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
  max-f = max+(-f)
proof
  max-f = max-(R_EAL f) by Th30;
  then max-f = max+(-R_EAL f) by MESFUNC2:14;
  then max-f = max+(R_EAL -f) by Th28;
  hence thesis by Th30;
end;
