reserve X for ComplexUnitarySpace;
reserve x, y, w, g, g1, g2 for Point of X;
reserve z for Complex;
reserve p, q, r, M, M1, M2 for Real;
reserve seq, seq1, seq2, seq3 for sequence of X;
reserve k,n,m for Nat;
reserve Nseq for increasing sequence of NAT;

theorem
  (seq1 - seq2) ^\k = (seq1 ^\k) - (seq2 ^\k)
proof
  thus (seq1 - seq2) ^\k = (seq1 + (-seq2)) ^\k by CSSPACE:64
    .= (seq1 ^\k) + ((-seq2) ^\k) by Th86
    .= (seq1 ^\k) + -(seq2 ^\k) by Th87
    .= (seq1 ^\k) - (seq2 ^\k) by CSSPACE:64;
end;
