theorem
  dom f = dom (max+f - max-f) & dom f = dom (max+f + max-f)
proof
  dom f = dom (max+(R_EAL f)-max-(R_EAL f)) by MESFUNC2:17;
  then dom f = dom (R_EAL(max+f)-max-(R_EAL f)) by Th30;
  then dom f = dom (R_EAL(max+f)-R_EAL(max-f)) by Th30;
  then dom f = dom (R_EAL(max+f - max-f)) by Th23;
  hence dom f =dom (max+f - max-f);
  dom f = dom (max+(R_EAL f)+max-(R_EAL f)) by MESFUNC2:17;
  then dom f = dom (R_EAL(max+f)+max-(R_EAL f)) by Th30;
  then dom f = dom (R_EAL(max+f)+R_EAL(max-f)) by Th30;
  then dom f = dom (R_EAL(max+f + max-f)) by Th23;
  hence thesis;
end;
