\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{t10\_matrix\_5 (TMMTaXC8GFevGK9mFMxMahb2gi2ncnYYJyr)}
\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 $ k7\_matrix\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v33\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_matrix\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_group\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_complfld : {\iota}$ be given.
Let $ k6\_complex1 : {\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 $ v36\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_matrix\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_matrix\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v33\_algstr\_0~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v5\_group\_1~X0){\unicdcdcdhd}(\\
(v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v4\_vectsp\_1~\\
X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_matrix\_1~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~(k3\_finseq\_2~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}(k6\_matrix\_3~X0~X1~(k1\_group\_1~X0)=X1))\end{array}
\label{hyp:ehjdpfngbgehchjgihpffd}
\end{equation}
Assume the following.
\begin{equation}
{{{k1\_group\_1}~{k1\_complfld}}={k6\_complex1}}\label{hyp:ehidpfdgpgngahmgggmgeg}
\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}
\begin{array}{c}(\preoh v6\_struct\_0~k1\_complfld){\unicdcdcdhd}((v13\_algstr\_0~k1\_complfld){\unicdcdcdhd}((\\
v33\_algstr\_0~k1\_complfld){\unicdcdcdhd}((v36\_algstr\_0~k1\_complfld){\unicdcdcdhd}((v3\_group\_1~\\
k1\_complfld){\unicdcdcdhd}((v5\_group\_1~k1\_complfld){\unicdcdcdhd}((v3\_vectsp\_1~k1\_complfld){\unicdcdcdhd}\\
((v5\_vectsp\_1~k1\_complfld){\unicdcdcdhd}((v6\_vectsp\_1~k1\_complfld){\unicdcdcdhd}((v2\_rlvect\_1~\\
k1\_complfld){\unicdcdcdhd}((v3\_rlvect\_1~k1\_complfld){\unicdcdcdhd}(v4\_rlvect\_1~k1\_complfld)))))))))))\end{array}
\label{hyp:ggdgddpfdgpgngahmgggmgeg}
\end{equation}
Assume the following.
\begin{equation}
{{({{v36\_algstr\_0}~{k1\_complfld}})}{\unicdcdcdhd}{({{v4\_vectsp\_1}~{k1\_complfld}})}}\label{hyp:ggdgcdpfdgpgngahmgggmgeg}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v2\_struct\_0}~{k1\_complfld}}}})}{\unicdcdcdhd}{({{v36\_algstr\_0}~{k1\_complfld}})}}\label{hyp:ggdgbdpfdgpgngahmgggmgeg}
\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\_matrix\_5~X0)){\unicdcdcdhd}(m2\_finseq\_1~(k1\_matrix\_5~X0)~\\
(k3\_finseq\_2~(u1\_struct\_0~k1\_complfld))))\end{array}
\label{hyp:egehpflgbdpfngbgehchjgihpffd}
\end{equation}
Assume the following.
\begin{equation}
{{({{v36\_algstr\_0}~{k1\_complfld}})}{\unicdcdcdhd}{({{l6\_algstr\_0}~{k1\_complfld}})}}\label{hyp:egehpflgbdpfdgpgngahmgggmgeg}
\end{equation}
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}({\unicdcdadad} X2 .  ((v1\_matrix\_1~\\
X2){\unicdcdcdhd}(m2\_finseq\_1~X2~(k3\_finseq\_2~k2\_numbers))){\unicdbdjdcd}((X2=k7\_matrix\_5~\\
X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~k1\_complfld)){\unicdbdjdcd}\\
((X3=X0){\unicdbdjdcd}(X2=k2\_matrix\_5~(k6\_matrix\_3~k1\_complfld~(k1\_matrix\_5~\\
X1)~X3)))))))\end{array}
\label{hyp:eghdpfngbgehchjgihpffd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_complex1}={np\_\_1}}\label{hyp:egedpfdgpgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_matrix\_1~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~(k3\_finseq\_2~(u1\_struct\_0~\\
k1\_complfld)))){\unicdbdjdcd}(k2\_matrix\_5~X0=X0)\end{array}
\label{hyp:egcdpfngbgehchjgihpffd}
\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}\\
(k1\_matrix\_5~X0=X0)\end{array}
\label{hyp:egbdpfngbgehchjgihpffd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{X0}})}}}\label{hyp:dgdgbdpfihdgngahmgihpfad}
\end{equation}
\begin{theorem}\label{thm:ehbdadpfngbgehchjgihpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_matrix\_1~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~(k3\_finseq\_2~k2\_numbers))){\unicdbdjdcd}\\
(k7\_matrix\_5~np\_\_1~X0=X0)\end{array}$$
\end{theorem}
\end{document}
