reserve p, q, x, y for Real,
  n for Nat;

theorem Th9:
  for f, g, h, k being real-valued FinSequence holds (f+g)-(h+k) = (f-h)+(g-k)
proof
  let f, g, h, k be real-valued FinSequence;
  thus f+g-(h+k) = f+(g+-(h+k)) by RVSUM_1:15
    .= f+(g+(-h+-k)) by RVSUM_1:26
    .= f+(-h+(g+-k)) by RVSUM_1:15
    .= f+-h+(g+-k) by RVSUM_1:15
    .= (f-h)+(g+-k)
    .= (f-h) + (g-k);
end;
