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
  seq is convergent implies lim (seq - x) = (lim seq) - x
proof
  assume seq is convergent;
  then lim (seq + (-x)) = (lim seq) + (-x) by Th17;
  then lim (seq - x) = (lim seq) + (-x) by BHSP_1:56;
  hence thesis by RLVECT_1:def 11;
end;
