theorem
  for f being Function st X c= dom f & f is one-to-one holds f"(f.:X) = X
proof
  let f be Function such that
A1: X c= dom f and
A2: f is one-to-one;
  thus f"(f.:X) c= X by A2,Th81;
  let x be object;
  assume
A3: x in X;
  then f.x in f.:X by A1,Def6;
  hence thesis by A1,A3,Def7;
end;
