\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{t41\_matrix14 (TMWr9rEcmnyLD6hNGJHjLfo7BLpHX9TT7PZ)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\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 $ 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 $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_group\_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 $ m1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\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 $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_matrix\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_matrix\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k5\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ l4\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v9\_struct\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l5\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l4\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~\\
X1){\unicdcdcdhd}((\preoh v6\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v33\_algstr\_0~X1){\unicdcdcdhd}\\
((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}((v3\_group\_1~\\
X1){\unicdcdcdhd}((v5\_group\_1~X1){\unicdcdcdhd}((v4\_vectsp\_1~X1){\unicdcdcdhd}((v5\_vectsp\_1~X1){\unicdcdcdhd}(\\
l6\_algstr\_0~X1)))))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_matrix\_1~X2~(u1\_struct\_0~\\
X1)~X0~X0){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X0~k6\_numbers){\unicdcdcdhd}((k3\_matrix\_1~(u1\_struct\_0~\\
X1)~X2~np\_\_1~np\_\_1{\unicdcdgdad}k4\_struct\_0~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_matrix\_1~X3~\\
(u1\_struct\_0~X1)~X0~X0){\unicdbdjdcd}(\preoh (v1\_matrix\_6~X3~X0~X1){\unicdcdcdhd}((k3\_matrix\_1~\\
(u1\_struct\_0~X1)~(k4\_matrix\_6~X0~X1~X3~X2)~np\_\_1~np\_\_1=k5\_struct\_0~\\
X1){\unicdcdcdhd}(({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k5\_numbers){\unicdbdjdcd}((r1\_xxreal\_0~\\
X4~X0){\unicdbdjdcd}((r1\_xxreal\_0~X4~np\_\_1){\unicdcdcdid}(k3\_matrix\_1~(u1\_struct\_0~X1)~\\
(k4\_matrix\_6~X0~X1~X3~X2)~X4~np\_\_1=k4\_struct\_0~X1)))){\unicdcdcdhd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~k5\_numbers){\unicdbdjdcd}(((r1\_xxreal\_0~X4~X0){\unicdcdcdhd}(k3\_matrix\_1~\\
(u1\_struct\_0~X1)~X2~np\_\_1~X4=k4\_struct\_0~X1)){\unicdbdjdcd}((r1\_xxreal\_0~X4~\\
np\_\_1){\unicdcdcdid}(k3\_matrix\_1~(u1\_struct\_0~X1)~(k4\_matrix\_6~X0~X1~X3~X2)~\\
np\_\_1~X4=k4\_struct\_0~X1))))))))))))\end{array}
\label{hyp:ehedadpfngbgehchjgihbded}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~\\
X1){\unicdcdcdhd}((\preoh v6\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v33\_algstr\_0~X1){\unicdcdcdhd}\\
((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}((v3\_group\_1~\\
X1){\unicdcdcdhd}((v5\_group\_1~X1){\unicdcdcdhd}((v4\_vectsp\_1~X1){\unicdcdcdhd}((v5\_vectsp\_1~X1){\unicdcdcdhd}(\\
l6\_algstr\_0~X1)))))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_matrix\_1~X2~(u1\_struct\_0~\\
X1)~X0~X0){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X0~k6\_numbers){\unicdcdcdhd}((k3\_matrix\_1~(u1\_struct\_0~\\
X1)~X2~np\_\_1~np\_\_1{\unicdcdgdad}k4\_struct\_0~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_matrix\_1~X3~\\
(u1\_struct\_0~X1)~X0~X0){\unicdbdjdcd}(\preoh (v1\_matrix\_6~X3~X0~X1){\unicdcdcdhd}((k3\_matrix\_1~\\
(u1\_struct\_0~X1)~(k4\_matrix\_6~X0~X1~X2~X3)~np\_\_1~np\_\_1=k5\_struct\_0~\\
X1){\unicdcdcdhd}(({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k5\_numbers){\unicdbdjdcd}((r1\_xxreal\_0~\\
X4~X0){\unicdbdjdcd}((r1\_xxreal\_0~X4~np\_\_1){\unicdcdcdid}(k3\_matrix\_1~(u1\_struct\_0~X1)~\\
(k4\_matrix\_6~X0~X1~X2~X3)~np\_\_1~X4=k4\_struct\_0~X1)))){\unicdcdcdhd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~k5\_numbers){\unicdbdjdcd}(((r1\_xxreal\_0~X4~X0){\unicdcdcdhd}(k3\_matrix\_1~\\
(u1\_struct\_0~X1)~X2~X4~np\_\_1=k4\_struct\_0~X1)){\unicdbdjdcd}((r1\_xxreal\_0~X4~\\
np\_\_1){\unicdcdcdid}(k3\_matrix\_1~(u1\_struct\_0~X1)~(k4\_matrix\_6~X0~X1~X2~X3)~\\
X4~np\_\_1=k4\_struct\_0~X1))))))))))))\end{array}
\label{hyp:ehddjdpfngbgehchjgihbded}
\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 .  ((\preoh v6\_struct\_0~X0){\unicdcdcdhd}(l4\_struct\_0~X0)){\unicdbdjdcd}(\preoh v9\_struct\_0~\\
(k5\_struct\_0~X0)~X0)\end{array}
\label{hyp:ggdgbdbdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{{v9\_struct\_0}~{({{k4\_struct\_0}~{X0}})}}~{X0}})}}}\label{hyp:ggdgbdadpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l6\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l2\_algstr\_0}~{X0}})}{\unicdcdcdhd}{({{l5\_algstr\_0}~{X0}})}})}}}\label{hyp:egehpfmggdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l5\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l4\_algstr\_0}~{X0}})}{\unicdcdcdhd}{({{l4\_struct\_0}~{X0}})}})}}}\label{hyp:egehpfmgfdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l4\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{({{l2\_struct\_0}~{X0}})}{\unicdcdcdhd}{({{l3\_struct\_0}~{X0}})}})}}}\label{hyp:egehpfmgedpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v7\_ordinal1~X0){\unicdcdcdhd}\\
(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((\preoh v6\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}\\
((v33\_algstr\_0~X1){\unicdcdcdhd}((v3\_group\_1~X1){\unicdcdcdhd}((v5\_group\_1~X1){\unicdcdcdhd}((v2\_rlvect\_1~\\
X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}((v4\_vectsp\_1~X1){\unicdcdcdhd}\\
((v5\_vectsp\_1~X1){\unicdcdcdhd}(l6\_algstr\_0~X1)))))))))))){\unicdcdcdhd}((m1\_matrix\_1~\\
X2~(u1\_struct\_0~X1)~X0~X0){\unicdcdcdhd}(m1\_matrix\_1~X3~(u1\_struct\_0~X1)~X0~X0)))){\unicdbdjdcd}\\
(m1\_matrix\_1~(k4\_matrix\_6~X0~X1~X2~X3)~(u1\_struct\_0~X1)~X0~X0)\end{array}
\label{hyp:egehpflgedpfngbgehchjgihpfgd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehedbdpfngbgehchjgihbded}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~\\
X1){\unicdcdcdhd}((\preoh v6\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v33\_algstr\_0~X1){\unicdcdcdhd}\\
((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}((v3\_group\_1~\\
X1){\unicdcdcdhd}((v5\_group\_1~X1){\unicdcdcdhd}((v4\_vectsp\_1~X1){\unicdcdcdhd}((v5\_vectsp\_1~X1){\unicdcdcdhd}(\\
l6\_algstr\_0~X1)))))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_matrix\_1~X2~(u1\_struct\_0~\\
X1)~X0~X0){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X0~k6\_numbers){\unicdcdcdhd}((k3\_matrix\_1~(u1\_struct\_0~\\
X1)~X2~np\_\_1~np\_\_1{\unicdcdgdad}k4\_struct\_0~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_matrix\_1~X3~\\
(u1\_struct\_0~X1)~X0~X0){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_matrix\_1~X4~(u1\_struct\_0~\\
X1)~X0~X0){\unicdbdjdcd}(\preoh (v1\_matrix\_6~X3~X0~X1){\unicdcdcdhd}((v1\_matrix\_6~X4~X0~X1){\unicdcdcdhd}((k3\_matrix\_1~\\
(u1\_struct\_0~X1)~(k4\_matrix\_6~X0~X1~(k4\_matrix\_6~X0~X1~X3~X2)~X4)~\\
np\_\_1~np\_\_1=k5\_struct\_0~X1){\unicdcdcdhd}(({\unicdcdadad} X5 .  (m1\_subset\_1~X5~k5\_numbers){\unicdbdjdcd}\\
((r1\_xxreal\_0~X5~X0){\unicdbdjdcd}((r1\_xxreal\_0~X5~np\_\_1){\unicdcdcdid}(k3\_matrix\_1~(u1\_struct\_0~\\
X1)~(k4\_matrix\_6~X0~X1~(k4\_matrix\_6~X0~X1~X3~X2)~X4)~X5~np\_\_1=k4\_struct\_0~\\
X1)))){\unicdcdcdhd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~k5\_numbers){\unicdbdjdcd}((r1\_xxreal\_0~\\
X5~X0){\unicdbdjdcd}((r1\_xxreal\_0~X5~np\_\_1){\unicdcdcdid}(k3\_matrix\_1~(u1\_struct\_0~X1)~\\
(k4\_matrix\_6~X0~X1~(k4\_matrix\_6~X0~X1~X3~X2)~X4)~np\_\_1~X5=k4\_struct\_0~\\
X1))))))))))))))\end{array}$$
\end{theorem}
\end{document}
