\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}
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\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t48\_eqrel\_1 (TMW1GXEXuvxhTwnkTTREcwJP433Xs2xGMjw)}
\maketitle
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_funct\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_funct\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (m1\_subset\_1~X2~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(k7\_relset\_1~X0~X1~X2~X3=k7\_relat\_1~\\
X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k10\_funct\_3}~{X0}}~{X1}}={{{k8\_funct\_3}~{X0}}~{X1}}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdadpfggfhogdgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_relat\_1~(k8\_funct\_3~X0~X1)){\unicdcdcdhd}(v1\_funct\_1~\\
(k8\_funct\_3~X0~X1))\end{array}
\label{hyp:egehpflgidpfggfhogdgehpfdd}
\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~(\\
k1\_funct\_3~X0)){\unicdcdcdhd}(v1\_funct\_1~(k1\_funct\_3~X0)))\end{array}
\label{hyp:egehpflgbdpfggfhogdgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_funct\_1~(k10\_funct\_3~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~\\
(k10\_funct\_3~X0~X1)~(k2\_zfmisc\_1~X0~X1)~X1){\unicdcdcdhd}(m1\_subset\_1~(k10\_funct\_3~\\
X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)~X1))))\end{array}
\label{hyp:egehpflgbdadpfggfhogdgehpfdd}
\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}((X2=k8\_funct\_3~X0~X1){\unicdbdjded}((k9\_xtuple\_0~X2=k2\_zfmisc\_1~X0~\\
X1){\unicdcdcdhd}({\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((X3 \in X0){\unicdcdcdhd}(X4 \in X1)){\unicdbdjdcd}(k1\_binop\_1~X2~\\
X3~X4=X4))))\end{array}
\label{hyp:egfdpfggfhogdgehpfdd}
\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\_funct\_3~X0){\unicdbdjded}((k9\_xtuple\_0~\\
X1=k1\_zfmisc\_1~(k9\_xtuple\_0~X0)){\unicdcdcdhd}({\unicdcdadad} X2 .  (r1\_tarski~X2~(\\
k9\_xtuple\_0~X0)){\unicdbdjdcd}(k1\_funct\_1~X1~X2=k7\_relat\_1~X0~X2)))))\end{array}
\label{hyp:egbdpfggfhogdgehpfdd}
\end{equation}
\begin{theorem}\label{thm:ehedidpffgbhchfgmgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (r1\_tarski~X0~(k2\_zfmisc\_1~X1~\\
X2)){\unicdbdjdcd}(k1\_funct\_1~(k1\_funct\_3~(k10\_funct\_3~X1~X2))~X0=k7\_relset\_1~\\
(k2\_zfmisc\_1~X1~X2)~X2~(k10\_funct\_3~X1~X2)~X0)\end{array}$$
\end{theorem}
\end{document}
