\relax 
\providecommand\hyper@newdestlabel[2]{}
\@writefile{toc}{\contentsline {chapter}{\numberline {A}Deductive systems}{207}{appendix.A}\protected@file@percent }
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{chap:dedsys}{{A}{207}{Deductive systems}{appendix.A}{}}
\newlabel{chap:dedsys@cref}{{[appendix][1][2147483647]A}{[1][207][]207}}
\@writefile{toc}{\contentsline {section}{\numberline {A.1}Trees and free algebras}{207}{section.A.1}\protected@file@percent }
\newlabel{sec:trees}{{A.1}{207}{Trees and free algebras}{section.A.1}{}}
\newlabel{sec:trees@cref}{{[subappendix][1][2147483647,1]A.1}{[1][207][]207}}
\newlabel{thm:tree-ind}{{A.1.1}{208}{}{thm.A.1.1}{}}
\newlabel{thm:tree-ind@cref}{{[thm][1][2147483647,1,1]A.1.1}{[1][208][]208}}
\newlabel{thm:tree-rec}{{A.1.2}{208}{}{thm.A.1.2}{}}
\newlabel{thm:tree-rec@cref}{{[thm][2][2147483647,1,1]A.1.2}{[1][208][]208}}
\newlabel{ex:wf-rigid}{{A.1.1}{209}{}{@ex.A.1.1}{}}
\newlabel{ex:wf-rigid@cref}{{[@ex][1][2147483647,1,1]A.1.1}{[1][209][]209}}
\newlabel{ex:natw}{{A.1.2}{209}{}{@ex.A.1.2}{}}
\newlabel{ex:natw@cref}{{[@ex][2][2147483647,1,1]A.1.2}{[1][209][]209}}
\@writefile{toc}{\contentsline {section}{\numberline {A.2}Indexed trees}{209}{section.A.2}\protected@file@percent }
\newlabel{sec:indexed-trees}{{A.2}{209}{Indexed trees}{section.A.2}{}}
\newlabel{sec:indexed-trees@cref}{{[subappendix][2][2147483647,1]A.2}{[1][209][]209}}
\newlabel{ex:multi-sorted-W}{{A.2.1}{209}{}{@ex.A.2.1}{}}
\newlabel{ex:multi-sorted-W@cref}{{[@ex][1][2147483647,1,2]A.2.1}{[1][209][]209}}
\@writefile{toc}{\contentsline {section}{\numberline {A.3}Free algebras with axioms}{210}{section.A.3}\protected@file@percent }
\newlabel{sec:axioms}{{A.3}{210}{Free algebras with axioms}{section.A.3}{}}
\newlabel{sec:axioms@cref}{{[subappendix][3][2147483647,1]A.3}{[1][209][]210}}
\newlabel{thm:free-monoid}{{A.3.1}{210}{}{thm.A.3.1}{}}
\newlabel{thm:free-monoid@cref}{{[thm][1][2147483647,1,3]A.3.1}{[1][210][]210}}
\newlabel{thm:tree-quotient}{{A.3.2}{212}{}{thm.A.3.2}{}}
\newlabel{thm:tree-quotient@cref}{{[thm][2][2147483647,1,3]A.3.2}{[1][211][]212}}
\newlabel{ex:tree-quotient}{{A.3.1}{212}{}{@ex.A.3.1}{}}
\newlabel{ex:tree-quotient@cref}{{[@ex][1][2147483647,1,3]A.3.1}{[1][212][]212}}
\newlabel{ex:infop-ac}{{A.3.2}{212}{}{@ex.A.3.2}{}}
\newlabel{ex:infop-ac@cref}{{[@ex][2][2147483647,1,3]A.3.2}{[1][212][]212}}
\@writefile{toc}{\contentsline {section}{\numberline {A.4}Rules and deductive systems}{212}{section.A.4}\protected@file@percent }
\newlabel{sec:rules}{{A.4}{212}{Rules and deductive systems}{section.A.4}{}}
\newlabel{sec:rules@cref}{{[subappendix][4][2147483647,1]A.4}{[1][212][]212}}
\@writefile{toc}{\contentsline {section}{\numberline {A.5}Terms}{213}{section.A.5}\protected@file@percent }
\newlabel{sec:terms}{{A.5}{213}{Terms}{section.A.5}{}}
\newlabel{sec:terms@cref}{{[subappendix][5][2147483647,1]A.5}{[1][213][]213}}
\newlabel{defn:terms}{{A.5.2}{215}{}{defn.A.5.2}{}}
\newlabel{defn:terms@cref}{{[defn][2][2147483647]A.5.2}{[1][215][]215}}
\newlabel{item:terms-uniq}{{(a)}{215}{}{Item.312}{}}
\newlabel{item:terms-uniq@cref}{{[enumi][1][2147483647](a)}{[1][215][]215}}
\newlabel{item:term-wf}{{(b)}{215}{}{Item.313}{}}
\newlabel{item:term-wf@cref}{{[enumi][2][2147483647](b)}{[1][215][]215}}
\citation{gp:asib}
\citation{gp:aswvb}
\citation{pg:freshml}
\citation{crole:alpha}
\newlabel{thm:term-system}{{A.5.3}{216}{}{lem.A.5.3}{}}
\newlabel{thm:term-system@cref}{{[lem][3][2147483647]A.5.3}{[1][215][]216}}
\@writefile{toc}{\contentsline {section}{\numberline {A.6}Variable binding and $\ensuremath  {\your@alpha }\xspace  $-equivalence}{216}{section.A.6}\protected@file@percent }
\newlabel{sec:alpha}{{A.6}{216}{Variable binding and $\alpha $-equivalence}{section.A.6}{}}
\newlabel{sec:alpha@cref}{{[subappendix][6][2147483647,1]A.6}{[1][216][]216}}
\@writefile{brf}{\backcite{gp:asib,gp:aswvb,pg:freshml}{{217}{A.6}{section.A.6}}}
\@writefile{brf}{\backcite{crole:alpha}{{217}{A.6}{section.A.6}}}
\newlabel{eq:alpha-gen}{{A.6.1}{217}{Variable binding and $\alpha $-equivalence}{equation.A.6.1}{}}
\newlabel{eq:alpha-gen@cref}{{[equation][1][2147483647,1,6]A.6.1}{[1][217][]217}}
\newlabel{thm:alpha-adm}{{A.6.2}{218}{}{lem.A.6.2}{}}
\newlabel{thm:alpha-adm@cref}{{[lem][2][2147483647]A.6.2}{[1][218][]218}}
\newlabel{item:alpha-eqvadm}{{(a)}{218}{}{Item.314}{}}
\newlabel{item:alpha-eqvadm@cref}{{[enumi][1][2147483647](a)}{[1][218][]218}}
\newlabel{item:alpha-bindadm}{{(b)}{218}{}{Item.315}{}}
\newlabel{item:alpha-bindadm@cref}{{[enumi][2][2147483647](b)}{[1][218][]218}}
\newlabel{item:alpha-gen-inv}{{(c)}{218}{}{Item.316}{}}
\newlabel{item:alpha-gen-inv@cref}{{[enumi][3][2147483647](c)}{[1][218][]218}}
\newlabel{item:alpha-refl}{{(d)}{218}{}{Item.317}{}}
\newlabel{item:alpha-refl@cref}{{[enumi][4][2147483647](d)}{[1][218][]218}}
\newlabel{item:alpha-symm}{{(e)}{218}{}{Item.318}{}}
\newlabel{item:alpha-symm@cref}{{[enumi][5][2147483647](e)}{[1][218][]218}}
\newlabel{item:alpha-trans}{{(f)}{218}{}{Item.319}{}}
\newlabel{item:alpha-trans@cref}{{[enumi][6][2147483647](f)}{[1][218][]218}}
\newlabel{item:alpha-rename}{{(g)}{218}{}{Item.320}{}}
\newlabel{item:alpha-rename@cref}{{[enumi][7][2147483647](g)}{[1][218][]218}}
\@setckpt{dedsys}{
\setcounter{page}{221}
\setcounter{equation}{2}
\setcounter{enumi}{7}
\setcounter{enumii}{2}
\setcounter{enumiii}{0}
\setcounter{enumiv}{0}
\setcounter{footnote}{3}
\setcounter{mpfootnote}{0}
\setcounter{part}{0}
\setcounter{chapter}{1}
\setcounter{section}{6}
\setcounter{subsection}{0}
\setcounter{subsubsection}{0}
\setcounter{paragraph}{0}
\setcounter{subparagraph}{0}
\setcounter{figure}{0}
\setcounter{table}{0}
\setcounter{parentequation}{0}
\setcounter{section@level}{1}
\setcounter{Item}{320}
\setcounter{Hfootnote}{20}
\setcounter{bookmark@seq@number}{74}
\setcounter{thm}{2}
\setcounter{@ex}{0}
}
