reserve X for RealUnitarySpace;
reserve x, y, z, g, g1, g2 for Point of X;
reserve a, q, r for Real;
reserve seq, seq1, seq2, seq9 for sequence of X;
reserve k, n, m, m1, m2 for Nat;

theorem Th16:
  seq is convergent implies lim (- seq) = - (lim seq)
proof
  assume seq is convergent;
  then lim ((-1) * seq) = (-1) * (lim seq) by Th15;
  then lim (- seq) = (-1) * (lim seq) by BHSP_1:55;
  hence thesis by RLVECT_1:16;
end;
