theorem Th17:
  rng(f +* g) c= rng f \/ rng g
proof
  let y be object;
  assume y in rng(f +* g);
  then consider x being object such that
A1: x in dom (f +* g) and
A2: y = (f +* g).x by FUNCT_1:def 3;
  x in dom f & not x in dom g or x in dom g by A1,Th12;
  then x in dom f & (f +* g).x = f.x or x in dom g & (f +* g).x = g.x by Th11
,Th13;
  then y in rng f or y in rng g by A2,FUNCT_1:def 3;
  hence thesis by XBOOLE_0:def 3;
end;
