Homework Assignment 3
                               CS 389r
                         Unique Number: 53540
                             Spring, 2026

                       Given:  February 3, 2026
                        Due:  February 12, 2026


This homework asks for solutions to problems 39 -- 47.  You should
work these proofs out on paper, and turn in your work.  Your proofs
should look similar to the example proof of:

  (equal (tree-copy x) x)

given in the R-AND-I-STRUCTURAL-INDUCTION section of the online, class
notes.  It is important that you identify the variable(s) on which you
are inducting, and that you make clear how you are using the Principle
of Structural Induction.

Note!  This homework will take a lot of time!

After this assignment, we will begin using the ACL2 Proof Builder
instead of performing "hand proofs".