1 #LyX 2.3 created this file. For more info see http://www.lyx.org/
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96 Department of Mathematics
97 \begin_inset Newline newline
101 \begin_inset Newline newline
107 \begin_layout Current Address
116 http://www.lehigh.edu/~dlj0/dlj0.html
119 \begin_layout Keywords
124 To Emmanuel, for forcing me to fix this, and Jean-Marc, for making it possible,
126 Also to Mate, who suggested numerous improvements.
129 \begin_layout Dedicatory
133 \begin_layout Translator
137 \begin_layout Subjectclass
138 Primary: 12G34, Secondary: 09G87
141 \begin_layout Abstract
142 This is not very abstract.
143 Note that the abstract must be part of the title stuff for AMS.
145 is aware of that since version 0.12.1.
150 \begin_layout Section
154 \begin_layout Standard
155 This file, and any amsart-* \SpecialChar LyX
156 file, can be converted to either of the numbering
157 schemes by simply changing the document class in the
172 \begin_layout Enumerate
173 amsart - The standard AMS-article format.
174 All results and similar statements are numbered as
175 \begin_inset Formula $(n.m)$
178 , where the first number refers to the section, and the second refers to
179 the total number of results (Theorems, Corollaries, Propositions, Definitions
180 and Remarks, etc.) in that section.
181 There are also many (but not all) environments available unnumbered, which
182 is occasionally needed.
183 Unnumbered environments indicated by an asterisk at the end.
186 \begin_layout Enumerate
187 amsart-seq - Here, numbering for each type of statement is in its own sequence,
188 with no reference to the section number.
189 There are also many (but not all) environments available unnumbered, which
190 is occasionally needed.
193 \begin_layout Theorem
194 This is a numbered theorem
207 \begin_layout Standard
209 Note that two occurrences of the same environment, like two definitions,
210 need to be separated somehow.
211 For the moment, the best way is to include a paragraph with a %, in the
213 environment, if you really want two definitions (or whatever) together,
214 with no intervening text of another sort.
217 \begin_layout Theorem*
218 This is an unnumbered theorem
230 \begin_layout Corollary
238 \begin_layout Corollary*
239 Unnumbered corollary.
243 \begin_layout Standard
247 \begin_layout Plain Layout
257 \begin_layout Corollary*
258 A second, with no intervening text.
259 Note the % to force a separation.
266 \begin_layout Proposition
270 \begin_layout Proposition*
274 \begin_layout Conjecture
278 \begin_layout Conjecture*
279 So wild I didn't number it.
282 \begin_layout Criterion
286 \begin_layout Algorithm
287 first this, then the next
295 Bald statement of fact.
296 Unnumbered environments are often used for emphasis, or in a short presentation
297 that doesn't require numbered results.
305 \begin_layout Definition
306 a word means exactly what I say it means.
309 \begin_layout Definition*
313 \begin_layout Standard
327 \begin_layout Example
328 This should be an example.
331 \begin_layout Standard
348 \begin_layout Condition
352 \begin_layout Problem
353 I don't know what to write is the problem.
357 I think this will be useful.
361 I did it the way the documentation said to.
365 It may need more work yet.
368 \begin_layout Standard
369 More plain text, in standard format.
372 \begin_layout Theorem
373 This is a second numbered theorem
380 \begin_layout Standard
384 \begin_layout Corollary
396 \begin_layout Proposition
400 \begin_layout Conjecture
404 \begin_layout Criterion
408 \begin_layout Notation
409 \begin_inset Formula $S=\mathbb{R}$
415 \begin_layout Summary
416 In the end, will it matter?
419 \begin_layout Acknowledgement
420 Thanks to Mattias Ettrich.
421 Without him I never would have learned \SpecialChar LaTeX
426 If this works, then the rest will.
429 \begin_layout Conclusion
434 Here goes another proof.
437 \begin_layout Standard
441 \begin_layout Section
445 \begin_layout Standard
446 This tries out the section environments.
449 \begin_layout Theorem
457 \begin_layout Standard
461 \begin_layout Corollary
463 First one of this section.
474 \begin_layout Proposition
478 \begin_layout Conjecture
482 \begin_layout Criterion
486 \begin_layout Subsection
490 \begin_layout Standard
491 With more results therein.
494 \begin_layout Theorem
495 This is a theorem, maybe the fourth one.
502 \begin_layout Standard
506 \begin_layout Corollary
518 \begin_layout Proposition
522 \begin_layout Conjecture
526 \begin_layout Criterion
530 \begin_layout Standard
534 \begin_layout Theorem
542 \begin_layout Standard
547 I believe this is true.
558 \begin_layout Proposition
562 \begin_layout Conjecture
566 \begin_layout Criterion
570 \begin_layout Subsubsection
571 This is the subsection with results.
574 \begin_layout Standard
575 The quick, brown fox jumped over the lazy dog.
578 \begin_layout Theorem
579 This is a theorem - sixth in the series
586 \begin_layout Standard
590 \begin_layout Corollary
602 \begin_layout Proposition
606 \begin_layout Conjecture
610 \begin_layout Criterion
614 \begin_layout Bibliography
615 \begin_inset CommandInset bibitem
629 \begin_layout Bibliography
630 \begin_inset CommandInset bibitem
637 American Mathematical Society,
639 Instructions for preparation of papers and monographs: AMS-\SpecialChar LaTeX
645 \begin_layout Bibliography
646 \begin_inset CommandInset bibitem
653 American Mathematical Society,