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The "Rule of Allowability"

I am so frequently asked whether a particular theorem or homework problem can be used in the proof of some other homework problem that I decided to give a complete listing of the "Rule of Allowability" that was first discussed in the 1997 FAQ's. So here is the official answer:

In the proof of homework problem k on the assignment that deals with Topic Number n (see below) you may use:

Any theorem that appears in the textbook or the lecture notes in section of the book which was covered in a Topic Number less than n.

This does not include theorems that appear in the textbook, but appear in a section of the textbook which was not covered (e.g. you can't use a result from Chapter 4.6 in a problem that is in Chapter 6.2 because we don't officially cover Chapter 4.6 [see below])

Any theorem that appears in the same section of the textbook or lecture notes (Topic Number n) EXCEPT if the question is asking you to prove all or part of the theorem you want to use, or any part of a theorem on which the proof of the theorem you want to use depends (i.e. no circular arguments).

Any theorem which was proven in lecture prior to covering the current assignment's topic.

Any theorem which is proven completely in the FAQ's or the Lecture Notes, including the theorem you are trying to prove. If the complete proof is given (including the reasons for all statements) you should simply reference the appropriate location in the FAQ's or Lecture Notes, don't recopy the whole proof. If the proof in the FAQ's or Lecture notes is given without reasons, or with some reasons missing, you may use the proof but you must supply the missing reasons. In that situation you must copy the entire proof and supply the reasons, indicating the source of the proof you are copying (FAQ's or Lecture Notes) at the top of the proof. If the proof has an error in it and you reference it, your solution will be marked wrong even if it is a proof from the Lecture Notes, textbook, or FAQ. It is your responsibility to ensure that any proof you hand in is correct, even those you reference, and that includes convincing yourself that there are no typos or other errors in the argument.

The results of any previously assigned homework problem, whether or not you got it correct.

This can include assigned problems in the same section you are working on, except were explicitly noted.
The results of homework problems which were NOT assigned may not be used without proving them first.

Any lemma you prove in your current assignment (whose proof is correct).

You may not use a lemma or result that you proved in a previous homework assignment, unless it was an assigned problem.

You many not use any other theorems or lemmas, including ones found in other books, ones from sections of our textbook that we haven't covered yet or won't cover, ones that are mentioned in passing in lecture or in the FAQ's without proof, or ones from previous semesters or other sections of the course, whether or not I was the instructor. You may also not use answers to problems given in the back of the textbook, as most of these are not complete proofs, but rather just hints about proofs. The recipes on the recipe sheet are recipes that are derived from theorems and definitions in the Lecture Notes and textbook, so that it is allowable to use a given recipe only if it is allowable to use the theorem or definition from which it is derived in accordance with Rules #1-6 above.

**List of Topics**
Topic Number	Activity
1	Introduction and Toy Proofs
2	Logic - Appendix A
3	Logic cont.
4	Sets and Functions -Appendix B
5	Set and Functions cont.
6	Chapter 1.1
7	Induction - Appendix C
8	Chapter 1.2
9	Chapter 1.3
10	Equivalence Relations -Appendix D
11	Chapter 2.1
12	Chapter 2.2
13	Chapter 2.3
14	Chapter 3.1
15	Chapter 3.2
16	Chapter 3.3
17	Chapter 4.1
18	Chapter 4.2
19	Chapter 4.3
20	Chapter 4.4
21	Chapter 5.1
22	Chapter 5.2
23	Chapter 5.3
24	Chapter 6.1
25	Chapter 6.2
26	Chapter 7.1
27	Chapter 7.2
28	Chapter 7.3
29	Chapter 7.4
30	Chapter 7.5
31	Chapter 7.6
32	Chapter 7.7
33	Chapter 7.8
34	Chapter 7.9
35	Lectures on Rubik's Cube, Maple etc.