
theorem
  for L be right_zeroed non empty addLoopStr for p,q be
  Polynomial of L for n be Element of NAT holds (n is_at_least_length_of p & n
  is_at_least_length_of q) implies n is_at_least_length_of p+q
proof
  let L be right_zeroed non empty addLoopStr;
  let p,q be Polynomial of L;
  let n be Element of NAT;
  assume
A1: n is_at_least_length_of p & n is_at_least_length_of q;
  let i be Nat;
  assume i>=n;
  then
A2: p.i = 0.L & q.i = 0.L by A1;
  thus (p+q).i = 0.L + 0.L by A2,NORMSP_1:def 2
    .= 0.L by RLVECT_1:def 4;
end;
