%% %% Ein Beispiel der DANTE-Edition %% Mathematiksatz mit LaTeX %% 3. Auflage %% Beispiel 09-23-1 auf Seite 205. %% Copyright (C) 2018 Herbert Voss %% %% It may be distributed and/or modified under the conditions %% of the LaTeX Project Public License, either version 1.3 %% of this license or (at your option) any later version. %% See http://www.latex-project.org/lppl.txt for details. %% %% ==== % Show page(s) 1 %% %% \documentclass[10pt]{exaartplain} \pagestyle{empty} \setlength\textwidth{352.81416pt} \AtBeginDocument{\setlength\parindent{0pt}} %StartShownPreambleCommands \usepackage{prooftrees, amsmath, turnstile} \newcommand*\tnot{\mathord{\sim}} \newcommand*\lif{\mathbin{\rightarrow}} \newcommand*\liff{\mathbin{\leftrightarrow}} \newcommand*\elim{\,\text{E}} %StopShownPreambleCommands \begin{document} \begin{prooftree} {to prove={(\exists x)((\forall y)(Py \lif x = y) \land Px) \sststile{}{} (\exists x)(\forall y)(Py \liff x = y)}} [{(\exists x)((\forall y)(Py \lif x = y) \land Px)}, checked=a, just=Pr., name=pr [{\lnot (\exists x)(\forall y)(Py \liff x = y)}, subs=a, just=Conc.~neg., name=neg conc [{(\forall y)(Py \lif a = y) \land Pa}, checked, just=$\exists\elim$:pr [{(\forall y)(Py \lif a = y)}, subs=b, just=$\land\elim$:!u, name=mark [Pa, just=$\land\elim$:!uu, name=simple [{\lnot (\forall y)(Py \liff a = y)}, checked=b, just=$\lnot\exists\elim$:neg conc [{\lnot (Pb \liff a = b)}, checked, just=$\lnot\forall\elim$:!u [Pb, just=$\liff\elim$:!u, name=to Pb or not to Pb [a \neq b, just=$\liff\elim$:!u [{Pb \lif a = b}, checked, just=$\forall\elim$:mark, move by=1 [\lnot Pb, close={:to Pb or not to Pb,!c}, just=$\lif\elim$:!u ] [{a = b} [a \neq a, close={:!c}, just={$=\elim$:{!uuu,!u}} ] ] ] ] ] [\lnot Pb [{a = b}[Pb, just={$=\elim$:{simple,!u}}, close={:to Pb or not to Pb,!c}]] ]]]]]]]] \end{prooftree} \end{document}