\contentsline {section}{\numberline {1}Introduction}{3}{section.1}
\contentsline {subsection}{\numberline {1.1}About LogiWeb}{3}{subsection.1.1}
\contentsline {subsection}{\numberline {1.2}About the proof system}{3}{subsection.1.2}
\contentsline {section}{\numberline {2}The Deduction Algorithm}{5}{section.2}
\contentsline {section}{\numberline {3}Supporting Lemmas}{5}{section.3}
\contentsline {subsection}{\numberline {3.1}Corollary $C1.10a$}{6}{subsection.3.1}
\contentsline {subsection}{\numberline {3.2}Corollary $C1.10(b)$}{6}{subsection.3.2}
\contentsline {subsection}{\numberline {3.3}Lemma ${A1'}^*$}{6}{subsection.3.3}
\contentsline {subsection}{\numberline {3.4}Lemma ${A2'}^*$}{7}{subsection.3.4}
\contentsline {subsection}{\numberline {3.5}Lemma $Double Hypothesis$}{7}{subsection.3.5}
\contentsline {subsection}{\numberline {3.6}Lemma $L1.8$}{8}{subsection.3.6}
\contentsline {subsection}{\numberline {3.7}Lemma $Tautology 1$}{8}{subsection.3.7}
\contentsline {section}{\numberline {4}The Main Proofs }{9}{section.4}
\contentsline {subsection}{\numberline {4.1}Lemma $L3.2(b)'$}{9}{subsection.4.1}
\contentsline {subsection}{\numberline {4.2}Lemma $L3.2(c)'$}{9}{subsection.4.2}
\contentsline {subsection}{\numberline {4.3}Lemma $L3.2(d)'$}{10}{subsection.4.3}
\contentsline {subsection}{\numberline {4.4}Lemma $L3.2(f)'$}{10}{subsection.4.4}
\contentsline {subsubsection}{\numberline {4.4.1}The base case of $L3.2(f)'$}{10}{subsubsection.4.4.1}
\contentsline {subsubsection}{\numberline {4.4.2}The induction step of $L3.2(f)'$}{11}{subsubsection.4.4.2}
\contentsline {subsection}{\numberline {4.5}Lemma $L3.2(g)'$}{12}{subsection.4.5}
\contentsline {subsubsection}{\numberline {4.5.1}Base case of $L3.2(g)'$}{12}{subsubsection.4.5.1}
\contentsline {subsubsection}{\numberline {4.5.2}Induction step of $L3.2(g)'$}{13}{subsubsection.4.5.2}
\contentsline {subsection}{\numberline {4.6}Lemma $L3.2(h)'$}{14}{subsection.4.6}
\contentsline {subsubsection}{\numberline {4.6.1}Base case of $L3.2(h)'$}{15}{subsubsection.4.6.1}
\contentsline {subsubsection}{\numberline {4.6.2}Induction step of $L3.2(h)'$}{15}{subsubsection.4.6.2}
\contentsline {section}{\numberline {5}Conclusion}{17}{section.5}
\contentsline {section}{\numberline {A}The name of the page}{18}{section.A}
\contentsline {section}{\numberline {B}The Bibliography}{18}{section.B}