reserve
  X for non empty set,
  FX for Filter of X,
  SFX for Subset-Family of X;

theorem Th43:
  for L being non empty 1-sorted, B being set,
  s being sequence of the carrier of L holds
  sequence_to_net(s) is_eventually_in B iff
  ex i being Element of sequence_to_net(s) st for j being Element of
  sequence_to_net(s) st i <= j holds (sequence_to_net(s)).j in B;
