reserve X for non empty UNITSTR;
reserve a, b for Real;
reserve x, y for Point of X;
reserve X for RealUnitarySpace;
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
  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 Th44;
end;
