\documentclass{article}
\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t42\_funct\_5 (TMGvLshGGTULoS9YrEUJ6VPaeTqFGNeap4G)}
\maketitle
Let $ k1\_funct\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k3\_funct\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{{k4\_xboole\_0}~{X0}}~{k1\_xboole\_0}}={X0}}}\label{hyp:ehddpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(k9\_xtuple\_0~k1\_xboole\_0=k1\_xboole\_0){\unicdcdcdhd}(k10\_xtuple\_0~k1\_xboole\_0=\\
k1\_xboole\_0)\end{array}
\label{hyp:ehddidpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~k1\_xboole\_0){\unicdcdcdhd}((v5\_relat\_1~k1\_xboole\_0~\\
X0){\unicdcdcdhd}((v1\_funct\_1~k1\_xboole\_0){\unicdcdcdhd}(v5\_ordinal1~k1\_xboole\_0)))\end{array}
\label{hyp:ehddadpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}(({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \\
\preoh k4\_tarski~X1~X2 \in k9\_xtuple\_0~X0){\unicdbdjdcd}((k1\_funct\_5~X0=k1\_xboole\_0){\unicdcdcdhd}\\
(k3\_funct\_5~X0=k1\_xboole\_0)))\end{array}
\label{hyp:ehcdhdpfggfhogdgehpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2=k4\_xboole\_0~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in X2){\unicdbdjded}((X3 \in X0){\unicdcdcdhd}(\preoh X3 \in X1)))\end{array}
\label{hyp:egfdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k4\_tarski~X0~X1=k2\_tarski~(k2\_tarski~X0~\\
X1)~(k1\_tarski~X0)\end{array}
\label{hyp:egfdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
{{k1\_xboole\_0}={{the}~{({{\uniddcgcg} X0 : {\iota} .  {{v1\_xboole\_0}~{X0}}})}}}\label{hyp:egcdpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehedcdpfggfhogdgehpffd}
$$\begin{array}{c}(k1\_funct\_5~k1\_xboole\_0=k1\_xboole\_0){\unicdcdcdhd}(k3\_funct\_5~k1\_xboole\_0=\\
k1\_xboole\_0)\end{array}$$
\end{theorem}
\end{document}
