\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\_3 (TMMheUUuGFXjYLtM8aK7qeErCaRPaBeRXiP)}
\maketitle
Let $ k2\_matrix\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_matrix\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_enumset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (k3\_finseq\_1~(k3\_matrix\_2~\\
X0~X1~X2~X3)=np\_\_2){\unicdcdcdhd}((k1\_matrix\_1~(k3\_matrix\_2~X0~X1~X2~X3)=np\_\_2){\unicdcdcdhd}\\
(k2\_matrix\_1~(k3\_matrix\_2~X0~X1~X2~X3)=k2\_zfmisc\_1~(k2\_finseq\_1~\\
np\_\_2)~(k2\_finseq\_1~np\_\_2)))\end{array}
\label{hyp:ehddpfngbgehchjgihpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(k2\_finseq\_1~np\_\_1=k1\_tarski~np\_\_1){\unicdcdcdhd}(k2\_finseq\_1~np\_\_2=k2\_tarski~\\
np\_\_1~np\_\_2)\end{array}
\label{hyp:ehcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  k2\_zfmisc\_1~(k2\_tarski~\\
X0~X1)~(k2\_tarski~X2~X3)=k2\_enumset1~(k4\_tarski~X0~X2)~(k4\_tarski~\\
X0~X3)~(k4\_tarski~X1~X2)~(k4\_tarski~X1~X3)\end{array}
\label{hyp:ehcdddpfngdgbgchehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdpfdhahchfgdgehpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  k2\_matrix\_1~(k3\_matrix\_2~\\
X0~X1~X2~X3)=k2\_enumset1~(k4\_tarski~np\_\_1~np\_\_1)~(k4\_tarski~np\_\_1~\\
np\_\_2)~(k4\_tarski~np\_\_2~np\_\_1)~(k4\_tarski~np\_\_2~np\_\_2)\end{array}$$
\end{theorem}
\end{document}
