
theorem Th32:
  for L be non empty ZeroStr for z0 be Element of L holds <%z0%>.0
  = z0 & for n be Element of NAT st n >= 1 holds <%z0%>.n = 0.L
proof
  let L be non empty ZeroStr;
  let z0 be Element of L;
  thus <%z0%>.0 = z0 by ALGSEQ_1:def 5;
  let n be Element of NAT;
A1: len <%z0%> <= 1 by ALGSEQ_1:def 5;
  assume n >= 1;
  hence thesis by A1,ALGSEQ_1:8,XXREAL_0:2;
end;
