\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{t2\_sprect\_1 (TMVmctRk5JvcxFEJ4bCNJD12Cg8pLtwjPNK)}
\maketitle
Let $ v3\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k10\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_zfmisc\_1~X0)){\unicdbdjdcd}({\unicdcdaddd} X1 .  \\
(m1\_subset\_1~X1~X0){\unicdcdcdhd}(X0=k1\_tarski~X1))\end{array}
\label{hyp:ehedgdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{{k2\_tarski}~{X0}}~{X0}}={{k1\_tarski}~{X0}}}}\label{hyp:ehcdjdpffgogfhngdhfgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (k1\_tarski~X0=k2\_tarski~X1~X2){\unicdbdjdcd}\\
(X1=X2)\end{array}
\label{hyp:mgddpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k10\_xtuple\_0~(k10\_finseq\_1~X0~X1)=k2\_tarski~\\
X0~X1\end{array}
\label{hyp:mgbdddpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_relat\_1~(k10\_finseq\_1~X0~X1)){\unicdcdcdhd}(v1\_funct\_1~\\
(k10\_finseq\_1~X0~X1))\end{array}
\label{hyp:ggdgidpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {\preoh{{{v1\_xboole\_0}~{({{{k2\_tarski}~{X0}}~{X1}})}}}}}}\label{hyp:ggdgddpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v3\_funct\_1~X0))){\unicdbdjdcd}\\
(v1\_zfmisc\_1~(k10\_xtuple\_0~X0))\end{array}
\label{hyp:ggdgbdcdpfggfhogdgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdpfdhahchfgdgehpfbd}
${{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{v3\_funct\_1}~{({{{k10\_finseq\_1}~{X0}}~{X1}})}})}{\unicdbdjdcd}{({{X0}={X1}})}}}}$.
\end{theorem}
\end{document}
