reserve T, X, Y for Subset of HP-WFF;
reserve p, q, r, s for Element of HP-WFF;

theorem
  T is Hilbert_theory implies HP_TAUT c= T
proof
  assume
A1: T is Hilbert_theory;
  HP_TAUT c= CnPos(T) by Th10,XBOOLE_1:2;
  hence thesis by A1,Th12;
end;
