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
  the carrier of R <> {0.R} implies for k ex p being AlgSequence of R st
  len p = k
proof
  set D = the carrier of R;
  assume D <> {0.R};
  then consider t being object such that
A1: t in D and
A2: t <> 0.R by ZFMISC_1:35;
  reconsider y=t as Element of R by A1;
  let k;
  deffunc F(Nat) = y;
  consider p being AlgSequence of R such that
A3: len p <= k & for i st i < k holds p.i=F(i) from AlgSeqLambdaF;
  for i st i < k holds p.i<>0.R by A2,A3;
  then len p >= k by Th2;
  hence thesis by A3,XXREAL_0:1;
end;
