# Formal Mathematical Proofs in TeX

## QED -Right-justified end-of-proof mark

It is now conventional to indicate the end of a mathematical proof by putting a little square on the far right hand side of the page.
I have only seen two ways of doing this:
• a naïve one, "\hfill $\square$", that sometimes works, but frequently puts the square on the left of the next line; and
• a character-by-character copy of the macros that I wrote for my Cambridge PhD thesis in 1986, with the help of Chris Thompson of the University Computing Service.
The code of mine that has been copied around the world for 20 years ensures that the square does on the right (of the next line) even when the last line of the proof takes up the whole of a line.
See the documentation for why this is not as simple as you might expect.
This package also allows you to put \qed in various mathematical environments such as eqnarray.
It has "bells and whistles" for a Proof LATEX environment.
Also for "theorems as commands" such as \Theorem instead of \begin{Theorem}...\end{Theorem}.
The macros: QED.sty and the manual. This is also available in DVI, PDF, compressed PostScript and compressed PostScript A4 booklet.

## Proof trees

The macros: prooftree.sty and the manual.
My most popular macro package. People come up to me at conferences to say how useful it is, whereas the commutative diagrams package attracts abuse.
A little secret: whilst the diagrams package took years of experimentation, the proof tree package was written in an afternoon!

## Proof boxes

The macros: boxproof.sty.
The manual and some examples as DVI, PDF, compressed PostScript and A5 PS booklet, and its LATEX source.

This is www.PaulTaylor.EU/proofs/index.html and it was derived from proofs/index.tex which was last modified on 22 July 2007.