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;

theorem
  R_EAL f - R_EAL g = R_EAL f + R_EAL -g
proof
  R_EAL f - R_EAL g = R_EAL(f-g) by Th23
    .=R_EAL(f + -g);
  hence thesis by Th23;
end;
