Formal Mathematical Proofs in TeX
Paul Taylor
1986-2003
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.