reserve X for non empty CUNITSTR;
reserve a, b for Complex;
reserve x, y for Point of X;
reserve X for ComplexUnitarySpace;
reserve x, y, z, u, v for Point of X;
reserve seq, seq1, seq2, seq3 for sequence of X;
reserve  n for Nat;

theorem
  seq1 - seq2 = - (seq2 - seq1)
proof
  now
    let n be Element of NAT;
    thus (seq1 - seq2).n = seq1.n - seq2.n by NORMSP_1:def 3
      .= - (seq2.n - seq1.n) by RLVECT_1:33
      .= - (seq2 - seq1).n by NORMSP_1:def 3
      .= (- (seq2 - seq1)).n by BHSP_1:44;
  end;
  hence thesis by FUNCT_2:63;
end;
