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Theorems and such
After a couple of declarations, you can do this:
\begin{theorem}
Herding cats is hard.
\end{theorem}
Theorem 1.Herding cats is hard.
\begin{lemma}[Smith, 1972]
Herding alligators is harder,
and much more dangerous besides.
\end{lemma}
Lemma 1 (Smith, 1972).Herding alligators is harder, and much
more dangerous besides.
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Creating theorem types
Before using theorem and lemma, I had to do this:
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
The rst argument is the internal name, so the word you put
in the \begin{} and \end{} statements. The second argument is
the external name, so it appears in the document before the
number.
Each theorem type has its own counter (hence Theorem 1 and
Lemma 1 in the previous example).
Put these declarations in preamble.tex.
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Several types, one counter
\newtheorem{prop}{Proposition}
\newtheorem{propdef}[prop]{Proposition-Definition}
The optional argument [prop] says that Proposition-Denitions
should be numbered in the same series as Propositions.
\begin{prop}[Lucas, 1977]
Swordplay obviates acting.
\end{prop}
\begin{propdef}[Lucas, 1999]
There exist painfully inane characters. A maximal such
character in a film is \emph{of Jar-Jar type}.
\end{propdef}
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Several times, one counter (continued)
Proposition-Denitions and Propositions are not numbered
separately:
Proposition 1 (Lucas, 1977).Swordplay obviates acting.
Proposition-Denition 2 (Lucas, 1999).There exist painfully
inane characters. A maximal such character in a lm is of Jar-Jar
type.
Note also that we used emph instead of textit.
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Counting within sections, subsections, etc.
You can do
\newtheorem{remark}{Remark}[section]
to make Remarks numbered separately within each section
(\Remark 5.3"for the third Remark in Section 5).
Similarly \newtheorem{remark}{Remark}[subsection] would make
\Remark 5.2.1" and the like.
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More with theorems: styles and numbering
You can use three built-in \styles" to specify how you want
your theorem heading to appear. You can also dene your own
if these aren’t enough. Additionally, using an * makes a theorem
type unnumbered.
\theoremstyle{plain}% default
\newtheorem{thm}{Theorem}[section]
\newtheorem{lem}[thm]{Lemma}
\newtheorem{prop}[thm]{Proposition}
\newtheorem*{cor}{Corollary}
\newtheorem*{KL}{Kleins Lemma}
16
More with theorems (continued)
\theoremstyle{definition}
\newtheorem{defn}{Definition}[section]
\newtheorem{conj}{Conjecture}[section]
\newtheorem{exmp}{Example}[section]
\theoremstyle{remark}
\newtheorem*{rem}{Remark}
\newtheorem*{note}{Note}
\newtheorem{case}{Case}
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Proof environment
The proof environment automatically places a QED symbol at
the end of your proof:
\begin{proof}[Proof of the Main Theorem]
Combining Lemma~\ref{lem:smith} and Definition~\ref{def:smith},
we see that $\mu(x)=17$.
\end{proof}
Proof of the Main Theorem. Combining Lemma 1 and Denition 3,
we see that (x) = 17.
For some reason, amsmath doesn’t appear to contain the proof
environment, so you might need to add \usepackage{amsthm} to
preamble.tex.
18
Moving the QED
Sometimes, the box appears on an empty line:
Proof.
G(t) = L !t
+t
(t)
\begin{proof}
\begin{equation*}
G(t)=L\gamma!\,t^{-\gamma}+t^{-\delta}\eta(t) \qedhere
\end{equation*}
\end{proof}
Proof.
G(t) = L !t
+t
(t)
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Part II: breaking and stacking
 multline, for breaking lines in long equations
 gather and align, for several equations in one display
 pmatrix and variants, for matrices
 \substack, for stacking conditions under big operators
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