theorem
  z in rng(g*f) implies z in rng g
proof
  assume z in rng(g*f);
  then consider x being object such that
A1: x in dom(g*f) and
A2: z = (g*f).x by Def3;
  f.x in dom g & (g*f).x = g.(f.x) by A1,Th11,Th12;
  hence thesis by A2,Def3;
end;
