
theorem
  for X being non empty set, i being object, x being Element of X
  holds proj({i} --> X,i).({i} --> x) = x
proof
  let X be non empty set, i be object, x be Element of X;
  {i} --> x in product ({i} --> X) by Th13;
  then {i} --> x in dom proj({i} --> X,i) by CARD_3:def 16;
  hence proj({i} --> X,i).({i} --> x) = ({i} --> x).i by CARD_3:def 16
    .= (i .--> x).i by FUNCOP_1:def 9
    .= x by FUNCOP_1:72;
end;
