\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{t47\_quatern2 (TMTxPRFXH5dp72uPcopb6cyyPQbtjthrGRe)}
\maketitle
Let $ k8\_quatern2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k16\_quatern2 : {\iota}$ be given.
Let $ v1\_quaterni : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_quatern2 : {\iota}$ be given.
Let $ k6\_quatern2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_quatern2 : {\iota}$ be given.
Let $ k7\_quatern2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k22\_quaterni : {\iota}$ be given.
Let $ v6\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_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 $ 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 $ v3\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l6\_algstr\_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 $ l1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_quaterni : {\iota}$ be given.
Let $ u1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_quatern2 : {\iota}$ be given.
Let $ u2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k12\_quatern2 : {\iota}$ be given.
Let $ g6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ u3\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}((X0{\unicdcdgdad}k1\_quatern2){\unicdbdjdcd}(k6\_quatern2~\\
X0~X0=k2\_quatern2))\end{array}
\label{hyp:ehddddpfbhfhbgehfgchogcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_quaterni}~{X0}})}{\unicdbdjdcd}{({{{k8\_quatern2}~{X0}}={{k7\_quatern2}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpfbhfhbgehfgchogcd}
\end{equation}
Assume the following.
\begin{equation}
{{k2\_quatern2}={k22\_quaterni}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfbhfhbgehfgchogcd}
\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}
\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 .  {{({{l2\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l2\_struct\_0}~{X0}})}{\unicdcdcdhd}{({{l1\_algstr\_0}~{X0}})}})}}}\label{hyp:egehpfmgcdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_quaterni}~{k22\_quaterni}}\label{hyp:egehpflgcdcdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{({{v36\_algstr\_0}~{k16\_quatern2}})}{\unicdcdcdhd}{({{l6\_algstr\_0}~{k16\_quatern2}})}}\label{hyp:egehpflgbdgdpfbhfhbgehfgchogcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(k7\_quatern2~X0=k6\_quatern2~k2\_quatern2~\\
X0)\end{array}
\label{hyp:egcdpfbhfhbgehfgchogcd}
\end{equation}
Assume the following.
\begin{equation}
{{k22\_quaterni}={np\_\_1}}\label{hyp:egbdidpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v36\_algstr\_0~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)){\unicdbdjdcd}((X0=k16\_quatern2){\unicdbdjded}\\
((u1\_struct\_0~X0=k1\_quaterni){\unicdcdcdhd}((u1\_algstr\_0~X0=k10\_quatern2){\unicdcdcdhd}\\
((u2\_algstr\_0~X0=k12\_quatern2){\unicdcdcdhd}((k5\_struct\_0~X0=k2\_quatern2){\unicdcdcdhd}\\
(k4\_struct\_0~X0=k1\_quatern2))))))\end{array}
\label{hyp:egbdadpfbhfhbgehfgchogcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l6\_algstr\_0~X0){\unicdbdjdcd}((v36\_algstr\_0~X0){\unicdbdjdcd}(X0=g6\_algstr\_0~\\
(u1\_struct\_0~X0)~(u1\_algstr\_0~X0)~(u2\_algstr\_0~X0)~(u3\_struct\_0~\\
X0)~(u2\_struct\_0~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghddgdpfbgmghgdhehchpfad}
\end{equation}
\begin{theorem}\label{thm:ehedhdpfbhfhbgehfgchogcd}
${{{k8\_quatern2}~{({{k5\_struct\_0}~{k16\_quatern2}})}}={{k5\_struct\_0}~{k16\_quatern2}}}$.
\end{theorem}
\end{document}
