\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{l34\_matrix11 (TMaSWgFU7XcBDVB54rW2MUcG8ZbZZ7UoNyr)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_matrix\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_matrix11 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_finseq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_matrix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
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 .  ((v1\_matrix\_1~X2){\unicdcdcdhd}(m2\_finseq\_1~X2~(k3\_finseq\_2~\\
X0))){\unicdbdjdcd}(((k3\_finseq\_1~X1=k3\_finseq\_1~X2){\unicdcdcdhd}(k1\_matrix\_1~X1=k1\_matrix\_1~\\
X2)){\unicdbdjdcd}(k2\_matrix\_1~X1=k2\_matrix\_1~X2)))\end{array}
\label{hyp:ehfdfdpfngbgehchjgihpfed}
\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}
\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 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
((v7\_ordinal1~X0){\unicdcdcdhd}((v7\_ordinal1~X1){\unicdcdcdhd}((v7\_ordinal1~X2){\unicdcdcdhd}((\preoh v1\_xboole\_0~\\
X3){\unicdcdcdhd}((m1\_matrix\_1~X4~X3~X1~X2){\unicdcdcdhd}(m1\_finseq\_1~X5~X3)))))){\unicdbdjdcd}(m1\_matrix\_1~\\
(k3\_matrix11~X0~X1~X2~X3~X4~X5)~X3~X1~X2)\end{array}
\label{hyp:egehpflgddpfngbgehchjgihbdbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v7\_ordinal1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (\preoh v1\_xboole\_0~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_matrix\_1~X4~X3~X1~X2){\unicdbdjdcd}({\unicdcdadad} X5 .  (m2\_finseq\_1~X5~X3){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(m1\_matrix\_1~X6~X3~X1~X2){\unicdbdjdcd}(((k3\_finseq\_1~X5=k1\_matrix\_1~X4){\unicdbdjdcd}(\\
(X6=k3\_matrix11~X0~X1~X2~X3~X4~X5){\unicdbdjded}((k3\_finseq\_1~X6=k3\_finseq\_1~\\
X4){\unicdcdcdhd}((k1\_matrix\_1~X6=k1\_matrix\_1~X4){\unicdcdcdhd}({\unicdcdadad} X7 .  (v7\_ordinal1~\\
X7){\unicdbdjdcd}({\unicdcdadad} X8 .  (v7\_ordinal1~X8){\unicdbdjdcd}((k4\_tarski~X7~X8 \in k2\_matrix\_1~\\
X4){\unicdbdjdcd}(((X7{\unicdcdgdad}X0){\unicdbdjdcd}(k3\_matrix\_1~X3~X6~X7~X8=k3\_matrix\_1~X3~X4~X7~X8)){\unicdcdcdhd}\\
((X7=X0){\unicdbdjdcd}(k3\_matrix\_1~X3~X6~X0~X8=k1\_funct\_1~X5~X8)))))))))){\unicdcdcdhd}\\
((k3\_finseq\_1~X5{\unicdcdgdad}k1\_matrix\_1~X4){\unicdbdjdcd}((X6=k3\_matrix11~X0~X1~X2~X3~\\
X4~X5){\unicdbdjded}(X6=X4))))))))))\end{array}
\label{hyp:egddpfngbgehchjgihbdbd}
\end{equation}
\begin{theorem}\label{thm:mgddedpfngbgehchjgihbdbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(\preoh v1\_xboole\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_matrix\_1~X4~X2~X1~X0){\unicdbdjdcd}({\unicdcdadad} X5 .  (m2\_finseq\_1~X5~X2){\unicdbdjdcd}((k2\_matrix\_1~\\
X4=k2\_matrix\_1~(k3\_matrix11~X3~X1~X0~X2~X4~X5)){\unicdcdcdhd}((k3\_finseq\_1~X4=\\
k3\_finseq\_1~(k3\_matrix11~X3~X1~X0~X2~X4~X5)){\unicdcdcdhd}(k1\_matrix\_1~X4=k1\_matrix\_1~\\
(k3\_matrix11~X3~X1~X0~X2~X4~X5)))))))))\end{array}$$
\end{theorem}
\end{document}
