reserve X for RealUnitarySpace,
  x, g, g1, h for Point of X,
  a, p, r, M, M1, M2 for Real,
  seq, seq1, seq2, seq3 for sequence of X,
  Nseq for increasing sequence of NAT,

  k, l, l1, l2, l3, n, m, m1, m2 for Nat;

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;
