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;
