
theorem
  for f being Function, A being set st f is one-to-one & A c= dom (f")
  holds f.:(f".:A) = A
proof
  let f be Function, A be set;
  assume that
A1: f is one-to-one and
A2: A c= dom (f");
  f"".:(f".:A)=A by A1,A2,FUNCT_1:107;
  hence thesis by A1,FUNCT_1:43;
end;
