reserve A for set,
  C for non empty set,
  B for Subset of A,
  x for Element of A,
  f,g for Function of A,C;

theorem Th5:
  for f,g being Function holds g c= f implies f +* g = f
proof
  let f,g be Function;
  assume
A1: g c= f;
  then dom g c= dom f by GRFUNC_1:2;
  then
A2: dom f = dom f \/ dom g by XBOOLE_1:12;
  for x be object st x in dom f holds (x in dom g implies f.x = g.x) & (not x
  in dom g implies f.x = f.x) by A1,GRFUNC_1:2;
  hence thesis by A2,FUNCT_4:def 1;
end;
