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 ;
reserve X for non empty set,
  S for SigmaField of X,
  f,g for PartFunc of X,REAL,
  A for Element of S;
reserve X for non empty set,
  Y for set,
  S for SigmaField of X,
  f,g,h for PartFunc of X,REAL,
  A for Element of S,
  r for Real;

theorem Th60:
  for x be object st x in dom(f+g+h) holds (f+g+h).x=f.x+g.x+h.x
proof
  let x be object;
  assume
A1: x in dom(f+g+h);
  dom(f+g+h) = dom(f+g) /\ dom h by VALUED_1:def 1;
  then x in dom(f+g) by A1,XBOOLE_0:def 4;
  then f.x + g.x + h.x = (f+g).x + h.x by VALUED_1:def 1;
  hence thesis by A1,VALUED_1:def 1;
end;
