reserve f,g,h for Function,
  A for set;
reserve F for Function,
  B,x,y,y1,y2,z for set;
reserve x,z for object;
reserve X for non empty set,
  Y for set,
  F for BinOp of X,
  f,g,h for Function of Y,X,
  x,x1,x2 for Element of X;
reserve Y for non empty set,
  F for BinOp of X,
  f,g,h for Function of Y,X,
  x,x1,x2 for Element of X;
reserve Y for set,
  F for BinOp of X,
  f,g,h for Function of Y,X,
  x,x1,x2 for Element of X;
reserve Y for non empty set,
  F for BinOp of X,
  f,g,h for Function of Y,X,
  x,x1,x2 for Element of X;
reserve Y for set,
  F for BinOp of X,
  f,g,h for Function of Y,X,
  x,x1,x2 for Element of X;
reserve Y for non empty set,
  F for BinOp of X,
  f,g,h for Function of Y,X,
  x,x1,x2 for Element of X;
reserve Y for set,
  F for BinOp of X,
  f,g,h for Function
  of Y,X,
  x,x1,x2 for Element of X;

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;
