reserve X for non empty set,
  Y for set,
  S for SigmaField of X,
  F for sequence of S,
  f,g for PartFunc of X,REAL,
  A,B for Element of S,
  r,s for Real,
  a for Real,
  n for Nat;
reserve X for non empty set,
  S for SigmaField of X,
  f,g for PartFunc of X,REAL,
  A for Element of S,
  r for Real,
  p for Rational;
reserve X for non empty set,
  f,g for PartFunc of X,REAL,
  r for Real ;

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;
