theorem
  ( Al is countable &
  still_not-bound_in X is finite & X |= p ) implies X |- p
proof
  assume
A1: Al is countable;
  assume
A2: still_not-bound_in X is finite;
  assume
A3: X |= p;
  assume
A4: not X |- p;
  reconsider Y = X \/ {'not' p} as Subset of CQC-WFF(Al);
A5: still_not-bound_in Y is finite by A2,Th36;
  Y is Consistent by A4,HENMODEL:9;
  then ex CZ,JH1 st ( JH1,valH(Al) |= Y) by A1,A5,Th34;
  hence contradiction by A3,Th37;
end;
