theorem Th11:
  S is_convergent_in_metrspace_to x implies lim S = x
proof
  assume S is_convergent_in_metrspace_to x; then
  S is convergent & for r st 0 < r ex m st for n st m <= n holds dist(S.n,
  x) < r;
  hence thesis by TBSP_1:def 3;
end;
