\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\_matrixr2 (TMRgdnqQPMHu1Q3VTi5jN14MmkGjUy8FEub)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_finseq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_matrix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_matrix\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (v7\_ordinal1~\\
X2){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_matrix\_1~X3){\unicdcdcdhd}(m2\_finseq\_1~X3~(k3\_finseq\_2~\\
X0))){\unicdbdjdcd}(((r1\_xxreal\_0~np\_\_1~X1){\unicdcdcdhd}((r1\_xxreal\_0~X1~(k3\_finseq\_1~\\
X3)){\unicdcdcdhd}((r1\_xxreal\_0~np\_\_1~X2){\unicdcdcdhd}(r1\_xxreal\_0~X2~(k1\_matrix\_1~X3))))){\unicdbdjdcd}\\
(k4\_tarski~X1~X2 \in k2\_matrix\_1~X3))))\end{array}
\label{hyp:ehddgdpfngbgehchjgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((v1\_matrix\_1~X1){\unicdcdcdhd}\\
(m1\_finseq\_1~X1~(k3\_finseq\_2~X0))){\unicdcdcdhd}((v7\_ordinal1~X2){\unicdcdcdhd}(v7\_ordinal1~\\
X3))){\unicdbdjdcd}(m1\_subset\_1~(k3\_matrix\_1~X0~X1~X2~X3)~X0)\end{array}
\label{hyp:egehpflgddpfngbgehchjgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_matrix\_1~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~(k3\_finseq\_2~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v7\_ordinal1~\\
X3){\unicdbdjdcd}((k4\_tarski~X2~X3 \in k2\_matrix\_1~X1){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~X0){\unicdbdjdcd}((X4=k3\_matrix\_1~X0~X1~X2~X3){\unicdbdjded}({\unicdcdaddd} X5 .  (m2\_finseq\_1~\\
X5~X0){\unicdcdcdhd}((X5=k1\_funct\_1~X1~X2){\unicdcdcdhd}(X4=k1\_funct\_1~X5~X3))))))))\end{array}
\label{hyp:egfdpfngbgehchjgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehcdpfngbgehchjgihchcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k5\_numbers){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_matrix\_1~\\
X3){\unicdcdcdhd}(m2\_finseq\_1~X3~(k3\_finseq\_2~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_finseq\_1~\\
X4~X0){\unicdbdjdcd}(((X4=k1\_funct\_1~X3~X1){\unicdcdcdhd}((r1\_xxreal\_0~np\_\_1~X1){\unicdcdcdhd}((r1\_xxreal\_0~\\
X1~(k3\_finseq\_1~X3)){\unicdcdcdhd}((r1\_xxreal\_0~np\_\_1~X2){\unicdcdcdhd}((r1\_xxreal\_0~X2~\\
(k1\_matrix\_1~X3)){\unicdcdcdhd}(k3\_finseq\_1~X4=k1\_matrix\_1~X3)))))){\unicdbdjdcd}(k3\_matrix\_1~\\
X0~X3~X1~X2=k1\_funct\_1~X4~X2))))))\end{array}$$
\end{theorem}
\end{document}
