theorem Th10:
  S is convergent implies ex x st S is_convergent_in_metrspace_to x
proof
  assume S is convergent;
  then consider x such that
A1: for r st 0 < r ex m st for n st m <= n holds dist(S.n,x) < r;
  S is_convergent_in_metrspace_to x by A1;
  hence thesis;
end;
