1 #LyX 2.4 created this file. For more info see https://www.lyx.org/
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98 Department of Mathematics
99 \begin_inset Newline newline
103 \begin_inset Newline newline
109 \begin_layout Current Address
118 http://www.lehigh.edu/~dlj0/dlj0.html
121 \begin_layout Keywords
126 To Emmanuel, for forcing me to fix this, and Jean-Marc, for making it possible,
128 Also to Mate, who suggested numerous improvements.
131 \begin_layout Dedicatory
135 \begin_layout Translator
139 \begin_layout Subjectclass
140 Primary: 12G34, Secondary: 09G87
143 \begin_layout Abstract
144 This is not very abstract.
145 Note that the abstract must be part of the title stuff for AMS.
147 is aware of that since version 0.12.1.
152 \begin_layout Section
156 \begin_layout Standard
157 This file, and any amsart-* \SpecialChar LyX
158 file, can be converted to either of the numbering
159 schemes by simply changing the document class in the
174 \begin_layout Enumerate
175 amsart - The standard AMS-article format.
176 All results and similar statements are numbered as
177 \begin_inset Formula $(n.m)$
180 , where the first number refers to the section, and the second refers to
181 the total number of results (Theorems, Corollaries, Propositions, Definitions
182 and Remarks, etc.) in that section.
183 There are also many (but not all) environments available unnumbered, which
184 is occasionally needed.
185 Unnumbered environments indicated by an asterisk at the end.
188 \begin_layout Enumerate
189 amsart-seq - Here, numbering for each type of statement is in its own sequence,
190 with no reference to the section number.
191 There are also many (but not all) environments available unnumbered, which
192 is occasionally needed.
195 \begin_layout Theorem
196 This is a numbered theorem
209 \begin_layout Standard
211 Note that two occurrences of the same environment, like two definitions,
212 need to be separated somehow.
213 For the moment, the best way is to include a paragraph with a %, in the
215 environment, if you really want two definitions (or whatever) together,
216 with no intervening text of another sort.
219 \begin_layout Theorem*
220 This is an unnumbered theorem
232 \begin_layout Corollary
240 \begin_layout Corollary*
241 Unnumbered corollary.
245 \begin_layout Standard
249 \begin_layout Plain Layout
259 \begin_layout Corollary*
260 A second, with no intervening text.
261 Note the % to force a separation.
268 \begin_layout Proposition
272 \begin_layout Proposition*
276 \begin_layout Conjecture
280 \begin_layout Conjecture*
281 So wild I didn't number it.
284 \begin_layout Criterion
288 \begin_layout Algorithm
289 first this, then the next
297 Bald statement of fact.
298 Unnumbered environments are often used for emphasis, or in a short presentation
299 that doesn't require numbered results.
307 \begin_layout Definition
308 a word means exactly what I say it means.
311 \begin_layout Definition*
315 \begin_layout Standard
329 \begin_layout Example
330 This should be an example.
333 \begin_layout Standard
350 \begin_layout Condition
354 \begin_layout Problem
355 I don't know what to write is the problem.
359 I think this will be useful.
363 I did it the way the documentation said to.
367 It may need more work yet.
370 \begin_layout Standard
371 More plain text, in standard format.
374 \begin_layout Theorem
375 This is a second numbered theorem
382 \begin_layout Standard
386 \begin_layout Corollary
398 \begin_layout Proposition
402 \begin_layout Conjecture
406 \begin_layout Criterion
410 \begin_layout Notation
411 \begin_inset Formula $S=\mathbb{R}$
417 \begin_layout Summary
418 In the end, will it matter?
421 \begin_layout Acknowledgement
422 Thanks to Mattias Ettrich.
423 Without him I never would have learned \SpecialChar LaTeX
428 If this works, then the rest will.
431 \begin_layout Conclusion
436 Here goes another proof.
439 \begin_layout Standard
443 \begin_layout Section
447 \begin_layout Standard
448 This tries out the section environments.
451 \begin_layout Theorem
459 \begin_layout Standard
463 \begin_layout Corollary
465 First one of this section.
476 \begin_layout Proposition
480 \begin_layout Conjecture
484 \begin_layout Criterion
488 \begin_layout Subsection
492 \begin_layout Standard
493 With more results therein.
496 \begin_layout Theorem
497 This is a theorem, maybe the fourth one.
504 \begin_layout Standard
508 \begin_layout Corollary
520 \begin_layout Proposition
524 \begin_layout Conjecture
528 \begin_layout Criterion
532 \begin_layout Standard
536 \begin_layout Theorem
544 \begin_layout Standard
549 I believe this is true.
560 \begin_layout Proposition
564 \begin_layout Conjecture
568 \begin_layout Criterion
572 \begin_layout Subsubsection
573 This is the subsection with results.
576 \begin_layout Standard
577 The quick, brown fox jumped over the lazy dog.
580 \begin_layout Theorem
581 This is a theorem - sixth in the series
588 \begin_layout Standard
592 \begin_layout Corollary
604 \begin_layout Proposition
608 \begin_layout Conjecture
612 \begin_layout Criterion
616 \begin_layout Bibliography
617 \begin_inset CommandInset bibitem
631 \begin_layout Bibliography
632 \begin_inset CommandInset bibitem
639 American Mathematical Society,
641 Instructions for preparation of papers and monographs: AMS-\SpecialChar LaTeX
647 \begin_layout Bibliography
648 \begin_inset CommandInset bibitem
655 American Mathematical Society,