
theorem Th33:
  for L be non empty ZeroStr for z0 be Element of L st z0 <> 0.L
  holds len <%z0%> = 1
proof
  let L be non empty ZeroStr;
  let z0 be Element of L;
  assume z0 <> 0.L;
  then <%z0%>.0 <> 0.L by ALGSEQ_1:def 5;
  then <%z0%> <> <%0.L%> by ALGSEQ_1:def 5;
  then len <%z0%> <> 0 by ALGSEQ_1:14;
  then
A1: len <%z0%> >= 0+1 by NAT_1:13;
  assume len <%z0%> <> 1;
  then len <%z0%> > 1 by A1,XXREAL_0:1;
  hence contradiction by ALGSEQ_1:def 5;
end;
