Theorems, lemmas, propositions, corollaries, definitions and examples
are all "theorem-like objects''. They are
set in the same style, and numbered in a single sequence using the
chapter number and a theorem counter that starts at 1 with each
chapter. The macros are \thm, \lem, \prop, \cor,
\defn and \example. They take an optional parameter delimited
by `(' and `)' (not by the usual $\TeX$ braces). The parameter
is an optional title for the theorem-like object—for example,
\thm (Bolzano-Weierstrass) Every bounded
sequence \dots
produces:
Warning. You may get nasty, inscrutable error messages if \thm
(or another of these macros) is immediately followed by something
`strange', especially by a group delimited by {...}. The
following doesn't work:
\example {\em Don't try this at home!\/} Here is an example\dots
This works fine:
\example\relax{\em That's better.\/} Here is\dots
Each theorem-like object must be followed by one of these macros:
\endthm, \enddef, \endexample, or \endthmnoproof.
The first three mark the end of the corresponding theorem-like object;
the ends of examples and definitions will be followed by a small
hollow square. The macro \endthmnoproof also inserts a hollow
square after the statement of the theorem, lemma, etc.
If a proof is provided, it should begin with \proof and end with
\endproof. A solid square will be inserted at the end of the proof.
The macro \proof goes
between the statement of the theorem and the proof.
Your text may include a list of claims or steps or remarks of some kind. These are set like this:
\beginclaimlist
\item{Claim 1.} You need not use the word "claim''.
\item{Claim 2.} Each claim may include more than one paragraph.
\endclaimlist
producing this:
Claim 1. You need not use the word "claim''.
Claim 2. Each claim may include more than one paragraph.
Remark. If you want to write a single claim or
remark, you may use a claimlist with only one item, or you may
use the macro pair \remark and \endremark; this paragraph
starts with \remark{Remark} and ends with \endremark. A
remark may consist of more than one paragraph, though there is no
indication that the remark has ended.
Every theorem-like object generates an entry in a special index file (see page 5.2). This can be used to produce an index of all theorem-like objects, separate from the main index; this manual includes a brief example. For more information about producing indices, see chapter 5. (To see how to generate all these nifty cross references, see chapter 4.)