
theorem Th24:
  for L be add-associative right_zeroed right_complementable
distributive non empty doubleLoopStr for p be Polynomial of L holds len (0.L*
  p) = 0
proof
  let L be add-associative right_zeroed right_complementable distributive non
  empty doubleLoopStr;
  let p be Polynomial of L;
  0 is_at_least_length_of (0.L*p)
  proof
    let i be Nat;
    assume i>=0;
    reconsider ii=i as Element of NAT by ORDINAL1:def 12;
    thus (0.L*p).i = 0.L*p.ii by Def4
      .= 0.L;
  end;
  hence thesis by ALGSEQ_1:def 3;
end;
