let X be Subset of HP-WFF; :: thesis: X c= CnPos X
let a be object ; :: according to TARSKI:def 3 :: thesis: ( not a in X or a in CnPos X )
assume A1: a in X ; :: thesis: a in CnPos X
then reconsider t = a as Element of HP-WFF ;
for T being Subset of HP-WFF st T is Hilbert_theory & X c= T holds
t in T by A1;
hence a in CnPos X by Def11; :: thesis: verum