\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}
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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{t51\_matrixc1 (TMTxQTYgGcfQCczfoZ4s5PeAgvfybDp9qmY)}
\maketitle
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\_numbers : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k12\_matrixc1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_matrix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_matrixc1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_matrixc1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k17\_rvsum\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_matrix\_1~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~(k3\_finseq\_2~k2\_numbers))){\unicdbdjdcd}\\
(k11\_matrixc1~X0=k10\_matrixc1~(k4\_matrix\_1~k2\_numbers~X0))\end{array}
\label{hyp:ehfdadpfngbgehchjgihdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_matrix\_1~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~(k3\_finseq\_2~k2\_numbers))){\unicdbdjdcd}\\
((\preoh r1\_xxreal\_0~(k3\_finseq\_1~X0)~k6\_numbers){\unicdbdjdcd}(k17\_rvsum\_1~(k10\_matrixc1~\\
X0)=k17\_rvsum\_1~(k11\_matrixc1~X0)))\end{array}
\label{hyp:ehedjdpfngbgehchjgihdgbd}
\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}
{\preoh{{{v1\_xboole\_0}~{k2\_numbers}}}}\label{hyp:ggdgcdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_matrix\_1~X1){\unicdcdcdhd}\\
(m1\_finseq\_1~X1~(k3\_finseq\_2~X0)))){\unicdbdjdcd}((v1\_matrix\_1~(k4\_matrix\_1~\\
X0~X1)){\unicdcdcdhd}(m2\_finseq\_1~(k4\_matrix\_1~X0~X1)~(k3\_finseq\_2~X0)))\end{array}
\label{hyp:egehpflgedpfngbgehchjgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_matrix\_1~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~(k3\_finseq\_2~k2\_numbers))){\unicdbdjdcd}\\
(k12\_matrixc1~X0=k17\_rvsum\_1~(k10\_matrixc1~X0))\end{array}
\label{hyp:egbdbdpfngbgehchjgihdgbd}
\end{equation}
\begin{theorem}\label{thm:ehfdbdpfngbgehchjgihdgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_matrix\_1~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~(k3\_finseq\_2~k2\_numbers))){\unicdbdjdcd}\\
((\preoh r1\_xxreal\_0~(k3\_finseq\_1~X0)~k6\_numbers){\unicdbdjdcd}(k12\_matrixc1~X0=\\
k12\_matrixc1~(k4\_matrix\_1~k2\_numbers~X0)))\end{array}$$
\end{theorem}
\end{document}
