Part 8
An Interesting Example of Part_btwn() and Concatenation

This is an interesting example of using Prt_btwn () and concatenation. It shows that the removal of a substring from a string produces one of the original strings.

Prt_btwn (| a |, | a | + 1, a o <x>) = Prt_btwn (0, 1, <x> o a) = <x>;
Prt_btwn (0, | a |, a o <x>) = Prt_btwn (1, | a | + 1, <x> o a) = a ;

Example:
α = <1, 4 > ; | α | = 2; x = 7; α o <x> = <1, 4, 7>; <x> o α = <7, 1, 4>;
Prt_btwn (2, 3, <1, 4, 7>) = Prt_btwn (0, 1, <7, 1, 4>) = <x>;
Prt_Btwn (0, 2, <1, 4, 7>) = Prt_btwn (1, 3, <7, 1, 4>) = α;