
theorem Th5:
  for L be non empty ZeroStr for p be Polynomial of L st len p = 0
  holds p = 0_.(L)
proof
  let L be non empty ZeroStr;
  let p be Polynomial of L;
  assume len p = 0;
  then
A1: 0 is_at_least_length_of p by ALGSEQ_1:def 3;
A2: now
    let x be object;
    assume x in dom p;
    then reconsider i=x as Element of NAT by NORMSP_1:12;
    i >= 0;
    hence p.x = 0.L by A1;
  end;
  dom p = NAT by NORMSP_1:12;
  hence thesis by A2,FUNCOP_1:11;
end;
