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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
\begin_inset Newline newline
\end_inset

Lehigh University
\begin_inset Newline newline
\end_inset

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.
 \SpecialChar 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-* \SpecialChar 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
 \SpecialChar 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 Plain Layout

%
\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 \SpecialChar 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
\begin_inset CommandInset bibitem
LatexCommand bibitem
key "1"
literal "true"

\end_inset

Johnson, D.
 L.
 
\emph on
Out of my head
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LatexCommand bibitem
key "2"
literal "true"

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American Mathematical Society, 
\emph on
Instructions for preparation of papers and monographs: AMS-\SpecialChar LaTeX

\emph default
, (1997).
\end_layout

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\begin_inset CommandInset bibitem
LatexCommand bibitem
key "3"
literal "true"

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American Mathematical Society, 
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