\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{l72\_matrix\_9 (TMFJXcp8rkQD2zVEiaBmfBHatRSena1CSbj)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ m1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_matrix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_setwiseo : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k12\_matrix\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k15\_matrix\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_matrix\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ m1\_matrix\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k11\_matrix\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_finsop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k10\_matrix\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ u2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\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}(\\
(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)))))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_matrix\_2~X2~(k12\_matrix\_2~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_matrix\_1~X3~(u1\_struct\_0~X1)~X0~X0){\unicdbdjdcd}(({\unicdcdaddd} X4 .  \\
(m1\_subset\_1~X4~k5\_numbers){\unicdcdcdhd}((X4 \in k2\_finseq\_1~X0){\unicdcdcdhd}({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~k5\_numbers){\unicdbdjdcd}((X5 \in k2\_finseq\_1~X0){\unicdbdjdcd}(k1\_funct\_1~\\
(k9\_matrix\_1~(u1\_struct\_0~X1)~X3~X4)~X5=k4\_struct\_0~X1))))){\unicdbdjdcd}(\\
k3\_funct\_2~(k12\_matrix\_2~X0)~(u1\_struct\_0~X1)~(k1\_matrix\_9~X0~\\
X1~X3)~X2=k4\_struct\_0~X1)))))\end{array}
\label{hyp:ehfdcdpfngbgehchjgihpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\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}(\\
(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)))))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_matrix\_1~X2~(u1\_struct\_0~\\
X1)~X0~X0){\unicdbdjdcd}(({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~k5\_numbers){\unicdcdcdhd}((X3 \in k2\_finseq\_1~\\
X0){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k5\_numbers){\unicdbdjdcd}((X4 \in k2\_finseq\_1~\\
X0){\unicdbdjdcd}(k1\_funct\_1~(k9\_matrix\_1~(u1\_struct\_0~X1)~X2~X3)~X4=k4\_struct\_0~\\
X1))))){\unicdbdjdcd}(k7\_setwiseo~(k12\_matrix\_2~X0)~(u1\_struct\_0~X1)~(u1\_algstr\_0~\\
X1)~(k15\_matrix\_2~(k12\_matrix\_2~X0))~(k11\_matrix\_3~X0~X1~X2)=k4\_struct\_0~\\
X1))))\end{array}
\label{hyp:ehfdbdpfngbgehchjgihpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\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}(\\
(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)))))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_matrix\_2~X2~(k12\_matrix\_2~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_matrix\_1~X3~(u1\_struct\_0~X1)~X0~X0){\unicdbdjdcd}(({\unicdcdaddd} X4 .  \\
(m1\_subset\_1~X4~k5\_numbers){\unicdcdcdhd}((X4 \in k2\_finseq\_1~X0){\unicdcdcdhd}({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~k5\_numbers){\unicdbdjdcd}((X5 \in k2\_finseq\_1~X0){\unicdbdjdcd}(k1\_funct\_1~\\
(k9\_matrix\_1~(u1\_struct\_0~X1)~X3~X4)~X5=k4\_struct\_0~X1))))){\unicdbdjdcd}(\\
k3\_funct\_2~(k12\_matrix\_2~X0)~(u1\_struct\_0~X1)~(k11\_matrix\_3~X0~\\
X1~X3)~X2=k4\_struct\_0~X1)))))\end{array}
\label{hyp:ehfdadpfngbgehchjgihpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((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))){\unicdbdjdcd}((v1\_funct\_1~(k1\_matrix\_9~X0~X1~X2)){\unicdcdcdhd}((v1\_funct\_2~(k1\_matrix\_9~\\
X0~X1~X2)~(k12\_matrix\_2~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~(k1\_matrix\_9~\\
X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k12\_matrix\_2~X0)~(u1\_struct\_0~\\
X1))))))\end{array}
\label{hyp:egehpflgbdpfngbgehchjgihpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((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))){\unicdbdjdcd}((v1\_funct\_1~(k11\_matrix\_3~X0~X1~X2)){\unicdcdcdhd}((v1\_funct\_2~(\\
k11\_matrix\_3~X0~X1~X2)~(k12\_matrix\_2~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~\\
(k11\_matrix\_3~X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k12\_matrix\_2~\\
X0)~(u1\_struct\_0~X1))))))\end{array}
\label{hyp:egehpflgbdbdpfngbgehchjgihpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\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}(\\
(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)))))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_matrix\_1~X2~(u1\_struct\_0~\\
X1)~X0~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k12\_matrix\_2~\\
X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k12\_matrix\_2~X0)~(u1\_struct\_0~X1)))))){\unicdbdjdcd}((X3=k1\_matrix\_9~X0~\\
X1~X2){\unicdbdjded}({\unicdcdadad} X4 .  (m1\_matrix\_2~X4~(k12\_matrix\_2~X0)){\unicdbdjdcd}(k3\_funct\_2~\\
(k12\_matrix\_2~X0)~(u1\_struct\_0~X1)~X3~X4=k1\_finsop\_1~(u1\_struct\_0~\\
X1)~(k10\_matrix\_3~X0~X1~X2~X4)~(u2\_algstr\_0~X1)))))))\end{array}
\label{hyp:egbdpfngbgehchjgihpfjd}
\end{equation}
\begin{theorem}\label{thm:mghdcdpfngbgehchjgihpfjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((\preoh v6\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v33\_algstr\_0~X1){\unicdcdcdhd}(\\
(v3\_group\_1~X1){\unicdcdcdhd}((v5\_group\_1~X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~\\
X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}((v4\_vectsp\_1~X1){\unicdcdcdhd}((v5\_vectsp\_1~X1){\unicdcdcdhd}\\
(l6\_algstr\_0~X1)))))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_matrix\_1~X2~(u1\_struct\_0~\\
X1)~X0~X0){\unicdbdjdcd}(({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~k5\_numbers){\unicdcdcdhd}((X3 \in k2\_finseq\_1~\\
X0){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k5\_numbers){\unicdbdjdcd}((X4 \in k2\_finseq\_1~\\
X0){\unicdbdjdcd}(k1\_funct\_1~(k9\_matrix\_1~(u1\_struct\_0~X1)~X2~X3)~X4=k4\_struct\_0~\\
X1))))){\unicdbdjdcd}(k7\_setwiseo~(k12\_matrix\_2~X0)~(u1\_struct\_0~X1)~(u1\_algstr\_0~\\
X1)~(k15\_matrix\_2~(k12\_matrix\_2~X0))~(k1\_matrix\_9~X0~X1~X2)=k4\_struct\_0~\\
X1))))\end{array}$$
\end{theorem}
\end{document}
