reserve r,t for Real;
reserve i for Integer;
reserve k,n for Nat;
reserve p for Polynomial of F_Real;
reserve e for Element of F_Real;
reserve L for non empty ZeroStr;
reserve z,z0,z1,z2 for Element of L;

theorem Th26:
  z2 <> 0.L implies len <%z0,z1,z2%> = 3
  proof
    assume z2 <> 0.L;
    then <%z0,z1,z2%>.2 <> 0.L by Th23;
    then
A1: for n being Nat st n is_at_least_length_of <%z0,z1,z2%> holds 2+1 <= n
    by NAT_1:13;
    3 is_at_least_length_of <%z0,z1,z2%> by Th24;
    hence thesis by A1,ALGSEQ_1:def 3;
  end;
