reserve x,y,z,X for set,
  T for Universe;

theorem Th19:
  for S being non empty 1-sorted, N being net of S, X st N
  is_eventually_in X holds N is_often_in X
proof
  let S be non empty 1-sorted, N be net of S, X;
  given i being Element of N such that
A1: for j being Element of N st i <= j holds N.j in X;
  let j be Element of N;
  consider z being Element of N such that
A2: i <= z & j <= z by Def3;
  take z;
  thus thesis by A1,A2;
end;
