#This file was created by <cfog> Tue Jan  6 11:05:02 1998
#LyX 0.12 (C) 1995-1997 Matthias Ettrich and the LyX Team
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\layout Title

Test of AMS-Art Style
\layout Author

David L.
 Johnson
\layout Address

Department of Mathematics
\newline 
Lehigh University
\newline 
Bethlehem, PA 18015
\layout Current Address

Home
\layout Email

dlj0@lehigh.edu
\layout URL

http://www.lehigh.edu/~dlj0/dlj0.html
\layout Keywords

Test
\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.
\layout Dedicatory

To my wife.
\layout Translator

Joe
\layout Subjectclass

Primary: 12G34, Secondary: 09G87
\layout Abstract

This is not very abstract.
 Note that the abstract must be part of the title stuff for AMS.
 For some reason LyX doesn't really put it there, yet.
 That should be fixed eventually.
\layout Section

Introduction
\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:
\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.
\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.
\layout Theorem

This is a numbered theorem
\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.
 
\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.
\layout Theorem*

This is an unnumbered theorem
\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.
\layout Corollary

First corollary.
\layout Proof

Its proof.
\layout Corollary*

Unnumbered corollary.
 
\layout LaTeX

%
\layout Corollary*

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

Lemma number 1
\layout Proposition

First proposition.
\layout Proposition*

Unnumbered version.
\layout Conjecture

A wild guess.
\layout Conjecture*

So wild I didn't number it.
\layout Criterion

Need some criteria
\layout Algorithm

first this, then the next
\layout Fact

Not fiction.
\layout Fact*

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

It stands to reason.
\layout Definition

a word means exactly what I say it means.
\layout Definition*

Unnumbered.
\layout Standard

Plain text.
 Plain text.
 Plain text.
 Plain text.
 Plain text.
 Plain text.
 Plain text.
 Plain text.
 Plain text.
 Plain text.
 
\layout Example

This should be an example.
\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.
 
\layout Condition

If you say so.
\layout Problem

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

I think this will be useful.
\layout Claim

I did it the way the documentation said to.
\layout Note

It may need more work yet.
\layout Standard

More plain text, in standard format.
\layout Theorem

This is a second numbered theorem
\layout Proof

Here is its proof.
\layout Standard

More text.
\layout Corollary

Second corollary.
\layout Proof

Its proof.
\layout Lemma

Lemma number 2
\layout Proposition

Second proposition.
\layout Conjecture

A wild guess.
\layout Criterion

Need some criteria
\layout Notation


\begin_inset Formula \( S=\mathbb {R} \)
\end_inset 

.
\layout Summary

In the end, will it matter?
\layout Acknowledgement

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

If this works, then the rest will.
\layout Conclusion

It seems to work.
\layout Proof

Here goes another proof.
\layout Standard

Plain text.
\layout Section

Next try.
\layout Standard

This tries out the section environments.
\layout Theorem

This is a theorem
\layout Proof

Here is its proof.
\layout Standard

More text.
\layout Corollary

Third corollary.
 First one of this section.
\layout Proof

Its proof.
\layout Lemma

Lemma number 3
\layout Proposition

Third proposition.
\layout Conjecture

A wild guess.
\layout Criterion

Need some criteria
\layout Subsection

This is a subsection
\layout Standard

With more results therein.
\layout Theorem

This is a theorem, maybe the fourth one.
\layout Proof

Here is its proof.
\layout Standard

More text.
\layout Corollary

Fourth corollary.
\layout Proof

Its proof.
\layout Lemma

Lemma number 4
\layout Proposition

Fourth proposition.
\layout Conjecture

A wild guess.
\layout Criterion

Need some criteria
\layout Standard

More random text.
\layout Theorem

This is a theorem
\layout Proof

Here is its proof.
\layout Standard

More text.
\layout Claim

I believe this is true.
\layout Proof

Its proof.
\layout Lemma

Lemma number 5
\layout Proposition

Fifth proposition.
\layout Conjecture

A wild guess.
\layout Criterion

Need some criteria
\layout Subsubsection

This is the subsection with results.
\layout Standard

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

This is a theorem - sixth in the series
\layout Proof

Here is its proof.
\layout Standard

More text.
\layout Corollary

Sixth corollary.
\layout Proof

Its proof.
\layout Lemma

Lemma number 6
\layout Proposition

Sixth proposition.
\layout Conjecture

A wild guess.
\layout Criterion

Need some criteria
\layout Bibliography
\bibitem {1}

Johnson, D.
 L.
 
\emph on 
Out of my head
\layout Bibliography
\bibitem {2}

American Mathematical Society, 
\emph on 
Instructions for preparation of papers and monographs: AMS-LaTeX
\emph default 
, (1997).
\layout Bibliography
\bibitem {3}

American Mathematical Society, 
\layout Standard

\the_end
