theorem
  for x being set st x in dom f & max+f.x = 0 holds max-f.x = -(f.x)
proof
  let x be set;
  assume that
A1: x in dom f and
A2: max+f.x =0;
  0 = max+(R_EAL f).x by A2,Th30;
  then max-(R_EAL f).x =-((R_EAL f).x) by A1,MESFUNC2:20;
  then max-f.x =-((R_EAL f).x) by Th30;
  hence thesis by SUPINF_2:2;
end;
