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;
