\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}
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\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{t15\_matrixr1 (TMdBmCRkoKw73v721fn4ncj5RPEo5Z1DqV2)}
\maketitle
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_rvsum\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_rvsum\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_rvsum\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_finseq\_1~X0~k1\_numbers){\unicdbdjdcd}(k8\_rvsum\_1~X0~(k5\_euclid~\\
(k3\_finseq\_1~X0))=X0)\end{array}
\label{hyp:ehfdpfngbgehchjgihchbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_finseq\_1~X0~k1\_numbers){\unicdbdjdcd}((k4\_rvsum\_1~X0~(k6\_rvsum\_1~\\
X0)=k5\_euclid~(k3\_finseq\_1~X0)){\unicdcdcdhd}(k8\_rvsum\_1~X0~X0=k5\_euclid~\\
(k3\_finseq\_1~X0)))\end{array}
\label{hyp:ehddpfngbgehchjgihchbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_finseq\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_1~\\
X1~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~k1\_numbers){\unicdbdjdcd}(((k3\_finseq\_1~\\
X0=k3\_finseq\_1~X1){\unicdcdcdhd}(k3\_finseq\_1~X1=k3\_finseq\_1~X2)){\unicdbdjdcd}(k8\_rvsum\_1~\\
X0~(k8\_rvsum\_1~X1~X2)=k4\_rvsum\_1~(k8\_rvsum\_1~X0~X1)~X2))))\end{array}
\label{hyp:ehbdddpfngbgehchjgihchbd}
\end{equation}
\begin{theorem}\label{thm:ehbdfdpfngbgehchjgihchbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_finseq\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_1~\\
X1~k1\_numbers){\unicdbdjdcd}((k3\_finseq\_1~X0=k3\_finseq\_1~X1){\unicdbdjdcd}(X0=k4\_rvsum\_1~\\
(k8\_rvsum\_1~X0~X1)~X1)))\end{array}$$
\end{theorem}
\end{document}
