let L be non empty ZeroStr ; for z0, z1 being Element of L st z1 <> 0. L holds
len <%z0,z1%> = 2
let z0, z1 be Element of L; ( z1 <> 0. L implies len <%z0,z1%> = 2 )
assume
z1 <> 0. L
; len <%z0,z1%> = 2
then
<%z0,z1%> . 1 <> 0. L
by Th38;
then A1:
for n being Nat st n is_at_least_length_of <%z0,z1%> holds
1 + 1 <= n
by NAT_1:13;
2 is_at_least_length_of <%z0,z1%>
by Th38;
hence
len <%z0,z1%> = 2
by A1, ALGSEQ_1:def 3; verum