reserve i,k,l,m,n for Nat,
  x for set;
reserve R for non empty ZeroStr;
reserve p,q for AlgSequence of R;

theorem Th2:
  (for i st i < k holds p.i<>0.R) implies len p>=k
proof
  assume
A1: for i st i < k holds p.i<>0.R;
  for i st i<k holds len p>i
  proof
    let i;
    assume i<k;
    then p.i<>0.R by A1;
    hence thesis by Th1;
  end;
  hence thesis;
end;
