\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{t6\_matrix\_9 (TMTX4icPYCSeX6eNxq8945ApQrH23nepeZD)}
\maketitle
Let $ k12\_matrix\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_finseq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_finseq\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k3\_finseq\_5~(k10\_finseq\_1~X0~X1)=k10\_finseq\_1~\\
X1~X0\end{array}
\label{hyp:ehgdbdpfggjgogdhfgbhpffd}
\end{equation}
Assume the following.
\begin{equation}
{{{k1\_finseq\_2}~{np\_\_2}}={{{k10\_finseq\_1}~{np\_\_1}}~{np\_\_2}}}\label{hyp:ehfdcdpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k12\_matrix\_2~np\_\_2=k2\_tarski~(k10\_finseq\_1~np\_\_1~np\_\_2)~(k10\_finseq\_1~\\
np\_\_2~np\_\_1)\end{array}
\label{hyp:ehddpfngbgehchjgihpfhd}
\end{equation}
\begin{theorem}\label{thm:ehgdpfngbgehchjgihpfjd}
$$\begin{array}{c}k12\_matrix\_2~np\_\_2=k2\_tarski~(k1\_finseq\_2~np\_\_2)~(k3\_finseq\_5~\\
(k1\_finseq\_2~np\_\_2))\end{array}$$
\end{theorem}
\end{document}
