\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\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{t12\_matrixc1 (TMVLJXpsvuNVW9vYqAkUdT38a9HgWRPDiuB)}
\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 $ k1\_matrixc1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_matrix\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_matrix\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k15\_complex1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_complex1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_complex1 : {\iota}$ be given.
Let $ k19\_binop\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v1\_int\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xcmplx\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_matrix\_1~X1){\unicdcdcdhd}(\\
m2\_finseq\_1~X1~(k3\_finseq\_2~k2\_numbers))){\unicdbdjdcd}(k1\_matrixc1~(k7\_matrix\_5~\\
X0~X1)=k7\_matrix\_5~(k15\_complex1~X0)~(k1\_matrixc1~X1)))\end{array}
\label{hyp:ehfdpfngbgehchjgihdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xcmplx\_0~X0){\unicdbdjdcd}(k15\_complex1~(k4\_xcmplx\_0~X0)=\\
k10\_complex1~(k15\_complex1~X0))\end{array}
\label{hyp:ehddddpfdgpgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
{{{k15\_complex1}~{k6\_complex1}}={k6\_complex1}}\label{hyp:ehddadpfdgpgngahmgfgihbd}
\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}\\
(k7\_matrix\_5~(k19\_binop\_2~np\_\_1)~X0=k4\_matrix\_5~X0)\end{array}
\label{hyp:ehbdbdpfngbgehchjgihdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_1){\unicdcdcdhd}(m2\_subset\_1~np\_\_1~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_1~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_1~k1\_numbers))\end{array}
\label{hyp:dhahdgbdpfogfhngfgchbgmgdh}
\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}
{{\unicdcdadad} X0 .  {{({{v1\_int\_1}~{X0}})}{\unicdbdjdcd}{({{{k19\_binop\_2}~{X0}}={{k4\_xcmplx\_0}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdjdpfcgjgogpgahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_numbers){\unicdbdjdcd}(k10\_complex1~X0=k4\_xcmplx\_0~\\
X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdadpfdgpgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
{{v6\_membered}~{k4\_ordinal1}}\label{hyp:ggdggdpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k6\_complex1}}~{k2\_numbers}}\label{hyp:egehpflggdpfdgpgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{({{k4\_xcmplx\_0}~{X0}})}})}}}\label{hyp:egehpflgedpfihdgngahmgihpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_matrix\_1~X0){\unicdcdcdhd}(m1\_finseq\_1~X0~(k3\_finseq\_2~k2\_numbers))){\unicdbdjdcd}\\
((v1\_matrix\_1~(k1\_matrixc1~X0)){\unicdcdcdhd}(m2\_finseq\_1~(k1\_matrixc1~X0)~\\
(k3\_finseq\_2~k2\_numbers)))\end{array}
\label{hyp:egehpflgbdpfngbgehchjgihdgbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_complex1}={np\_\_1}}\label{hyp:egedpfdgpgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k2\_numbers}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{X0}})}}}\label{hyp:dgdgddpfihdgngahmgihpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v6\_membered}~{X0}})}{\unicdbdjdcd}{({{v5\_membered}~{X0}})}}}\label{hyp:dgdgbdpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v5\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
(v1\_int\_1~X1))\end{array}
\label{hyp:dgdgbdgdpfngfgngcgfgchfgeg}
\end{equation}
\begin{theorem}\label{thm:ehbdcdpfngbgehchjgihdgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_matrix\_1~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~(k3\_finseq\_2~k2\_numbers))){\unicdbdjdcd}\\
(k1\_matrixc1~(k4\_matrix\_5~X0)=k4\_matrix\_5~(k1\_matrixc1~X0))\end{array}$$
\end{theorem}
\end{document}
