## 3. 6 ARRN (Arrangement of Quantitization Symbols and Parentheses)

Let us first look at the examples.

Example 1 a1 : (All x) ((Exist y) (f(x,y))) by

...;.............

a2 : (All x) (Exist y) (f(x,y)) by ARRN (a1) ;
Therefore, ARRN is used to take out the unnecessary parentheses in between
the quantitization blocks. Also, it can be used to insert parentheses.

Example 2 a1 : (All x) (All y) (g(x,y)) by ...;

...............
a2 : (All x) ((All y) (g(x,y))) by ARRN (a1) ;
Thus, ARRN is an abbreviation of arrange.