theorem
  ( ex k st for n st n >= k holds seq1.n = seq2.n ) implies seq1
  is_compared_to seq2
proof
  assume ex k st for n st n >= k holds seq1.n = seq2.n;
  then consider m such that
A1: for n st n >= m holds seq1.n = seq2.n;
  let r such that
A2: r > 0;
  take k = m;
  let n;
  assume n >= k;
  then dist((seq1.n), (seq2.n)) = dist((seq1.n), (seq1.n)) by A1
    .= 0 by CSSPACE:50;
  hence thesis by A2;
end;
