theorem Th37:
  X |= p implies not J,v |= X \/ {'not' p}
proof
  assume
A1: X |= p;
  assume
A2: J,v |= X \/ {'not' p};
  then
A3: J,v |= X by Th35,XBOOLE_1:7;
A4: {'not' p} c= X \/ {'not' p} by XBOOLE_1:7;
  'not' p in {'not' p} by TARSKI:def 1;
  then J,v |= 'not' p by A2,A4,CALCUL_1:def 11;
  then not J,v |= p by VALUAT_1:17;
  hence contradiction by A1,A3,CALCUL_1:def 12;
end;
