
theorem Th27:
  for S being non empty 1-sorted, N being non empty NetStr over S, X being set
  st rng the mapping of N c= X holds N is_eventually_in X
proof
  let S be non empty 1-sorted, N be non empty NetStr over S;
  let X be set such that
A1: rng the mapping of N c= X;
  set i = the Element of N;
  take i;
  let j be Element of N;
  N.j in rng the mapping of N by FUNCT_2:4;
  hence thesis by A1;
end;
