reserve P,Q,X,Y,Z for set, p,x,x9,x1,x2,y,z for object;
reserve D for non empty set;
reserve A,B for non empty set;
reserve Y for non empty set,
  f for Function of X,Y,
  p for PartFunc of Y,Z,
  x for Element of X;
reserve g for Function of X,X;
reserve X,Y for non empty set,
  Z,S,T for set,
  f for Function of X,Y,
  g for PartFunc of Y,Z,
  x for Element of X;

theorem
  for H being Function of D, [:A,B:], d being Element of D holds H.d = [
  pr1 H.d,pr2 H.d]
proof
  let H be Function of D, [:A,B:], d be Element of D;
  thus H.d = [(H.d)`1,(H.d)`2] by MCART_1:21
    .= [(H.d)`1,pr2 H.d] by Def6
    .= [pr1 H.d,pr2 H.d] by Def5;
end;
