theorem Th5:
  for A be real-bounded Subset of REAL holds 0 <= xvol A
proof
  let A be real-bounded Subset of REAL;
  per cases;
  suppose A <> {};
    then 0<= vol A by INTEGRA1:9;
    hence 0 <= xvol A by Def2;
  end;
  suppose A = {};
    hence 0 <= xvol A by Def2;
  end;
end;
