theorem
  abs f = max+f + max-f
proof
  abs f = R_EAL(abs f);
  then abs f = |. R_EAL f .| by Th44;
  then abs f = max+(R_EAL f) + max-(R_EAL f) by MESFUNC2:24;
  then abs f = R_EAL(max+f)+max-(R_EAL f) by Th30;
  then abs f = R_EAL(max+f)+R_EAL(max-f) by Th30;
  then abs f = R_EAL(max+f + max-f) by Th23;
  hence thesis;
end;
