\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{t36\_matrix\_6 (TMG16tErCPMSGc8mYaLAsZmdECJH6pSCNeZ)}
\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 $ 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\_matrix\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r2\_matrix\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ 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 .  \\
(v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_matrix\_1~X2~(u1\_struct\_0~X0)~\\
X1~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_matrix\_1~X3~(u1\_struct\_0~X0)~X1~X1){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_matrix\_1~X4~(u1\_struct\_0~X0)~X1~X1){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_matrix\_1~\\
X5~(u1\_struct\_0~X0)~X1~X1){\unicdbdjdcd}(((r2\_matrix\_6~X1~X0~X4~X2){\unicdcdcdhd}(r2\_matrix\_6~\\
X1~X0~X5~X3)){\unicdbdjdcd}(r2\_matrix\_6~X1~X0~(k4\_matrix\_6~X1~X0~X4~X5)~(k4\_matrix\_6~\\
X1~X0~X3~X2))))))))\end{array}
\label{hyp:ehbdedpfngbgehchjgihpfgd}
\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}\\
((r2\_matrix\_6~X0~X1~X2~X3){\unicdbdjdcd}(r2\_matrix\_6~X0~X1~X3~X2))\end{array}
\label{hyp:dhjhngngfgehchjhpfchcdpfngbgehchjgihpfgd}
\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}(m1\_matrix\_1~(k5\_matrix\_6~X0~X1~X2)~(u1\_struct\_0~X1)~X0~\\
X0)\end{array}
\label{hyp:egehpflgfdpfngbgehchjgihpfgd}
\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}
\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}((v1\_matrix\_6~X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_matrix\_1~X3~\\
(u1\_struct\_0~X1)~X0~X0){\unicdbdjdcd}((X3=k5\_matrix\_6~X0~X1~X2){\unicdbdjded}(r2\_matrix\_6~\\
X0~X1~X3~X2))))))\end{array}
\label{hyp:egedpfngbgehchjgihpfgd}
\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}((v1\_matrix\_6~X2~X0~X1){\unicdbdjded}({\unicdcdaddd} X3 .  (m1\_matrix\_1~X3~\\
(u1\_struct\_0~X1)~X0~X0){\unicdcdcdhd}(r2\_matrix\_6~X0~X1~X2~X3)))))\end{array}
\label{hyp:egddpfngbgehchjgihpfgd}
\end{equation}
\begin{theorem}\label{thm:ehddgdpfngbgehchjgihpfgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((\preoh v6\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v33\_algstr\_0~X1){\unicdcdcdhd}(\\
(v3\_group\_1~X1){\unicdcdcdhd}((v5\_group\_1~X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~\\
X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}((v4\_vectsp\_1~X1){\unicdcdcdhd}((v5\_vectsp\_1~X1){\unicdcdcdhd}\\
(l6\_algstr\_0~X1)))))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_matrix\_1~X2~(u1\_struct\_0~\\
X1)~X0~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_matrix\_1~X3~(u1\_struct\_0~X1)~X0~X0){\unicdbdjdcd}\\
(((v1\_matrix\_6~X2~X0~X1){\unicdcdcdhd}(v1\_matrix\_6~X3~X0~X1)){\unicdbdjdcd}((v1\_matrix\_6~\\
(k4\_matrix\_6~X0~X1~X2~X3)~X0~X1){\unicdcdcdhd}(k5\_matrix\_6~X0~X1~(k4\_matrix\_6~\\
X0~X1~X2~X3)=k4\_matrix\_6~X0~X1~(k5\_matrix\_6~X0~X1~X3)~(k5\_matrix\_6~\\
X0~X1~X2)))))))\end{array}$$
\end{theorem}
\end{document}
