
theorem
  for S being 1-sorted for T being non empty 1-sorted for f being
  Function of S,T st f is bijective holds f" is bijective
proof
  let S be 1-sorted;
  let T be non empty 1-sorted;
  let f be Function of S,T;
  assume
A1: f is bijective;
  then
A2: rng f = [#]T by FUNCT_2:def 3;
  then rng (f") = [#]S by A1,TOPS_2:49;
  then
A3: f" is onto by FUNCT_2:def 3;
  f" is one-to-one by A1,A2,TOPS_2:50;
  hence thesis by A3;
end;
