1 #LyX 2.1 created this file. For more info see http://www.lyx.org/
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88 Department of Mathematics
89 \begin_inset Newline newline
93 \begin_inset Newline newline
99 \begin_layout Current Address
108 http://www.lehigh.edu/~dlj0/dlj0.html
111 \begin_layout Keywords
116 To Emmanuel, for forcing me to fix this, and Jean-Marc, for making it possible,
118 Also to Mate, who suggested numerous improvements.
121 \begin_layout Dedicatory
125 \begin_layout Translator
129 \begin_layout Subjectclass
130 Primary: 12G34, Secondary: 09G87
133 \begin_layout Abstract
134 This is not very abstract.
135 Note that the abstract must be part of the title stuff for AMS.
136 LyX is aware of that since version 0.12.1.
141 \begin_layout Section
145 \begin_layout Standard
146 This file, and any amsart-* LyX file, can be converted to either of the
147 numbering schemes by simply changing the document class in the
162 \begin_layout Enumerate
163 amsart - The standard AMS-article format.
164 All results and similar statements are numbered as
165 \begin_inset Formula $(n.m)$
168 , where the first number refers to the section, and the second refers to
169 the total number of results (Theorems, Corollaries, Propositions, Definitions
170 and Remarks, etc.) in that section.
171 There are also many (but not all) environments available unnumbered, which
172 is occasionally needed.
173 Unnumbered environments indicated by an asterisk at the end.
176 \begin_layout Enumerate
177 amsart-seq - Here, numbering for each type of statement is in its own sequence,
178 with no reference to the section number.
179 There are also many (but not all) environments available unnumbered, which
180 is occasionally needed.
183 \begin_layout Theorem
184 This is a numbered theorem
197 \begin_layout Standard
199 Note that two occurrences of the same environment, like two definitions,
200 need to be separated somehow.
201 For the moment, the best way is to include a paragraph with a %, in the
202 LaTeX environment, if you really want two definitions (or whatever) together,
203 with no intervening text of another sort.
206 \begin_layout Theorem*
207 This is an unnumbered theorem
219 \begin_layout Corollary
227 \begin_layout Corollary*
228 Unnumbered corollary.
232 \begin_layout Standard
236 \begin_layout Plain Layout
246 \begin_layout Corollary*
247 A second, with no intervening text.
248 Note the % to force a separation.
255 \begin_layout Proposition
259 \begin_layout Proposition*
263 \begin_layout Conjecture
267 \begin_layout Conjecture*
268 So wild I didn't number it.
271 \begin_layout Criterion
275 \begin_layout Algorithm
276 first this, then the next
284 Bald statement of fact.
285 Unnumbered environments are often used for emphasis, or in a short presentation
286 that doesn't require numbered results.
294 \begin_layout Definition
295 a word means exactly what I say it means.
298 \begin_layout Definition*
302 \begin_layout Standard
316 \begin_layout Example
317 This should be an example.
320 \begin_layout Standard
337 \begin_layout Condition
341 \begin_layout Problem
342 I don't know what to write is the problem.
346 I think this will be useful.
350 I did it the way the documentation said to.
354 It may need more work yet.
357 \begin_layout Standard
358 More plain text, in standard format.
361 \begin_layout Theorem
362 This is a second numbered theorem
369 \begin_layout Standard
373 \begin_layout Corollary
385 \begin_layout Proposition
389 \begin_layout Conjecture
393 \begin_layout Criterion
397 \begin_layout Notation
398 \begin_inset Formula $S=\mathbb{R}$
404 \begin_layout Summary
405 In the end, will it matter?
408 \begin_layout Acknowledgement
409 Thanks to Mattias Ettrich.
410 Without him I never would have learned LaTeX.
414 If this works, then the rest will.
417 \begin_layout Conclusion
422 Here goes another proof.
425 \begin_layout Standard
429 \begin_layout Section
433 \begin_layout Standard
434 This tries out the section environments.
437 \begin_layout Theorem
445 \begin_layout Standard
449 \begin_layout Corollary
451 First one of this section.
462 \begin_layout Proposition
466 \begin_layout Conjecture
470 \begin_layout Criterion
474 \begin_layout Subsection
478 \begin_layout Standard
479 With more results therein.
482 \begin_layout Theorem
483 This is a theorem, maybe the fourth one.
490 \begin_layout Standard
494 \begin_layout Corollary
506 \begin_layout Proposition
510 \begin_layout Conjecture
514 \begin_layout Criterion
518 \begin_layout Standard
522 \begin_layout Theorem
530 \begin_layout Standard
535 I believe this is true.
546 \begin_layout Proposition
550 \begin_layout Conjecture
554 \begin_layout Criterion
558 \begin_layout Subsubsection
559 This is the subsection with results.
562 \begin_layout Standard
563 The quick, brown fox jumped over the lazy dog.
566 \begin_layout Theorem
567 This is a theorem - sixth in the series
574 \begin_layout Standard
578 \begin_layout Corollary
590 \begin_layout Proposition
594 \begin_layout Conjecture
598 \begin_layout Criterion
602 \begin_layout Bibliography
603 \begin_inset CommandInset bibitem
616 \begin_layout Bibliography
617 \begin_inset CommandInset bibitem
623 American Mathematical Society,
625 Instructions for preparation of papers and monographs: AMS-LaTeX
630 \begin_layout Bibliography
631 \begin_inset CommandInset bibitem
637 American Mathematical Society,