\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{t28\_quatern3 (TMGAqBWgiRjKPniBwNfvxcYRNn14iQva3jY)}
\maketitle
Let $ v1\_quaterni : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k25\_quaterni : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k5\_square\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_quatern2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k31\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_quaterni : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k8\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k17\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k18\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k19\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k20\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_quaterni : {\iota}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(k20\_quaterni~(k25\_quaterni~(k10\_real\_1~\\
np\_\_1~(k5\_square\_1~(k3\_quatern2~X0)))~(k31\_quaterni~X0))=k1\_real\_1~\\
(k8\_real\_1~(k10\_real\_1~np\_\_1~(k5\_square\_1~(k3\_quatern2~X0)))~\\
(k20\_quaterni~X0)))\end{array}
\label{hyp:ehcdhdpfbhfhbgehfgchogdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(k19\_quaterni~(k25\_quaterni~(k10\_real\_1~\\
np\_\_1~(k5\_square\_1~(k3\_quatern2~X0)))~(k31\_quaterni~X0))=k1\_real\_1~\\
(k8\_real\_1~(k10\_real\_1~np\_\_1~(k5\_square\_1~(k3\_quatern2~X0)))~\\
(k19\_quaterni~X0)))\end{array}
\label{hyp:ehcdgdpfbhfhbgehfgchogdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(k18\_quaterni~(k25\_quaterni~(k10\_real\_1~\\
np\_\_1~(k5\_square\_1~(k3\_quatern2~X0)))~(k31\_quaterni~X0))=k1\_real\_1~\\
(k8\_real\_1~(k10\_real\_1~np\_\_1~(k5\_square\_1~(k3\_quatern2~X0)))~\\
(k18\_quaterni~X0)))\end{array}
\label{hyp:ehcdfdpfbhfhbgehfgchogdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(X0=k6\_quaterni~(k17\_quaterni~X0)~\\
(k18\_quaterni~X0)~(k19\_quaterni~X0)~(k20\_quaterni~X0))\end{array}
\label{hyp:ehcdedpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(k17\_quaterni~(k25\_quaterni~(k10\_real\_1~\\
np\_\_1~(k5\_square\_1~(k3\_quatern2~X0)))~(k31\_quaterni~X0))=k8\_real\_1~\\
(k10\_real\_1~np\_\_1~(k5\_square\_1~(k3\_quatern2~X0)))~(k17\_quaterni~\\
X0))\end{array}
\label{hyp:ehcdedpfbhfhbgehfgchogdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_1){\unicdcdcdhd}(m2\_subset\_1~np\_\_1~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_1~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_1~k1\_numbers))\end{array}
\label{hyp:dhahdgbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{{v3\_membered}~{k1\_numbers}}\label{hyp:ggdgddpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k1\_numbers){\unicdcdcdhd}(v1\_quaterni~\\
X1)){\unicdbdjdcd}(v1\_quaterni~(k25\_quaterni~X0~X1))\end{array}
\label{hyp:ggdgbdddpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(m1\_subset\_1~(k5\_square\_1~\\
X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgfdpfdhbhfhbgchfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(m1\_subset\_1~(k3\_quatern2~X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgddpfbhfhbgehfgchogcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(m1\_subset\_1~(k31\_quaterni~X0)~k1\_quaterni)\end{array}
\label{hyp:egehpflgddbdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k1\_numbers){\unicdcdcdhd}(v1\_xreal\_0~\\
X1)){\unicdbdjdcd}(m1\_subset\_1~(k10\_real\_1~X0~X1)~k1\_numbers)\end{array}
\label{hyp:egehpflgbdadpfchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_quaterni}})}{\unicdbdjdcd}{({{v1\_quaterni}~{X0}})}}}\label{hyp:dgdgbdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
(v1\_xreal\_0~X1))\end{array}
\label{hyp:dgdgbdedpfngfgngcgfgchfgeg}
\end{equation}
\begin{theorem}\label{thm:ehcdidpfbhfhbgehfgchogdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(k25\_quaterni~(k10\_real\_1~np\_\_1~\\
(k5\_square\_1~(k3\_quatern2~X0)))~(k31\_quaterni~X0)=k6\_quaterni~\\
(k8\_real\_1~(k10\_real\_1~np\_\_1~(k5\_square\_1~(k3\_quatern2~X0)))~\\
(k17\_quaterni~X0))~(k1\_real\_1~(k8\_real\_1~(k10\_real\_1~np\_\_1~(k5\_square\_1~\\
(k3\_quatern2~X0)))~(k18\_quaterni~X0)))~(k1\_real\_1~(k8\_real\_1~\\
(k10\_real\_1~np\_\_1~(k5\_square\_1~(k3\_quatern2~X0)))~(k19\_quaterni~\\
X0)))~(k1\_real\_1~(k8\_real\_1~(k10\_real\_1~np\_\_1~(k5\_square\_1~(k3\_quatern2~\\
X0)))~(k20\_quaterni~X0))))\end{array}$$
\end{theorem}
\end{document}
