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
  seq1 is convergent & lim seq1 = g1 & seq2 is convergent & lim seq2 =
  g2 implies dist((seq1 - seq2) , (g1 - g2)) is convergent & lim dist((seq1 -
  seq2) , (g1 - g2)) = 0
proof
  assume
  seq1 is convergent & lim seq1 = g1 & seq2 is convergent & lim seq2 = g2;
  then seq1 - seq2 is convergent & lim (seq1 - seq2) = g1 - g2 by Th4,Th14;
  hence thesis by Th24;
end;
