This is pdfeTeX, Version 3.141592-1.21a-2.2 (Web2C 7.5.4) (format=latex 2009.4.25) 6 NOV 2012 17:52 entering extended mode **all (./all.tex LaTeX2e <2003/12/01> Babel and hyphenation patterns for american, french, german, ngerman, b ahasa, basque, bulgarian, catalan, croatian, czech, danish, dutch, esperanto, e stonian, finnish, greek, icelandic, irish, italian, latin, magyar, norsk, polis h, portuges, romanian, russian, serbian, slovak, slovene, spanish, swedish, tur kish, ukrainian, nohyphenation, loaded. (./body.tex (/Users/cp/svn/hilbertbernays/trunk/article.cls Document Class: article 1999/01/07 v1.4a Standard LaTeX document class (/Users/cp/svn/hilbertbernays/trunk/size12.clo File: size12.clo 2000/05/19 v1.4b Standard LaTeX file (size option) ) \c@part=\count79 \c@section=\count80 \c@subsection=\count81 \c@subsubsection=\count82 \c@paragraph=\count83 \c@subparagraph=\count84 \c@figure=\count85 \c@table=\count86 \abovecaptionskip=\skip41 \belowcaptionskip=\skip42 \bibindent=\dimen102 ) (/Users/cp/Library/TeX/texmf/tex/latex/latexlib/dina4.sty) (/Users/cp/Library/TeX/texmf/tex/latex/latexlib/header.tex (/Users/cp/svn/hilbertbernays/trunk/headerhot.tex \disp=\skip43 \textwidthminustwomm=\skip44 \textwidthminushalfcm=\skip45 \textwidthminusonecm=\skip46 \textwidthminustwocm=\skip47 \textwidthminusfourcm=\skip48 \textwidthminussixcm=\skip49 \yinibox=\box26 ) (/Users/cp/Library/TeX/texmf/tex/latex/latexlib/headerproof.tex)) (/Users/cp/Library/TeX/texmf/tex/latex/latexlib/header12pt.tex) (/Users/cp/svn/hilbertbernays/trunk/headernames.tex (/Users/cp/svn/hilbertbernays/trunk/amssymb.sty Package: amssymb 2002/01/22 v2.2d (/Users/cp/svn/hilbertbernays/trunk/amsfonts.sty Package: amsfonts 2001/10/25 v2.2f \@emptytoks=\toks14 \symAMSa=\mathgroup4 \symAMSb=\mathgroup5 LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold' (Font) U/euf/m/n --> U/euf/b/n on input line 132. )) (/Users/cp/svn/hilbertbernays/trunk/fontenc.sty Package: fontenc 2004/02/22 v1.99f Standard LaTeX package (/Users/cp/svn/hilbertbernays/trunk/t1enc.def File: t1enc.def 2004/02/22 v1.99f Standard LaTeX file LaTeX Font Info: Redeclaring font encoding T1 on input line 43. )) (/Users/cp/svn/hilbertbernays/trunk/specialfonts.tex) (/Users/cp/svn/hilbertbernays/trunk/headernamesrest.tex)) (/Users/cp/svn/hilbertbernays/trunk/headerforformulas.tex) (/Users/cp/Library/TeX/texmf/tex/latex/latexlib/headernosugarterms.tex) LaTeX Warning: Unused global option(s): [mssymb]. No file all.aux. \openout1 = `all.aux'. LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 46. LaTeX Font Info: ... okay on input line 46. LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 46. LaTeX Font Info: ... okay on input line 46. LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 46. LaTeX Font Info: ... okay on input line 46. LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 46. LaTeX Font Info: ... okay on input line 46. LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 46. LaTeX Font Info: ... okay on input line 46. LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 46. LaTeX Font Info: ... okay on input line 46. LaTeX Font Info: Try loading font information for T1+cmtt on input line 83. (/Users/cp/svn/hilbertbernays/trunk/t1cmtt.fd File: t1cmtt.fd 1999/05/25 v2.5h Standard LaTeX font definitions ) LaTeX Font Info: Try loading font information for U+msa on input line 92. (/Users/cp/svn/hilbertbernays/trunk/umsa.fd File: umsa.fd 2002/01/19 v2.2g AMS font definitions ) LaTeX Font Info: Try loading font information for U+msb on input line 92. (/Users/cp/svn/hilbertbernays/trunk/umsb.fd File: umsb.fd 2002/01/19 v2.2g AMS font definitions ) [1 ] (./all.toc ! Missing $ inserted. $ l.10 ...onfluence, and Church-Rosser-Property}{18} ? q OK, entering \batchmode... ! Extra }, or forgotten $. \@dottedtocline ...\nobreak \hskip -\leftskip {#4} \nobreak \leaders \hbox {$... l.10 ...onfluence, and Church-Rosser-Property}{18} I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Missing $ inserted. $ l.10 ...onfluence, and Church-Rosser-Property}{18} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ) \tf@toc=\write3 \openout3 = `all.toc'. ! Missing } inserted. } l.206 \tableofcontents \nopagebreak I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. LaTeX Warning: Reference `bibliography' on page 1 undefined on input line 207. [1] (/Users/cp/Library/TeX/texmf/tex/latex/latexlib/headerpagenumber.tex) LaTeX Warning: Citation `kaplan' on page 1 undefined on input line 449. LaTeX Warning: Reference `itemtwo' on page 1 undefined on input line 469. LaTeX Warning: Reference `itemone' on page 1 undefined on input line 490. LaTeX Warning: Citation `kaplan' on page 1 undefined on input line 500. LaTeX Warning: Citation `kaplan' on page 1 undefined on input line 512. LaTeX Warning: Citation `kaplan' on page 1 undefined on input line 515. LaTeX Warning: Citation `kaplan' on page 1 undefined on input line 522. LaTeX Warning: Reference `appendixproofs' on page 1 undefined on input line 544 . [1] LaTeX Warning: Reference `section morebasic' on page 2 undefined on input line 593. ! Undefined control sequence. ...power of a relation\/})}\\ A^{\oast } & := & \displaystyle \bi... l.683 } % The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Overfull \hbox (4.86742pt too wide) in paragraph at lines 723--753 []$ \T1/cmr/m/n/12 de-notes the multi-set con-tain-ing an element `$\OML/cmm/m /it/12 a$\T1/cmr/m/n/12 ' ex-actly $ \OMS/cmsy/m/n/12 j[]j $\T1/cmr/m/n/12 - [] Underfull \vbox (badness 10000) has occurred while \output is active [] [2] Underfull \vbox (badness 10000) has occurred while \output is active [] [3] ! Undefined control sequence. ...,\sigsorts ,\sigarity \restrictedto {\consfunsym }) l.804 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: Environment example undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.810 \begin{example} [Signature with Constructor Sub-signature]\mbox{}\\\lab... Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. \@sharp ->\{\identminus , \ident {memberp} \} l.826 \}} \\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.862 \sigarity(\identminus ) & The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: \begin{document} ended by \end{example}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.881 \end{example} Your command was ignored. Type I to replace it with another command, or to continue without it. Underfull \vbox (badness 7203) has occurred while \output is active [] [4] ! Undefined control sequence. l.938 As exhibited in \Av enhaus\&Becker\cite{SR-92-11}, The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Citation `SR-92-11' on page 5 undefined on input line 938. LaTeX Warning: Citation `order-sorted' on page 5 undefined on input line 942. ! Undefined control sequence. l.943 or Smolka\etal \cite{ordersortedtwo}: The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Citation `ordersortedtwo' on page 5 undefined on input line 943. ! Undefined control sequence. l.995 given by (\simplemath {s\in\sigsorts}) The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.995 given by (\simplemath{s\in \sigsorts}) I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.995 given by (\simplemath{s\in\sigsorts} ) I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Undefined control sequence. l.1008 \simplemath {s\in\sigsorts}, The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.1015 \end{sloppypar} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. Overfull \hbox (144.71802pt too wide) in paragraph at lines 984--1015 \U/msb/m/n/12 S\OT1/cmr/m/n/12 ) [] \OML/cmm/m/it/12 ; [] ; [] ; and [] :Toav oidconfusion \OT1/cmr/m/n/12 : [] Overfull \hbox (472.45023pt too wide) in paragraph at lines 984--1015 \OML/cmm/m/it/12 Notethat [] for[]; whereas [] :Ourcustomofreusingthesymbolofaf amilyfortheunionofitsrangesnowallowstowrite \OMS/cmsy/m/n/12 T \OML/cmm/m/it/12 asashorthandfor [] :$ [] ! Missing } inserted. } l.1015 \end{sloppypar} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Undefined control sequence. l.1025 \OCC {t} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \OCC l.1027 \bigmath{\OCC{x}=\{\emptyset\}} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \OCC l.1034 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. q\in \OCC {t_{i}}\setwithstop l.1034 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1055 For $P\subseteq\OCC {t}$, The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1066 $\forall p,q\in\OCC {t}: The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Underfull \hbox (badness 10000) in paragraph at lines 1073--1085 [] [5] LaTeX Warning: Citation `kaplan84' on page 6 undefined on input line 1103. LaTeX Warning: Citation `kaplan' on page 6 undefined on input line 1123. LaTeX Warning: Citation `der' on page 6 undefined on input line 1130. LaTeX Warning: Reference `footnotea' on page 6 undefined on input line 1140. ! LaTeX Error: Environment example undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.1153 \begin{example} \label{exb}\mbox{} Your command was ignored. Type I to replace it with another command, or to continue without it. LaTeX Warning: Reference `exa' on page 6 undefined on input line 1154. ! Undefined control sequence. l.1157 \identminus \x\zero&\eqcolon&\x\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1157 \identminus\x \zero&\eqcolon&\x\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1157 \identminus\x\zero &\eqcolon&\x\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1157 \identminus\x\zero&\eqcolon &\x\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1157 \identminus\x\zero&\eqcolon&\x \\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \identminus l.1158 \identminus \s\x\s\y&\eqcolon&\identminus\x\y\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1158 \identminus\s \x\s\y&\eqcolon&\identminus\x\y\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1158 \identminus\s\x \s\y&\eqcolon&\identminus\x\y\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1158 \identminus\s\x\s \y&\eqcolon&\identminus\x\y\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1158 \identminus\s\x\s\y &\eqcolon&\identminus\x\y\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1158 \identminus\s\x\s\y&\eqcolon &\identminus\x\y\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1158 \identminus\s\x\s\y&\eqcolon&\identminus \x\y\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1158 ...dentminus\s\x\s\y&\eqcolon&\identminus\x \y\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1158 ...ntminus\s\x\s\y&\eqcolon&\identminus\x\y \\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \mbp l.1160 \mbp \x\nil&\eqcolon&\false\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1160 \mbp\x \nil&\eqcolon&\false\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1160 \mbp\x\nil &\eqcolon&\false\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1160 \mbp\x\nil&\eqcolon &\false\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1160 \mbp\x\nil&\eqcolon&\false \\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \mbp l.1161 \mbp \x\cns\y\el&\eqcolon&\true &\rs&\x\eqcolon\y\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1161 \mbp\x \cns\y\el&\eqcolon&\true &\rs&\x\eqcolon\y\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1161 \mbp\x\cns \y\el&\eqcolon&\true &\rs&\x\eqcolon\y\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1161 \mbp\x\cns\y \el&\eqcolon&\true &\rs&\x\eqcolon\y\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1161 \mbp\x\cns\y\el &\eqcolon&\true &\rs&\x\eqcolon\y\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1161 \mbp\x\cns\y\el&\eqcolon &\true &\rs&\x\eqcolon\y\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1161 \mbp\x\cns\y\el&\eqcolon&\true &\rs&\x\eqcolon\y\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1161 ...mbp\x\cns\y\el&\eqcolon&\true &\rs&\x \eqcolon\y\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1161 ...s\y\el&\eqcolon&\true &\rs&\x\eqcolon \y\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1161 ...y\el&\eqcolon&\true &\rs&\x\eqcolon\y \\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \mbp l.1162 \mbp \x\cns\y\el&\eqcolon&\mbp\x\el&\rs&\x\necolon\y\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1162 \mbp\x \cns\y\el&\eqcolon&\mbp\x\el&\rs&\x\necolon\y\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1162 \mbp\x\cns \y\el&\eqcolon&\mbp\x\el&\rs&\x\necolon\y\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1162 \mbp\x\cns\y \el&\eqcolon&\mbp\x\el&\rs&\x\necolon\y\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1162 \mbp\x\cns\y\el &\eqcolon&\mbp\x\el&\rs&\x\necolon\y\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1162 \mbp\x\cns\y\el&\eqcolon &\mbp\x\el&\rs&\x\necolon\y\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1162 \mbp\x\cns\y\el&\eqcolon&\mbp \x\el&\rs&\x\necolon\y\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1162 \mbp\x\cns\y\el&\eqcolon&\mbp\x \el&\rs&\x\necolon\y\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1162 \mbp\x\cns\y\el&\eqcolon&\mbp\x\el &\rs&\x\necolon\y\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1162 ...mbp\x\cns\y\el&\eqcolon&\mbp\x\el&\rs&\x \necolon\y\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1162 ...s\y\el&\eqcolon&\mbp\x\el&\rs&\x\necolon \y\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.1162 ...y\el&\eqcolon&\mbp\x\el&\rs&\x\necolon\y \\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \comment l.1163 \comment {%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing } inserted. } l.1164 ... \\ I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Misplaced \crcr. \endarray ->\crcr \egroup \egroup l.1179 \end{array} I can't figure out why you would want to use a tab mark or \cr or \span just now. If something like a right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Extra }, or forgotten \endgroup. \endarray ->\crcr \egroup \egroup l.1179 \end{array} I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! LaTeX Error: \begin{document} ended by \end{example}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.1183 \end{example} Your command was ignored. Type I to replace it with another command, or to continue without it. LaTeX Warning: Citation `kaplan' on page 6 undefined on input line 1203. ! LaTeX Error: Environment example undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.1211 \begin{example} \mbox{}\\ Your command was ignored. Type I to replace it with another command, or to continue without it. LaTeX Warning: Citation `kaplan' on page 6 undefined on input line 1227. ! LaTeX Error: \begin{document} ended by \end{example}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.1234 \end{example} Your command was ignored. Type I to replace it with another command, or to continue without it. Underfull \vbox (badness 1509) has occurred while \output is active [] [6] ! LaTeX Error: Environment example undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.1251 \begin{example} \mbox{} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: \begin{document} ended by \end{example}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.1267 \end{example} Your command was ignored. Type I to replace it with another command, or to continue without it. LaTeX Warning: Citation `kaplan' on page 7 undefined on input line 1319. LaTeX Warning: Citation `kaplan' on page 7 undefined on input line 1324. LaTeX Warning: Citation `kaplan' on page 7 undefined on input line 1336. ! LaTeX Error: Environment example undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.1385 \begin{example} \label{exc} Your command was ignored. Type I to replace it with another command, or to continue without it. LaTeX Warning: Reference `exb' on page 7 undefined on input line 1386. ! Undefined control sequence. \minuspp \zeropp {\spp x}\:\eqcolon \zeropp l.1395 ...minuspp\zeropp{\spp x}\:\eqcolon\zeropp} . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: \begin{document} ended by \end{example}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.1406 \end{example} Your command was ignored. Type I to replace it with another command, or to continue without it. [7] ! LaTeX Error: Environment example undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.1415 \begin{example} \label{exnew} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: \begin{document} ended by \end{example}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.1423 \end{example} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. l.1426 \comment {------------------------------------------------------------... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Citation `bg2' on page 8 undefined on input line 1431. LaTeX Warning: Citation `kaplan' on page 8 undefined on input line 1434. LaTeX Warning: Citation `beckerctrs' on page 8 undefined on input line 1446. LaTeX Warning: Citation `kaplan' on page 8 undefined on input line 1449. LaTeX Warning: Citation `bg2' on page 8 undefined on input line 1450. LaTeX Warning: Citation `kaplan' on page 8 undefined on input line 1475. ! LaTeX Error: Environment example undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.1480 \begin{example} \label{exd} Your command was ignored. Type I to replace it with another command, or to continue without it. LaTeX Warning: Reference `exb' on page 8 undefined on input line 1481. ! Undefined control sequence. l.1485 \ident{0}, \ident{s}, and \identminus \ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Citation `kaplan' on page 8 undefined on input line 1489. ! Undefined control sequence. \mbp l.1493 \bigmath{\mbp\succ\true,\false}} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \mbp \succ \true ,\false l.1493 \bigmath{\mbp\succ\true,\false}} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \mbp \succ \true ,\false l.1493 \bigmath{\mbp\succ\true,\false}} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...} \\ & \{\ident {b}\} \\ & \{\false \}\cup \setwith {\mbppp x ... l.1517 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...oes not occur in }l))} \\ & \{\true \} \cup \setwith {\mbppp x... l.1517 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ... {a},\ \ident {b}\ \}\\ &\{\ \false \comma \mbppp {\ident {a}}... l.1531 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...\ident {b}}\nilpp \ \}\\ &\{\ \true \}\cup \setwith {\mbppp x ... l.1531 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...,\ident {b}\}\ \wedge \ l\not =\nil )\setwithstop l.1531 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \mbp l.1540 ...}\:\cns\ident{b}\:\nil\:\congru\:\false} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \mbp \ident {a}\:\cns \ident {b}\:\nil \:\congru \:\false l.1540 ...}\:\cns\ident{b}\:\nil\:\congru\:\false} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \mbp \ident {a}\:\cns \ident {b}\:\nil \:\congru \:\false l.1540 ...}\:\cns\ident{b}\:\nil\:\congru\:\false} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...\ident {b}\:\nil \:\congru \:\false l.1540 ...}\:\cns\ident{b}\:\nil\:\congru\:\false} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \mbp l.1542 ...\:\cns\ident{b}\:\nil\ \not\sim\ \false} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \mbp \ident {a}\:\cns \ident {b}\:\nil \ \not \sim \ \false l.1542 ...\:\cns\ident{b}\:\nil\ \not\sim\ \false} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \mbp \ident {a}\:\cns \ident {b}\:\nil \ \not \sim \ \false l.1542 ...\:\cns\ident{b}\:\nil\ \not\sim\ \false} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...dent {b}\:\nil \ \not \sim \ \false l.1542 ...\:\cns\ident{b}\:\nil\ \not\sim\ \false} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: \begin{document} ended by \end{example}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.1553 \end{example} Your command was ignored. Type I to replace it with another command, or to continue without it. Underfull \vbox (badness 10000) has occurred while \output is active [] [8] Underfull \vbox (badness 10000) has occurred while \output is active [] [9] ! Undefined control sequence. ...}} {\ident {nil}}} \ \not =\ \false l.1581 \ \not=\ \false} . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...}} {\ident {nil}}} \ \not =\ \false l.1592 \ \not=\ \false} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Citation `wirth1' on page 10 undefined on input line 1625. LaTeX Warning: Reference `defsemantics' on page 10 undefined on input line 1635 . ! Undefined control sequence. l.1642 \mbp -rule The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `itemone' on page 10 undefined on input line 1665. LaTeX Warning: Reference `itemtwo' on page 10 undefined on input line 1671. ! Undefined control sequence. l.1681 for which the application ``\simplemath {\ident{f}(t_0,\ldots,t_{n-1})}'' The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.1681 ...e application ``\simplemath{\ident{f}(t_ 0,\ldots,t_{n-1})}'' I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.1681 ...implemath{\ident{f}(t_0,\ldots,t_{n-1})} '' I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Missing $ inserted. $ l.1682 to some constructor ground terms $t_ 0$, \ldots, $t_{n-1}$ is an undef... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX Warning: Citation `kapur1' on page 10 undefined on input line 1697. LaTeX Warning: Citation `kapur2' on page 10 undefined on input line 1697. LaTeX Warning: Citation `kapur1' on page 10 undefined on input line 1709. LaTeX Warning: Citation `kapur1' on page 10 undefined on input line 1748. ! Undefined control sequence. ...\zeropredicatepp \zeropp \:\eqcolon \truepp l.1748 } \@. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \zeropredicatepp {\spp x}\:\eqcolon \falsepp \ \} l.1748 } \@. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...set \ \vdash \ \,\zeropp \:\eqcolon \spp \zeropp l.1748 } \@. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \R \ \nvdash \ \,\zeropp \:\eqcolon \spp \zeropp l.1748 } \@. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Citation `kapur2' on page 10 undefined on input line 1749. ! Undefined control sequence. kh=(\algebra \restrictedto {\tgcons _s})_{s\in \sigsorts } l.1770 ...estrictedto{\tgcons_s})_{s\in\sigsorts}} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. [10] LaTeX Warning: Reference `itemtwo' on page 11 undefined on input line 1787. LaTeX Warning: Reference `theorem monotony1' on page 11 undefined on input line 1796. [11] LaTeX Warning: Reference `itemtwo' on page 12 undefined on input line 1830. LaTeX Warning: Reference `itemone' on page 12 undefined on input line 1830. LaTeX Warning: Citation `kaplan' on page 12 undefined on input line 1834. LaTeX Warning: Reference `section reduction relation' on page 12 undefined on i nput line 1835. LaTeX Warning: Citation `kaplan' on page 12 undefined on input line 1857. LaTeX Warning: Reference `exd' on page 12 undefined on input line 1864. ! Undefined control sequence. \mbppp x {\cnspp y l} \:\eqcolon \mbppp x l \:\rs \x \necolon \y... l.1889 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...y l} \:\eqcolon \mbppp x l \:\rs \x \necolon \y \comma \DEF \x... l.1889 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...qcolon \mbppp x l \:\rs \x \necolon \y \comma \DEF \x \comma \... l.1889 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...lon \mbppp x l \:\rs \x \necolon \y \comma \DEF \x \comma \DEF... l.1889 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...\:\rs \x \necolon \y \comma \DEF \x \comma \DEF \y \ ; l.1889 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...on \y \comma \DEF \x \comma \DEF \y \ ; l.1889 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \true l.1895 is neither \bigmath{\true} nor \bigmath{\false} now, but undefined in... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \false l.1895 ...her \bigmath{\true} nor \bigmath{\false} now, but undefined instead. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `exc' on page 12 undefined on input line 1898. LaTeX Warning: Reference `exnew' on page 12 undefined on input line 1913. LaTeX Warning: Citation `kaplan' on page 12 undefined on input line 1928. LaTeX Warning: Citation `kaplan' on page 12 undefined on input line 1939. [12] LaTeX Warning: Citation `bg2' on page 13 undefined on input line 1950. LaTeX Warning: Citation `beckerctrs' on page 13 undefined on input line 1961. LaTeX Warning: Citation `kaplan' on page 13 undefined on input line 1965. LaTeX Warning: Citation `bg2' on page 13 undefined on input line 1966. ! Undefined control sequence. \orpp \truepp Y\:\eqcolon \truepp l.2005 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Citation `waltherLPAR92' on page 13 undefined on input line 2017 . ! Undefined control sequence. \citeinka ->Biundo\etal \cite {inka} l.2017 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Citation `inka' on page 13 undefined on input line 2017. LaTeX Warning: Citation `bm1' on page 13 undefined on input line 2017. ! Undefined control sequence. \citezhang ->Zhang\etal \cite {zhang} l.2017 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Citation `zhang' on page 13 undefined on input line 2017. LaTeX Warning: Citation `wirth1' on page 13 undefined on input line 2017. ! Undefined control sequence. \DEF \cpp {x_0}{x_{n-1}} l.2028 \bigmath{\DEF\cpp{x_0}{x_{n-1}}} holds for The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Citation `bm1' on page 13 undefined on input line 2040. LaTeX Warning: Citation `walther termination' on page 13 undefined on input lin e 2040. ! Undefined control sequence. \citeSR ->\Av enhaus\&Becker\cite {SR-92-11} l.2047 as in \citeSR \ where it is shown that The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Citation `SR-92-11' on page 13 undefined on input line 2047. LaTeX Warning: Reference `theorem joinable due to small variables' on page 13 u ndefined on input line 2050. Overfull \hbox (0.31215pt too wide) in paragraph at lines 2054--2068 \T1/cmr/m/n/12 tive-conditional equa-tions and for ex-press-ing (in-duc-tive) p rop-er-ties with first-order/Gentzen [] ! Undefined control sequence. l.2069 \comment { The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Underfull \vbox (badness 10000) has occurred while \output is active [] [13] LaTeX Warning: Citation `bm1' on page 14 undefined on input line 2077. LaTeX Warning: Citation `inka' on page 14 undefined on input line 2080. Overfull \hbox (35.6553pt too wide) in paragraph at lines 2089--2096 \T1/cmr/m/n/12 ta-tion) and ` $\OML/cmm/m/it/12 x \OT1/cmr/m/n/12 = \OML/cmm/m/ it/12 y[]\OT1/cmss/m/n/12 s \OML/cmm/m/it/12 x \OT1/cmr/m/n/12 = \OT1/cmss/m/n/ 12 s \OML/cmm/m/it/12 y$ \T1/cmr/m/n/12 ' (where Boyer&Moore take `[]' [] LaTeX Warning: Reference `item nr 1' on page 14 undefined on input line 2103. [14] LaTeX Warning: Reference `section terms' on page 15 undefined on input line 215 4. LaTeX Warning: Citation `SR-92-11' on page 15 undefined on input line 2162. ! Undefined control sequence. ...}{\vt }:(\sigma \tau )\restrictedto \X =\mu \restrictedto \X )... l.2223 } %math The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...\restrictedto \X =\mu \restrictedto \X ) \ \} \\ \end {array} l.2223 } %math The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Citation `wirth1' on page 15 undefined on input line 2234. LaTeX Warning: Citation `wgctrslncs' on page 15 undefined on input line 2234. LaTeX Warning: Citation `SR-92-11' on page 15 undefined on input line 2234. LaTeX Warning: Reference `unificationappendix' on page 15 undefined on input li ne 2251. [15] ! Undefined control sequence. ...,\sigsorts ,\sigarity \restrictedto {\consfunsym }) l.2281 ...s,\sigarity\restrictedto{\consfunsym}) } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.2309 } I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Missing $ inserted. $ l.2309 } I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Missing $ inserted. $ l.2309 } I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Missing $ inserted. $ l.2309 } I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! LaTeX Error: \mathcal allowed only in math mode. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.2309 } You're in trouble here. Try typing to proceed. If that doesn't work, type X to quit. ! Missing $ inserted. $ l.2309 } I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Missing $ inserted. $ l.2309 } I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Missing $ inserted. $ l.2309 } I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Missing $ inserted. $ l.2309 } I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! LaTeX Error: \mathcal allowed only in math mode. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.2309 } You're in trouble here. Try typing to proceed. If that doesn't work, type X to quit. LaTeX Warning: Reference `section terms' on page 16 undefined on input line 231 9. ! Undefined control sequence. {(\id \restrictedto {\algebra \SIGsort {s}})_{s\in \sigsorts }}\m... l.2388 } \@. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.2393 Let \simplemath {\X\!\subseteq\!\V}. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.2393 Let \simplemath{\X\! \subseteq\!\V}. I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.2393 Let \simplemath{\X\!\subseteq\!\V} . I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. LaTeX Font Warning: Command \em invalid in math mode on input line 2395. ! LaTeX Error: Command \itshape invalid in math mode. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.2395 {\em term algebra over} $\X$ and \sig/\cons/\V\@. Please use the math alphabet \mathit instead of the \itshape command. ! You can't use `\spacefactor' in math mode. \@->\spacefactor \@m l.2395 ...m algebra over} $\X$ and \sig/\cons/\V\@ . Sorry, but I'm not programmed to handle this case; I'll just pretend that you didn't ask for it. If you're in the wrong mode, you might be able to return to the right one by typing `I}' or `I$' or `I\par'. Missing character: There is no è in font cmex10! ! Missing $ inserted. $ l.2396 ...erm algebra has $\vtvarsigmaindex{s}\cap \tsigX$ as the I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! LaTeX Error: Environment lemma undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.2443 \begin{lemma} [Substitution-Lemma]\label{substitutionlemma}\mbox{}\\ Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. l.2446 For \simplemath {t\in\vt} and \simplemath{\sigma\in\Xsubst}: The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.2446 For \simplemath{t\in \vt} and \simplemath{\sigma\in\Xsubst}: I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.2446 For \simplemath{t\in\vt} and \simplemath{\sigma\in\Xsubst}: I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Undefined control sequence. l.2446 For \simplemath{t\in\vt} and \simplemath {\sigma\in\Xsubst}: The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.2449 } I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! LaTeX Error: \begin{document} ended by \end{lemma}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.2450 \end{lemma} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing } inserted. } l.2450 \end{lemma} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. Overfull \hbox (66.7563pt too wide) in paragraph at lines 2392--2451 \T1/cmr/m/n/12 Let $\OT1/cmr/m/n/12 X$$ \OMS/cmsy/m/n/12 ^^R \OT1/cmr/m/n/12 V \OML/cmm/m/it/12 :Weuse[] todenotethe[]$$\OT1/cmr/m/n/12 X$$\OML/cmm/m/it/12 an d[]=[]=\OT1/cmr/m/n/12 V\OML/cmm/m/it/12 :Thistermalgebrahas$$\OMS/cmsy/m/n/12 T []$$\[]$ [] Underfull \vbox (badness 2134) has occurred while \output is active [] [16] ! Undefined control sequence. l.2455 \simplemath {\varsigma\in\{\SIG,\CONS\}}; The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.2455 \simplemath{\varsigma \in\{\SIG,\CONS\}}; I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.2455 \simplemath{\varsigma\in\{\SIG,\CONS\}} ; I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Undefined control sequence. l.2456 \simplemath {\dunno\in\{\sig,\cons\}}; The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Font Warning: Command \em invalid in math mode on input line 2459. ! LaTeX Error: Command \itshape invalid in math mode. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.2459 {\em $\varsigma\mbox{\rm:}\dunno$-term-generated}\/ \udiff Please use the math alphabet \mathit instead of the \itshape command. ! Missing } inserted. } l.2459 {\em $ \varsigma\mbox{\rm:}\dunno$-term-generated}\/ \udiff I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing $ inserted. $ l.2459 {\em $\varsigma \mbox{\rm:}\dunno$-term-generated}\/ \udiff I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. Underfull \hbox (badness 10000) in paragraph at lines 2453--2468 \T1/cmr/m/n/12 For $\OML/cmm/m/it/12 & \OMS/cmsy/m/n/12 2 f[]\OML/cmm/m/it/12 ; \OMS/cmsy/m/n/12 Cg\OT1/cmr/m/n/12 ; []; \OML/cmm/m/it/12 a[]=[] \OMS/cmsy/m/n /12 ^^@ \OML/cmm/m/it/12 algebra \OMS/cmsy/m/n/12 A \OML/cmm/m/it/12 iscalled [] ! Undefined control sequence. l.2483 ...}\!\sim_{s_{j}}\!b} for some \simplemath {j\leq n}, then The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.2483 ...m_{s_{j}}\!b} for some \simplemath{j\leq n}, then I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.2483 ...s_{j}}\!b} for some \simplemath{j\leq n} , then I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Missing $ inserted. $ l.2489 I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! LaTeX Error: Environment theorem undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.2539 \begin{theorem} [Homomorphism-Theorem]\label{Homomorphism-Theorem}\mbo... Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: \begin{document} ended by \end{theorem}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.2568 \end{theorem} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. l.2574 \simplemath {\X\tightsubseteq\V}; and The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.2575 \simplemath {\kappa\in\SUBST{\X}{\algebra}}:\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.2575 \simplemath{\kappa \in\SUBST{\X}{\algebra}}:\\ I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.2575 \simplemath{\kappa\in\SUBST{\X}{\algebra}} :\\ I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. LaTeX Font Warning: Command \em invalid in math mode on input line 2577. ! LaTeX Error: Command \itshape invalid in math mode. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.2577 {\em initial in $\rm K$} Please use the math alphabet \mathit instead of the \itshape command. ! Missing } inserted. } l.2577 {\em initial in $ \rm K$} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Extra }, or forgotten $. } l.2577 {\em initial in $\rm K$} I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Undefined control sequence. l.2581 for all \simplemath {\balgebra\in{\rm K}} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Font Warning: Command \em invalid in math mode on input line 2584. ! LaTeX Error: Command \itshape invalid in math mode. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.2584 {\em free for\/ $\rm K$ over $\X$ \wrt\ $\kappa$} Please use the math alphabet \mathit instead of the \itshape command. ! Missing } inserted. } l.2584 {\em free for\/ $ \rm K$ over $\X$ \wrt\ $\kappa$} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing $ inserted. $ l.2584 ...ee for\/ $\rm K$ over $\X$ \wrt\ $\kappa $} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Undefined control sequence. \id \restrictedto {A}\subseteq R l.2732 ...\bigmath{\id\restrictedto{A}\subseteq R} . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.2768 $<\!\cup\,\id\restrictedto {A}$. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.2772 Let \simplemath {\X\tightsubseteq\V}\@. A relation $R$ on \vt\ is called: The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Overfull \hbox (13.74318pt too wide) in paragraph at lines 2779--2785 [][] [] [17] ! Undefined control sequence. l.2787 ...in R:\forall t\in\tsigX:\forall p\in\OCC {t}: The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Overfull \hbox (15.56563pt too wide) in paragraph at lines 2809--2810 [][] [] ! Undefined control sequence. ...s A\ \subseteq \ (\id \restrictedto {A}\cup R\cup R^{-1}) l.2818 ... (\id\restrictedto{A}\cup R\cup R^{-1})} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...ll t:\exists t':((t,t')\in R^{\oast }\ \wedge \ t'\not \in \DO... l.2830 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...rmeq t'$\udiff \ $\exists p\in \OCC {t'}: t=t'/p l.2850 ...'$\udiff\ $\exists p\in\OCC{t'}: t=t'/p} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Citation `dershowitz2' on page 18 undefined on input line 2928. ! LaTeX Error: Environment lemma undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.2961 \begin{lemma} \label{newmanlemma}\mbox{} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: \begin{document} ended by \end{lemma}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.2963 \end{lemma} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: Environment lemma undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.2967 \begin{lemma} \mbox{} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: \begin{document} ended by \end{lemma}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.2969 \end{lemma} Your command was ignored. Type I to replace it with another command, or to continue without it. [18] ! LaTeX Error: Environment definition undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.2977 \begin{definition} [Syntax of CRS]\label{defrules}\mbox{} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. l.2981 ...subset of the {\em set of rules} \rules \ over\/ \sig/\cons/\/\V, The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `defrulescontinu' on page 19 undefined on input line 2 982. ! Undefined control sequence. \rules \ \subseteq \ \direqvsig \times (\condlit )^{\ast }\ , l.2987 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...erms nor the literals ``\simplemath {s\boldequal t}'', ``\simp... l.3119 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...th {s\boldequal t}'', ``\simplemath {u\boldunequal v}'', ``\si... l.3119 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ... {u\boldunequal v}'', ``\simplemath {\Def \,w}'' themselves. \... l.3119 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: \begin{sloppypar} on input line 2976 ended by \end{definition}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3130 \end{definition} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: Environment definition undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3166 \begin{definition} [Semantics of CRS]\label{defsemantics}\mbox{} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: \begin{document} ended by \end{definition}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3204 \end{definition} Your command was ignored. Type I to replace it with another command, or to continue without it. Underfull \hbox (badness 10000) in paragraph at lines 3186--3205 [] Underfull \vbox (badness 10000) has occurred while \output is active [] [19] LaTeX Warning: Reference `fundamental corollary' on page 20 undefined on input line 3220. ! LaTeX Error: Environment definition undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3227 \begin{definition} \label{defhqlconsql}\mbox{} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. \algebra \restrictedto {\consfunsym \uplus (\{\CONS \}\!\times \s... l.3243 ...nsym\uplus(\{\CONS\}\!\times\sigsorts)}} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \balgebra \restrictedto {\consfunsym \uplus (\{\CONS \}\!\times \... l.3245 ...nsym\uplus(\{\CONS\}\!\times\sigsorts)}} \@. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: \begin{document} ended by \end{definition}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3287 \end{definition} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: Environment lemma undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3295 \begin{lemma} \label{lemmacongruisall}\mbox{} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. \balgebra \restrictedto {\consfunsym \uplus (\{\CONS \}\!\times \... l.3315 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: \begin{document} ended by \end{lemma}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3317 \end{lemma} Your command was ignored. Type I to replace it with another command, or to continue without it. LaTeX Warning: Citation `kaplan' on page 20 undefined on input line 3326. LaTeX Warning: Citation `kaplan' on page 20 undefined on input line 3326. ! LaTeX Error: Environment lemma undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3331 \begin{lemma} \label{lemmatheor}\mbox{} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: \begin{document} ended by \end{lemma}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3344 \end{lemma} Your command was ignored. Type I to replace it with another command, or to continue without it. [20] LaTeX Warning: Reference `newtheoremmodel' on page 21 undefined on input line 3 433. LaTeX Warning: Reference `section terms' on page 21 undefined on input line 343 3. LaTeX Warning: Reference `theorem monotony1' on page 21 undefined on input line 3433. ! LaTeX Error: Environment definition undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3436 \nopagebreak \begin{definition} [Set of Rules] Your command was ignored. Type I to replace it with another command, or to continue without it. LaTeX Warning: Reference `defrules' on page 21 undefined on input line 3438. ! Undefined control sequence. \rules l.3442 \bigmath{\rules\ :=} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: \begin{document} ended by \end{definition}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3466 \end{definition} Your command was ignored. Type I to replace it with another command, or to continue without it. LaTeX Warning: Reference `section motivation' on page 21 undefined on input lin e 3520. [21] ! LaTeX Error: Environment definition undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3530 \nopagebreak \begin{definition} [Our Reduction Relation \red] Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. l.3533 Let\/ \simplemath {\X\tightsubseteq\V}. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...\Xsubst \!\!: \exists p\!\in \!\OCC {s}\!\!:\! \left (\begin {... l.3550 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. u\footnotenotconflu v l.3618 } %footnotetext The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...efltrans \hat {u}\footnotenotconflu \hat {v}\footnoteantireflt... l.3618 } %footnotetext The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: Environment example undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3618 } %footnotetext Your command was ignored. Type I to replace it with another command, or to continue without it. LaTeX Warning: Reference `defred' on page 22 undefined on input line 3618. ! LaTeX Error: \begin{document} ended by \end{example}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3618 } %footnotetext Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: \begin{document} ended by \end{definition}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3619 \end{definition} Your command was ignored. Type I to replace it with another command, or to continue without it. LaTeX Warning: Reference `defred' on page 22 undefined on input line 3651. ! Undefined control sequence. ...\Xsubst \!\!: \exists p\!\in \!\OCC {s}\!\!:\! \left (\begin {... l.3667 \end{array}\right).} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `defred' on page 22 undefined on input line 3674. LaTeX Warning: Reference `defred' on page 22 undefined on input line 3684. LaTeX Warning: Reference `appendixproofs' on page 22 undefined on input line 36 91. Underfull \vbox (badness 10000) has occurred while \output is active [] [22] ! LaTeX Error: Environment corollary undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3701 \begin{corollary} [Monotonicity of \red\ \wrt\ Replacement] Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: \begin{document} ended by \end{corollary}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3706 \end{corollary} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: Environment corollary undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3707 \begin{corollary} [Stability of \red]\label{corollary stable}\mbox{}\\ Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: \begin{document} ended by \end{corollary}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3710 \end{corollary} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: Environment lemma undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3723 \begin{lemma} \label{lemma about conskeeping}\mbox{}\\ Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: \begin{document} ended by \end{lemma}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3727 \end{lemma} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: Environment lemma undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3730 \begin{lemma} \label{lemma about sortkeeping}\mbox{} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: \begin{document} ended by \end{lemma}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3734 \end{lemma} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: Environment lemma undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3737 \begin{lemma} \label{lemma about groundconskeeping}\mbox{} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: \begin{document} ended by \end{lemma}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3741 \end{lemma} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: Environment lemma undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3744 \begin{lemma} \label{lemma about conflu}\mbox{} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: \begin{document} ended by \end{lemma}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3750 \end{lemma} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: Environment lemma undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3753 \begin{lemma} [Monotonicity of \redindex{\beta} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: \begin{document} ended by \end{lemma}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3771 \end{lemma} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: Environment lemma undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3774 \begin{lemma} [Fulfilledness Test may be Simple] Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: \begin{document} ended by \end{lemma}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3813 \end{lemma} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: Environment lemma undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3817 \begin{lemma} \label{lemma about ground reduction}\mbox{} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. l.3820 For all \simplemath {\beta\preceq\omega\tightplus\omega}: The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.3820 For all \simplemath{\beta \preceq\omega\tightplus\omega}: I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.3820 ...math{\beta\preceq\omega\tightplus\omega} : I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Undefined control sequence. l.3828 for \simplemath {C\in\Xcondlit}: The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: \begin{sloppypar} on input line 3816 ended by \end{lemma}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3839 \end{lemma} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ l.3839 \end{lemma} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.3839 \end{lemma} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. LaTeX Warning: Reference `example why strange negation' on page 23 undefined on input line 3854. LaTeX Warning: Reference `itemtwo' on page 23 undefined on input line 3860. LaTeX Warning: Reference `section motivation' on page 23 undefined on input lin e 3861. ! LaTeX Error: Environment definition undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3864 \begin{definition} [\Def-Moderate Conditional Rule Systems (\Def-MCRS)] Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: \begin{document} ended by \end{definition}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3875 \end{definition} Your command was ignored. Type I to replace it with another command, or to continue without it. Underfull \vbox (badness 10000) has occurred while \output is active [] [23] ! LaTeX Error: Environment theorem undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3910 \begin{theorem} \label{newtheoremmodel}\mbox{}\\ Your command was ignored. Type I to replace it with another command, or to continue without it. LaTeX Warning: Reference `defhqlconsql' on page 24 undefined on input line 3917 . LaTeX Warning: Reference `footnote of newtheoremmodel about weakened confluence ' on page 24 undefined on input line 3928. LaTeX Warning: Reference `theorem sem confl' on page 24 undefined on input line 3956. LaTeX Warning: Reference `footnote cf defhqlconsql' on page 24 undefined on inp ut line 3964. LaTeX Warning: Reference `footnote cf defhqlconsql' on page 24 undefined on inp ut line 3974. ! LaTeX Error: \begin{document} ended by \end{theorem}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3978 \end{theorem} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: Environment corollary undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3980 \begin{corollary} \label{fundamental corollary}\mbox{} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: \begin{document} ended by \end{corollary}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3989 \end{corollary} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: Environment theorem undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3994 \begin{theorem} \label{theorem monotony1}\mbox{}\\ Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. l.3997 Let\/ \simplemath {\X\tightsubseteq\V}\@. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.3999 and \simplemath {\X'\tightsubseteq\V'} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \restrictedto l.4006 ...nsym',\sigsorts',\sigarity'\restrictedto {\consfunsym'}) \\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \restrictedto l.4007 \V'\restrictedto {\sigsortstimes}&\V ... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \footnotenotconflu _{_{\R ,\X }} l.4073 } : The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \footnotenotconflu _{_{\R ,\X }} l.4073 } : The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: \begin{document} ended by \end{theorem}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4099 \end{theorem} Your command was ignored. Type I to replace it with another command, or to continue without it. [24] LaTeX Warning: Citation `der' on page 25 undefined on input line 4115. ! LaTeX Error: Environment definition undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4122 \begin{definition} [Critical Peaks and Joinability] Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. l.4157 p\in\OCC {l_{1}}\ \wedge\ l_{1}/p\not\in\V The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: \begin{document} ended by \end{definition}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4231 \end{definition} Your command was ignored. Type I to replace it with another command, or to continue without it. Overfull \hbox (0.51344pt too wide) in paragraph at lines 4122--4232 []$ [] ! LaTeX Error: Environment lemma undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4236 \begin{lemma} [Joinability of Critical Peaks is Necessary for Confluence] Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. l.4239 and\/ \simplemath {\X\tightsubseteq\V}. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: \begin{document} ended by \end{lemma}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4242 \end{lemma} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: Environment lemma undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4246 \begin{lemma} [ Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. l.4255 \simplemath {\X\tightsubseteq\V}; The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: \begin{document} ended by \end{lemma}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4275 \end{lemma} Your command was ignored. Type I to replace it with another command, or to continue without it. LaTeX Warning: Citation `der' on page 25 undefined on input line 4281. LaTeX Warning: Citation `der' on page 25 undefined on input line 4287. LaTeX Warning: Citation `der' on page 25 undefined on input line 4292. LaTeX Warning: Citation `der' on page 25 undefined on input line 4295. LaTeX Warning: Citation `plaisted' on page 25 undefined on input line 4301. LaTeX Warning: Citation `der' on page 25 undefined on input line 4315. LaTeX Warning: Citation `der' on page 25 undefined on input line 4354. LaTeX Warning: Citation `der' on page 25 undefined on input line 4354. LaTeX Warning: Citation `der' on page 25 undefined on input line 4354. LaTeX Warning: Citation `der' on page 25 undefined on input line 4357. LaTeX Warning: Citation `der' on page 25 undefined on input line 4358. LaTeX Warning: Reference `ex theorem of little use' on page 25 undefined on inp ut line 4361. LaTeX Warning: Reference `theoremconfluence' on page 25 undefined on input line 4365. LaTeX Warning: Reference `theorem joinable due to small variables' on page 25 u ndefined on input line 4365. LaTeX Warning: Citation `der' on page 25 undefined on input line 4372. Underfull \vbox (badness 10000) has occurred while \output is active [] [25] ! LaTeX Error: Environment theorem undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4381 \begin{theorem} [Syntactic Confluence Criterion] Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. l.4383 ...RS over \sig/\cons/\/\V\ and \simplemath {\X\tightsubseteq\V}. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: \begin{document} ended by \end{theorem}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4387 \end{theorem} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: Environment example undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4402 \begin{example} \label{ex theorem of little use}\mbox{} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: \begin{document} ended by \end{example}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4426 \end{example} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: Environment theorem undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4434 \begin{theorem} [Semantic Confluence Criterion]\label{theorem sem confl} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. l.4436 ...RS over \sig/\cons/\/\V\ and \simplemath {\X\tightsubseteq\V}. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `footnote of newtheoremmodel about weakened confluence ' on page 26 undefined on input line 4455. ! LaTeX Error: \begin{document} ended by \end{theorem}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4480 \end{theorem} Your command was ignored. Type I to replace it with another command, or to continue without it. [26] ! LaTeX Error: Environment lemma undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4494 \begin{lemma} [Reducibility of Ground Terms is Not Co-semi-decidable] Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: \begin{document} ended by \end{lemma}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4506 \end{lemma} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: Environment lemma undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4511 \begin{lemma} [Reducibility of Ground Terms is Not Semi-decidable] Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: \begin{sloppypar} on input line 4510 ended by \end{lemma}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4524 \end{lemma} Your command was ignored. Type I to replace it with another command, or to continue without it. LaTeX Warning: Citation `kaplan84' on page 27 undefined on input line 4530. ! LaTeX Error: Environment theorem undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4536 \begin{theorem} \label{lemma computable}\mbox{} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: \begin{document} ended by \end{theorem}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4564 \end{theorem} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: Environment corollary undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4566 \begin{corollary} \label{corollary normal form and reducibility}\mbox{} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: \begin{document} ended by \end{corollary}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4573 \end{corollary} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. l.4592 \comment {%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \supertermX l.4608 ...krightarrow\ \subseteq\ \hookrightarrow} , The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \repl {t}{p}{l}\supertermeqX l\hookrightarrow u l.4612 ...}{p}{l}\supertermeqX l\hookrightarrow u} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: Environment lemma undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4625 \begin{lemma} \label{lemmaa} Your command was ignored. Type I to replace it with another command, or to continue without it. Underfull \vbox (badness 3646) has occurred while \output is active [] [27] LaTeX Warning: Reference `item does not hold in general if' on page 28 undefine d on input line 4641. ! LaTeX Error: \begin{document} ended by \end{lemma}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4651 \end{lemma} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: Environment lemma undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4655 \begin{lemma} \label{lemmab}\mbox{} Your command was ignored. Type I to replace it with another command, or to continue without it. LaTeX Warning: Reference `lemmaa' on page 28 undefined on input line 4657. LaTeX Warning: Reference `lemmaa itema' on page 28 undefined on input line 4657 . LaTeX Warning: Reference `lemmaa' on page 28 undefined on input line 4671. LaTeX Warning: Reference `lemmaa itemc' on page 28 undefined on input line 4671 . LaTeX Warning: Reference `lemmaa' on page 28 undefined on input line 4671. LaTeX Warning: Reference `lemmaa itemb' on page 28 undefined on input line 4671 . ! LaTeX Error: \begin{document} ended by \end{lemma}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4681 \end{lemma} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. l.4688 \simplemath { The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.4689 s\in \tsigX\ \wedge\ I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Undefined control sequence. l.4692 \exists p\!\in\!\OCC {s}\!\!: The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Extra }, or forgotten $. l.4693 } I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Missing $ inserted. $ l.4697 } I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. Underfull \vbox (badness 10000) has occurred while \output is active [] [28] ! LaTeX Error: Environment lemma undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4713 \begin{lemma} \label{lemma variable extension}\mbox{}\\ Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: \begin{document} ended by \end{lemma}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4718 \end{lemma} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: Environment lemma undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4728 \begin{lemma} \label{lemmaa} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. l.4732 Define \simplemath {\ \succ\ :=} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.4732 Define \simplemath{\ \succ \ :=} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.4732 Define \simplemath{\ \succ\ :=} I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Undefined control sequence. l.4733 \simplemath {(\rightrightarrows\cup\superterm)^{\oplus}}. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.4735 \begin{enumerate} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Missing \endgroup inserted. \endgroup l.4735 \begin{enumerate} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. Overfull \hbox (112.88615pt too wide) in paragraph at lines 4729--4735 []\T1/cmr/m/n/12 Let $\U/msa/m/n/12 ^^S$ \T1/cmr/m/n/12 be a sort-invariant[] a nd $\OMS/cmsy/m/n/12 T$\T1/cmr/m/n/12 -mono-tonic relation on $\OMS/cmsy/m/n/12 T$\T1/cmr/m/n/12 . Define $\OMS/cmsy/m/n/12 ^^_ \OT1/cmr/m/n/12 := []\OML/cmm /m/it/12 :Nowthefollowingholds \OT1/cmr/m/n/12 :$ [] ! LaTeX Error: Lonely \item--perhaps a missing list environment. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4738 \item\label {lemmaa itemc} Try typing to proceed. If that doesn't work, type X to quit. ! LaTeX Error: Lonely \item--perhaps a missing list environment. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4745 \item\label {lemmaa itemd} Try typing to proceed. If that doesn't work, type X to quit. LaTeX Warning: Reference `item does not hold in general if' on page 29 undefine d on input line 4746. ! LaTeX Error: Lonely \item--perhaps a missing list environment. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4750 \item\label {lemmaa itema} Try typing to proceed. If that doesn't work, type X to quit. ! LaTeX Error: Lonely \item--perhaps a missing list environment. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4755 \item\label {lemmaa itemb} Try typing to proceed. If that doesn't work, type X to quit. ! LaTeX Error: \begin{document} ended by \end{enumerate}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4758 \end{enumerate} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing } inserted. } l.4758 \end{enumerate} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! LaTeX Error: \begin{document} ended by \end{lemma}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4759 \end{lemma} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing } inserted. } l.4759 \end{lemma} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.4759 \end{lemma} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.4759 \end{lemma} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.4759 \end{lemma} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Extra \endgroup. \endgroup l.4759 \end{lemma} Things are pretty mixed up, but I think the worst is over. ! LaTeX Error: Environment lemma undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4762 \begin{lemma} \label{lemmab}\mbox{} Your command was ignored. Type I to replace it with another command, or to continue without it. LaTeX Warning: Reference `lemmaa' on page 29 undefined on input line 4764. LaTeX Warning: Reference `lemmaa itema' on page 29 undefined on input line 4764 . LaTeX Warning: Reference `lemma variable extension' on page 29 undefined on inp ut line 4770. LaTeX Warning: Reference `lemmaa' on page 29 undefined on input line 4774. LaTeX Warning: Reference `lemmaa itemc' on page 29 undefined on input line 4774 . ! LaTeX Error: \begin{document} ended by \end{lemma}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4784 \end{lemma} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. l.4787 \comment {%%%%% The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: Environment definition undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4818 \begin{definition} [Termination-Pair]\label{defterminationpair}\mbox{}\\ Your command was ignored. Type I to replace it with another command, or to continue without it. LaTeX Warning: Reference `exampletp' on page 29 undefined on input line 4848. LaTeX Warning: Reference `exampletp itemdrei' on page 29 undefined on input lin e 4848. LaTeX Warning: Reference `definition alignment' on page 29 undefined on input l ine 4878. LaTeX Warning: Reference `lemmaa' on page 29 undefined on input line 4878. LaTeX Warning: Reference `lemmab' on page 29 undefined on input line 4878. ! LaTeX Error: \begin{document} ended by \end{definition}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4882 \end{definition} Your command was ignored. Type I to replace it with another command, or to continue without it. [29] ! LaTeX Error: Environment example undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4887 \begin{example} \label{exampletp}\mbox{} Your command was ignored. Type I to replace it with another command, or to continue without it. LaTeX Warning: Reference `lemmaa' on page 30 undefined on input line 4896. LaTeX Warning: Reference `lemmaa itemb' on page 30 undefined on input line 4896 . ! Undefined control sequence. ... \!\vt \!\!\!:\forall p\!\in \!\OCC {t}\!\!: (t/p\!\in \!\vtsi... l.4908 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...t\tightin \vt $ and $p\tightin \OCC {t}$ with \bigmath {t/p\in... l.4932 }.} \nopagebreak The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \varrho :=\sigma \restrictedto {\VAR {t',t''}}\cup \xi ^{-1}\res... l.4932 }.} \nopagebreak The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...t',t''}}\cup \xi ^{-1}\restrictedto {\V \setminus \VAR {t',t''}} l.4932 }.} \nopagebreak The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: \begin{document} ended by \end{example}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4938 \end{example} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: Environment definition undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4959 \begin{definition} [Alignment of a Rule \wrt\ a Termination-Pair] Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. l.4964 $\kurzregel\in\rules $ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.4965 ...d\/ {\em aligned with }$(>,\rhd)$ \bdiff The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: \begin{document} ended by \end{definition}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.4969 \end{definition} Your command was ignored. Type I to replace it with another command, or to continue without it. LaTeX Warning: Citation `derdecreasing' on page 30 undefined on input line 4975 . LaTeX Warning: Citation `der' on page 30 undefined on input line 4975. LaTeX Warning: Reference `footnote on transitive closure' on page 30 undefined on input line 4993. LaTeX Warning: Citation `derdecreasing' on page 30 undefined on input line 5007 . ! LaTeX Error: Environment example undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5010 \begin{example} [\mbox{\rm$\rhd:=\superterm Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. l.5031 \simplemath {\rhd}\,:~~\mbox{} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.5031 \simplemath{\rhd }\,:~~\mbox{} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.5031 \simplemath{\rhd} \,:~~\mbox{} I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! LaTeX Error: \begin{document} ended by \end{example}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5043 \end{example} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ l.5043 \end{example} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.5043 \end{example} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. LaTeX Warning: Reference `exampletp itemzwei' on page 30 undefined on input lin e 5046. LaTeX Warning: Reference `exampletp' on page 30 undefined on input line 5046. LaTeX Warning: Reference `exampletp itemeins' on page 30 undefined on input lin e 5048. LaTeX Warning: Reference `exampletp' on page 30 undefined on input line 5048. LaTeX Warning: Reference `exampletp itemzwei' on page 30 undefined on input lin e 5051. LaTeX Warning: Reference `exampletp' on page 30 undefined on input line 5051. Overfull \hbox (336.83228pt too wide) in paragraph at lines 5010--5054 \U/msa/m/n/12 B \OT1/cmr/m/n/12 : [] [][] [] \OML/cmm/m/it/12 isimpossiblesin cealignmentofthesecondrulerequires [] ; whichalsoforbids [] ; sincethenweget [] :$ [] [30] LaTeX Warning: Citation `der' on page 31 undefined on input line 5077. ! LaTeX Error: Environment definition undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5080 \begin{definition} [Compatibility of a CRS with a Termination-Pair]% Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. l.5085 over\/ \sig/\/\V\ \bdiff \ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: \begin{document} ended by \end{definition}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5109 \end{definition} Your command was ignored. Type I to replace it with another command, or to continue without it. LaTeX Warning: Reference `defcompat' on page 31 undefined on input line 5154. ! LaTeX Error: Environment definition undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5160 \begin{definition} % Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. l.5165 over\/ \sig/\/\V\ \bdiff \ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \simplemath l.5170 \simplemath { The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.5172 \left (\begin{array}{l@{\ (\ }r@{\ \Rightarrow\ }l@{\ )\ }} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.5199 } \nopagebreak I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! LaTeX Error: \begin{document} ended by \end{definition}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5200 \nopagebreak \end{definition} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ l.5200 \nopagebreak \end{definition} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.5200 \nopagebreak \end{definition} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! LaTeX Error: Environment definition undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5204 \begin{definition} % Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. l.5209 over\/ \sig/\/\V\ \bdiff \ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \simplemath l.5215 \simplemath { The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.5217 \left (\begin{array}{l@{}c@{}r@{}c@{}l@{}c@{}} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.5245 } I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! LaTeX Error: \begin{document} ended by \end{definition}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5246 \end{definition} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ l.5246 \end{definition} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.5246 \end{definition} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. LaTeX Warning: Citation `der' on page 31 undefined on input line 5266. LaTeX Warning: Reference `defcompat' on page 31 undefined on input line 5271. LaTeX Warning: Reference `deflrcompat' on page 31 undefined on input line 5279. LaTeX Warning: Reference `defdccompat' on page 31 undefined on input line 5279. LaTeX Warning: Reference `defcompat' on page 31 undefined on input line 5285. ! Undefined control sequence. l.5290 \comment {%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Underfull \vbox (badness 10000) has occurred while \output is active [] [31] ! LaTeX Error: Environment definition undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5293 \begin{definition} [\redindex{\R,{\rm normal}}]\mbox{}\\ Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. l.5305 \exists p\!\in\!\OCC {s}\!\!:\! The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.5309 t\ \ \ \ =\ \replac {$s$}{$p$}{$r\sigma$} ... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing } inserted. } l.5309 t\ \ \ \ =\ \replac{$ s$}{$p$}{$r\sigma$} ... I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Extra }, or forgotten $. } l.5309 t\ \ \ \ =\ \replac{$s$} {$p$}{$r\sigma$} ... I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Missing } inserted. } l.5309 t\ \ \ \ =\ \replac{$s$}{$ p$}{$r\sigma$} ... I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Extra }, or forgotten $. } l.5309 t\ \ \ \ =\ \replac{$s$}{$p$} {$r\sigma$} ... I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Missing } inserted. } l.5309 t\ \ \ \ =\ \replac{$s$}{$p$}{$ r\sigma$} ... I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing $ inserted. $ l.5309 t\ \ \ \ =\ \replac{$s$}{$p$}{$r\sigma $} ... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Missing \cr inserted. \cr l.5309 t\ \ \ \ =\ \replac{$s$}{$p$}{$r\sigma$} ... I'm guessing that you meant to end an alignment here. ! Missing $ inserted. $ l.5309 t\ \ \ \ =\ \replac{$s$}{$p$}{$r\sigma$} ... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Misplaced alignment tab character &. l.5309 ...a$} & I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Missing $ inserted. $ l.5310 \wedge ... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Misplaced \cr. \reserved@c ->\ifnum 0=`{\fi }${}\cr l.5311 \sigma \mbox{ is {\bf normal} \wrt\ }l,\redshortsub ... I can't figure out why you would want to use a tab mark or \cr or \span just now. If something like a right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.5311 ...,\redshortsub & I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced \cr. \reserved@c ->\ifnum 0=`{\fi }${}\cr l.5313 \multicolumn {2}{@{}l@{}} I can't figure out why you would want to use a tab mark or \cr or \span just now. If something like a right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced \omit. \multispan ->\omit \@multispan l.5314 ... is {\bf fulfilled \wrt\ }}\redshortsub} \\ I expect to see \omit only after tab marks or the \cr of an alignment. Proceed, and I'll ignore this case. ! Misplaced \span. \sp@n ->\span \omit \advance \@multicnt \m@ne l.5314 ... is {\bf fulfilled \wrt\ }}\redshortsub} \\ I can't figure out why you would want to use a tab mark or \cr or \span just now. If something like a right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced \omit. \sp@n ->\span \omit \advance \@multicnt \m@ne l.5314 ... is {\bf fulfilled \wrt\ }}\redshortsub} \\ I expect to see \omit only after tab marks or the \cr of an alignment. Proceed, and I'll ignore this case. ! Missing \endgroup inserted. \endgroup l.5314 ... is {\bf fulfilled \wrt\ }}\redshortsub} \\ I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! You can't use `macro parameter character #' in display math mode. \@preamble ->$$$\relax \@sharp $\hfil $$ l.5314 ... is {\bf fulfilled \wrt\ }}\redshortsub} \\ Sorry, but I'm not programmed to handle this case; I'll just pretend that you didn't ask for it. If you're in the wrong mode, you might be able to return to the right one by typing `I}' or `I$' or `I\par'. ! Display math should end with $$. \hfil l.5314 ... is {\bf fulfilled \wrt\ }}\redshortsub} \\ The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ l.5314 ... is {\bf fulfilled \wrt\ }}\redshortsub} \\ I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Display math should end with $$. \endgroup l.5314 ... is {\bf fulfilled \wrt\ }}\redshortsub} \\ The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing } inserted. } l.5314 ... is {\bf fulfilled \wrt\ }}\redshortsub} \\ I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Misplaced \crcr. \endarray ->\crcr \egroup \egroup l.5315 \end{array} \right)\! I can't figure out why you would want to use a tab mark or \cr or \span just now. If something like a right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Extra }, or forgotten \right. \endarray ->\crcr \egroup \egroup l.5315 \end{array} \right)\! I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Extra }, or forgotten \right. \endarray ->\crcr \egroup \egroup l.5315 \end{array} \right)\! I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! LaTeX Error: \begin{document} ended by \end{array}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5315 \end{array} \right)\! Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing \right. inserted. \right . l.5315 \end{array} \right)\! I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing $ inserted. $ l.5315 \end{array} \right)\! I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing $ inserted. $ l.5315 \end{array}\right )\! I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra \right. l.5315 \end{array}\right) \! I'm ignoring a \right that had no matching \left. ! LaTeX Error: \begin{document} ended by \end{definition}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5325 \end{definition} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing } inserted. } l.5325 \end{definition} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Extra \endgroup. \endgroup l.5325 \end{definition} Things are pretty mixed up, but I think the worst is over. ! LaTeX Error: Environment sublemma undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5326 \begin{sublemma} \label{sublemma reducibility the same} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: \begin{document} ended by \end{sublemma}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5337 \end{sublemma} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: Environment lemma undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5342 \begin{lemma} \label{lemma goebel 1}\mbox{}\\ Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: \begin{document} ended by \end{lemma}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5350 \end{lemma} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: Environment definition undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5354 \begin{definition} % Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. l.5359 over\/ \sig/\/\V\ \bdiff \ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. {\SUBSYM }({\VAR {((l,r),C)}},{\tvsig [\cap \tgsig ]}) l.5366 ...BST{\VAR{((l,r),C)}}{\tvsig[\cap\tgsig]} :\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: \begin{document} ended by \end{definition}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5389 \end{definition} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Too many }'s. l.5391 } %comment%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%... You've closed more groups than you opened. Such booboos are generally harmless, so keep going. Overfull \hbox (264.16281pt too wide) in paragraph at lines 5300--5393 $\OML/cmm/m/it/12 s[]t$ \T1/cmr/m/n/12 if $ \OMS/cmsy/m/n/12 9\OT1/cmr/m/n/1 2 ((\OML/cmm/m/it/12 l; r\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 ; C\OT1/cmr/m/n/12 ) \OMS/cmsy/m/n/12 2 \OT1/cmr/m/n/12 R : \OMS/cmsy/m/n/12 9\OML/cmm/m/it/12 ^^[ \OMS/cmsy/m/n/12 2 [] \OT1/cmr/m/n/12 : \OMS/cmsy/m/n/12 9\OML/cmm/m/it /12 p \OMS/cmsy/m/n/12 2 \OML/cmm/m/it/12 s \OT1/cmr/m/n/12 : []$$ $\T1/cm r/m/n/12 , [] Underfull \vbox (badness 10000) has occurred while \output is active [] [32] ! LaTeX Error: Environment lemma undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5397 \begin{lemma} \label{lemma about termination}\mbox{} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. l.5402 Now we have \simplemath {\redsubY\subseteq\ >} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.5402 Now we have \simplemath{\redsubY\subseteq \ >} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.5402 ...e have \simplemath{\redsubY\subseteq\ >} I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Undefined control sequence. l.5404 \simplemath { The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! You can't use `\spacefactor' in math mode. \@->\spacefactor \@m l.5413 }~over\/~\sig/\/\V\@ . Sorry, but I'm not programmed to handle this case; I'll just pretend that you didn't ask for it. If you're in the wrong mode, you might be able to return to the right one by typing `I}' or `I$' or `I\par'. ! LaTeX Error: \begin{document} ended by \end{lemma}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5414 \end{lemma} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ l.5414 \end{lemma} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. Missing character: There is no è in font cmex10! ! Missing } inserted. } l.5414 \end{lemma} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. Overfull \hbox (223.7372pt too wide) in paragraph at lines 5397--5415 \T1/cmr/m/n/12 As-sume that R is Y-compa-tible with T. Now we have $[][]$$\OMS/ cmsy/m/n/12 ^^R \OML/cmm/m/it/12 > and[]; whichisnoetherian:Furthermore; \OT1/c mr/m/n/12 R \OML/cmm/m/it/12 is\OT1/cmr/m/n/12 X \OMS/cmsy/m/n/12 ^^@ [] Overfull \hbox (106.6601pt too wide) in paragraph at lines 5397--5415 \OML/cmm/m/it/12 compa\T1/cmr/m/n/12 -\OML/cmm/m/it/12 tible []with []\OT1/cmr/ m/n/12 T\OML/cmm/m/it/12 and\OT1/cmr/m/n/12 V \OMS/cmsy/m/n/12 ^^@ \OML/cmm/m/i t/12 compa\T1/cmr/m/n/12 -\OML/cmm/m/it/12 tible withthetermination \OMS/cmsy/m /n/12 ^^@ \OML/cmm/m/it/12 pair [] [] []over [][]=\OT1/cmr/m/n/12 V\OML/cmm/m/ it/12 :$ [] ! LaTeX Error: Environment definition undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5423 \begin{definition} \label{def weakly joinable}\mbox{} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. \simplemath l.5426 \\\simplemath { The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.5427 \forall \tau\in\Xsubst: I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.5428 } I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Missing $ inserted. $ l.5454 } I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! LaTeX Error: \begin{document} ended by \end{definition}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5455 \end{definition} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing } inserted. } l.5455 \end{definition} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. Underfull \hbox (badness 10000) in paragraph at lines 5423--5456 [] ! LaTeX Error: Environment theorem undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5467 \begin{theorem} [Syntactic Confluence Test] Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: \begin{document} ended by \end{theorem}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5489 \end{theorem} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. l.5495 Theorem~5.1 in \Av enhaus\&Becker\cite{SR-92-11}, The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Citation `SR-92-11' on page 33 undefined on input line 5495. LaTeX Warning: Reference `theoremconfluence' on page 33 undefined on input line 5496. LaTeX Warning: Reference `theorem quasi overlay joinable' on page 33 undefined on input line 5499. ! LaTeX Error: Environment theorem undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5502 \begin{theorem} [Syntactic Confluence Test] Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. \simplemath l.5511 \\\simplemath { The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.5512 \forall \kurzregel\in\R: I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.5514 } I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Missing $ inserted. $ l.5533 } I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! LaTeX Error: \begin{document} ended by \end{theorem}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5549 \end{theorem} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing } inserted. } l.5549 \end{theorem} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! LaTeX Error: Environment lemma undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5553 \begin{lemma} \label{lemma about semi-decidable reducibility}\mbox{}\\ Your command was ignored. Type I to replace it with another command, or to continue without it. LaTeX Warning: Reference `lemma not semi' on page 33 undefined on input line 55 60. [33] ! LaTeX Error: \begin{sloppypar} on input line 5552 ended by \end{lemma}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5587 \end{lemma} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: Environment lemma undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5598 \begin{lemma} [Reducibility of Ground Terms is Still Not Co-semi-decid... Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: \begin{document} ended by \end{lemma}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5609 \end{lemma} Your command was ignored. Type I to replace it with another command, or to continue without it. LaTeX Warning: Reference `corollary normal form and reducibility' on page 34 un defined on input line 5615. ! LaTeX Error: Environment lemma undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5618 \begin{lemma} \label{lemma about decidable reducibility}\mbox{}\\ Your command was ignored. Type I to replace it with another command, or to continue without it. LaTeX Warning: Reference `lemma still not co-semi' on page 34 undefined on inpu t line 5627. LaTeX Warning: Reference `lemma not co-semi' on page 34 undefined on input line 5634. LaTeX Warning: Reference `lemma not semi' on page 34 undefined on input line 56 34. ! LaTeX Error: \begin{document} ended by \end{lemma}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5658 \end{lemma} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. ...esep \ignorespaces \Cf \ Kapur\etal \cite {ground counfluence}... l.5668 } . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Citation `ground counfluence' on page 34 undefined on input line 5668. ! LaTeX Error: Environment lemma undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5675 \begin{lemma} [Confluence of \redshortsub\ is Not Semi-decidable]% Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: \begin{document} ended by \end{lemma}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5683 \end{lemma} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. l.5686 \comment {%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: Environment lemma undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5688 \begin{lemma} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: \begin{document} ended by \end{lemma}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5716 \end{lemma} Your command was ignored. Type I to replace it with another command, or to continue without it. [34] [35] ! LaTeX Error: Environment definition undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5724 \begin{definition} [Syntax of Formulas]\label{def formulas}\mbox{}\\ Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. l.5725 Let\/ \simplemath {\X\tightsubseteq\V}. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \Xformulas l.5729 ...:=\Xatoms^{\ast}\times\Xatoms^{\ast}\ ,} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.5736 \comment {and (when we list\/ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.5737 \simplemath {\Gamma} or \simplemath{\Delta}) The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.5737 \simplemath{\Gamma } or \simplemath{\Delta}) I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.5737 \simplemath{\Gamma} or \simplemath{\Delta}) I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Undefined control sequence. l.5737 \simplemath{\Gamma} or \simplemath {\Delta}) The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Extra }, or forgotten $. l.5741 } %comment I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! LaTeX Error: \begin{document} ended by \end{definition}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5742 \end{definition} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ l.5742 \end{definition} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.5742 \end{definition} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.5742 \end{definition} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! LaTeX Error: Environment definition undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5744 \begin{definition} [Validity of Formulas in \Algebra s] Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. l.5746 Let\/ \simplemath {\X\tightsubseteq\V}; The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.5750 An atom \simplemath {(u\boldequal v)\in\Xatoms} is\/ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.5750 An atom \simplemath{(u\boldequal v)\in \Xatoms} is\/ I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.5750 ...m \simplemath{(u\boldequal v)\in\Xatoms} is\/ I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. LaTeX Font Warning: Command \em invalid in math mode on input line 5751. ! LaTeX Error: Command \itshape invalid in math mode. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5751 {\em true \wrt\ \simplemath{\algebra_{\kappa}}} Please use the math alphabet \mathit instead of the \itshape command. ! Undefined control sequence. l.5751 {\em true \wrt\ \simplemath {\algebra_{\kappa}}} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.5755 \simplemath {(\DEF u)\in\Xatoms} (with \bigmath{u\in\tsigX_s}; The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Font Warning: Command \em invalid in math mode on input line 5757. ! LaTeX Error: Command \itshape invalid in math mode. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5757 {\em true \wrt\ \simplemath{\algebra_{\kappa}}} Please use the math alphabet \mathit instead of the \itshape command. ! Undefined control sequence. l.5757 {\em true \wrt\ \simplemath {\algebra_{\kappa}}} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.5761 I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Undefined control sequence. l.5763 A formula \simplemath {\gd\in\Xformulas} is The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.5763 A formula \simplemath{\gd\in \Xformulas} is I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Undefined control sequence. l.5763 A formula \simplemath{\gd\in\Xformulas } is The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Extra }, or forgotten $. l.5763 A formula \simplemath{\gd\in\Xformulas} is I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. LaTeX Font Warning: Command \em invalid in math mode on input line 5764. ! LaTeX Error: Command \itshape invalid in math mode. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5764 {\em valid in \algebra} \udiff\ \bigmath{\forall\kappa\in\SUBST{\X}{\... Please use the math alphabet \mathit instead of the \itshape command. ! Missing $ inserted. $ l.5776 } I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! LaTeX Error: \begin{document} ended by \end{definition}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5777 \end{definition} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing } inserted. } l.5777 \end{definition} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.5777 \end{definition} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! LaTeX Error: Environment example undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5787 \begin{example} Your command was ignored. Type I to replace it with another command, or to continue without it. LaTeX Warning: Reference `exa' on page 36 undefined on input line 5789. ! Undefined control sequence. \begin {array}[t]{lclcl} \mbp \x \nil &\eqcolon &\false \\ \mbp ... l.5806 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \begin {array}[t]{lclcl} \mbp \x \nil &\eqcolon &\false \\ \mbp ... l.5806 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \begin {array}[t]{lclcl} \mbp \x \nil &\eqcolon &\false \\ \mbp ... l.5806 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...y}[t]{lclcl} \mbp \x \nil &\eqcolon &\false \\ \mbp \x \cns \y... l.5806 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...lcl} \mbp \x \nil &\eqcolon &\false \\ \mbp \x \cns \y \el &\e... l.5806 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \mbp l.5806 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...x \nil &\eqcolon &\false \\ \mbp \x \cns \y \el &\eqcolon &\tr... l.5806 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...l &\eqcolon &\false \\ \mbp \x \cns \y \el &\eqcolon &\true &\... l.5806 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...\eqcolon &\false \\ \mbp \x \cns \y \el &\eqcolon &\true &\rs ... l.5806 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...olon &\false \\ \mbp \x \cns \y \el &\eqcolon &\true &\rs &\x ... l.5806 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...se \\ \mbp \x \cns \y \el &\eqcolon &\true &\rs &\x \eqcolon \... l.5806 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...mbp \x \cns \y \el &\eqcolon &\true &\rs &\x \eqcolon \y \\ \m... l.5806 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...ns \y \el &\eqcolon &\true &\rs &\x \eqcolon \y \\ \mbp \x \cn... l.5806 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ... &\eqcolon &\true &\rs &\x \eqcolon \y \\ \mbp \x \cns \y \el ... l.5806 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...eqcolon &\true &\rs &\x \eqcolon \y \\ \mbp \x \cns \y \el &\e... l.5806 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \mbp l.5806 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...rue &\rs &\x \eqcolon \y \\ \mbp \x \cns \y \el &\eqcolon &\mb... l.5806 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...\rs &\x \eqcolon \y \\ \mbp \x \cns \y \el &\eqcolon &\mbp \x ... l.5806 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ... &\x \eqcolon \y \\ \mbp \x \cns \y \el &\eqcolon &\mbp \x \el... l.5806 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ... \eqcolon \y \\ \mbp \x \cns \y \el &\eqcolon &\mbp \x \el &\r... l.5806 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...\y \\ \mbp \x \cns \y \el &\eqcolon &\mbp \x \el &\rs &\x \nec... l.5806 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...\mbp \x \cns \y \el &\eqcolon &\mbp \x \el &\rs &\x \necolon \... l.5806 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...p \x \cns \y \el &\eqcolon &\mbp \x \el &\rs &\x \necolon \y \... l.5806 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ... \cns \y \el &\eqcolon &\mbp \x \el &\rs &\x \necolon \y \comm... l.5806 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...\el &\eqcolon &\mbp \x \el &\rs &\x \necolon \y \comma \DEF \x... l.5806 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...olon &\mbp \x \el &\rs &\x \necolon \y \comma \DEF \x \comma \... l.5806 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...n &\mbp \x \el &\rs &\x \necolon \y \comma \DEF \x \comma \DEF... l.5806 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...&\rs &\x \necolon \y \comma \DEF \x \comma \DEF \y \\ \end {ar... l.5806 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...on \y \comma \DEF \x \comma \DEF \y \\ \end {array} l.5806 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \im \mbp \x \el \eqcolon \true \comma \mbp \x \el \eqcolon \false l.5811 ...colon\true\comma\mbp\x\el\eqcolon\false} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \im \mbp \x \el \eqcolon \true \comma \mbp \x \el \eqcolon \false l.5811 ...colon\true\comma\mbp\x\el\eqcolon\false} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \im \mbp \x \el \eqcolon \true \comma \mbp \x \el \eqcolon \false l.5811 ...colon\true\comma\mbp\x\el\eqcolon\false} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \im \mbp \x \el \eqcolon \true \comma \mbp \x \el \eqcolon \false l.5811 ...colon\true\comma\mbp\x\el\eqcolon\false} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \im \mbp \x \el \eqcolon \true \comma \mbp \x \el \eqcolon \false l.5811 ...colon\true\comma\mbp\x\el\eqcolon\false} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...p \x \el \eqcolon \true \comma \mbp \x \el \eqcolon \false l.5811 ...colon\true\comma\mbp\x\el\eqcolon\false} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...x \el \eqcolon \true \comma \mbp \x \el \eqcolon \false l.5811 ...colon\true\comma\mbp\x\el\eqcolon\false} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...l \eqcolon \true \comma \mbp \x \el \eqcolon \false l.5811 ...colon\true\comma\mbp\x\el\eqcolon\false} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...n \true \comma \mbp \x \el \eqcolon \false l.5811 ...colon\true\comma\mbp\x\el\eqcolon\false} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ... \comma \mbp \x \el \eqcolon \false l.5811 ...colon\true\comma\mbp\x\el\eqcolon\false} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `fundamental corollary' on page 36 undefined on input line 5822. ! Undefined control sequence. l.5823 ... new constructor constant\/ \strangelist \ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \mbp l.5826 ...strangelist\notcongrusubemptyset\:\true} and The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \mbp \zero \strangelist \notcongrusubemptyset \:\true l.5826 ...strangelist\notcongrusubemptyset\:\true} and The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \mbp \zero \strangelist \notcongrusubemptyset \:\true l.5826 ...strangelist\notcongrusubemptyset\:\true} and The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...elist \notcongrusubemptyset \:\true l.5826 ...strangelist\notcongrusubemptyset\:\true} and The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \mbp l.5827 ...trangelist\notcongrusubemptyset\:\false} ). The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \mbp \zero \strangelist \notcongrusubemptyset \:\false l.5827 ...trangelist\notcongrusubemptyset\:\false} ). The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \mbp \zero \strangelist \notcongrusubemptyset \:\false l.5827 ...trangelist\notcongrusubemptyset\:\false} ). The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...list \notcongrusubemptyset \:\false l.5827 ...trangelist\notcongrusubemptyset\:\false} ). The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: \begin{document} ended by \end{example}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5832 \end{example} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: Environment definition undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5835 \begin{definition} [Inductive Substitutions]\mbox{}\\ Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. ...gcons \ \wedge \ \tau \restrictedto {\Vsig }=\id \restrictedto... l.5843 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...rictedto {\Vsig }=\id \restrictedto {\Vsig } \setwithstop l.5843 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: \begin{document} ended by \end{definition}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5844 \end{definition} Your command was ignored. Type I to replace it with another command, or to continue without it. Underfull \vbox (badness 10000) has occurred while \output is active [] [36] ! LaTeX Error: Environment definition undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5847 \begin{definition} [Type-A/B/C-inductive Validity]\mbox{}\\ Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. l.5851 Let\/ \simplemath {\gd\in\formulas}. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.5851 Let\/ \simplemath{\gd\in \formulas}. I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Undefined control sequence. l.5851 Let\/ \simplemath{\gd\in\formulas }. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Extra }, or forgotten $. l.5851 Let\/ \simplemath{\gd\in\formulas} . I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. LaTeX Font Warning: Command \em invalid in math mode on input line 5854. ! LaTeX Error: Command \itshape invalid in math mode. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5854 \ldots\ {\em type-A-inductively valid \wrt\ \R} \udiff\ Please use the math alphabet \mathit instead of the \itshape command. ! Missing $ inserted. $ l.5859 } I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! LaTeX Error: \begin{document} ended by \end{definition}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5882 \end{definition} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing } inserted. } l.5882 \end{definition} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. LaTeX Warning: Reference `theorem monotony2' on page 37 undefined on input line 5899. ! Undefined control sequence. l.5951 by nonempty antecedents `\simplemath {\Gamma}' The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.5951 by nonempty antecedents `\simplemath{\Gamma }' I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.5951 ...onempty antecedents `\simplemath{\Gamma} ' I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Missing $ inserted. $ l.5953 I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. Underfull \vbox (badness 10000) has occurred while \output is active [] [37] ! LaTeX Error: Environment example undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5960 \begin{example} [Type-A \boldunequal\ Type-B] Your command was ignored. Type I to replace it with another command, or to continue without it. LaTeX Warning: Reference `ex why cons-term-generated' on page 38 undefined on i nput line 5962. ! Undefined control sequence. l.5965 ...ht have the intuition that\/ \simplemath {\:\true} and\/ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.5965 ...have the intuition that\/ \simplemath{\: \true} and\/ I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Undefined control sequence. l.5965 ...the intuition that\/ \simplemath{\:\true } and\/ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Extra }, or forgotten $. l.5965 ...he intuition that\/ \simplemath{\:\true} and\/ I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Undefined control sequence. l.5966 \simplemath {\:\false} are not the same; \ie\ that The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.5966 \simplemath{\:\false } are not the same; \ie\ that The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \true \eqcolon \false \im l.5967 \\\linemath{\true\eqcolon\false\im} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \true \eqcolon \false \im l.5967 \\\linemath{\true\eqcolon\false\im} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \true \eqcolon \false \im l.5967 \\\linemath{\true\eqcolon\false\im} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.5971 (not even for \simplemath {\R=\emptyset}). The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.5975 I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. Overfull \hbox (120.36107pt too wide) in paragraph at lines 5964--5975 \OML/cmm/m/it/12 shouldbeinductivelyvalid:Thisformula; however; isnotvalidinthe trivial[]=[] \OMS/cmsy/m/n/12 ^^@ \OML/cmm/m/it/12 algebra; andthereforenottype \OMS/cmsy/m/n/12 ^^@ [] Overfull \hbox (194.73389pt too wide) in paragraph at lines 5964--5975 \OML/cmm/m/it/12 minimal; wecanexcludeitbyrequiringthemodelsunderconsiderationt obeconstructor \OMS/cmsy/m/n/12 ^^@ \OML/cmm/m/it/12 minimal:Indeed; theabovefo rmulaistype \OMS/cmsy/m/n/12 ^^@ [] ! Undefined control sequence. l.5980 \simplemath {\:\s\zero} with \simplemath{\:\zero} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.5980 \simplemath{\: \s\zero} with \simplemath{\:\zero} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Undefined control sequence. l.5980 \simplemath{\:\s \zero} with \simplemath{\:\zero} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.5980 \simplemath{\:\s\zero } with \simplemath{\:\zero} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Extra }, or forgotten $. l.5980 \simplemath{\:\s\zero} with \simplemath{\:\zero} I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Undefined control sequence. l.5980 \simplemath{\:\s\zero} with \simplemath {\:\zero} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.5980 ...math{\:\s\zero} with \simplemath{\:\zero } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.5981 but do not identify \simplemath {\:\true} with \simplemath{\:\false}): The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.5981 but do not identify \simplemath{\:\true } with \simplemath{\:\false}): The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.5981 ...fy \simplemath{\:\true} with \simplemath {\:\false}): The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.5981 ...emath{\:\true} with \simplemath{\:\false }): The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \im \mbp \zero \cns \s \zero \nil \eqcolon \false l.5982 ...m\mbp\zero\cns\s\zero\nil\eqcolon\false} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \im \mbp \zero \cns \s \zero \nil \eqcolon \false l.5982 ...m\mbp\zero\cns\s\zero\nil\eqcolon\false} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \im \mbp \zero \cns \s \zero \nil \eqcolon \false l.5982 ...m\mbp\zero\cns\s\zero\nil\eqcolon\false} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \im \mbp \zero \cns \s \zero \nil \eqcolon \false l.5982 ...m\mbp\zero\cns\s\zero\nil\eqcolon\false} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \im \mbp \zero \cns \s \zero \nil \eqcolon \false l.5982 ...m\mbp\zero\cns\s\zero\nil\eqcolon\false} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \im \mbp \zero \cns \s \zero \nil \eqcolon \false l.5982 ...m\mbp\zero\cns\s\zero\nil\eqcolon\false} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...p \zero \cns \s \zero \nil \eqcolon \false l.5982 ...m\mbp\zero\cns\s\zero\nil\eqcolon\false} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ... \cns \s \zero \nil \eqcolon \false l.5982 ...m\mbp\zero\cns\s\zero\nil\eqcolon\false} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: \begin{document} ended by \end{example}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5983 \end{example} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ l.5983 \end{example} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.5983 \end{example} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.5983 \end{example} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! LaTeX Error: Environment lemma undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5991 \begin{lemma} \label{lemma inductive validity A and B}\mbox{}\\ Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. l.5993 Let\/ $\gd\in\formulas $. Now \wrt\ \R\ the \fol\ holds: The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: \begin{document} ended by \end{lemma}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.6011 \end{lemma} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: Environment example undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.6019 \begin{example} [Type-B \boldunequal\ Type-C] Your command was ignored. Type I to replace it with another command, or to continue without it. LaTeX Warning: Reference `exa' on page 38 undefined on input line 6021. LaTeX Warning: Reference `exa' on page 38 undefined on input line 6022. ! Undefined control sequence. l.6029 ...tively valid (not even for\/ \simplemath {\R=\emptyset}): The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.6029 ...(not even for\/ \simplemath{\R=\emptyset }): I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.6029 ...not even for\/ \simplemath{\R=\emptyset} ): I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Missing $ inserted. $ l.6033 } I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Undefined control sequence. ...unno}\:\im \ident {dunno}\:\eqcolon \true \comma \ident {dunno... l.6033 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...:\im \ident {dunno}\:\eqcolon \true \comma \ident {dunno}\:\eq... l.6033 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...rue \comma \ident {dunno}\:\eqcolon \false \ . l.6033 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...mma \ident {dunno}\:\eqcolon \false \ . l.6033 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: \begin{document} ended by \end{example}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.6034 \end{example} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing } inserted. } l.6034 \end{example} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! LaTeX Error: Environment lemma undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.6042 \begin{lemma} \label{lemma inductive validity B and C}\mbox{}\\ Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. l.6044 Let\/ $\gd\in\formulas $. Now \wrt\ \R\ the \fol\ holds: The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.6053 ...atom \bigmath{(\DEF u)} in\/ \simplemath {\Gamma} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.6053 ...igmath{(\DEF u)} in\/ \simplemath{\Gamma } I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.6053 ...gmath{(\DEF u)} in\/ \simplemath{\Gamma} I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Missing $ inserted. $ l.6058 I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Missing } inserted. } l.6058 I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. Overfull \hbox (49.60834pt too wide) in paragraph at lines 6053--6058 []\T1/cmr/m/n/12 If for each atom $\OT1/cmr/m/n/12 ([]\OML/cmm/m/it/12 u\OT1/c mr/m/n/12 )$ \T1/cmr/m/n/12 in $\OML/cmm/m/it/12 ^^@theformula\OT1/cmr/m/n/12 \ [] []\OML/cmm/m/it/12 istype \OMS/cmsy/m/n/12 ^^@ \OML/cmm/m/it/12 C \OMS/cms y/m/n/12 ^^@ \OML/cmm/m/it/12 inductivelyvalid; thentype \OMS/cmsy/m/n/12 ^^@ [] ! LaTeX Error: \begin{document} ended by \end{lemma}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.6060 \end{lemma} Your command was ignored. Type I to replace it with another command, or to continue without it. [38] ! LaTeX Error: Environment example undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.6064 \begin{example} [Type-C \boldunequal\ Type-D] Your command was ignored. Type I to replace it with another command, or to continue without it. LaTeX Warning: Reference `ex why cons-term-generated' on page 39 undefined on i nput line 6066. LaTeX Warning: Reference `ex why cons-term-generated' on page 39 undefined on i nput line 6068. ! Undefined control sequence. l.6069 \simplemath {\cdr} and add the rule\/ \bigmath{\cdr\cns\x\el\eqcolon\el}. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.6069 \simplemath{\cdr } and add the rule\/ \bigmath{\cdr\cns\x\el\eqcolon\el}. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \cdr l.6069 ...ule\/ \bigmath{\cdr\cns\x\el\eqcolon\el} . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \cdr \cns \x \el \eqcolon \el l.6069 ...ule\/ \bigmath{\cdr\cns\x\el\eqcolon\el} . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \cdr \cns \x \el \eqcolon \el l.6069 ...ule\/ \bigmath{\cdr\cns\x\el\eqcolon\el} . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \cdr \cns \x \el \eqcolon \el l.6069 ...ule\/ \bigmath{\cdr\cns\x\el\eqcolon\el} . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \cdr \cns \x \el \eqcolon \el l.6069 ...ule\/ \bigmath{\cdr\cns\x\el\eqcolon\el} . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \cdr \cns \x \el \eqcolon \el l.6069 ...ule\/ \bigmath{\cdr\cns\x\el\eqcolon\el} . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \cdr l.6070 ... the intuition that\/ \bigmath{\cdr\nil} is still undefined The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \cdr \nil l.6070 ... the intuition that\/ \bigmath{\cdr\nil} is still undefined The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \DEF \cdr \nil \im \nlmath \cdr \nil \eqcolon \nil \im \headroom ... l.6072 ...dr\nil\eqcolon\nil\im\headroom\footroom} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \DEF \cdr \nil \im \nlmath \cdr \nil \eqcolon \nil \im \headroom ... l.6072 ...dr\nil\eqcolon\nil\im\headroom\footroom} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \cdr l.6072 ...dr\nil\eqcolon\nil\im\headroom\footroom} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \DEF \cdr \nil \im \nlmath \cdr \nil \eqcolon \nil \im \headroom ... l.6072 ...dr\nil\eqcolon\nil\im\headroom\footroom} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...\nil \im \nlmath \cdr \nil \eqcolon \nil \im \headroom \footroom l.6072 ...dr\nil\eqcolon\nil\im\headroom\footroom} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...\im \nlmath \cdr \nil \eqcolon \nil \im \headroom \footroom l.6072 ...dr\nil\eqcolon\nil\im\headroom\footroom} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `fundamental corollary' on page 39 undefined on input line 6082. ! Undefined control sequence. \cdr l.6085 the rule\/ \bigmath{\cdr\nil\eqcolon\nil} . They are type-D-inductivel... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \cdr \nil \eqcolon \nil l.6085 the rule\/ \bigmath{\cdr\nil\eqcolon\nil} . They are type-D-inductivel... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \cdr \nil \eqcolon \nil l.6085 the rule\/ \bigmath{\cdr\nil\eqcolon\nil} . They are type-D-inductivel... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \cdr \nil \eqcolon \nil l.6085 the rule\/ \bigmath{\cdr\nil\eqcolon\nil} . They are type-D-inductivel... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: \begin{document} ended by \end{example}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.6087 \end{example} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: Environment definition undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.6089 \begin{definition} [Type-D-inductive Validity]\mbox{}\\ Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. l.6091 Let\/ \simplemath {\gd\in\formulas}. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.6091 Let\/ \simplemath{\gd\in \formulas}. I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Undefined control sequence. l.6091 Let\/ \simplemath{\gd\in\formulas }. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Extra }, or forgotten $. l.6091 Let\/ \simplemath{\gd\in\formulas} . I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. LaTeX Font Warning: Command \em invalid in math mode on input line 6094. ! LaTeX Error: Command \itshape invalid in math mode. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.6094 {\em type-D-inductively valid \wrt\ \R} \udiff\ Please use the math alphabet \mathit instead of the \itshape command. ! LaTeX Error: \begin{document} ended by \end{definition}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.6098 \end{definition} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ l.6098 \end{definition} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.6098 \end{definition} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. LaTeX Warning: Reference `newtheoremmodel' on page 39 undefined on input line 6 102. LaTeX Warning: Reference `ex different: C and D' on page 39 undefined on input line 6119. ! LaTeX Error: Environment lemma undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.6123 \begin{lemma} \label{lemma inductive validity C and D}\mbox{}\\ Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. l.6125 Let\/ $\gd\in\formulas $. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `theorem sem confl' on page 39 undefined on input line 6153. ! Undefined control sequence. ...rement to confluence of \simplemath {\redsubVsig \cap (D_{_{\V... l.6153 } , then The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.6153 } , then I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. ...Vsig }}\!\tighttimes D_{_{\Vsig }})} for \simplemath { D_{_{\V... l.6153 } , then I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Undefined control sequence. ...mes D_{_{\Vsig }})} for \simplemath { D_{_{\Vsig }} := \setwit... l.6153 } , then The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Extra }, or forgotten $. \@footnotetext ...rut \strutbox }\color@endgroup } l.6153 } , then I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Missing $ inserted. $ l.6156 I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. Overfull \hbox (42.45784pt too wide) in paragraph at lines 6153--6156 \T1/cmr/m/n/10 to con-flu-ence of []$[][]$$\OMS/cmsy/m/n/10 \\OT1/cmr/m/n/10 (\ OML/cmm/m/it/10 D[] []D[]\OT1/cmr/m/n/10 )\OML/cmm/m/it/10 for[]:|; thentype \O MS/cmsy/m/n/10 ^^@ [] LaTeX Warning: Reference `footnote of theorem Birkhoff about weakened confluenc e' on page 39 undefined on input line 6168. ! Undefined control sequence. ...emptyset \^^Mas well as \simplemath {D_{_{\Vsig }}} with \bigm... l.6168 } and The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.6168 } and I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. ... well as \simplemath {D_{_{\Vsig }}} with \bigmath {D_{_{\empt... l.6168 } and I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Extra }, or forgotten $. \@footnotetext ...rut \strutbox }\color@endgroup } l.6168 } and I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Missing $ inserted. $ l.6174 I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. Underfull \hbox (badness 10000) in paragraph at lines 6168--6174 [][]\T1/cmr/m/n/10 Footnote [] is ap-pli-ca-ble here if we replace []$[][]$ wit h $[][]$ as well as [] Overfull \hbox (90.79257pt too wide) in paragraph at lines 6168--6174 \T1/cmr/m/n/10 D$[]\OML/cmm/m/it/10 with [] :|andforeach [] theformula\OT1/cmr/ m/n/10 \ [] []\OML/cmm/m/it/10 istype \OMS/cmsy/m/n/10 ^^@ [] Underfull \hbox (badness 10000) in paragraph at lines 6168--6174 \OML/cmm/m/it/10 D \OMS/cmsy/m/n/10 ^^@ \OML/cmm/m/it/10 inductivelyvalid; then type \OMS/cmsy/m/n/10 ^^@ \OML/cmm/m/it/10 D \OMS/cmsy/m/n/10 ^^@ \OML/cmm/m/it /10 inductivevalidityof[] impliestype \OMS/cmsy/m/n/10 ^^@ \OML/cmm/m/it/10 C \ OMS/cmsy/m/n/10 ^^@ [] ! Missing } inserted. } l.6175 \end{enumerate} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.6175 \end{enumerate} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.6175 \end{enumerate} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.6175 \end{enumerate} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! LaTeX Error: \begin{document} ended by \end{lemma}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.6176 \end{lemma} Your command was ignored. Type I to replace it with another command, or to continue without it. Underfull \vbox (badness 10000) has occurred while \output is active [] [39] ! LaTeX Error: Environment lemma undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.6184 \begin{lemma} \label{lemma inductive validity D}\mbox{}\\ Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. l.6186 Let\/ $\gd\in\formulas $. Now the following two items are logically eq... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \simplemath l.6194 \simplemath { The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.6195 \forall \tau\in\Vsigsubst: I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.6196 } I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Missing $ inserted. $ l.6225 } I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. Overfull \hbox (7.13863pt too wide) in paragraph at lines 6195--6226 []$ [] ! Missing } inserted. } l.6227 \end{enumerate} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! LaTeX Error: \begin{document} ended by \end{lemma}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.6228 \end{lemma} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: Environment corollary undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.6238 \begin{corollary} (of Lemma~\ref{lemma inductive validity A and B})\\ Your command was ignored. Type I to replace it with another command, or to continue without it. LaTeX Warning: Reference `lemma inductive validity A and B' on page 40 undefine d on input line 6238. ! LaTeX Error: \begin{document} ended by \end{corollary}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.6254 \end{corollary} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: Environment corollary undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.6256 \begin{corollary} Your command was ignored. Type I to replace it with another command, or to continue without it. LaTeX Warning: Reference `lemma inductive validity B and C' on page 40 undefine d on input line 6257. ! LaTeX Error: \begin{document} ended by \end{corollary}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.6272 \end{corollary} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: Environment corollary undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.6274 \begin{corollary} Your command was ignored. Type I to replace it with another command, or to continue without it. LaTeX Warning: Reference `lemma inductive validity C and D' on page 40 undefine d on input line 6275. ! LaTeX Error: \begin{document} ended by \end{corollary}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.6291 \end{corollary} Your command was ignored. Type I to replace it with another command, or to continue without it. LaTeX Warning: Citation `kr2' on page 40 undefined on input line 6304. ! Undefined control sequence. l.6305 as well as in Bouhoula\etal \cite{bouhoula}. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Citation `bouhoula' on page 40 undefined on input line 6305. ! Undefined control sequence. l.6308 Zhang\etal \cite{zhang} can be described as The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Citation `zhang' on page 40 undefined on input line 6308. ! Undefined control sequence. ...a subset of our set of rules \rules \@finalstrut \strutbox l.6321 of rules \rules} , The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Citation `bg1' on page 40 undefined on input line 6326. LaTeX Warning: Citation `bg2' on page 40 undefined on input line 6328. LaTeX Warning: Citation `GaSt92' on page 40 undefined on input line 6330. LaTeX Warning: Citation `padawitz' on page 40 undefined on input line 6342. LaTeX Warning: Citation `kr1' on page 40 undefined on input line 6343. LaTeX Warning: Citation `kr2' on page 40 undefined on input line 6344. LaTeX Warning: Citation `bevers&lewi' on page 40 undefined on input line 6353. ! Undefined control sequence. l.6359 type-A\comment {-inductive validity}, which is obviously The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Citation `kapur1' on page 40 undefined on input line 6363. LaTeX Warning: Citation `kapur2' on page 40 undefined on input line 6363. LaTeX Warning: Reference `section motivation' on page 40 undefined on input lin e 6364. LaTeX Warning: Reference `footnote Kapur&Musser' on page 40 undefined on input line 6365. LaTeX Warning: Citation `kapur1' on page 40 undefined on input line 6367. LaTeX Warning: Citation `kapur2' on page 40 undefined on input line 6372. LaTeX Warning: Reference `footnote all symbols constructors' on page 40 undefin ed on input line 6373. ! Undefined control sequence. \im u\:\eqcolon v l.6375 ...f the form ``\bigmath{\im u\:\eqcolon v} '') The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.6380 type-B\comment {-inductive validity}. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. [40] LaTeX Warning: Reference `ex different: A and B' on page 41 undefined on input line 6388. LaTeX Warning: Reference `ex different: B and C' on page 41 undefined on input line 6389. LaTeX Warning: Reference `section motivation' on page 41 undefined on input lin e 6396. LaTeX Warning: Reference `ex different: A and B' on page 41 undefined on input line 6398. ! Undefined control sequence. \mbp l.6400 ...ns\s\zero\nil\congrusubemptyset\:\false} '' The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \mbp \zero \cns \s \zero \nil \congrusubemptyset \:\false l.6400 ...ns\s\zero\nil\congrusubemptyset\:\false} '' The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \mbp \zero \cns \s \zero \nil \congrusubemptyset \:\false l.6400 ...ns\s\zero\nil\congrusubemptyset\:\false} '' The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \mbp \zero \cns \s \zero \nil \congrusubemptyset \:\false l.6400 ...ns\s\zero\nil\congrusubemptyset\:\false} '' The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \mbp \zero \cns \s \zero \nil \congrusubemptyset \:\false l.6400 ...ns\s\zero\nil\congrusubemptyset\:\false} '' The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \mbp \zero \cns \s \zero \nil \congrusubemptyset \:\false l.6400 ...ns\s\zero\nil\congrusubemptyset\:\false} '' The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...ro \nil \congrusubemptyset \:\false l.6400 ...ns\s\zero\nil\congrusubemptyset\:\false} '' The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \im \mbp \zero \cns \s \zero \nil \eqcolon \false l.6402 ...m\mbp\zero\cns\s\zero\nil\eqcolon\false} '' The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \im \mbp \zero \cns \s \zero \nil \eqcolon \false l.6402 ...m\mbp\zero\cns\s\zero\nil\eqcolon\false} '' The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \im \mbp \zero \cns \s \zero \nil \eqcolon \false l.6402 ...m\mbp\zero\cns\s\zero\nil\eqcolon\false} '' The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \im \mbp \zero \cns \s \zero \nil \eqcolon \false l.6402 ...m\mbp\zero\cns\s\zero\nil\eqcolon\false} '' The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \im \mbp \zero \cns \s \zero \nil \eqcolon \false l.6402 ...m\mbp\zero\cns\s\zero\nil\eqcolon\false} '' The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \im \mbp \zero \cns \s \zero \nil \eqcolon \false l.6402 ...m\mbp\zero\cns\s\zero\nil\eqcolon\false} '' The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...p \zero \cns \s \zero \nil \eqcolon \false l.6402 ...m\mbp\zero\cns\s\zero\nil\eqcolon\false} '' The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ... \cns \s \zero \nil \eqcolon \false l.6402 ...m\mbp\zero\cns\s\zero\nil\eqcolon\false} '' The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `lemma inductive validity D' on page 41 undefined on i nput line 6409. LaTeX Warning: Reference `lemma inductive validity C and D' on page 41 undefine d on input line 6411. ! Undefined control sequence. l.6412 for showing type-C\comment {-inductive validity}. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `ex different: B and C' on page 41 undefined on input line 6413. Underfull \vbox (badness 2393) has occurred while \output is active [] [41] ! LaTeX Error: Environment theorem undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.6450 \begin{theorem} {\bf Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. \restrictedto l.6481 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \restrictedto l.6481 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...w constructor constant \strangelist \ of sort \ident {list} to... l.6491 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `ex why cons-term-generated' on page 42 undefined on i nput line 6491. LaTeX Warning: Reference `theorem monotony1' on page 42 undefined on input line 6502. Underfull \hbox (badness 10000) in paragraph at lines 6457--6505 [] ! Undefined control sequence. \ident {nicep}\:\eqcolon \true \ \rulesugar \ \:\true \necolon \f... l.6536 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \ident {nicep}\:\eqcolon \true \ \rulesugar \ \:\true \necolon \f... l.6536 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...qcolon \true \ \rulesugar \ \:\true \necolon \false \comma \DE... l.6536 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...rue \ \rulesugar \ \:\true \necolon \false \comma \DEF \false ... l.6536 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...rulesugar \ \:\true \necolon \false \comma \DEF \false \comma ... l.6536 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ... \necolon \false \comma \DEF \false \comma \DEF \true l.6536 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...comma \DEF \false \comma \DEF \true l.6536 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \begin {array}[t]{l} \true \eqcolon \false \im \\ \im \ident {ni... l.6536 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \begin {array}[t]{l} \true \eqcolon \false \im \\ \im \ident {ni... l.6536 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...{array}[t]{l} \true \eqcolon \false \im \\ \im \ident {nicep}\... l.6536 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...\im \\ \im \ident {nicep}\:\eqcolon \true ,\\ \end {array} l.6536 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ... \im \ident {nicep}\:\eqcolon \true ,\\ \end {array} l.6536 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...ray}[t]{l} \ident {dunno}\:\eqcolon \true \\ \ident {dunno}\:\... l.6536 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...]{l} \ident {dunno}\:\eqcolon \true \\ \ident {dunno}\:\eqcolo... l.6536 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...n \true \\ \ident {dunno}\:\eqcolon \false .\\ \end {array} l.6536 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ... \\ \ident {dunno}\:\eqcolon \false .\\ \end {array} l.6536 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `theorem sem confl' on page 42 undefined on input line 6560. ! Undefined control sequence. l.6565 Now, for \/ $\gd\in\formulas $, we have: The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \comment l.6589 \comment {%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `theorem sem confl' on page 42 undefined on input line 6625. ! Undefined control sequence. ...s This means that each \simplemath {\Vsigsubst }-instance of ... l.6642 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `ex different: C and D' on page 42 undefined on input line 6642. ! Undefined control sequence. \cdr l.6642 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \cdr \nil \eqcolon \nil l.6642 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \cdr \nil \eqcolon \nil l.6642 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \cdr \nil \eqcolon \nil l.6642 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: \begin{document} ended by \end{theorem}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.6648 \end{theorem} Your command was ignored. Type I to replace it with another command, or to continue without it. Underfull \vbox (badness 10000) has occurred while \output is active [] [42] Overfull \vbox (0.2148pt too high) has occurred while \output is active [] [43] LaTeX Warning: Citation `kapur1' on page 44 undefined on input line 6766. LaTeX Warning: Citation `kapur2' on page 44 undefined on input line 6766. LaTeX Warning: Citation `Zh88' on page 44 undefined on input line 6768. LaTeX Warning: Citation `kaplan' on page 44 undefined on input line 6773. LaTeX Warning: Citation `kaplan' on page 44 undefined on input line 6786. ! Undefined control sequence. l.6826 J\"urgen \Av enhaus The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Citation `wg1' on page 44 undefined on input line 6842. LaTeX Warning: Citation `wgctrslncs' on page 44 undefined on input line 6847. LaTeX Warning: Citation `wg1' on page 44 undefined on input line 6866. LaTeX Warning: Reference `newtheoremmodel' on page 44 undefined on input line 6 866. LaTeX Warning: Reference `theorem sem confl' on page 44 undefined on input line 6866. LaTeX Warning: Reference `lemma variable extension' on page 44 undefined on inp ut line 6866. LaTeX Warning: Reference `theorem joinable due to small variables' on page 44 u ndefined on input line 6866. LaTeX Warning: Reference `section results for compatible' on page 44 undefined on input line 6866. LaTeX Warning: Reference `section inductive validity' on page 44 undefined on i nput line 6866. [44] LaTeX Warning: Reference `lemmacongruisall' on page 45 undefined on input line 6875. Underfull \hbox (badness 10000) in paragraph at lines 6875--6876 [] ! Undefined control sequence. l.6880 Due to \simplemath {\kernel{\algebra}=\kernel{\balgebra}}, The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.6887 \simplemath {t\in\gtsigindex{s}}, The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.6887 \simplemath{t\in \gtsigindex{s}}, I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.6887 \simplemath{t\in\gtsigindex{s}} , I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Undefined control sequence. l.6889 \simplemath {t'\in\gtconsindex{s}} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! You can't use `\spacefactor' in math mode. \@->\spacefactor \@m l.6895 ...ra\ only if it is true \wrt\ \balgebra\@ . Sorry, but I'm not programmed to handle this case; I'll just pretend that you didn't ask for it. If you're in the wrong mode, you might be able to return to the right one by typing `I}' or `I$' or `I\par'. LaTeX Warning: Reference `substitutionlemma' on page 45 undefined on input line 6903. ! You can't use `\spacefactor' in math mode. \@->\spacefactor \@m l.6907 ...gebra\ is a \Model\ of all rules of \R\@ . Sorry, but I'm not programmed to handle this case; I'll just pretend that you didn't ask for it. If you're in the wrong mode, you might be able to return to the right one by typing `I}' or `I$' or `I\par'. Missing character: There is no è in font cmex10! Missing character: There is no è in font cmex10! ! Missing $ inserted. $ l.6909 Let $\kappa $ be any \algebra-valuation of \V\@. I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. Overfull \hbox (665.38782pt too wide) in paragraph at lines 6880--6915 []\OML/cmm/m/it/12 ; thenthereissome[]with [] ; bywhichweget [] :Thus\OT1/cmr/m /n/12 `$[]\T1/cmr/m/n/12 t$[]\OML/cmm/m/it/12 istruew:r:t: \OMS/cmsy/m/n/12 A \ OML/cmm/m/it/12 onlyifitistruew:r:t: \OMS/cmsy/m/n/12 B\OML/cmm/m/it/12 :Since\ OT1/cmr/m/n/12 `[] []\OML/cmm/m/it/12 occursasapositiveliteralintheconditionsof therulesonly; \OMS/cmsy/m/n/12 A \OML/cmm/m/it/12 isa[]=[] \OMS/cmsy/m/n/12 ^^@ [] Underfull \hbox (badness 10000) in paragraph at lines 6880--6915 \OML/cmm/m/it/12 model ofallgroundinstancesoftherulesof\OT1/cmr/m/n/12 R\OML/cm m/m/it/12 ; whichimpliesthat\OMS/cmsy/m/n/12 A \OML/cmm/m/it/12 isa[]=[] \OMS/c msy/m/n/12 ^^@ [] LaTeX Warning: Reference `Homomorphism-Theorem' on page 45 undefined on input l ine 6919. ! Missing } inserted. } l.6926 \end{enumerate} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. LaTeX Warning: Reference `lemmatheor' on page 45 undefined on input line 6931. Underfull \hbox (badness 10000) in paragraph at lines 6931--6932 [] LaTeX Warning: Reference `lemmacongruisall' on page 45 undefined on input line 6939. LaTeX Warning: Reference `substitutionlemma' on page 45 undefined on input line 6966. LaTeX Warning: Reference `lemmacongruisall' on page 45 undefined on input line 6966. [45] LaTeX Warning: Reference `defred' on page 46 undefined on input line 7023. Underfull \hbox (badness 10000) in paragraph at lines 7023--7024 [] LaTeX Warning: Reference `defred' on page 46 undefined on input line 7027. LaTeX Warning: Reference `defred' on page 46 undefined on input line 7033. LaTeX Warning: Reference `defred' on page 46 undefined on input line 7054. ! Undefined control sequence. l.7061 \simplemath { The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.7062 (\red\cap (\tcs\times\vt)) I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.7065 } I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Missing $ inserted. $ l.7066 I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Missing } inserted. } l.7066 I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. LaTeX Warning: Reference `defred' on page 46 undefined on input line 7072. LaTeX Warning: Reference `defrulescontinu' on page 46 undefined on input line 7 081. LaTeX Warning: Reference `defrulescontinu' on page 46 undefined on input line 7 085. LaTeX Warning: Reference `correctnessofdefproof item 1' on page 46 undefined on input line 7089. LaTeX Warning: Reference `correctnessofdefproof item 2' on page 46 undefined on input line 7090. LaTeX Warning: Reference `defrulescontinu' on page 46 undefined on input line 7 091. LaTeX Warning: Reference `correctnessofdefproof item 3' on page 46 undefined on input line 7094. LaTeX Warning: Reference `defrulescontinu' on page 46 undefined on input line 7 095. LaTeX Warning: Reference `correctnessofdefproof item 4' on page 46 undefined on input line 7098. LaTeX Warning: Reference `correctnessofdefproof item 1' on page 46 undefined on input line 7106. LaTeX Warning: Reference `correctnessofdefproof item 3' on page 46 undefined on input line 7112. LaTeX Warning: Reference `correctnessofdefproof item 5' on page 46 undefined on input line 7112. LaTeX Warning: Reference `correctnessofdefproof item 6A' on page 46 undefined o n input line 7116. LaTeX Warning: Reference `correctnessofdefproof item 6A' on page 46 undefined o n input line 7119. LaTeX Warning: Reference `correctnessofdefproof item 6B' on page 46 undefined o n input line 7120. LaTeX Warning: Reference `correctnessofdefproof item 2' on page 46 undefined on input line 7121. LaTeX Warning: Reference `correctnessofdefproof item 5' on page 46 undefined on input line 7125. LaTeX Warning: Reference `correctnessofdefproof item 7' on page 46 undefined on input line 7125. LaTeX Warning: Reference `defred' on page 46 undefined on input line 7128. [46] LaTeX Warning: Reference `lemma about conskeeping' on page 47 undefined on inpu t line 7135. LaTeX Warning: Reference `correctnessofdefproof item 8' on page 47 undefined on input line 7137. LaTeX Warning: Reference `correctnessofdefproof item 3' on page 47 undefined on input line 7138. LaTeX Warning: Reference `correctnessofdefproof item 2' on page 47 undefined on input line 7140. LaTeX Warning: Reference `defred' on page 47 undefined on input line 7141. LaTeX Warning: Reference `lemma about conskeeping' on page 47 undefined on inpu t line 7143. LaTeX Warning: Reference `lemma about sortkeeping' on page 47 undefined on inpu t line 7147. LaTeX Warning: Reference `defrulescontinu' on page 47 undefined on input line 7 148. LaTeX Warning: Reference `lemma about conskeeping' on page 47 undefined on inpu t line 7154. LaTeX Warning: Reference `lemma about sortkeeping' on page 47 undefined on inpu t line 7155. LaTeX Warning: Reference `lemma about groundconskeeping' on page 47 undefined o n input line 7159. LaTeX Warning: Reference `defrulescontinu' on page 47 undefined on input line 7 160. LaTeX Warning: Reference `lemma about conskeeping' on page 47 undefined on inpu t line 7166. LaTeX Warning: Reference `lemma about groundconskeeping' on page 47 undefined o n input line 7167. LaTeX Warning: Reference `lemma about conflu' on page 47 undefined on input lin e 7171. LaTeX Warning: Reference `lemma about conskeeping' on page 47 undefined on inpu t line 7172. LaTeX Warning: Reference `lemma about conflu' on page 47 undefined on input lin e 7173. LaTeX Warning: Reference `lemma monotonic wrt ordinals' on page 47 undefined on input line 7177. LaTeX Warning: Reference `correctnessofdefproof item 4' on page 47 undefined on input line 7179. LaTeX Warning: Reference `correctnessofdefproof item 8' on page 47 undefined on input line 7179. LaTeX Warning: Reference `lemma about conflu' on page 47 undefined on input lin e 7219. LaTeX Warning: Reference `lemma monotonic wrt ordinals' on page 47 undefined on input line 7228. LaTeX Warning: Reference `lemma normal form fulfilledness testing' on page 47 u ndefined on input line 7233. LaTeX Warning: Reference `lemma about groundconskeeping' on page 47 undefined o n input line 7242. LaTeX Warning: Reference `lemma about groundconskeeping' on page 47 undefined o n input line 7248. LaTeX Warning: Reference `lemma normal form fulfilledness testing' on page 47 u ndefined on input line 7249. LaTeX Warning: Reference `lemma about ground reduction' on page 47 undefined on input line 7254. ! Undefined control sequence. l.7256 \simplemath {\tau\in\SUBST{\Y}{\tX}} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.7256 \simplemath{\tau \in\SUBST{\Y}{\tX}} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.7256 \simplemath{\tau\in\SUBST{\Y}{\tX}} I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Undefined control sequence. \tau \restrictedto {\X }\subseteq \id l.7258 \bigmath{\tau\restrictedto{\X}\subseteq\id} . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.7259 Using this $\tau $ in combination with Corollary~\ref{corollary stable} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX Warning: Reference `corollary stable' on page 47 undefined on input line 7259. ! Undefined control sequence. l.7260 ...etting rid of variables from \simplemath {\Y\tightsetminus\X} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `corollary stable' on page 47 undefined on input line 7264. LaTeX Warning: Reference `lemma about ground reduction' on page 47 undefined on input line 7265. ! Missing } inserted. } l.7266 \end{proof} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. LaTeX Warning: Reference `newtheoremmodel' on page 47 undefined on input line 7 279. ! Undefined control sequence. l.7283 ...algebra\ is a \Model\ of \R; \simplemath {\mu\in\SUBST{\X}{\calgebr... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.7283 ...bra\ is a \Model\ of \R; \simplemath{\mu \in\SUBST{\X}{\calgebra}}; I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.7283 ...\simplemath{\mu\in\SUBST{\X}{\calgebra}} ; I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Missing $ inserted. $ l.7291 } I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX Warning: Reference `item funda c' on page 47 undefined on input line 7294 . ! Undefined control sequence. l.7297 \simplemath {\sigma\in\Xsubst}. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.7297 \simplemath{\sigma \in\Xsubst}. I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.7297 \simplemath{\sigma\in\Xsubst} . I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. LaTeX Warning: Reference `substitutionlemma' on page 47 undefined on input line 7298. ! Missing $ inserted. $ l.7303 confluence of $\redsub[\cap (D_{_{\X}}\tighttimes D_{_{\X}})]$, I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX Warning: Reference `lemma about groundconskeeping' on page 47 undefined o n input line 7305. ! Undefined control sequence. l.7307 \simplemath {\kurzregel\in\R}; The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.7307 \simplemath{\kurzregel\in \R}; I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.7307 \simplemath{\kurzregel\in\R} ; I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Undefined control sequence. l.7308 \simplemath {\sigma\in\Xsubst}: The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.7327 } I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Undefined control sequence. \algebra \restrictedto {\consfunsym \uplus (\{\CONS \}\!\times \s... l.7333 ...nsym\uplus(\{\CONS\}\!\times\sigsorts)}} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \calgebra \restrictedto {\consfunsym \uplus (\{\CONS \}\!\times \... l.7335 ...nsym\uplus(\{\CONS\}\!\times\sigsorts)}} \@. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. {h}\morphcolon {\algebra \restrictedto {\consfunsym \uplus (\{\CO... l.7343 .../(\congrusub\cap(\tcc\tighttimes\tcc)))} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.7345 (\simplemath {s\in\sigsorts}; \simplemath{A\in\algebra\CONSsort{s}}): The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.7345 (\simplemath{s\in \sigsorts}; \simplemath{A\in\algebra\CONSsort{s}}): I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.7345 (\simplemath{s\in\sigsorts} ; \simplemath{A\in\algebra\CONSsort{s}}): I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Undefined control sequence. l.7345 (\simplemath{s\in\sigsorts}; \simplemath {A\in\algebra\CONSsort{s}}): The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \calgebra \restrictedto {\consfunsym \uplus (\{\CONS \}\!\times \... l.7351 ...nsym\uplus(\{\CONS\}\!\times\sigsorts)}} . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.7352 Let $\mu $ be a \calgebra-valuation of \X\ I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX Warning: Reference `lemma about sortkeeping' on page 47 undefined on inpu t line 7374. LaTeX Warning: Reference `item funda c' on page 47 undefined on input line 7382 . ! Undefined control sequence. l.7384 If \simplemath {\calgebra\in\rm K}; \simplemath{\mu\in\SUBST{\X}{\cal... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.7384 If \simplemath{\calgebra\in \rm K}; \simplemath{\mu\in\SUBST{\X}{\cal... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.7384 If \simplemath{\calgebra\in\rm K} ; \simplemath{\mu\in\SUBST{\X}{\cal... I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Undefined control sequence. l.7384 ...mplemath{\calgebra\in\rm K}; \simplemath {\mu\in\SUBST{\X}{\calgebr... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.7385 $\redsubemptyset[\cap (D_{_{\emptyset}}\tighttimes D_{_{\emptyset}})]$ I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Undefined control sequence. l.7401 If \simplemath {\omega\preceq\beta} and The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.7401 If \simplemath{\omega \preceq\beta} and I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.7401 If \simplemath{\omega\preceq\beta} and I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Undefined control sequence. p\in \OCC {s} l.7408 \bigmath{p\in\OCC{s}} ; with The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `substitutionlemma' on page 47 undefined on input line 7415. ! Undefined control sequence. l.7417 \bigmath{C\sigma} is true \wrt\ \simplemath {\calgebra_{\mu}}. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.7418 Three cases for $L$ in $C\sigma $: I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Undefined control sequence. l.7426 by the existence of some \simplemath {\hat{u}\in\gtconsindex{s'}} with The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.7426 by the existence of some \simplemath{\hat {u}\in\gtconsindex{s'}} with I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.7426 ... \simplemath{\hat{u}\in\gtconsindex{s'}} with I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Undefined control sequence. l.7427 \simplemath { The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.7432 $\calgebra_ {\mu}(u)=\calgebra_{\mu}(\hat{u})\in\calgebra\CONSsort{s'}$. I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Undefined control sequence. l.7449 By \simplemath {\omega\preceq\beta} and Lemma~\ref{lemma about conflu} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.7449 By \simplemath{\omega \preceq\beta} and Lemma~\ref{lemma about conflu} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.7449 By \simplemath{\omega\preceq\beta} and Lemma~\ref{lemma about conflu} I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. LaTeX Warning: Reference `lemma about conflu' on page 47 undefined on input lin e 7449. LaTeX Warning: Reference `lemma about ground reduction' on page 47 undefined on input line 7452. ! Missing $ inserted. $ l.7457 $\redsubemptyset[\cap (D_{_{\emptyset}}\tighttimes D_{_{\emptyset}})]$) I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX Warning: Reference `item funda c' on page 47 undefined on input line 7459 . ! Undefined control sequence. l.7460 (for \simplemath {\X:=\emptyset}), The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.7460 (for \simplemath{\X:=\emptyset }), I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.7460 (for \simplemath{\X:=\emptyset} ), I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! You can't use `\spacefactor' in math mode. \@->\spacefactor \@m l.7462 ...also a constructor-minimum model of \R\@ . Sorry, but I'm not programmed to handle this case; I'll just pretend that you didn't ask for it. If you're in the wrong mode, you might be able to return to the right one by typing `I}' or `I$' or `I\par'. LaTeX Font Warning: Command \em invalid in math mode on input line 7470. ! LaTeX Error: Command \itshape invalid in math mode. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.7470 is (by ({\em \ref{item funda c}\/})) a \Model\ of \R\@.~~\hfill\Qed{Cl... Please use the math alphabet \mathit instead of the \itshape command. LaTeX Warning: Reference `item funda c' on page 47 undefined on input line 7470 . ! You can't use `\spacefactor' in math mode. \@->\spacefactor \@m l.7470 ...ref{item funda c}\/})) a \Model\ of \R\@ .~~\hfill\Qed{Claim~2} Sorry, but I'm not programmed to handle this case; I'll just pretend that you didn't ask for it. If you're in the wrong mode, you might be able to return to the right one by typing `I}' or `I$' or `I\par'. Missing character: There is no è in font cmex10! Missing character: There is no è in font cmex10! ! Missing $ inserted. $ l.7472 If $\redsubemptyset[\cap (D_{_{\emptyset}}\tighttimes D_{_{\emptyset}... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Undefined control sequence. l.7475 Suppose \simplemath {\calgebra\in{\rm K}} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.7475 Suppose \simplemath{\calgebra\in {\rm K}} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.7475 Suppose \simplemath{\calgebra\in{\rm K}} I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Missing $ inserted. $ l.7476 and $\mu $ to be a \calgebra-valuation of \X\@. I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX Warning: Reference `Homomorphism-Theorem' on page 47 undefined on input l ine 7481. LaTeX Warning: Reference `lemma about ground reduction' on page 47 undefined on input line 7497. LaTeX Warning: Reference `item funda a' on page 47 undefined on input line 7498 . LaTeX Warning: Reference `item funda c' on page 47 undefined on input line 7499 . LaTeX Warning: Reference `item funda b' on page 47 undefined on input line 7500 . LaTeX Warning: Reference `item funda c' on page 47 undefined on input line 7502 . LaTeX Warning: Reference `item funda a' on page 47 undefined on input line 7503 . Underfull \hbox (badness 4108) in paragraph at lines 7279--7504 []$ \T1/cmr/m/n/12 By the Axiom of Choice, each element of $[]\OT1/cmr/m/n/12 ( V\OML/cmm/m/it/12 ; \OMS/cmsy/m/n/12 A\OT1/cmr/m/n/12 )$ \T1/cmr/m/n/12 can be [] Underfull \hbox (badness 7151) in paragraph at lines 7279--7504 \T1/cmr/m/n/12 writ-ten $\OML/cmm/m/it/12 ^^[ \OMS/cmsy/m/n/12 ^^N A[]$ \T1/c mr/m/n/12 for some $\OML/cmm/m/it/12 ^^[ \OMS/cmsy/m/n/12 2 []\OML/cmm/m/it/12 :Thus\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 bytheSubstitution \OMS/cmsy/m/n/12 ^^@ [] Overfull \hbox (160.92538pt too wide) in paragraph at lines 7279--7504 \OML/cmm/m/it/12 Lemma\OT1/cmr/m/n/12 ([])\OML/cmm/m/it/12 and [] \OT1/cmr/m/n/ 12 )\OML/cmm/m/it/12 ; for\OMS/cmsy/m/n/12 A \OML/cmm/m/it/12 beinga[]=[] \OMS/ cmsy/m/n/12 ^^@ \OML/cmm/m/it/12 model of\OT1/cmr/m/n/12 R \OML/cmm/m/it/12 iti ssufficienttonotethat\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 byconfluenceof$$[][]$\T1 /cmr/m/n/12 [$\OMS/cmsy/m/n/12 \\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 D[][]D[]\OT1/ cmr/m/n/12 )]$\T1/cmr/m/n/12 , [] Underfull \hbox (badness 10000) in paragraph at lines 7279--7504 \T1/cmr/m/n/12 homomorphism $\OML/cmm/m/it/12 h[][][][]$ \T1/cmr/m/n/12 given [] Underfull \hbox (badness 2452) in paragraph at lines 7279--7504 \T1/cmr/m/n/12 by (s$\OMS/cmsy/m/n/12 2 \U/msb/m/n/12 S\OT1/cmr/m/n/12 ; []) : [] \OML/cmm/m/it/12 :Thusweonlyhavetofinda[] \OMS/cmsy/m/n/12 ^^@ [] Overfull \hbox (533.38742pt too wide) in paragraph at lines 7279--7504 \OML/cmm/m/it/12 ^^Land$\T1/cmr/m/n/12 s$[][]$t$\OML/cmm/m/it/12 ; thenwealread yhave [] :Otherwisethereare [] \OT1/cmr/m/n/12 ; [] ; [] ; \OML/cmm/m/it/12 w ith [] \OT1/cmr/m/n/12 ; [] ; \OML/cmm/m/it/12 and [] fulfilledw:r:t: []:As\OM S/cmsy/m/n/12 C \OML/cmm/m/it/12 isa[]=[] \OMS/cmsy/m/n/12 ^^@ [] Overfull \hbox (259.54759pt too wide) in paragraph at lines 7279--7504 \OML/cmm/m/it/12 model of\OT1/cmr/m/n/12 R\OML/cmm/m/it/12 ; for [] \OT1/cmr/m/ n/12 (\OML/cmm/m/it/12 bytheSubstitution \OMS/cmsy/m/n/12 ^^@ \OML/cmm/m/it/12 Lemma\OT1/cmr/m/n/12 ([]))\OML/cmm/m/it/12 weonlyhavetoshowthatthecondition [] istruew:r:t: []:Threecasesfor$\T1/cmr/m/n/12 L$\OML/cmm/m/it/12 in$\T1/cmr/m/n/ 12 C$\OML/cmm/m/it/12 ^^[$\T1/cmr/m/n/12 : [] Underfull \hbox (badness 1796) in paragraph at lines 7279--7504 \T1/cmr/m/n/12 If $\OML/cmm/m/it/12 L \OT1/cmr/m/n/12 = (\OML/cmm/m/it/12 u[]v\ OT1/cmr/m/n/12 )$\T1/cmr/m/n/12 , by $\OML/cmm/m/it/12 u \OMS/cmsy/m/n/12 #[] \OML/cmm/m/it/12 v$ \T1/cmr/m/n/12 the in-duc-tion hypo-thesis im-plies $\OMS /cmsy/m/n/12 C[]\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 u\OT1/cmr/m/n/12 ) = [] Underfull \hbox (badness 1960) in paragraph at lines 7279--7504 \OMS/cmsy/m/n/12 C[]\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 v\OT1/cmr/m/n/12 )$ \T1/c mr/m/n/12 . If $\OML/cmm/m/it/12 L \OT1/cmr/m/n/12 = ([] \OML/cmm/m/it/12 u\OT1 /cmr/m/n/12 )$ \T1/cmr/m/n/12 with $\OML/cmm/m/it/12 u \OMS/cmsy/m/n/12 2 []$\T 1/cmr/m/n/12 , by the exist-ence of some $[] \OMS/cmsy/m/n/12 2 [] Underfull \hbox (badness 2617) in paragraph at lines 7279--7504 []\OML/cmm/m/it/12 with[]theinductionhypothesisimplies$$\OMS/cmsy/m/n/12 C$$[]\ OT1/cmr/m/n/12 (\OML/cmm/m/it/12 u\OT1/cmr/m/n/12 ) = \OMS/cmsy/m/n/12 C[]\OT1/ cmr/m/n/12 ([]) \OMS/cmsy/m/n/12 2 C[]$\T1/cmr/m/n/12 . If [] Overfull \hbox (111.71295pt too wide) in paragraph at lines 7279--7504 \OML/cmm/m/it/12 ^^LandLemma [][]weknowthat [] \OT1/cmr/m/n/12 ; \OML/cmm/m/it/ 12 thenbyLemma [][] [] \OT1/cmr/m/n/12 ; \OML/cmm/m/it/12 andtherefore\OT1/cmr/ m/n/12 (\OML/cmm/m/it/12 byconfluenceof$$[][]$\T1/cmr/m/n/12 [$\OMS/cmsy/m/n/12 \\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 D[][]D[]\OT1/cmr/m/n/12 )]$\T1/cmr/m/n/12 ) [] Underfull \hbox (badness 10000) in paragraph at lines 7279--7504 [][][]$ \T1/cmr/m/n/12 . Be-cause of ([]) (for $\OT1/cmr/m/n/12 X$\T1/cmr/m/n/1 2 :=$\OMS/cmsy/m/n/12 ;\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 ; \OMS/cmsy/m/n/12 C \ OML/cmm/m/it/12 mustbenotonlyaconstructor \OMS/cmsy/m/n/12 ^^@ [] Overfull \hbox (311.92902pt too wide) in paragraph at lines 7279--7504 \OML/cmm/m/it/12 minimalmodelbutalsoaconstructor \OMS/cmsy/m/n/12 ^^@ \OML/cmm/ m/it/12 minimummodelof\OT1/cmr/m/n/12 R\OML/cmm/m/it/12 :Hence [] simplybecause [] \OT1/cmr/m/n/12 ; [] ; \OML/cmm/m/it/12 and\OMS/cmsy/m/n/12 I \OML/cmm/m/i t/12 is\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 by\OT1/cmr/m/n/12 ([]))\OML/cmm/m/it/1 2 a[]=[] \OMS/cmsy/m/n/12 ^^@ [] [47] ! Missing } inserted. } l.7504 \end{proof} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.7504 \end{proof} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.7504 \end{proof} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.7504 \end{proof} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.7504 \end{proof} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.7504 \end{proof} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.7504 \end{proof} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.7504 \end{proof} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.7504 \end{proof} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.7504 \end{proof} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. Underfull \vbox (badness 10000) has occurred while \output is active [] [48] LaTeX Warning: Reference `theorem monotony1' on page 49 undefined on input line 7511. LaTeX Warning: Reference `footnote signature does not matter' on page 49 undefi ned on input line 7512. ! Undefined control sequence. l.7515 \simplemath { The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.7516 \forall i\in\N\!\!: I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.7519 \forall t\!\!:} I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Missing $ inserted. $ l.7528 } I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX Warning: Reference `lemma about conskeeping' on page 49 undefined on inpu t line 7536. ! Undefined control sequence. p\in \OCC {s'} l.7559 \bigmath{p\in\OCC{s'}} with The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. p\in \OCC {s} l.7605 \bigmath{p\in\OCC{s}} with The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `lemma about conflu' on page 49 undefined on input lin e 7627. ! Missing } inserted. } l.7633 \end{proof} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. LaTeX Warning: Reference `lemma necessary' on page 49 undefined on input line 7 637. LaTeX Warning: Reference `lemma necessary' on page 49 undefined on input line 7 663. LaTeX Warning: Reference `lemma quasi overlay joinable' on page 49 undefined on input line 7668. LaTeX Warning: Reference `corollary monotonic' on page 49 undefined on input li ne 7697. Underfull \hbox (badness 10000) in paragraph at lines 7668--7707 [] Underfull \vbox (badness 10000) has occurred while \output is active [] [49] LaTeX Warning: Reference `theorem quasi overlay joinable' on page 50 undefined on input line 7713. ! Undefined control sequence. l.7727 (with \simplemath {x_{\bar{s}}\in\Vsigindex{\bar{s}}} for The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.7727 (with \simplemath{x_ {\bar{s}}\in\Vsigindex{\bar{s}}} for I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.7727 ...emath{x_{\bar{s}}\in\Vsigindex{\bar{s}}} for I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Undefined control sequence. l.7728 \simplemath {\bar{s}\in\sigsorts}):\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.7737 $s_ {\rm new}$ when rewriting terms of an I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. Underfull \hbox (badness 3503) in paragraph at lines 7715--7761 \OML/cmm/m/it/12 Sincethesortrestrictionsdonotallow[]tomakeanyuseoftermsoftheso rt$\T1/cmr/m/n/12 s$[]$ when [] ! Undefined control sequence. \Pi \subseteq \OCC {u} l.7774 \bigmath{\Pi\subseteq\OCC{u}} with The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `lemmaa' on page 50 undefined on input line 7791. ! Undefined control sequence. l.7817 \simplemath {\beta\tightplus1}. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.7817 \simplemath{\beta \tightplus1}. I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.7817 \simplemath{\beta\tightplus1} . I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Missing $ inserted. $ l.7819 I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Undefined control sequence. l.7829 \simplemath { The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.7830 \forall m\in\N:(v\antiredindexn{m}{\beta+1}u\implies m>n) I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.7831 } ) I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Missing $ inserted. $ l.7835 I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. Underfull \hbox (badness 10000) in paragraph at lines 7820--7835 \OML/cmm/m/it/12 v[]u[][]u$ $\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 n[]\OT1/cmr/bx/ n/12 N\OT1/cmr/m/n/12 )$ \T1/cmr/m/n/12 (with $\OMS/cmsy/m/n/12 8\OML/cmm/m/it /12 m \OMS/cmsy/m/n/12 2 \OT1/cmr/bx/n/12 N \OT1/cmr/m/n/12 : (\OML/cmm/m/it/12 v[]u [] m > [] ! Undefined control sequence. l.7864 $q\in\OCC {u}$; The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.7866 \simplemath {\mu_{1}\in\Xsubst}; with The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.7866 \simplemath{\mu _{1}\in\Xsubst}; with I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.7866 \simplemath{\mu_{1}\in\Xsubst} ; with I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Missing $ inserted. $ l.7867 $u/q=l_ {1}\mu_{1}$; I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. Underfull \vbox (badness 10000) has occurred while \output is active [] [50] Underfull \vbox (badness 10000) has occurred while \output is active [] [51] ! Undefined control sequence. p\in \Pi '\cap \OCC {l_{1}} l.7906 ...s some \bigmath{p\in\Pi'\cap\OCC{l_{1}}} with \bigmath{l_{1}/p\not... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.7911 Let $\varrho$ be given by (\simplemath {x\in\V}): $x\varrho:=$ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.7911 Let $\varrho$ be given by (\simplemath{x\in \V}): $x\varrho:=$ I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.7911 ...varrho$ be given by (\simplemath{x\in\V} ): $x\varrho:=$ I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Missing $ inserted. $ l.7911 ...iven by (\simplemath{x\in\V}): $x\varrho :=$ I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Undefined control sequence. l.7922 \simplemath {\Y:=\VAR{((l_{0},r_{0}),C_{0})\xi,((l_{1},r_{1}),C_{1})}}, The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.7923 \simplemath {\sigma:=\min\MGU{\msa(l_{0}\xi,l_{1}/p)\mse,\Y}} and The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.7923 \simplemath{\sigma :=\min\MGU{\msa(l_{0}\xi,l_{1}/p)\mse,\Y}} and I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.7923 ...\min\MGU{\msa(l_{0}\xi,l_{1}/p)\mse,\Y}} and I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Missing $ inserted. $ l.7924 $\varphi \in\Xsubst$ I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Undefined control sequence. \sigma \varphi \restrictedto {\Y }=\varrho \restrictedto {\Y } l.7926 ...strictedto{\Y}=\varrho\restrictedto{\Y}} . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...ictedto {\Y }=\varrho \restrictedto {\Y } l.7926 ...strictedto{\Y}=\varrho\restrictedto{\Y}} . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \forall p\in \Pi '\cap \OCC {l_{1}}:l_{1}/p\in \V l.8030 ...ll p\in\Pi'\cap\OCC{l_{1}}:l_{1}/p\in\V} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...scriptscriptstyle \N }}({\OCCSYMBOL [\vt ]}) l.8032 ...EF{\Gamma}{\V}{\FINITE{\OCCSYMBOL[\vt]}} by ($x\in\V$): The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `lemma about groundconskeeping' on page 52 undefined o n input line 8118. Underfull \hbox (badness 1275) in paragraph at lines 7898--8146 []$\T1/cmr/m/n/12 . Hence, for $[] \OT1/cmr/m/n/12 := []$ \T1/cmr/m/n/12 we g et $[] \OT1/cmr/m/n/12 =$ [] Underfull \hbox (badness 1902) in paragraph at lines 7898--8146 [][][]$ \T1/cmr/m/n/12 by $\OML/cmm/m/it/12 w[]s[]$ \T1/cmr/m/n/12 (by Sub-clai m 1). [] Overfull \vbox (16.41075pt too high) has occurred while \output is active [] [52] ! Undefined control sequence. p'\in \OCC {l_{0}}\ \wedge \ l_{0}/p'\not \in \V l.8161 ...n\OCC{l_{0}}\ \wedge\ l_{0}/p'\not\in\V} \\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.8175 \simplemath { The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.8176 l_ {1}\xi\varrho\!=\!l_{1}\xi\xi^{-1}\mu_{1}\!=\!u/q\!=\!u/pp'\!=\! I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.8178 } I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Undefined control sequence. l.8180 \simplemath {\Y:=\VAR{((l_1,r_1),C_1)\xi,((l_0,r_0),C_0)}}, The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.8181 \simplemath {\sigma:=\min\MGU{\msa(l_{1}\xi,l_{0}/p')\mse,\Y}} and The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.8182 $\varphi \in\Xsubst$ I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Undefined control sequence. \sigma \varphi \restrictedto {\Y }=\varrho \restrictedto {\Y } l.8184 ...strictedto{\Y}=\varrho\restrictedto{\Y}} . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...ictedto {\Y }=\varrho \restrictedto {\Y } l.8184 ...strictedto{\Y}=\varrho\restrictedto{\Y}} . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `lemma quasi overlay joinable' on page 53 undefined on input line 8233. LaTeX Warning: Reference `lemma about groundconskeeping' on page 53 undefined o n input line 8417. LaTeX Warning: Reference `theorem quasi overlay joinable' on page 53 undefined on input line 8440. Underfull \hbox (badness 10000) in paragraph at lines 8152--8442 \OT1/cmr/m/n/12 (\OML/cmm/m/it/12 l[]=p[]\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 %let []; []and$$' \OMS/cmsy/m/n/12 2 [] Underfull \hbox (badness 10000) in paragraph at lines 8152--8442 \T1/cmr/m/n/12 For $[] \OT1/cmr/m/n/12 := []$ \T1/cmr/m/n/12 we get $[][][]$ [] Underfull \hbox (badness 6608) in paragraph at lines 8152--8442 \T1/cmr/m/n/12 by $\OML/cmm/m/it/12 w[]s[]$ \T1/cmr/m/n/12 (by Sub-claim 5). Th us, for \T1/cmr/bx/n/12 Claim \T1/cmr/m/n/12 we only have to show [] Underfull \hbox (badness 2600) in paragraph at lines 8152--8442 \OML/cmm/m/it/12 v \OMS/cmsy/m/n/12 # []$\T1/cmr/m/n/12 . For $\OML/cmm/m/it/ 12 u[] \OT1/cmr/m/n/12 := []$ \T1/cmr/m/n/12 (Cf. Sub-claim 4) there is some [] Underfull \hbox (badness 10000) in paragraph at lines 8152--8442 \OML/cmm/m/it/12 w[]$ \T1/cmr/m/n/12 with $\OML/cmm/m/it/12 v[]w[][]u[]$ \T1/cm r/m/n/12 by Sub-claim 4 and $\OML/cmm/m/it/12 P\OT1/cmr/m/n/12 (\OML/cmm/m/it/1 2 v; u[]; s; s[]; ^^E \OMS/cmsy/m/n/12 n f\OML/cmm/m/it/12 p\OMS/cmsy/m/n/12 g \OT1/cmr/m/n/12 )$\T1/cmr/m/n/12 , which is [] Underfull \hbox (badness 6625) in paragraph at lines 8152--8442 \T1/cmr/m/n/12 smaller in the second or third po-si-tion. Finally, we get $\OML /cmm/m/it/12 w[] \OMS/cmsy/m/n/12 # []$ \T1/cmr/m/n/12 by [] Underfull \hbox (badness 10000) in paragraph at lines 8152--8442 \T1/cmr/m/n/12 (by Sub-claim 4), we get some $\OML/cmm/m/it/12 w$ \T1/cmr/m/n/1 2 with $\OML/cmm/m/it/12 v[]w[][]$ \T1/cmr/m/n/12 by $\OML/cmm/m/it/12 P\OT1/cm r/m/n/12 (\OML/cmm/m/it/12 v; u[]; l[]^^V[]; r[]^^V[];$ [] Underfull \hbox (badness 1210) in paragraph at lines 8152--8442 [] []\OMS/cmsy/m/n/12 j []\OT1/cmr/m/n/12 )$\T1/cmr/m/n/12 , which is smaller in the first po-si-tion by [] Overfull \vbox (32.55833pt too high) has occurred while \output is active [] [53] ! Missing } inserted. } l.8442 \end{proofparsep} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.8442 \end{proofparsep} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.8442 \end{proofparsep} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.8442 \end{proofparsep} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.8442 \end{proofparsep} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.8442 \end{proofparsep} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.8442 \end{proofparsep} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. LaTeX Warning: Reference `theorem sem confl' on page 54 undefined on input line 8445. ! Undefined control sequence. l.8466 rule $\kurzregel\in\R$, and a $p\in\OCC {t}$ with The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.8471 $C\sigma$ is true \wrt\ \simplemath {\algebra_{\kappa}}\@. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.8471 ...gma$ is true \wrt\ \simplemath{\algebra_ {\kappa}}\@. I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.8471 ...rue \wrt\ \simplemath{\algebra_{\kappa}} \@. I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! You can't use `\spacefactor' in math mode. \@->\spacefactor \@m l.8471 ...e \wrt\ \simplemath{\algebra_{\kappa}}\@ . Sorry, but I'm not programmed to handle this case; I'll just pretend that you didn't ask for it. If you're in the wrong mode, you might be able to return to the right one by typing `I}' or `I$' or `I\par'. Missing character: There is no è in font cmex10! ! Missing $ inserted. $ l.8472 For $(u\boldequal v)$ in $C\sigma $ we have I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Undefined control sequence. l.8480 \simplemath { The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.8481 \algebra_ {\kappa}(u)= I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.8483 } . I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Missing $ inserted. $ l.8484 For $(u\boldunequal v)$ in $C\sigma $ we know $\omega\preceq\gamma$ and I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX Warning: Reference `lemma about groundconskeeping' on page 54 undefined o n input line 8491. LaTeX Warning: Reference `lemma about groundconskeeping' on page 54 undefined o n input line 8519. ! Missing } inserted. } l.8538 \end{proof} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.8538 \end{proof} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. LaTeX Warning: Reference `lemma not co-semi' on page 54 undefined on input line 8541. LaTeX Warning: Reference `lemma not semi' on page 54 undefined on input line 85 41. ! Undefined control sequence. ...ape to the left of the head} & \nil \mbox {~~or~~} \ident {con... l.8605 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...pe to the right of the head} & \nil \mbox {~~or~~} \ident {con... l.8605 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Underfull \vbox (badness 1337) has occurred while \output is active [] [54] LaTeX Warning: Reference `lemma not semi' on page 55 undefined on input line 86 84. LaTeX Warning: Reference `lemma computable' on page 55 undefined on input line 8697. ! Undefined control sequence. l.8754 ...ules $\kurzregel\in\R$ and all $p\in\OCC {s}$ and all The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `lemma about groundconskeeping' on page 55 undefined o n input line 8804. LaTeX Warning: Reference `lemma variable extension' on page 55 undefined on inp ut line 8811. ! Undefined control sequence. l.8812 There exists some \simplemath {\tau\in\Xsubst}. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.8812 There exists some \simplemath{\tau \in\Xsubst}. I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.8812 ... exists some \simplemath{\tau\in\Xsubst} . I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Undefined control sequence. l.8813 ...how the \fol\ claims for all \simplemath {t,t'\in\vt}: The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.8817 For \simplemath {q\in\OCC{t}} and The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.8817 For \simplemath{q\in\OCC {t}} and The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `corollary stable' on page 55 undefined on input line 8822. LaTeX Warning: Reference `lemma about ground reduction' on page 55 undefined on input line 8824. ! Undefined control sequence. l.8827 There are \singlemath {\kurzregel\in\R}; \singlemath{\sigma\in\Vsubst}; The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.8827 ...singlemath{\kurzregel\in\R}; \singlemath {\sigma\in\Vsubst}; The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.8828 \singlemath {p\in\OCC{t/q}}; \singlemath{u\in\condterms{C}} with The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.8828 \singlemath{p\in\OCC {t/q}}; \singlemath{u\in\condterms{C}} with The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.8828 \singlemath{p\in\OCC{t/q}}; \singlemath {u\in\condterms{C}} with The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.8830 \singlemath {C\sigma} fulfilled \wrt\ \redshortsub. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `corollary stable' on page 55 undefined on input line 8831. ! Undefined control sequence. l.8832 \singlemath {C\sigma\tau} is fulfilled \wrt\ \redshortsub. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `lemma about ground reduction' on page 55 undefined on input line 8833. ! Undefined control sequence. l.8834 \singlemath {C\sigma\tau} is fulfilled \wrt\ \redsub. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.8835 Thus; since \simplemath {t\tau\in\tsigX}; \simplemath{\sigma\tau\in\Xs... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.8835 ...\simplemath{t\tau\in\tsigX}; \simplemath {\sigma\tau\in\Xsubst}; The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.8836 \simplemath {qp\in\OCC{t\tau}}; \bigmath{t\tau/qp=l\sigma\tau}; The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.8836 \simplemath{qp\in\OCC {t\tau}}; \bigmath{t\tau/qp=l\sigma\tau}; The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.8840 \end{proof} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. Overfull \hbox (1189.47693pt too wide) in paragraph at lines 8811--8840 []\OML/cmm/m/it/12 Thereare[]\OT1/cmr/m/n/12 ; []; []; []\OML/cmm/m/it/12 with [] \OT1/cmr/m/n/12 ; [] ; []\OML/cmm/m/it/12 fulfilledw:r:t: []:ByCorollary [] []; []isfulfilledw:r:t: []:ByLemma [][]; []isfulfilledw:r:t: []:Thus\OT1/cmr/m/ n/12 ; \OML/cmm/m/it/12 since[]\OT1/cmr/m/n/12 ; []; []; [] ; [] ; \OML/cmm/m /it/12 weget [] :$ [] [55] ! Missing } inserted. } l.8840 \end{proof} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. LaTeX Warning: Reference `lemmaa' on page 56 undefined on input line 8844. LaTeX Warning: Reference `lemmaa itemc' on page 56 undefined on input line 8845 . ! Undefined control sequence. \sigarity ({\iden a})=A l.8874 \bigmath{\sigarity({\iden a})=A} , The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \sigarity ({\iden f})=A\aritysugar B l.8875 ...ath{\sigarity({\iden f})=A\aritysugar B} , The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \sigarity ({\iden g})=A\aritysugar A l.8876 ...ath{\sigarity({\iden g})=A\aritysugar A} \@. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.8879 ${\iden f}\,{\iden a}\ \succ\ {\iden a}$ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.8879 ${\iden f}\,{\iden a}\ \succ\ {\iden a}$ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.8879 ${\iden f}\,{\iden a}\ \succ\ {\iden a}$ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. {\iden g}\,{\iden a}\ \succ \ {\iden a} l.8883 ...{{\iden g}\,{\iden a}\ \succ\ {\iden a}} but The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. {\iden g}\,{\iden a}\ \succ \ {\iden a} l.8883 ...{{\iden g}\,{\iden a}\ \succ\ {\iden a}} but The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. {\iden g}\,{\iden a}\ \succ \ {\iden a} l.8883 ...{{\iden g}\,{\iden a}\ \succ\ {\iden a}} but The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. {\iden f}\,{\iden g}\,{\iden a}\ \not \succ \ {\iden f}\,{\iden a} l.8884 ...den a}\ \not\succ\ {\iden f}\,{\iden a}} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. {\iden f}\,{\iden g}\,{\iden a}\ \not \succ \ {\iden f}\,{\iden a} l.8884 ...den a}\ \not\succ\ {\iden f}\,{\iden a}} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. {\iden f}\,{\iden g}\,{\iden a}\ \not \succ \ {\iden f}\,{\iden a} l.8884 ...den a}\ \not\succ\ {\iden f}\,{\iden a}} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ... g}\,{\iden a}\ \not \succ \ {\iden f}\,{\iden a} l.8884 ...den a}\ \not\succ\ {\iden f}\,{\iden a}} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ... a}\ \not \succ \ {\iden f}\,{\iden a} l.8884 ...den a}\ \not\succ\ {\iden f}\,{\iden a}} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `lemmaa itemd' on page 56 undefined on input line 8887 . LaTeX Warning: Reference `lemmaa itemc' on page 56 undefined on input line 8888 . ! Undefined control sequence. l.8889 $\rightrightarrows\,:=\{({\iden a},{\iden f}\,{\iden a})\}$ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.8889 $\rightrightarrows\,:=\{({\iden a},{\iden f}\,{\iden a})\}$ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.8889 ...arrows\,:=\{({\iden a},{\iden f}\,{\iden a})\}$ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. {\iden a}\ \rightrightarrows \^^M{\iden f}\,{\iden a}\ \superterm... l.8895 } \@. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...en a}\ \rightrightarrows \^^M{\iden f}\,{\iden a}\ \superterm ... l.8895 } \@. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...htrightarrows \^^M{\iden f}\,{\iden a}\ \superterm \ {\iden a} l.8895 } \@. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ... f}\,{\iden a}\ \superterm \ {\iden a} l.8895 } \@. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.8897 If one changes $\sigarity({\iden f})$ to be The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \sigarity ({\iden f})=A\aritysugar A l.8898 ...ath{\sigarity({\iden f})=A\aritysugar A} , The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `lemmaa itema' on page 56 undefined on input line 8902 . ! Undefined control sequence. l.8904 \simplemath {p\in\OCC{t}}; The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.8904 \simplemath{p\in \OCC{t}}; I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Undefined control sequence. l.8904 \simplemath{p\in\OCC {t}}; The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Extra }, or forgotten $. l.8904 \simplemath{p\in\OCC{t}} ; I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Undefined control sequence. l.8905 \simplemath {p\not=\emptyset} with The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! You can't use `\spacefactor' in math mode. \@->\spacefactor \@m l.8906 \bigmath{t'=t/p}\@ . Sorry, but I'm not programmed to handle this case; I'll just pretend that you didn't ask for it. If you're in the wrong mode, you might be able to return to the right one by typing `I}' or `I$' or `I\par'. Missing character: There is no è in font cmex10! ! Missing $ inserted. $ l.8907 ...nd \Vmonotonicity\ of $\rightrightarrows $ we get I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX Warning: Reference `lemmaa itemb' on page 56 undefined on input line 8910 . LaTeX Warning: Reference `lemmaa itema' on page 56 undefined on input line 8913 . ! Missing } inserted. } l.8919 \end{proof} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. LaTeX Warning: Reference `lemmab' on page 56 undefined on input line 8923. ! Undefined control sequence. ...ightarrows \cup \superterm )^{\oast }\,\circ \hookrightarrow )... l.8948 } \@. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. t_{k_{i}} (\rightrightarrows ^{\oast }\circ \superterm ^{\oast }... l.8956 } , The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...s ^{\oast }\circ \superterm ^{\oast }\ \circ \hookrightarrow )... l.8956 } , The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Citation `bd' on page 56 undefined on input line 8973. LaTeX Warning: Citation `bd' on page 56 undefined on input line 8976. LaTeX Warning: Reference `lemma about termination' on page 56 undefined on inpu t line 8986. LaTeX Warning: Reference `lemma monotonic wrt ordinals' on page 56 undefined on input line 8989. LaTeX Warning: Reference `lemma about ground reduction' on page 56 undefined on input line 8992. LaTeX Warning: Reference `lemma variable extension' on page 56 undefined on inp ut line 8994. LaTeX Warning: Reference `lemmaa' on page 56 undefined on input line 8997. LaTeX Warning: Reference `lemmab' on page 56 undefined on input line 8997. [56] LaTeX Warning: Reference `theoremconfluence' on page 57 undefined on input line 9011. LaTeX Font Warning: Command \em invalid in math mode on input line 9012. ! LaTeX Error: Command \itshape invalid in math mode. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.9012 ...{$({\em 1\/})\Rightarrow({\em 2\/})$:}}} Please use the math alphabet \mathit instead of the \itshape command. LaTeX Font Warning: Command \em invalid in math mode on input line 9012. ! LaTeX Error: Command \itshape invalid in math mode. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.9012 ...{$({\em 1\/})\Rightarrow({\em 2\/})$:}}} Please use the math alphabet \mathit instead of the \itshape command. LaTeX Warning: Reference `lemma necessary' on page 57 undefined on input line 9 013. LaTeX Font Warning: Command \em invalid in math mode on input line 9015. ! LaTeX Error: Command \itshape invalid in math mode. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.9015 ...d{$({\em 1\/})\Rightarrow({\em 2\/})$}}} Please use the math alphabet \mathit instead of the \itshape command. LaTeX Font Warning: Command \em invalid in math mode on input line 9015. ! LaTeX Error: Command \itshape invalid in math mode. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.9015 ...d{$({\em 1\/})\Rightarrow({\em 2\/})$}}} Please use the math alphabet \mathit instead of the \itshape command. LaTeX Font Warning: Command \em invalid in math mode on input line 9020. ! LaTeX Error: Command \itshape invalid in math mode. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.9020 ...{$({\em 2\/})\Rightarrow({\em 1\/})$:}}} Please use the math alphabet \mathit instead of the \itshape command. LaTeX Font Warning: Command \em invalid in math mode on input line 9020. ! LaTeX Error: Command \itshape invalid in math mode. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.9020 ...{$({\em 2\/})\Rightarrow({\em 1\/})$:}}} Please use the math alphabet \mathit instead of the \itshape command. LaTeX Warning: Reference `lemma about termination' on page 57 undefined on inpu t line 9033. ! Undefined control sequence. p,q\in \OCC {s} l.9036 \bigmath{p,q\in\OCC{s}} ; The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `lemma about sortkeeping' on page 57 undefined on inpu t line 9061. ! Undefined control sequence. \simplemath l.9065 \simplemath { The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.9066 \left \{\begin{array}{ll} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.9070 } and get I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! You can't use `\spacefactor' in math mode. \@->\spacefactor \@m l.9073 \bigmath{y\in\V}\@ . Sorry, but I'm not programmed to handle this case; I'll just pretend that you didn't ask for it. If you're in the wrong mode, you might be able to return to the right one by typing `I}' or `I$' or `I\par'. LaTeX Warning: Reference `corollary monotonic' on page 57 undefined on input li ne 9074. ! You can't use `\spacefactor' in math mode. \@->\spacefactor \@m l.9086 ...t_{1}=r_{1}\mu_{1}\refltrans r_{1}\nu}\@ . Sorry, but I'm not programmed to handle this case; I'll just pretend that you didn't ask for it. If you're in the wrong mode, you might be able to return to the right one by typing `I}' or `I$' or `I\par'. Missing character: There is no è in font cmex10! Missing character: There is no è in font cmex10! ! Missing $ inserted. $ l.9091 \underline{Claim:} $C_ {1}\nu$ is fulfilled. I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX Warning: Reference `lemma about groundconskeeping' on page 57 undefined o n input line 9120. LaTeX Warning: Reference `lemma about termination' on page 57 undefined on inpu t line 9121. ! Undefined control sequence. p\in \OCC {l_{1}};\ l_{1}/p\not \in \V l.9153 ...h{p\in\OCC{l_{1}};\ l_{1}/p\not\in\V}:}} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \sigma \tau \restrictedto \Y =\varrho \restrictedto \Y l.9192 } \@.\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...trictedto \Y =\varrho \restrictedto \Y l.9192 } \@.\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Font Warning: Command \em invalid in math mode on input line 9224. ! LaTeX Error: Command \itshape invalid in math mode. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.9224 ...; $({\em 2\/})\Rightarrow({\em 1\/})$}}} Please use the math alphabet \mathit instead of the \itshape command. LaTeX Font Warning: Command \em invalid in math mode on input line 9224. ! LaTeX Error: Command \itshape invalid in math mode. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.9224 ...; $({\em 2\/})\Rightarrow({\em 1\/})$}}} Please use the math alphabet \mathit instead of the \itshape command. ! Missing } inserted. } l.9226 \end{proof} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. LaTeX Warning: Reference `theorem joinable due to small variables' on page 57 u ndefined on input line 9232. LaTeX Warning: Reference `lemma about termination' on page 57 undefined on inpu t line 9233. LaTeX Warning: Reference `theoremconfluence' on page 57 undefined on input line 9235. Underfull \vbox (badness 10000) has occurred while \output is active [] [57] LaTeX Warning: Reference `lemma about semi-decidable reducibility' on page 58 u ndefined on input line 9588. LaTeX Warning: Reference `lemma about termination' on page 58 undefined on inpu t line 9592. ! Undefined control sequence. l.9596 of positions $p\in\OCC {s}$ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `lemma about groundconskeeping' on page 58 undefined o n input line 9621. ! Undefined control sequence. l.9623 and \R\ and \OCC {s} being finite, there can be only a finite number o... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `lemma still not co-semi' on page 58 undefined on inpu t line 9641. LaTeX Warning: Reference `lemma not co-semi' on page 58 undefined on input line 9643. LaTeX Warning: Reference `lemma not co-semi' on page 58 undefined on input line 9671. LaTeX Warning: Reference `lemma about decidable reducibility' on page 58 undefi ned on input line 9724. LaTeX Warning: Reference `lemma about semi-decidable reducibility' on page 58 u ndefined on input line 9726. LaTeX Warning: Reference `theoremconfluence' on page 58 undefined on input line 9727. Underfull \vbox (badness 1184) has occurred while \output is active [] [58] LaTeX Warning: Reference `lemma confluence not semi-decidable' on page 59 undef ined on input line 9733. LaTeX Warning: Reference `lemma still not co-semi' on page 59 undefined on inpu t line 9735. LaTeX Font Info: Try loading font information for OMS+cmr on input line 9762 . (/Users/cp/svn/hilbertbernays/trunk/omscmr.fd File: omscmr.fd 1999/05/25 v2.5h Standard LaTeX font definitions ) LaTeX Font Info: Font shape `OMS/cmr/m/n' in size <12> not available (Font) Font shape `OMS/cmsy/m/n' tried instead on input line 9762. LaTeX Warning: Reference `lemma not co-semi' on page 59 undefined on input line 9784. LaTeX Warning: Reference `lemma inductive validity A and B' on page 59 undefine d on input line 9889. ! Undefined control sequence. l.9896 Let \simplemath {\balgebra\in\rm M} and The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.9896 Let \simplemath{\balgebra\in \rm M} and I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.9896 Let \simplemath{\balgebra\in\rm M} and I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Undefined control sequence. l.9897 \simplemath {\mu\in\SUBST{\V}{\balgebra}}. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.9900 there must be some atom \simplemath {(u\boldequal v)} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.9901 or some atom \simplemath {(\DEF u)} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.9902 in \simplemath {\Delta} which is true \wrt\ \simplemath{\algebra_{\kap... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.9902 ...{\Delta} which is true \wrt\ \simplemath {\algebra_{\kappa}}. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.9909 for some \simplemath {s\in\sigsorts}. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.9911 \simplemath {\balgebra_{\mu}(u)} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.9913 \simplemath {\balgebra_{\kappa h}(u)} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.9915 \simplemath {h(\algebra_{\kappa}(u))\ } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.9917 \simplemath {\balgebra_{\mu}(u)} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.9919 \simplemath {h(\algebra_{\kappa}(v))} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.9921 \simplemath {\balgebra_{\mu}(v)\ } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.9924 \end{proof} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. Underfull \hbox (badness 4492) in paragraph at lines 9889--9924 []$ \T1/cmr/m/n/12 If no rule in R has a nega-tive con-di-tion, then there is s ome [] Underfull \hbox (badness 5064) in paragraph at lines 9889--9924 \OMS/cmsy/m/n/12 A$ \T1/cmr/m/n/12 being free in M over $\OT1/cmr/m/n/12 V$ \T1 /cmr/m/n/12 w.r.t. some $\OML/cmm/m/it/12 ^^T$\T1/cmr/m/n/12 . Then $\OMS/cmsy/ m/n/12 A$ \T1/cmr/m/n/12 is in K. Let $\OMS/cmsy/m/n/12 B$$2 [] Overfull \hbox (844.4705pt too wide) in paragraph at lines 9889--9924 \OT1/cmr/m/n/12 inductivelyvalidbyassumption\OML/cmm/m/it/12 ; \OT1/cmr/m/n/12 theremustbesomeatom[]orsomeatom[]in\OML/cmm/m/it/12 ^^A\OT1/cmr/m/n/12 whichist ruew\OML/cmm/m/it/12 :\OT1/cmr/m/n/12 r\OML/cmm/m/it/12 :\OT1/cmr/m/n/12 t\OML/ cmm/m/it/12 : []:\OT1/cmr/m/n/12 Thenwehave [] or [] forsome[]\OML/cmm/m/it/12 :\OT1/cmr/m/n/12 Thenwehave[][] [][] []andthen[][] [][] []or [] \OML/cmm/m/it/1 2 :$ [] ! Missing } inserted. } l.9924 \end{proof} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. LaTeX Warning: Reference `lemma inductive validity B and C' on page 59 undefine d on input line 9927. ! Undefined control sequence. l.9931 Let \simplemath {\chi\tightin\SUBST{\V}{\algebra}}. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.9931 Let \simplemath{\chi \tightin\SUBST{\V}{\algebra}}. I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.9931 ...lemath{\chi\tightin\SUBST{\V}{\algebra}} . I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Undefined control sequence. l.9932 ...xiom of Choice there is some \simplemath {\tau\tightin\Isubst} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.9933 with \simplemath {\chi=\tau\algebra_{\chi}}. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.9935 For \simplemath {A\in\atoms}: The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.9937 \uiff\ $A\tau $ is true \wrt\ \bigmath{\algebra_{\chi}}. I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX Warning: Reference `substitutionlemma' on page 59 undefined on input line 9939. ! Undefined control sequence. l.9941 \simplemath {u\in\vt}: The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.9941 \simplemath{u\in \vt}: I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.9941 \simplemath{u\in\vt} : I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Missing $ inserted. $ l.9946 } \Qed{Claim}\\ I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Undefined control sequence. l.9947 Now, if each atom \simplemath {A} in \simplemath{\Gamma} is true \wrt\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.9947 ... each atom \simplemath{A} in \simplemath {\Gamma} is true \wrt\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.9947 ...tom \simplemath{A} in \simplemath{\Gamma } is true \wrt\ I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.9947 ...om \simplemath{A} in \simplemath{\Gamma} is true \wrt\ I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Undefined control sequence. l.9951 \simplemath {A\tau} is true \wrt\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.9955 \simplemath {A} in \simplemath{\Delta} for which \simplemath{A\tau} is The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.9955 \simplemath{A} in \simplemath {\Delta} for which \simplemath{A\tau} is The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.9955 ...simplemath{\Delta} for which \simplemath {A\tau} is The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.9959 \simplemath {A} is The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! You can't use `\spacefactor' in math mode. \@->\spacefactor \@m l.9962 ...\ be a constructor-minimal model of \R\@ . Sorry, but I'm not programmed to handle this case; I'll just pretend that you didn't ask for it. If you're in the wrong mode, you might be able to return to the right one by typing `I}' or `I$' or `I\par'. ! Undefined control sequence. l.9965 (\simplemath {f\tightin\sigfunsym}); The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.9967 (\simplemath {s\tightin\sigsorts}); The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.9969 (\simplemath {s\tightin\sigsorts}). The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.9971 For \simplemath {\chi\in\SUBST{\V}{\balgebra}}; The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.9972 \simplemath {(u\boldequal v)\in\atoms}: The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \simplemath {(u\boldequal v)} is true \wrt \ \bigmath {\balgebra... l.9977 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...bra _{\chi }} \uiff \^^M\simplemath {(u\boldequal v)} is true ... l.9977 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.9979 For \simplemath {\chi\in\SUBST{\V}{\balgebra}}; The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.9980 \simplemath {(\DEF u)\in\atoms}: The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. If \simplemath {(\DEF u)} is true \wrt \ \bigmath {\balgebra _{\... l.9987 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...algebra _{\chi }}, then \simplemath {(\DEF u)} is true \wrt \ ... l.9987 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.9992 Let \simplemath {\tau\in\Isubst} and The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.9994 Now, suppose that for each atom \simplemath {A} in \simplemath{\Gamma}: The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.9994 ... each atom \simplemath{A} in \simplemath {\Gamma}: The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.9995 \simplemath {A\tau} is true \wrt\ \bigmath{\algebra_{\chi}}. Two cases: The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.9998 by Claim~1 we know that \simplemath {A\tau} is true \wrt\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `substitutionlemma' on page 59 undefined on input line 10000. ! Undefined control sequence. l.10001 \simplemath {A} is true \wrt\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10006 \simplemath {A} is true \wrt\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10009 there must be some atom \simplemath {A} in \simplemath{\Delta} which The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10009 ...some atom \simplemath{A} in \simplemath {\Delta} which The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `substitutionlemma' on page 59 undefined on input line 10012. ! Undefined control sequence. l.10012 ...ma(\ref{substitutionlemma}) \simplemath {A\tau} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10014 ... or by Claim~2 we know that \simplemath {A\tau} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.10016 \end{proof} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. Missing character: There is no è in font cmex10! Overfull \hbox (82.13336pt too wide) in paragraph at lines 9927--10016 \T1/cmr/m/n/12 Now, if each atom A in $\OML/cmm/m/it/12 ^^@istruew:r:t: [] ; t hen\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 byClaim\OT1/cmr/m/n/12 )[]\OML/cmm/m/it/12 istruew:r:t: [] ; too:Thus\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 since[] istype \O MS/cmsy/m/n/12 ^^@ [] Overfull \hbox (216.90361pt too wide) in paragraph at lines 9927--10016 \OML/cmm/m/it/12 B \OMS/cmsy/m/n/12 ^^@ \OML/cmm/m/it/12 inductivelyvalidbyassu mption\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 ; theremustbesomeatomAin^^Aforwhich[]is truew:r:t: [] :Then\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 byClaim\OT1/cmr/m/n/12 )\ OML/cmm/m/it/12 Aistruew:r:t: [] ; too:[] [] Underfull \hbox (badness 10000) in paragraph at lines 9927--10016 []\OML/cmm/m/it/12 Let\OMS/cmsy/m/n/12 A \OML/cmm/m/it/12 beaconstructor \OMS/c msy/m/n/12 ^^@ \OML/cmm/m/it/12 minimalmodelof\OT1/cmr/m/n/12 R\OML/cmm/m/it/12 :Definethe[]=[] \OMS/cmsy/m/n/12 ^^@ [] Underfull \hbox (badness 10000) in paragraph at lines 9927--10016 \OML/cmm/m/it/12 Bythesetwotrivialclaimsand [] \OT1/cmr/m/n/12 ; \OMS/cmsy/m/n/ 12 B \OML/cmm/m/it/12 isaconstructor \OMS/cmsy/m/n/12 ^^@ [] Underfull \hbox (badness 10000) in paragraph at lines 9927--10016 \OML/cmm/m/it/12 minimalmodelof\OT1/cmr/m/n/12 R\OML/cmm/m/it/12 ; which; ofcou rse; is\OMS/cmsy/m/n/12 C[][] ^^@ \OML/cmm/m/it/12 term \OMS/cmsy/m/n/12 ^^@ \O ML/cmm/m/it/12 gene\T1/cmr/m/n/12 - [] Overfull \hbox (93.10513pt too wide) in paragraph at lines 9927--10016 \OML/cmm/m/it/12 rated:Let[]and [] :Now; supposethatforeachatomAin^^@ \OT1/cmr/ m/n/12 : [] Overfull \hbox (123.78497pt too wide) in paragraph at lines 9927--10016 []\OML/cmm/m/it/12 istruew:r:t: [] :Twocases \OT1/cmr/m/n/12 : \OML/cmm/m/it/1 2 For [] ; byClaim []\OT1/cmr/m/n/12 1\OML/cmm/m/it/12 weknowthat[]istruew:r:t: [] ; andbytheSubstitution \OMS/cmsy/m/n/12 ^^@ [] Overfull \hbox (82.68416pt too wide) in paragraph at lines 9927--10016 \OML/cmm/m/it/12 inductivelyvalidbyassumption\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 ; theremustbesomeatomAin^^Awhichistruew:r:t: [] :BytheSubstitution \OMS/cmsy/m /n/12 ^^@ [] Underfull \vbox (badness 1137) has occurred while \output is active [] [59] ! Missing } inserted. } l.10016 \end{proof} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.10016 \end{proof} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.10016 \end{proof} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. LaTeX Warning: Reference `lemma inductive validity C and D' on page 60 undefine d on input line 10020. LaTeX Warning: Reference `newtheoremmodel' on page 60 undefined on input line 1 0028. LaTeX Warning: Reference `item funda c' on page 60 undefined on input line 1002 8. ! Undefined control sequence. l.10034 Let \simplemath {\mu\in\SUBST{\V}{\balgebra}}. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.10034 Let \simplemath{\mu \in\SUBST{\V}{\balgebra}}. I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.10034 ...simplemath{\mu\in\SUBST{\V}{\balgebra}} . I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. LaTeX Warning: Reference `newtheoremmodel' on page 60 undefined on input line 1 0039. ! Undefined control sequence. \mu \restrictedto {\Vsig }=\kappa h l.10041 \bigmath{\mu\restrictedto{\Vsig}=\kappa h} . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10043 there is some \simplemath {\tau\in\SUBST{\Vcons}{\gt}} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \mu \restrictedto {\Vcons }=\tau \balgebra =\tau \algebra \,h l.10044 ...{\Vcons}=\tau\balgebra=\tau\algebra\,h} . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10045 Define \simplemath {\chi\in\SUBST{\V}{\algebra}} by The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.10048 Now assume each atom $A$ in $\Gamma $ to be true \wrt\ I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Undefined control sequence. l.10049 \simplemath {\balgebra_{\mu}}. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.10049 \simplemath{\balgebra_ {\mu}}. I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.10049 \simplemath{\balgebra_{\mu}} . I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Undefined control sequence. l.10058 \simplemath {s\in\sigsorts}; The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10059 \simplemath {\hat{u},\hat{v}\in\gtconsindex{s}} with The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `newtheoremmodel' on page 60 undefined on input line 1 0087. LaTeX Warning: Reference `item funda c' on page 60 undefined on input line 1008 7. ! Undefined control sequence. l.10089 Hence (since \simplemath {\hat{u},\hat{v}\in\tgcons}) The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `lemma about ground reduction' on page 60 undefined on input line 10092. ! Missing $ inserted. $ l.10102 All in all, all atoms in $\Gamma $ are true \wrt\ to \bigmath{\algebr... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. Overfull \hbox (627.59761pt too wide) in paragraph at lines 10020--10118 \OML/cmm/m/it/12 morphism [] with [] :Furthermore; bytheAxiomofChoicethereisso me[]with [] :Define[]by [] :Wehave [] :Nowassumeeachatom$\T1/cmr/m/n/12 A$\OML/ cmm/m/it/12 in$$^^@$ [] Overfull \hbox (136.4367pt too wide) in paragraph at lines 10020--10118 \OML/cmm/m/it/12 inductivelyvalidbyassumption\OT1/cmr/m/n/12 )$\T1/cmr/m/n/12 A $\OML/cmm/m/it/12 istruew:r:t: [] :If [] ; then\OT1/cmr/m/n/12 (\OML/cmm/m/it/ 12 since\OT1/cmr/m/n/12 \ [] []\OML/cmm/m/it/12 and\OT1/cmr/m/n/12 \ [] []\OML/ cmm/m/it/12 aretype \OMS/cmsy/m/n/12 ^^@ [] Overfull \hbox (1159.27467pt too wide) in paragraph at lines 10020--10118 \OML/cmm/m/it/12 D \OMS/cmsy/m/n/12 ^^@ \OML/cmm/m/it/12 inductivelyvalidbyassu mption\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 therearesome[]\OT1/cmr/m/n/12 ; []\OML/ cmm/m/it/12 with [] and [] :Thenweget [] [] [] [] [] [] [] [] [] [] [] [] [] [] [] [] [] [] [] :Byconfluenceof [] andTheorem [][]\OT1/cmr/m/n/12 ([]) \OML/cmm/m/it/12 ; \OMS/cmsy/m/n/12 I \OML/cmm/m/it/12 andthereforealso\OMS/cms y/m/n/12 B \OML/cmm/m/it/12 isaconstructor \OMS/cmsy/m/n/12 ^^@ [] Overfull \hbox (541.04099pt too wide) in paragraph at lines 10020--10118 \OML/cmm/m/it/12 minim[]model:Hence\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 since[]\OT 1/cmr/m/n/12 ) [] ; \OML/cmm/m/it/12 i:e: [] :ByLemma [][]weget [] ; andthen [ ] [] [] [] [] [] [] :Thus$\T1/cmr/m/n/12 A$\OML/cmm/m/it/12 istruew:r:t: [] :Allinall; allatomsin$$^^@$ [] ! Missing } inserted. } l.10118 \end{proof} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.10118 \end{proof} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. LaTeX Warning: Reference `lemma inductive validity D' on page 60 undefined on i nput line 10122. ! Undefined control sequence. l.10123 Let \simplemath {\algebra\!:=\!\tVsig/\congrusubVsig}. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.10123 Let \simplemath{\algebra\! :=\!\tVsig/\congrusubVsig}. I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.10123 ...th{\algebra\!:=\!\tVsig/\congrusubVsig} . I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Undefined control sequence. l.10124 Let \simplemath {\kappa\!\tightin\!\SUBST{\Vsig}{\algebra}} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10126 \simplemath {x\!\mapsto\congrusubVsig\![\{x\}]}\@. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! You can't use `\spacefactor' in math mode. \@->\spacefactor \@m l.10126 ...th{x\!\mapsto\congrusubVsig\![\{x\}]}\@ . Sorry, but I'm not programmed to handle this case; I'll just pretend that you didn't ask for it. If you're in the wrong mode, you might be able to return to the right one by typing `I}' or `I$' or `I\par'. ! Undefined control sequence. l.10128 For \simplemath {\tau\in\Vsigsubst}; \simplemath{A\in\atoms}: The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10128 ...plemath{\tau\in\Vsigsubst}; \simplemath {A\in\atoms}: The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \simplemath {A} is true \wrt \^^M\bigmath {\algebra _{\tau \alge... l.10134 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ... _{\kappa }}} \uiff \^^M\simplemath {A\tau } is true \wrt \ \b... l.10134 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `substitutionlemma' on page 60 undefined on input line 10136. ! Undefined control sequence. (1)\simplemath {\implies }(2): l.10137 \\\underline{(1)\simplemath{\implies}(2):} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10138 Let \simplemath {\tau\in\Vsigsubst} and suppose that for each The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10139 \simplemath {(u\boldequal v)} in \simplemath{\Gamma} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10139 ...plemath{(u\boldequal v)} in \simplemath {\Gamma} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10141 \simplemath {(\DEF u)} in \simplemath{\Gamma} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10141 \simplemath{(\DEF u)} in \simplemath {\Gamma} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10142 we have some \simplemath {\hat{u}\in\tgcons} with The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10144 Then for each atom \simplemath {A} in \simplemath{\Gamma} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10144 ...each atom \simplemath{A} in \simplemath {\Gamma} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10145 we know that \simplemath {A\tau} is true \wrt\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10147 that \simplemath {A} is true \wrt\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10150 there is some \simplemath {A} in \simplemath{\Delta} which is true The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10150 ...e is some \simplemath{A} in \simplemath {\Delta} which is true The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10152 By Claim \simplemath {A\tau} is true \wrt\ \bigmath{\algebra_{\kappa}}. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10156 \simplemath {s\in\sigsorts} and some The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10157 \simplemath {\hat{u}\in\gtconsindex{s}=\tVsig\CONSsort{s}} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. (2)\simplemath {\implies }(1): l.10159 \\\underline{(2)\simplemath{\implies}(1):} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10160 Let \simplemath {\chi\in\SUBST{\V}{\algebra}}. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10161 Now suppose that each atom \simplemath {A} in \simplemath{\Gamma} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10161 ...each atom \simplemath{A} in \simplemath {\Gamma} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10163 ...iom of Choice there is some \simplemath {\tau\in\Vsigsubst} with The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10165 By Claim \simplemath {A\tau} is true \wrt\ \bigmath{\algebra_{\kappa}}. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10167 there is some \simplemath {A} in \simplemath{\Delta} such that The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10167 ...e is some \simplemath{A} in \simplemath {\Delta} such that The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10168 \simplemath {A\tau} is true The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10170 By Claim, \simplemath {A} is true \wrt\ \bigmath{\algebra_{\chi}}. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.10172 \end{proof} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. Missing character: There is no è in font cmex10! Overfull \hbox (1008.4199pt too wide) in paragraph at lines 10122--10172 []\OML/cmm/m/it/12 Let[]andsupposethatforeach[]in^^@wehave [] andforeach[]in^^@ wehavesome[]with [] :ThenforeachatomAin^^@weknowthat[]istruew:r:t: [] ; andthe n\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 byClaim\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 tha tAistruew:r:t: [] :Thus\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 since[] istype \OMS/c msy/m/n/12 ^^@ [] Overfull \hbox (151.09036pt too wide) in paragraph at lines 10122--10172 \OML/cmm/m/it/12 D \OMS/cmsy/m/n/12 ^^@ \OML/cmm/m/it/12 inductivelyvalidbyassu mption\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 ; thereissomeAin^^Awhichistruew:r:t: [ ] :ByClaim[]istruew:r:t: [] :Twocases \OT1/cmr/m/n/12 : [] Overfull \hbox (186.26501pt too wide) in paragraph at lines 10122--10172 \OML/cmm/m/it/12 For [] ; weget [] :For [] ; wegetsome[]andsome[]with [] :[] [] Overfull \hbox (1033.02893pt too wide) in paragraph at lines 10122--10172 []\OML/cmm/m/it/12 Let[]:NowsupposethateachatomAin^^@istruew:r:t: [] :BytheAxi omofChoicethereissome[]with [] :ByClaim[]istruew:r:t: [] :Thus\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 since\OT1/cmr/m/n/12 (2)\OML/cmm/m/it/12 holdsbyassumption\OT 1/cmr/m/n/12 )\OML/cmm/m/it/12 ; thereissomeAin^^Asuchthat[]istruew:r:t: [] :B yClaim; Aistruew:r:t: [] :$ [] ! Missing } inserted. } l.10172 \end{proof} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. Underfull \vbox (badness 10000) has occurred while \output is active [] [60] LaTeX Warning: Reference `theorem monotony2' on page 61 undefined on input line 10176. ! Undefined control sequence. ...gebra :=\algebraprime \restrictedto {\sigfunsym \uplus \sigsor... l.10180 } . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10181 Now an ``old'' formula \simplemath {\gd\in\formulas} is valid in \alg... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.10181 Now an ``old'' formula \simplemath{\gd\in \formulas} is valid in \alg... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Undefined control sequence. l.10181 ...d'' formula \simplemath{\gd\in\formulas } is valid in \algebra\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Extra }, or forgotten $. l.10181 ...'' formula \simplemath{\gd\in\formulas} is valid in \algebra\ I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! You can't use `\spacefactor' in math mode. \@->\spacefactor \@m l.10204 \algebra\ is a \Model\ of \R\@ . Sorry, but I'm not programmed to handle this case; I'll just pretend that you didn't ask for it. If you're in the wrong mode, you might be able to return to the right one by typing `I}' or `I$' or `I\par'. Missing character: There is no è in font cmex10! LaTeX Warning: Reference `newtheoremmodel' on page 61 undefined on input line 1 0212. LaTeX Warning: Reference `item funda c' on page 61 undefined on input line 1021 2. ! Undefined control sequence. ...hcolon {\algebraprime \restrictedto {\consfunsym '\uplus (\{\C... l.10223 } . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...ex {\R ',\emptyset }) \restrictedto {\consfunsym '\uplus (\{\C... l.10223 } . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. {h}\morphcolon {\algebra \restrictedto {\consfunsym \uplus (\{\CO... l.10229 ...tyset}\cap(\tgcons\tighttimes\tgcons))} . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `theorem monotony1' on page 61 undefined on input line 10235. LaTeX Warning: Reference `lemma about conflu' on page 61 undefined on input lin e 10235. ! Undefined control sequence. l.10254 by induction on \simplemath {\beta}; The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `Homomorphism-Theorem' on page 61 undefined on input l ine 10263. LaTeX Warning: Reference `lemma inductive validity D' on page 61 undefined on i nput line 10273. ! Undefined control sequence. l.10274 Let \simplemath {\tau'\in\SUBST{\V'}{\tVsigprime}} and suppose the pr... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `lemma inductive validity D' on page 61 undefined on i nput line 10275. ! Undefined control sequence. l.10276 \simplemath {\tau'}. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10277 There is a \simplemath {\tau\in\Isubstprime} and a The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10278 \simplemath {\sigma\in\SUBST{\Vsigprime}{\tVsigprime}} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \tau \restrictedto {\V }\in \Vsigsubst l.10280 ...ath{\tau\restrictedto{\V}\in\Vsigsubst} . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10281 For each atom \simplemath {(u\boldequal v)} in \simplemath{\Gamma} we The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10281 ...plemath{(u\boldequal v)} in \simplemath {\Gamma} we The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10284 \simplemath {\hat{u},\hat{v}\in\tgcons} with The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `theorem monotony1' on page 61 undefined on input line 10288. LaTeX Warning: Reference `corollary stable' on page 61 undefined on input line 10292. ! Undefined control sequence. l.10295 \simplemath {\ \hat{u}} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10297 \simplemath {u\tau\sigma} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10299 \simplemath {v\tau\sigma} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10301 \simplemath {\hat{v}\ }. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `lemma about ground reduction' on page 61 undefined on input line 10302. LaTeX Warning: Reference `theorem monotony1' on page 61 undefined on input line 10310. LaTeX Warning: Reference `lemma about ground reduction' on page 61 undefined on input line 10312. ! Undefined control sequence. l.10314 Furthermore, for each atom \simplemath {(\DEF u)} in \simplemath{\Gam... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10314 ...om \simplemath{(\DEF u)} in \simplemath {\Gamma} we The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10317 Thus there is a \simplemath {\hat{u}\in\tgcons} with The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10321 there is a literal \simplemath {(u\boldequal v)} in \simplemath{\Delt... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10321 ...plemath{(u\boldequal v)} in \simplemath {\Delta} with The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10322 ...subVsig v\tau} or a literal \simplemath {(\DEF u)} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10323 in \simplemath {\Delta} with \bigmath{u\tau\congrusubVsig\hat{u}} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10324 for some \simplemath {\hat{u}\in\tgcons}. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Reference `theorem monotony1' on page 61 undefined on input line 10325. LaTeX Warning: Reference `corollary stable' on page 61 undefined on input line 10329. ! Missing $ inserted. $ l.10333 \end{proof} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. Underfull \hbox (badness 10000) in paragraph at lines 10176--10333 \T1/cmr/m/n/12 Let $\OMS/cmsy/m/n/12 A[]$ \T1/cmr/m/n/12 be a []-algebra. Defin e the sig/cons-algebra $\OMS/cmsy/m/n/12 A$ [] Underfull \hbox (badness 10000) in paragraph at lines 10176--10333 \T1/cmr/m/n/12 by: $\OMS/cmsy/m/n/12 A \OT1/cmr/m/n/12 := [][]$ \T1/cmr/m/n/12 . Now an ``old'' formula $\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 ^^@; ^^A\OT1/cmr/m /n/12 )$$\OMS/cmsy/m/n/12 2 [] Overfull \hbox (749.52803pt too wide) in paragraph at lines 10176--10333 \OML/cmm/m/it/12 isvalidin\OMS/cmsy/m/n/12 A \OML/cmm/m/it/12 iff itisvalidin []:Furthermore; itsinductiveinstances [] donotdifferfor [] and [] since [] :Thu sforproving\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 A\OT1/cmr/m/n/12 )[\OML/cmm/m/it/1 2 and\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 B\OT1/cmr/m/n/12 )]\OML/cmm/m/it/12 ; it sufficestoshowthefol: \OT1/cmr/m/n/12 : [] Underfull \hbox (badness 10000) in paragraph at lines 10176--10333 \OML/cmm/m/it/12 ThisClaimisalsosufficientfor\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 C\OT1/cmr/m/n/12 ); \OML/cmm/m/it/12 becauseif[] is\OMS/cmsy/m/n/12 C[][] ^^@ \ OML/cmm/m/it/12 term \OMS/cmsy/m/n/12 ^^@ \OML/cmm/m/it/12 gene\T1/cmr/m/n/12 - [] Overfull \hbox (213.23256pt too wide) in paragraph at lines 10176--10333 []\OML/cmm/m/it/12 Aseachrulefrom\OT1/cmr/m/n/12 R \OML/cmm/m/it/12 canbetransl atedintoan\OT1/cmr/m/n/12 \\OML/cmm/m/it/12 old[]formula\OT1/cmr/m/n/12 (\OML/c mm/m/it/12 onwhich\OMS/cmsy/m/n/12 A \OML/cmm/m/it/12 and[] donotdiffer\OT1/cmr /m/n/12 (\OML/cmm/m/it/12 cf: above\OT1/cmr/m/n/12 ))\OML/cmm/m/it/12 ; \OMS/cm sy/m/n/12 A \OML/cmm/m/it/12 isa[]=[] \OMS/cmsy/m/n/12 ^^@ [] Overfull \hbox (566.15276pt too wide) in paragraph at lines 10176--10333 \OML/cmm/m/it/12 model of\OT1/cmr/m/n/12 R\OML/cmm/m/it/12 :Let$$[]$\T1/cmr/m/n /12 '$\OML/cmm/m/it/12 denotethegroundtermalgebraover$\T1/cmr/m/n/12 sig'/cons' $\OML/cmm/m/it/12 and[] denotethegroundtermalgebraover[]:Byconfluenceof [] andT heorem [][]\OT1/cmr/m/n/12 ([])\OML/cmm/m/it/12 ; [] isaconstructor \OMS/cmsy/ m/n/12 ^^@ [] Underfull \hbox (badness 10000) in paragraph at lines 10176--10333 \OML/cmm/m/it/12 minimummodelof[] w:r:t: $\T1/cmr/m/n/12 sig'/cons'$\OML/cmm/m/ it/12 :Thus; [] mustbeaconstructor \OMS/cmsy/m/n/12 ^^@ [] Overfull \hbox (673.97807pt too wide) in paragraph at lines 10176--10333 \OML/cmm/m/it/12 minim[]modelof[] w:r:t: $\T1/cmr/m/n/12 sig'/cons'$\OML/cmm/m/ it/12 ; too:Thereforetheremustbesome$\T1/cmr/m/n/12 cons'$\OMS/cmsy/m/n/12 ^^@\ OML/cmm/m/it/12 homomorphism [] :Bydefining [] \OT1/cmr/m/n/12 ( [] ; [] )\OML /cmm/m/it/12 ; wegeta[] \OMS/cmsy/m/n/12 ^^@ [] Overfull \hbox (1110.28143pt too wide) in paragraph at lines 10176--10333 \OML/cmm/m/it/12 homomorphism[]:Byconfluenceof [] andTheorem [][]\OT1/cmr/m/n/1 2 (1)\OML/cmm/m/it/12 andLemma [][]weget [] [] [] [] [] [] [] [] [] :Finall y; foreach[]=[] \OMS/cmsy/m/n/12 ^^@ [] Overfull \hbox (528.5998pt too wide) in paragraph at lines 10176--10333 \OML/cmm/m/it/12 model \OMS/cmsy/m/n/12 C \OML/cmm/m/it/12 of\OT1/cmr/m/n/12 R \OML/cmm/m/it/12 weget [] byinductionon^^L\OT1/cmr/m/n/12 ; \OML/cmm/m/it/12 th us [] \OT1/cmr/m/n/12 ; \OML/cmm/m/it/12 andthenbytheHomomorphism \OMS/cmsy/m/n /12 ^^@ [] Underfull \hbox (badness 10000) in paragraph at lines 10176--10333 []\OML/cmm/m/it/12 Wedotheprooffortheequivalentversionoftype \OMS/cmsy/m/n/12 ^ ^@ \OML/cmm/m/it/12 D \OMS/cmsy/m/n/12 ^^@ [] Overfull \hbox (4294.0485pt too wide) in paragraph at lines 10176--10333 \OML/cmm/m/it/12 inductivevaliditygivenbyLemma [][]\OT1/cmr/m/n/12 (2)\OML/cmm/ m/it/12 :Let[]andsupposethepremiseofLemma [][]\OT1/cmr/m/n/12 (2)\OML/cmm/m/it/ 12 toholdforthis[]:Thereisa[]anda[]suchthat [] :Notethat [] :Foreachatom[]in^^@ wehaveassumedthat\OT1/cmr/m/n/12 \ [] []\OML/cmm/m/it/12 and\OT1/cmr/m/n/12 \ [ ] []\OML/cmm/m/it/12 arevalidin [] :Thusthereare[]with [] and [] :ByTheorem [][ ]\OT1/cmr/m/n/12 (2)\OML/cmm/m/it/12 weget [] and [] ; andthenbyCorollary [][]a ndthesupposed [] get[][][] [][][] [][][] []:ByLemma [][]weget [] andthen\OT1/cm r/m/n/12 (\OML/cmm/m/it/12 byconfluenceof [] \OT1/cmr/m/n/12 ) [] \OML/cmm/m/it /12 ; andthenbyTheorem [][]\OT1/cmr/m/n/12 (1)\OML/cmm/m/it/12 weget [] andthen byLemma [][] [] :Furthermore; foreachatom[]in^^@wehaveassumedthat\OT1/cmr/m/n/1 2 \ [] []\OML/cmm/m/it/12 isvalidin [] :Thusthereisa[]with [] :Thus\OT1/cmr/m/n /12 (\OML/cmm/m/it/12 since[] istype \OMS/cmsy/m/n/12 ^^@ [] Overfull \hbox (889.65132pt too wide) in paragraph at lines 10176--10333 \OML/cmm/m/it/12 D \OMS/cmsy/m/n/12 ^^@ \OML/cmm/m/it/12 inductivelyvalidbyassu mption\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 ; thereisaliteral[]in^^Awith [] oralite ral[]in^^Awith [] forsome[]:ByTheorem [][]\OT1/cmr/m/n/12 (2)\OML/cmm/m/it/12 w eget [] or [] ; andthenbyCorollary [][] [] or [] :$ [] ! Missing } inserted. } l.10333 \end{proof} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. [61] ! Undefined control sequence. l.10348 \simplemath { The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.10349 \begin{array}{@{}llllll@{}} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Undefined control sequence. \mu \restrictedto {\V \setminus \{x\}}=\id \restrictedto {\V \set... l.10474 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ... \setminus \{x\}}=\id \restrictedto {\V \setminus \{x\}} l.10474 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...c]{ll} t(\xi \cup \id \restrictedto {\Vcons })&\mbox { if }y=x... l.10515 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.10538 \end{array} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! LaTeX Error: Environment lemma undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.10543 \begin{lemma} \label{lemma unification}\mbox{}\\ Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. l.10558 \singlemath {\mu\in\SUBST{\V}{\vt}} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.10558 \singlemath{\mu \in\SUBST{\V}{\vt}} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.10558 \singlemath{\mu\in\SUBST{\V}{\vt}} I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Undefined control sequence. l.10560 \simplemath {\repr{E}\mu\subseteq\id}. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.10561 If it terminates on $(E,\: \VARCONS{E,\X},\:\id)$ I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! LaTeX Error: \begin{sloppypar} on input line 10542 ended by \end{lemma}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.10568 \end{lemma} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing } inserted. } l.10568 \end{lemma} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. Underfull \hbox (badness 2941) in paragraph at lines 10543--10569 \T1/cmr/m/n/12 If it ter-mi-nates on $\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 E; []; ^^[\OT1/cmr/m/n/12 )$ \T1/cmr/m/n/12 with [], then there is no $\OML/cmm/m/it /12 ^^V \OMS/cmsy/m/n/12 2 [] [62] LaTeX Warning: Reference `lemma unification' on page 63 undefined on input line 10572. Underfull \hbox (badness 10000) in paragraph at lines 10572--10573 [] ! Undefined control sequence. x\mu =t(\xi \cup \id \restrictedto {\Vcons })=t\mu l.10654 ...(\xi\cup\id\restrictedto{\Vcons})=t\mu} using The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10675 $\sigma_n\restrictedto {\VAR{E_n}\cup(\Vcons\setminus \X_n)}\subseteq... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.10684 \simplemath {\pi_0\in\SUBST{\V}{\vt}}, The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.10684 \simplemath{\pi _0\in\SUBST{\V}{\vt}}, I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.10684 \simplemath{\pi_0\in\SUBST{\V}{\vt}} , I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Undefined control sequence. l.10686 \simplemath {\pi_n\in\SUBST{\V}{\vt}} with The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \pi _0\restrictedto {\X _0\cup \Vsig }=\sigma _n\restrictedto {\X... l.10687 ...gma_n\restrictedto{\X_0\cup\Vsig}\pi_n} . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...\cup \Vsig }=\sigma _n\restrictedto {\X _0\cup \Vsig }\pi _n l.10687 ...gma_n\restrictedto{\X_0\cup\Vsig}\pi_n} . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Missing $ inserted. $ l.10688 I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Missing } inserted. } l.10688 I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. Overfull \hbox (142.0137pt too wide) in paragraph at lines 10683--10688 []\T1/cmr/m/n/12 If $[]\OML/cmm/m/it/12 ^^Y[] \OMS/cmsy/m/n/12 ^^R []$ \T1/cm r/m/n/12 for some $\OML/cmm/m/it/12 ^^Y[] \OMS/cmsy/m/n/12 2 []\OML/cmm/m/it/12 ; thenthereissome[]with [] :[]$ [] [63] ! Undefined control sequence. ...n\mu = t(\xi \cup \id \restrictedto {\VARCONS {t}})\sigma _n\m... l.10800 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. t(\xi \cup \id \restrictedto {\VARCONS {t}})\mu = l.10803 ...\cup\id\restrictedto{\VARCONS{t}})\mu=} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. t(\xi \cup \id \restrictedto {\VARCONS {t}})=x\mu = l.10808 ...up\id\restrictedto{\VARCONS{t}})=x\mu=} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...UBST {\V }{\vt }: \mu \restrictedto {\X _n\cup \Vsig }\pi _{n+... l.10860 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...sig }\pi _{n+1}=\pi _n\restrictedto {\X _n\cup \Vsig } l.10860 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \pi _0\restrictedto {\X _0\cup \Vsig }=\sigma _n\restrictedto {\... l.10869 } . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...\cup \Vsig }=\sigma _n\restrictedto {\X _0\cup \Vsig }\pi _n =... l.10869 } . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...sig }\pi _n =\sigma _n\restrictedto {\X _0\cup \Vsig }\mu \pi ... l.10869 } . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ... _{n+1} =\sigma _{n+1}\restrictedto {\X _0\cup \Vsig }\pi _{n+1} l.10869 } . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...}:=(\xi ^{-1}\cup \id \restrictedto {\V \setminus \RAN {\xi }}... l.10873 ...strictedto{\V\setminus\RAN{\xi}})\pi_n} . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...{n+1}= t(\xi \cup \id \restrictedto {\VARCONS {t}}) (\xi ^{-1}... l.10893 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...}) (\xi ^{-1}\cup \id \restrictedto {\V \setminus \RAN {\xi }}... l.10893 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...xi \xi ^{-1} \cup \id \restrictedto {\VARCONS {t}}\id \restric... l.10905 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...dto {\VARCONS {t}}\id \restrictedto {\V \setminus \RAN {\xi }}... l.10905 } The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Text line contains an invalid character. l.10915 \bigmath{y\in(\X_n\!^^X \cup\!\Vsig)\setminus\VARSIG{t}}, A funny symbol that I can't read has just been input. Continue, and I'll forget that it ever happened. ! Undefined control sequence. \mu \restrictedto {\X }=\sigma \pi \restrictedto {\X } l.10991 } . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...edto {\X }=\sigma \pi \restrictedto {\X } l.10991 } . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Overfull \vbox (13.4703pt too high) has occurred while \output is active [] [64] ! Undefined control sequence. l.11017 J\"urgen \Av enhaus, Klaus Becker. The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.11020 \addressunikl . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.11022 \comment { The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.11057 \comment { The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.11062 \addressunikl . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.11096 \comment { The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.11103 \comment { The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.11131 \comment { The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.11138 \comment { The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.11157 \comment { The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. [65] ! Undefined control sequence. l.11163 \addressunikl . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.11172 \comment { The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.11177 \addressunikl . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.11180 \comment { The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.11189 \comment { The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.11198 \comment { The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.11219 \comment { The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.11243 \comment { The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.11270 \comment {%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.11276 \addressunikl . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. [66] ! Undefined control sequence. l.11293 \comment { The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.11330 \addressunikl . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Underfull \hbox (badness 1895) in paragraph at lines 11325--11331 []\T1/cmr/m/n/12 Claus-Peter Wirth. \T1/cmr/m/it/12 In-duc-tive Theorem Prov-in g in The-o-ries speci-fied by Posi- [] ! Undefined control sequence. l.11340 \addressunikl . The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Underfull \hbox (badness 5446) in paragraph at lines 11333--11341 []\T1/cmr/m/n/12 Claus-Peter Wirth, Bern-hard Gram-lich. \T1/cmr/m/it/12 A Cons tructor-Based Ap-proach for [] Underfull \hbox (badness 3954) in paragraph at lines 11333--11341 \T1/cmr/m/it/12 Positive/Negative-Conditional Equa-tional Speci-fi-ca-tions\T1/ cmr/m/n/12 . SEKI-Report SR--92--10 [] Underfull \hbox (badness 5446) in paragraph at lines 11343--11350 []\T1/cmr/m/n/12 Claus-Peter Wirth, Bern-hard Gram-lich. \T1/cmr/m/it/12 A Cons tructor-Based Ap-proach for [] ! Undefined control sequence. l.11357 \comment { The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. [67] (./all.aux) LaTeX Warning: There were undefined references. LaTeX Warning: Label(s) may have changed. Rerun to get cross-references right. ) ) (\end occurred inside a group at level 1) ### simple group (level 1) entered at line 5951 ({) ### bottom level Here is how much of TeX's memory you used: 5709 strings out of 94501 62980 string characters out of 1176137 124801 words of memory out of 1500000 8244 multiletter control sequences out of 10000+50000 37351 words of font info for 109 fonts, out of 1200000 for 2000 1187 hyphenation exceptions out of 8191 26i,27n,24p,366b,361s stack positions out of 5000i,500n,6000p,200000b,5000s Output written on all.dvi (69 pages, 372772 bytes).