI:def 1;
1 in {{},1} by TARSKI:def 2;
then not {{},1} \ A is empty by A1, XBOOLE_0:def 5;
hence ( not STS ({{},1},a) is almost_discrete & STS ({{},1},a) is strict & not STS ({{},1},a) is empty ) by Th35; :: thesis: verum