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

theorem Th6:
  p=<%0.R%> iff len p = 0
proof
  thus p=<%0.R%> implies len p = 0 by Lm2;
  thus len p=0 implies p=<%0.R%>
  proof
    assume len p=0;
    then len p=len <%0.R%> & for k st k < len p holds p.k = <%0.R%>.k
      by Lm2,NAT_1:2;
    hence thesis by Th4;
  end;
