\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}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t32\_funct\_5 (TMbpLRuPLtsnUHNry7ogFQWiB57t6KVS9S4)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_funct\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_funct\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (k2\_zfmisc\_1~X0~X1=k1\_xboole\_0){\unicdbdjded}((X0=\\
k1\_xboole\_0){\unicdcdcdid}(X1=k1\_xboole\_0))\end{array}
\label{hyp:ehjdadpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (k4\_tarski~X0~X1 \in \\
k2\_zfmisc\_1~X2~X3){\unicdbdjded}((X0 \in X2){\unicdcdcdhd}(X1 \in X3))\end{array}
\label{hyp:ehidhdpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~\\
X2)){\unicdbdjdcd}((k9\_xtuple\_0~X2=k2\_zfmisc\_1~X0~X1){\unicdbdjdcd}(k9\_xtuple\_0~(k2\_funct\_4~\\
X2)=k2\_zfmisc\_1~X1~X0))\end{array}
\label{hyp:ehedgdpfggfhogdgehpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~\\
X2)){\unicdbdjdcd}((k4\_tarski~X0~X1 \in k9\_xtuple\_0~(k2\_funct\_4~X2)){\unicdbdjdcd}(k1\_binop\_1~\\
(k2\_funct\_4~X2)~X0~X1=k1\_binop\_1~X2~X1~X0))\end{array}
\label{hyp:ehedddpfggfhogdgehpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}(r1\_tarski~(k10\_xtuple\_0~\\
(k2\_funct\_4~X0))~(k10\_xtuple\_0~X0))\end{array}
\label{hyp:ehedbdpfggfhogdgehpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}\\
(v1\_funct\_1~X3)){\unicdbdjdcd}(\preoh (k2\_zfmisc\_1~X0~X1{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}((k9\_xtuple\_0~\\
X3=k2\_zfmisc\_1~X0~X1){\unicdcdcdhd}((X2 \in X0){\unicdcdcdhd}({\unicdcdadad} X4 .  ((v1\_relat\_1~X4){\unicdcdcdhd}\\
(v1\_funct\_1~X4)){\unicdbdjdcd}(\preoh (k1\_funct\_1~(k1\_funct\_5~X3)~X2=X4){\unicdcdcdhd}((k9\_xtuple\_0~\\
X4=X1){\unicdcdcdhd}((r1\_tarski~(k10\_xtuple\_0~X4)~(k10\_xtuple\_0~X3)){\unicdcdcdhd}({\unicdcdadad} X5 .  \\
(X5 \in X1){\unicdbdjdcd}(k1\_funct\_1~X4~X5=k1\_binop\_1~X3~X2~X5)))))))))\end{array}
\label{hyp:ehcdjdpfggfhogdgehpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((r1\_tarski~X0~X1){\unicdcdcdhd}(r1\_tarski~\\
X1~X2)){\unicdbdjdcd}(r1\_tarski~X0~X2)\end{array}
\label{hyp:ehbdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}((v1\_relat\_1~(\\
k2\_funct\_4~X0)){\unicdcdcdhd}(v1\_funct\_1~(k2\_funct\_4~X0)))\end{array}
\label{hyp:egehpflgcdpfggfhogdgehpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}(k3\_funct\_5~X0=\\
k1\_funct\_5~(k2\_funct\_4~X0))\end{array}
\label{hyp:egddpfggfhogdgehpffd}
\end{equation}
\begin{theorem}\label{thm:ehddcdpfggfhogdgehpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}\\
(v1\_funct\_1~X3)){\unicdbdjdcd}(\preoh (k2\_zfmisc\_1~X0~X1{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}((k9\_xtuple\_0~\\
X3=k2\_zfmisc\_1~X0~X1){\unicdcdcdhd}((X2 \in X1){\unicdcdcdhd}({\unicdcdadad} X4 .  ((v1\_relat\_1~X4){\unicdcdcdhd}\\
(v1\_funct\_1~X4)){\unicdbdjdcd}(\preoh (k1\_funct\_1~(k3\_funct\_5~X3)~X2=X4){\unicdcdcdhd}((k9\_xtuple\_0~\\
X4=X0){\unicdcdcdhd}((r1\_tarski~(k10\_xtuple\_0~X4)~(k10\_xtuple\_0~X3)){\unicdcdcdhd}({\unicdcdadad} X5 .  \\
(X5 \in X0){\unicdbdjdcd}(k1\_funct\_1~X4~X5=k1\_binop\_1~X3~X5~X2)))))))))\end{array}$$
\end{theorem}
\end{document}
