1 #LyX 2.4 created this file. For more info see https://www.lyx.org/
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101 \begin_layout Address
102 Department of Mathematics
103 \begin_inset Newline newline
107 \begin_inset Newline newline
113 \begin_layout Current Address
122 http://www.lehigh.edu/~dlj0/dlj0.html
125 \begin_layout Keywords
130 To Emmanuel, for forcing me to fix this, and Jean-Marc, for making it possible,
132 Also to Mate, who suggested numerous improvements.
135 \begin_layout Dedicatory
139 \begin_layout Translator
143 \begin_layout Subjectclass
144 Primary: 12G34, Secondary: 09G87
147 \begin_layout Abstract
148 This is not very abstract.
149 Note that the abstract must be part of the title stuff for AMS.
151 is aware of that since version 0.12.1.
156 \begin_layout Section
160 \begin_layout Standard
161 This file, and any amsart-* \SpecialChar LyX
162 file, can be converted to either of the numbering
163 schemes by simply changing the document class in the
178 \begin_layout Enumerate
179 amsart - The standard AMS-article format.
180 All results and similar statements are numbered as
181 \begin_inset Formula $(n.m)$
184 , where the first number refers to the section, and the second refers to
185 the total number of results (Theorems, Corollaries, Propositions, Definitions
186 and Remarks, etc.) in that section.
187 There are also many (but not all) environments available unnumbered, which
188 is occasionally needed.
189 Unnumbered environments indicated by an asterisk at the end.
192 \begin_layout Enumerate
193 amsart-seq - Here, numbering for each type of statement is in its own sequence,
194 with no reference to the section number.
195 There are also many (but not all) environments available unnumbered, which
196 is occasionally needed.
199 \begin_layout Theorem
200 This is a numbered theorem
213 \begin_layout Standard
215 Note that two occurrences of the same environment, like two definitions,
216 need to be separated somehow.
217 For the moment, the best way is to include a paragraph with a %, in the
219 environment, if you really want two definitions (or whatever) together,
220 with no intervening text of another sort.
223 \begin_layout Theorem*
224 This is an unnumbered theorem
236 \begin_layout Corollary
244 \begin_layout Corollary*
245 Unnumbered corollary.
249 \begin_layout Standard
253 \begin_layout Plain Layout
263 \begin_layout Corollary*
264 A second, with no intervening text.
265 Note the % to force a separation.
272 \begin_layout Proposition
276 \begin_layout Proposition*
280 \begin_layout Conjecture
284 \begin_layout Conjecture*
285 So wild I didn't number it.
288 \begin_layout Criterion
292 \begin_layout Algorithm
293 first this, then the next
301 Bald statement of fact.
302 Unnumbered environments are often used for emphasis, or in a short presentation
303 that doesn't require numbered results.
311 \begin_layout Definition
312 a word means exactly what I say it means.
315 \begin_layout Definition*
319 \begin_layout Standard
333 \begin_layout Example
334 This should be an example.
337 \begin_layout Standard
354 \begin_layout Condition
358 \begin_layout Problem
359 I don't know what to write is the problem.
363 I think this will be useful.
367 I did it the way the documentation said to.
371 It may need more work yet.
374 \begin_layout Standard
375 More plain text, in standard format.
378 \begin_layout Theorem
379 This is a second numbered theorem
386 \begin_layout Standard
390 \begin_layout Corollary
402 \begin_layout Proposition
406 \begin_layout Conjecture
410 \begin_layout Criterion
414 \begin_layout Notation
415 \begin_inset Formula $S=\mathbb{R}$
421 \begin_layout Summary
422 In the end, will it matter?
425 \begin_layout Acknowledgement
426 Thanks to Mattias Ettrich.
427 Without him I never would have learned \SpecialChar LaTeX
432 If this works, then the rest will.
435 \begin_layout Conclusion
440 Here goes another proof.
443 \begin_layout Standard
447 \begin_layout Section
451 \begin_layout Standard
452 This tries out the section environments.
455 \begin_layout Theorem
463 \begin_layout Standard
467 \begin_layout Corollary
469 First one of this section.
480 \begin_layout Proposition
484 \begin_layout Conjecture
488 \begin_layout Criterion
492 \begin_layout Subsection
496 \begin_layout Standard
497 With more results therein.
500 \begin_layout Theorem
501 This is a theorem, maybe the fourth one.
508 \begin_layout Standard
512 \begin_layout Corollary
524 \begin_layout Proposition
528 \begin_layout Conjecture
532 \begin_layout Criterion
536 \begin_layout Standard
540 \begin_layout Theorem
548 \begin_layout Standard
553 I believe this is true.
564 \begin_layout Proposition
568 \begin_layout Conjecture
572 \begin_layout Criterion
576 \begin_layout Subsubsection
577 This is the subsection with results.
580 \begin_layout Standard
581 The quick, brown fox jumped over the lazy dog.
584 \begin_layout Theorem
585 This is a theorem - sixth in the series
592 \begin_layout Standard
596 \begin_layout Corollary
608 \begin_layout Proposition
612 \begin_layout Conjecture
616 \begin_layout Criterion
620 \begin_layout Bibliography
621 \begin_inset CommandInset bibitem
635 \begin_layout Bibliography
636 \begin_inset CommandInset bibitem
643 American Mathematical Society,
645 Instructions for preparation of papers and monographs: AMS-\SpecialChar LaTeX
651 \begin_layout Bibliography
652 \begin_inset CommandInset bibitem
659 American Mathematical Society,