theorem
  rng s c= dom (h2*h1) implies h2/*(h1/*s) = (h2*h1)/*s
proof
  assume
A1: rng s c= dom (h2*h1);
  now
    let n be Element of NAT;
A2: rng s c= dom h1 by A1,FUNCT_1:101;
    h1.:(rng s) c= dom h2 by A1,FUNCT_1:101;
    then
A3: rng (h1/*s) c= dom h2 by A2,Th30;
    s.n in rng s by Th28;
    then
A4: s.n in dom h1 by A1,FUNCT_1:11;
    thus ((h2*h1)/*s).n = (h2*h1).(s.n) by A1,FUNCT_2:108
      .= h2.(h1.(s.n)) by A4,FUNCT_1:13
      .= h2.((h1/*s).n) by A2,FUNCT_2:108
      .= (h2/*(h1/*s)).n by A3,FUNCT_2:108;
  end;
  hence thesis;
end;
