\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t1\_pralg\_2 (TMGD19CGZibZqpFz8oA317F6uEW91XLc2XR)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k1\_pralg\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_funct\_6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
{{{k10\_funct\_6}~{k1\_xboole\_0}}={k1\_xboole\_0}}\label{hyp:ehfdidpfggfhogdgehpfgd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{k1\_xboole\_0}}\label{hyp:ggdgbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (X1=k1\_tarski~X0){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}\\
(X2=X0))\end{array}
\label{hyp:egbdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}((X1=k1\_pralg\_2~X0){\unicdbdjded}(({\unicdcdadad} X2 .  \\
(X2 \in k9\_xtuple\_0~X1){\unicdbdjded}({\unicdcdaddd} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}(v1\_funct\_1~\\
X3)){\unicdcdcdhd}((X3 \in k9\_xtuple\_0~X0){\unicdcdcdhd}(X2=k10\_funct\_6~X3)))){\unicdcdcdhd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~X2)){\unicdbdjdcd}((X2 \in k9\_xtuple\_0~X1){\unicdbdjdcd}(k1\_funct\_1~\\
X1~X2=k1\_funct\_1~X0~(k10\_funct\_6~X2)))))))\end{array}
\label{hyp:egbdpfahchbgmghgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_relat\_1}~{X0}})}}}\label{hyp:dgdgbdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_funct\_1}~{X0}})}}}\label{hyp:dgdgbdpfggfhogdgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdpfahchbgmghgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}((k9\_xtuple\_0~\\
X0=k1\_tarski~k1\_xboole\_0){\unicdbdjdcd}(k1\_pralg\_2~X0=X0))\end{array}$$
\end{theorem}
\end{document}
