\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{t40\_quatern2 (TMUYq92AUgCzfnymRYaJ7JZkdedJxBwx5bM)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k16\_quatern2 : {\iota}$ be given.
Let $ k4\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_group\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_quatern2 : {\iota}$ be given.
Let $ k5\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_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 $ 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 $ l6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v34\_algstr\_0 : {{\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.
Assume the following.
\begin{equation}
{{{k1\_group\_1}~{k16\_quatern2}}={k2\_quatern2}}\label{hyp:ehddidpfbhfhbgehfgchogcd}
\end{equation}
Assume the following.
\begin{equation}
{{{k5\_struct\_0}~{k16\_quatern2}}={k2\_quatern2}}\label{hyp:ehddhdpfbhfhbgehfgchogcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}((v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}\\
((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k6\_algstr\_0~X0~\\
(k4\_algstr\_0~X0~(k5\_struct\_0~X0))~X1=k4\_algstr\_0~X0~X1))\end{array}
\label{hyp:mgedhdpfghfgdgehdhahpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v6\_struct\_0~k16\_quatern2){\unicdcdcdhd}((v13\_algstr\_0~k16\_quatern2){\unicdcdcdhd}\\
((v34\_algstr\_0~k16\_quatern2){\unicdcdcdhd}((v36\_algstr\_0~k16\_quatern2){\unicdcdcdhd}\\
((v2\_rlvect\_1~k16\_quatern2){\unicdcdcdhd}((v3\_rlvect\_1~k16\_quatern2){\unicdcdcdhd}(\\
(v4\_rlvect\_1~k16\_quatern2){\unicdcdcdhd}((v3\_group\_1~k16\_quatern2){\unicdcdcdhd}((v3\_vectsp\_1~\\
k16\_quatern2){\unicdcdcdhd}((v5\_vectsp\_1~k16\_quatern2){\unicdcdcdhd}(v6\_vectsp\_1~k16\_quatern2))))))))))\end{array}
\label{hyp:ggdggdpfbhfhbgehfgchogcd}
\end{equation}
Assume the following.
\begin{equation}
{{({{v36\_algstr\_0}~{k16\_quatern2}})}{\unicdcdcdhd}{({{v4\_vectsp\_1}~{k16\_quatern2}})}}\label{hyp:ggdgfdpfbhfhbgehfgchogcd}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v2\_struct\_0}~{k16\_quatern2}}}})}{\unicdcdcdhd}{({{v36\_algstr\_0}~{k16\_quatern2}})}}\label{hyp:ggdgedpfbhfhbgehfgchogcd}
\end{equation}
Assume the following.
\begin{equation}
{{({{v36\_algstr\_0}~{k16\_quatern2}})}{\unicdcdcdhd}{({{l6\_algstr\_0}~{k16\_quatern2}})}}\label{hyp:egehpflgbdgdpfbhfhbgehfgchogcd}
\end{equation}
\begin{theorem}\label{thm:ehedadpfbhfhbgehfgchogcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~k16\_quatern2)){\unicdbdjdcd}(k4\_algstr\_0~\\
k16\_quatern2~X0=k6\_algstr\_0~k16\_quatern2~(k4\_algstr\_0~k16\_quatern2~\\
(k1\_group\_1~k16\_quatern2))~X0)\end{array}$$
\end{theorem}
\end{document}
