Prove the following counterpart of Exercise 23. Let the set of productions involving the variable $A$ on the left be divided into two disjoint subsets
$A\rightarrow x_1A|x_2A|...|x_nA,$
and, $A\rightarrow y_1|y_2|...|y_m,$
where $A$ is not a suffix of any $y_i$. Show that the grammar obtained by replacing these productions with
$A\rightarrow y_i|Zy_i,$ $i=1,2,3,…,m$
$Z\rightarrow x_i|Zx_i,$ $i=1,2,3,…,n.$
is equivalent to the original grammar.
