theorem
  for X,Y,Z being non empty set for f being Function of X, [:Y,Z:] for x
  being Element of X holds f~.x =[(f.x)`2,(f.x)`1]
proof
  let X,Y,Z be non empty set;
  let f be Function of X, [:Y,Z:];
  let x be Element of X;
  x in X;
  then
A1: x in dom f by FUNCT_2:def 1;
  f.x = [(f.x)`1, (f.x)`2] by MCART_1:22;
  hence thesis by A1,Def1;
end;
