let D be non empty set ; for f, g being FinSequence of D st g is_odd_substring_of f, 0 holds
g is_odd_substring_of f,1
let f, g be FinSequence of D; ( g is_odd_substring_of f, 0 implies g is_odd_substring_of f,1 )
reconsider n = 0 as even Element of NAT ;
assume
g is_odd_substring_of f, 0
; g is_odd_substring_of f,1
then
g is_odd_substring_of f,n + 1
by Th16;
hence
g is_odd_substring_of f,1
; verum