theorem Th64:
  for G being set, H,I being non empty set for h being Function of G,H holds
  for h1 being Function of H,I holds
  h is bijective & h1 is bijective implies h1 * h is bijective
proof
  let G be set,H,I be non empty set;
  let h be Function of G,H, h1 be Function of H,I;
  assume that
A1: h is bijective and
A2: h1 is bijective;
  dom h1 = H & rng h = H by A1,FUNCT_2:def 3,def 1;
  then rng(h1 * h) = rng h1 by RELAT_1:28
    .= I by A2,FUNCT_2:def 3;
  hence thesis by A1,A2,FUNCT_2:def 3;
end;
