\relax \ifx\hyper@anchor\@undefined \global \let \oldcontentsline\contentsline \gdef \contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}} \global \let \oldnewlabel\newlabel \gdef \newlabel#1#2{\newlabelxx{#1}#2} \gdef \newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}} \AtEndDocument{\let \contentsline\oldcontentsline \let \newlabel\oldnewlabel} \else \global \let \hyper@last\relax \fi \bibstyle{plain} \citation{mendelson} \@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{3}{section.1}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.1}About LogiWeb}{3}{subsection.1.1}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.2}About the proof system}{3}{subsection.1.2}} \citation{mendelson} \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces The new version of the operators}}{4}{figure.1}} \newlabel{aaa}{{1}{4}{About the proof system\relax }{figure.1}{}} \citation{mendelson} \citation{mendelson} \@writefile{toc}{\contentsline {section}{\numberline {2}The Deduction Algorithm}{5}{section.2}} \newlabel{support}{{3}{5}{Supporting Lemmas\label {support}\relax }{section.3}{}} \@writefile{toc}{\contentsline {section}{\numberline {3}Supporting Lemmas}{5}{section.3}} \citation{mendelson} \@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Corollary $C1.10a$}{6}{subsection.3.1}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Corollary $C1.10(b)$}{6}{subsection.3.2}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Lemma ${A1'}^*$}{6}{subsection.3.3}} \citation{mendelson} \@writefile{toc}{\contentsline {subsection}{\numberline {3.4}Lemma ${A2'}^*$}{7}{subsection.3.4}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.5}Lemma $Double Hypothesis$}{7}{subsection.3.5}} \citation{mendelson} \@writefile{toc}{\contentsline {subsection}{\numberline {3.6}Lemma $L1.8$}{8}{subsection.3.6}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.7}Lemma $Tautology 1$}{8}{subsection.3.7}} \citation{mendelson} \newlabel{main.lemmas}{{4}{9}{The Main Proofs \label {main.lemmas}\relax }{section.4}{}} \@writefile{toc}{\contentsline {section}{\numberline {4}The Main Proofs }{9}{section.4}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.1}Lemma $L3.2(b)'$}{9}{subsection.4.1}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.2}Lemma $L3.2(c)'$}{9}{subsection.4.2}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.3}Lemma $L3.2(d)'$}{10}{subsection.4.3}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.4}Lemma $L3.2(f)'$}{10}{subsection.4.4}} \newlabel{f.base}{{4.4.1}{10}{The base case of $L3.2(f)'$\label {f.base}\relax }{subsubsection.4.4.1}{}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {4.4.1}The base case of $L3.2(f)'$}{10}{subsubsection.4.4.1}} \newlabel{f.hyp}{{4.4.2}{11}{The induction step of $L3.2(f)'$\label {f.hyp}\relax }{subsubsection.4.4.2}{}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {4.4.2}The induction step of $L3.2(f)'$}{11}{subsubsection.4.4.2}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.5}Lemma $L3.2(g)'$}{12}{subsection.4.5}} \newlabel{g.base}{{4.5.1}{12}{Base case of $L3.2(g)'$\label {g.base}\relax }{subsubsection.4.5.1}{}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {4.5.1}Base case of $L3.2(g)'$}{12}{subsubsection.4.5.1}} \newlabel{g.hyp}{{4.5.2}{13}{Induction step of $L3.2(g)'$\label {g.hyp}\relax }{subsubsection.4.5.2}{}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {4.5.2}Induction step of $L3.2(g)'$}{13}{subsubsection.4.5.2}} \newlabel{res.lemma}{{4.6}{14}{Lemma $L3.2(h)'$\label {res.lemma}\relax }{subsection.4.6}{}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.6}Lemma $L3.2(h)'$}{14}{subsection.4.6}} \newlabel{h.base}{{4.6.1}{15}{Base case of $L3.2(h)'$\label {h.base}\relax }{subsubsection.4.6.1}{}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {4.6.1}Base case of $L3.2(h)'$}{15}{subsubsection.4.6.1}} \newlabel{h.hyp}{{4.6.2}{15}{Induction step of $L3.2(h)'$\label {h.hyp}\relax }{subsubsection.4.6.2}{}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {4.6.2}Induction step of $L3.2(h)'$}{15}{subsubsection.4.6.2}} \@writefile{toc}{\contentsline {section}{\numberline {5}Conclusion}{17}{section.5}} \bibcite{mendelson}{Mendelson, 2001} \@writefile{toc}{\contentsline {section}{\numberline {A}The name of the page}{18}{section.A}} \@writefile{toc}{\contentsline {section}{\numberline {B}The Bibliography}{18}{section.B}}