reserve X for set;

theorem Th4:
  for X,Y being non empty set
  for f being Function of X,Y
  st f is bijective
  for y being Element of Y
  holds f.((f").y) = y
proof
  let X,Y be non empty set;
  let f be Function of X,Y;
  assume A1: f is bijective;
  let y be Element of Y;
  f is onto by A1;
  then reconsider g = f" as Function of Y,X by A1,FUNCT_2:25;
  y = (g").(g.y) by A1,FUNCT_2:26
   .= f.((f").y) by A1,FUNCT_1:43;
  hence thesis;
end;
