theorem
  for x being set st x in dom f & max-f.x = -(f.x) holds max+f.x = 0
proof
  let x be set;
  assume that
A1: x in dom f and
A2: max-f.x = -(f.x);
  -(f.x) = max-(R_EAL f).x by A2,Th30;
  then -((R_EAL f).x) = max-(R_EAL f).x by SUPINF_2:2;
  then max+(R_EAL f).x =0. by A1,MESFUNC2:21;
  hence thesis by Th30;
end;
