
theorem
  for n be non zero Nat,
      i be Nat,
      x be Point of REAL-NS n
    st 1 <= i <= n
  holds
    Proj(i,n) is_differentiable_in x
      &
    diff(Proj(i,n),x) = Proj(i,n)
proof
  let n be non zero Nat,
      i be Nat,
      x be Point of REAL-NS n;
  assume
  A1: 1 <= i <= n;

  n is non zero Element of NAT by ORDINAL1:def 12;
  then Proj(i,n) is Lipschitzian LinearOperator
        of REAL-NS n,REAL-NS 1 by A1,PDIFF_8:6;
  hence thesis by Th16;
end;
