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\begin_document
\begin_header
\textclass amsart
\language english
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\begin_body

\begin_layout Title

Test of AMS-Art Style
\end_layout

\begin_layout Author

David L.
 Johnson
\end_layout

\begin_layout Address

Department of Mathematics
\newline
Lehigh University
\newline
Bethlehem, PA 18015
\end_layout

\begin_layout Current Address

Home
\end_layout

\begin_layout Email

dlj0@lehigh.edu
\end_layout

\begin_layout URL

http://www.lehigh.edu/~dlj0/dlj0.html
\end_layout

\begin_layout Keywords

Test
\end_layout

\begin_layout Thanks

To Emmanuel, for forcing me to fix this, and Jean-Marc, for making it possible,
 and necessary.
 Also to Mate, who suggested numerous improvements.
\end_layout

\begin_layout Dedicatory

To my wife.
\end_layout

\begin_layout Translator

Joe
\end_layout

\begin_layout Subjectclass

Primary: 12G34, Secondary: 09G87
\end_layout

\begin_layout Abstract

This is not very abstract.
 Note that the abstract must be part of the title stuff for AMS.
 LyX is aware of that since version 0.12.1.
 Good.
 
\end_layout

\begin_layout Section

Introduction
\end_layout

\begin_layout Standard

This file, and any amsart-* LyX file, can be converted to either of the
 numbering schemes by simply changing the document class in the 
\family sans
\bar under
L
\bar default
ayout-
\bar under
D
\bar default
ocument
\family default
 popup.
 The styles are:
\end_layout

\begin_layout Enumerate

amsart - The standard AMS-article format.
 All results and similar statements are numbered as 
\begin_inset Formula $(n.m)$
\end_inset

, where the first number refers to the section, and the second refers to
 the total number of results (Theorems, Corollaries, Propositions, Definitions
 and Remarks, etc.) in that section.
 There are also many (but not all) environments available unnumbered, which
 is occasionally needed.
 Unnumbered environments indicated by an asterisk at the end.
\end_layout

\begin_layout Enumerate

amsart-seq - Here, numbering for each type of statement is in its own sequence,
 with no reference to the section number.
 There are also many (but not all) environments available unnumbered, which
 is occasionally needed.
\end_layout

\begin_layout Theorem

This is a numbered theorem
\end_layout

\begin_layout Proof

Here is its proof.
 Here is its proof.
 Here is its proof.
 Here is its proof.
 Here is its proof.
 Here is its proof.
 
\end_layout

\begin_layout Standard

More text.
 Note that two occurrences of the same environment, like two definitions,
 need to be separated somehow.
 For the moment, the best way is to include a paragraph with a %, in the
 LaTeX environment, if you really want two definitions (or whatever) together,
 with no intervening text of another sort.
\end_layout

\begin_layout Theorem*

This is an unnumbered theorem
\end_layout

\begin_layout Proof

Here is its proof.
 Here is its proof.
 Here is its proof.
 Here is its proof.
 Here is its proof.
 Here is its proof.
\end_layout

\begin_layout Corollary

First corollary.
\end_layout

\begin_layout Proof

Its proof.
\end_layout

\begin_layout Corollary*

Unnumbered corollary.
 
\end_layout

\begin_layout Standard


\begin_inset ERT
status collapsed

\begin_layout Standard
%
\end_layout

\end_inset


\end_layout

\begin_layout Corollary*

A second, with no intervening text.
 Note the % to force a separation.
\end_layout

\begin_layout Lemma

Lemma number 1
\end_layout

\begin_layout Proposition

First proposition.
\end_layout

\begin_layout Proposition*

Unnumbered version.
\end_layout

\begin_layout Conjecture

A wild guess.
\end_layout

\begin_layout Conjecture*

So wild I didn't number it.
\end_layout

\begin_layout Criterion

Need some criteria
\end_layout

\begin_layout Algorithm

first this, then the next
\end_layout

\begin_layout Fact

Not fiction.
\end_layout

\begin_layout Fact*

Bald statement of fact.
 Unnumbered environments are often used for emphasis, or in a short presentation
 that doesn't require numbered results.
 
\end_layout

\begin_layout Axiom

It stands to reason.
\end_layout

\begin_layout Definition

a word means exactly what I say it means.
\end_layout

\begin_layout Definition*

Unnumbered.
\end_layout

\begin_layout Standard

Plain text.
 Plain text.
 Plain text.
 Plain text.
 Plain text.
 Plain text.
 Plain text.
 Plain text.
 Plain text.
 Plain text.
 
\end_layout

\begin_layout Example

This should be an example.
\end_layout

\begin_layout Standard

Plain text.
 Plain text.
 Plain text.
 Plain text.
 Plain text.
 Plain text.
 Plain text.
 Plain text.
 Plain text.
 Plain text.
 Plain text.
 Plain text.
 Plain text.
 
\end_layout

\begin_layout Condition

If you say so.
\end_layout

\begin_layout Problem

I don't know what to write is the problem.
\end_layout

\begin_layout Remark

I think this will be useful.
\end_layout

\begin_layout Claim

I did it the way the documentation said to.
\end_layout

\begin_layout Note

It may need more work yet.
\end_layout

\begin_layout Standard

More plain text, in standard format.
\end_layout

\begin_layout Theorem

This is a second numbered theorem
\end_layout

\begin_layout Proof

Here is its proof.
\end_layout

\begin_layout Standard

More text.
\end_layout

\begin_layout Corollary

Second corollary.
\end_layout

\begin_layout Proof

Its proof.
\end_layout

\begin_layout Lemma

Lemma number 2
\end_layout

\begin_layout Proposition

Second proposition.
\end_layout

\begin_layout Conjecture

A wild guess.
\end_layout

\begin_layout Criterion

Need some criteria
\end_layout

\begin_layout Notation


\begin_inset Formula $S=\mathbb{R}$
\end_inset

.
\end_layout

\begin_layout Summary

In the end, will it matter?
\end_layout

\begin_layout Acknowledgement

Thanks to Mattias Ettrich.
 Without him I never would have learned LaTeX.
\end_layout

\begin_layout Case

If this works, then the rest will.
\end_layout

\begin_layout Conclusion

It seems to work.
\end_layout

\begin_layout Proof

Here goes another proof.
\end_layout

\begin_layout Standard

Plain text.
\end_layout

\begin_layout Section

Next try.
\end_layout

\begin_layout Standard

This tries out the section environments.
\end_layout

\begin_layout Theorem

This is a theorem
\end_layout

\begin_layout Proof

Here is its proof.
\end_layout

\begin_layout Standard

More text.
\end_layout

\begin_layout Corollary

Third corollary.
 First one of this section.
\end_layout

\begin_layout Proof

Its proof.
\end_layout

\begin_layout Lemma

Lemma number 3
\end_layout

\begin_layout Proposition

Third proposition.
\end_layout

\begin_layout Conjecture

A wild guess.
\end_layout

\begin_layout Criterion

Need some criteria
\end_layout

\begin_layout Subsection

This is a subsection
\end_layout

\begin_layout Standard

With more results therein.
\end_layout

\begin_layout Theorem

This is a theorem, maybe the fourth one.
\end_layout

\begin_layout Proof

Here is its proof.
\end_layout

\begin_layout Standard

More text.
\end_layout

\begin_layout Corollary

Fourth corollary.
\end_layout

\begin_layout Proof

Its proof.
\end_layout

\begin_layout Lemma

Lemma number 4
\end_layout

\begin_layout Proposition

Fourth proposition.
\end_layout

\begin_layout Conjecture

A wild guess.
\end_layout

\begin_layout Criterion

Need some criteria
\end_layout

\begin_layout Standard

More random text.
\end_layout

\begin_layout Theorem

This is a theorem
\end_layout

\begin_layout Proof

Here is its proof.
\end_layout

\begin_layout Standard

More text.
\end_layout

\begin_layout Claim

I believe this is true.
\end_layout

\begin_layout Proof

Its proof.
\end_layout

\begin_layout Lemma

Lemma number 5
\end_layout

\begin_layout Proposition

Fifth proposition.
\end_layout

\begin_layout Conjecture

A wild guess.
\end_layout

\begin_layout Criterion

Need some criteria
\end_layout

\begin_layout Subsubsection

This is the subsection with results.
\end_layout

\begin_layout Standard

The quick, brown fox jumped over the lazy dog.
\end_layout

\begin_layout Theorem

This is a theorem - sixth in the series
\end_layout

\begin_layout Proof

Here is its proof.
\end_layout

\begin_layout Standard

More text.
\end_layout

\begin_layout Corollary

Sixth corollary.
\end_layout

\begin_layout Proof

Its proof.
\end_layout

\begin_layout Lemma

Lemma number 6
\end_layout

\begin_layout Proposition

Sixth proposition.
\end_layout

\begin_layout Conjecture

A wild guess.
\end_layout

\begin_layout Criterion

Need some criteria
\end_layout

\begin_layout Bibliography
\bibitem {1}

Johnson, D.
 L.
 
\emph on
Out of my head
\end_layout

\begin_layout Bibliography
\bibitem {2}

American Mathematical Society, 
\emph on
Instructions for preparation of papers and monographs: AMS-LaTeX
\emph default
, (1997).
\end_layout

\begin_layout Bibliography
\bibitem {3}

American Mathematical Society, 
\end_layout

\end_body
\end_document
