theorem
  (seq1 - seq2) ^\k = (seq1 ^\k) - (seq2 ^\k)
proof
  thus (seq1 - seq2) ^\k = (seq1 + (-seq2)) ^\k by BHSP_1:49
    .= (seq1 ^\k) + ((-seq2) ^\k) by Th13
    .= (seq1 ^\k) + -(seq2 ^\k) by Th14
    .= (seq1 ^\k) - (seq2 ^\k) by BHSP_1:49;
end;
