theorem Th53:
  exp_R.th>0
proof
 now per cases;
    suppose
   th=0;
      hence thesis by Lm11;
    end;
    suppose
A1:   th<>0;
   now per cases by A1;
        suppose
       th<0;
          hence thesis by Th52;
        end;
        suppose
       th>0;
          hence thesis by Th51;
        end;
      end;
      hence thesis;
    end;
  end;
  hence thesis;
end;
