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%%
%% 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}
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