Homework Assignment 4
                               CS 389r
                         Unique Number: 51350
                             Spring, 2025

                       Given:  February 11, 2025
                        Due:  February 20, 2025


This homework asks that you use the ACL2 Proof Builder to perform
mechanical proofs for problems 40, 41, 43, 44, and 45.  We will
discuss the ACL2 Proof Builder in class on February 11th and 13th.

In addition, this homework asks for hand-written solutions to problems
48 and 49.  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.

Like HW 3, this homework will take quite a bit of time -- but this
homework is less labor intensive than HW 3.


One may use the ACL2 system on any of the public Linux machines.  For
a list of the ~170 available machines, see:

    https://apps.cs.utexas.edu/unixlabstatus/

When you have logged into one of these computers, the following command
will start ACL2:

   /p/bin/acl2


To use the proof builder, see the ACL2 documentation for the proof builder:

   https://www.cs.utexas.edu/~moore/acl2/v8-6/combined-manual/?topic=ACL2____PROOF-BUILDER

We will use a subset of the available commands; see:

   https://www.cs.utexas.edu/~moore/acl2/v8-6/combined-manual/?topic=ACL2____PROOF-BUILDER-COMMANDS-SHORT-LIST


For your homework, you may not use these proof-builder commands:

 ACL2-pc::bash
 ACL2-pc::prove

These two commands allow access to the automated portion of the ACL2
system; this would make your homework solutions a one-step process.

Although not needed for this assignment, you may use these two
commands only with the restrictions below.

 ACL2-pc::=
 ACL2-pc::claim

For the ``ACL2-pc::='' command, you may not provide any arguments.

For the ``ACL2-pc::claim'' command, your second argument must be 0.