theorem
  seq is convergent & lim seq<>0 implies ex seq1 st seq1 is subsequence
  of seq & seq1 is non-zero
proof
  assume seq is convergent & lim seq <>0;
  then consider k such that
A1: seq ^\k is non-zero by Th23;
  take seq ^\k;
  thus thesis by A1;
end;
