\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{t64\_matrixr2 (TMWpfSYTyxcM5V2Y2PCiQ1F463ZfBLaJD2B)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k5\_matrix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k4\_matrixr2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_matrix\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_matrix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ k4\_ordinal1 : {\iota}$ be given.
Let $ k4\_matrix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v6\_membered : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ k2\_matrixr1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k12\_matrix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_vectsp\_1 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}(({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k5\_numbers){\unicdbdjdcd}((k4\_tarski~X1~X1 \in k2\_matrix\_1~(k4\_matrixr2~X0)){\unicdbdjdcd}\\
(k3\_matrix\_1~k1\_numbers~(k4\_matrixr2~X0)~X1~X1=np\_\_1))){\unicdcdcdhd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k5\_numbers){\unicdbdjdcd}\\
((k4\_tarski~X1~X2 \in k2\_matrix\_1~(k4\_matrixr2~X0)){\unicdbdjdcd}((X1=X2){\unicdcdcdid}(k3\_matrix\_1~\\
k1\_numbers~(k4\_matrixr2~X0)~X1~X2=k6\_numbers))))))\end{array}
\label{hyp:ehgdddpfngbgehchjgihchcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k5\_numbers){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_matrix\_1~X2~X0~X1~X1){\unicdbdjdcd}(k5\_matrix\_1~X1~X0~(k5\_matrix\_1~\\
X1~X0~X2)=X2)))\end{array}
\label{hyp:ehcdjdpfngbgehchjgihchcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(\preoh v1\_xboole\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_matrix\_1~X3~X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_matrix\_1~X4~X2~X0~X1){\unicdbdjdcd}(({\unicdcdadad} X5 .  (v7\_ordinal1~X5){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(v7\_ordinal1~X6){\unicdbdjdcd}((k4\_tarski~X5~X6 \in k2\_matrix\_1~X3){\unicdbdjdcd}(k3\_matrix\_1~\\
X2~X3~X5~X6=k3\_matrix\_1~X2~X4~X5~X6)))){\unicdbdjdcd}(X3=X4))))))\end{array}
\label{hyp:ehcdhdpfngbgehchjgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (m1\_matrix\_1~X2~X1~X0~X0){\unicdbdjdcd}((k3\_finseq\_1~X2=X0){\unicdcdcdhd}((k1\_matrix\_1~\\
X2=X0){\unicdcdcdhd}(k2\_matrix\_1~X2=k2\_zfmisc\_1~(k2\_finseq\_1~X0)~(k2\_finseq\_1~\\
X0))))))\end{array}
\label{hyp:ehcdedpfngbgehchjgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\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 .  ((v7\_ordinal1~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~\\
X1){\unicdcdcdhd}(m1\_matrix\_1~X2~X1~X0~X0))){\unicdbdjdcd}(k5\_matrix\_1~X0~X1~X2=k4\_matrix\_1~\\
X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfngbgehchjgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{v6\_membered}~{k4\_ordinal1}}\label{hyp:ggdggdpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k1\_numbers}}}}\label{hyp:ggdgbdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v7\_ordinal1~\\
X1){\unicdcdcdhd}(v7\_ordinal1~X2))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_matrix\_1~X3~X0~X1~X2){\unicdbdjdcd}\\
((v1\_matrix\_1~X3){\unicdcdcdhd}(m2\_finseq\_1~X3~(k3\_finseq\_2~X0))))\end{array}
\label{hyp:egehpfngbdpfngbgehchjgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v7\_ordinal1~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~\\
X1){\unicdcdcdhd}(m1\_matrix\_1~X2~X1~X0~X0))){\unicdbdjdcd}(m1\_matrix\_1~(k5\_matrix\_1~X0~X1~\\
X2)~X1~X0~X0)\end{array}
\label{hyp:egehpflgfdpfngbgehchjgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}(m1\_matrix\_1~(k4\_matrixr2~\\
X0)~k1\_numbers~X0~X0)\end{array}
\label{hyp:egehpflgedpfngbgehchjgihchcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_matrix\_1~X1){\unicdcdcdhd}\\
(m2\_finseq\_1~X1~(k3\_finseq\_2~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_matrix\_1~\\
X2){\unicdcdcdhd}(m2\_finseq\_1~X2~(k3\_finseq\_2~X0))){\unicdbdjdcd}((X2=k4\_matrix\_1~X0~X1){\unicdbdjded}\\
((k3\_finseq\_1~X2=k1\_matrix\_1~X1){\unicdcdcdhd}(({\unicdcdadad} X3 .  (v7\_ordinal1~\\
X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (v7\_ordinal1~X4){\unicdbdjdcd}((k4\_tarski~X3~X4 \in k2\_matrix\_1~\\
X2){\unicdbdjded}(k4\_tarski~X4~X3 \in k2\_matrix\_1~X1)))){\unicdcdcdhd}({\unicdcdadad} X3 .  (v7\_ordinal1~\\
X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (v7\_ordinal1~X4){\unicdbdjdcd}((k4\_tarski~X4~X3 \in k2\_matrix\_1~\\
X1){\unicdbdjdcd}(k3\_matrix\_1~X0~X2~X3~X4=k3\_matrix\_1~X0~X1~X4~X3)))))))))\end{array}
\label{hyp:eggdpfngbgehchjgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}(k4\_matrixr2~X0=k2\_matrixr1~\\
(k12\_matrix\_1~k2\_vectsp\_1~X0))\end{array}
\label{hyp:egcdpfngbgehchjgihchcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjded}{({{X0} \in {k4\_ordinal1}})}}}\label{hyp:egbdcdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v6\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
(v7\_ordinal1~X1))\end{array}
\label{hyp:dgdgbdhdpfngfgngcgfgchfgeg}
\end{equation}
\begin{theorem}\label{thm:ehgdedpfngbgehchjgihchcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}(k5\_matrix\_1~X0~k1\_numbers~\\
(k4\_matrixr2~X0)=k4\_matrixr2~X0)\end{array}$$
\end{theorem}
\end{document}
