consider t being Element of T;
reconsider S = {t} as AntiChain_of_Prefixes by Th70;
take S ; :: thesis: S c= T
let x be set ; :: according to TARSKI:def 3 :: thesis: ( not x in S or x in T )
assume x in S ; :: thesis: x in T
then x = t by TARSKI:def 1;
hence x in T ; :: thesis: verum