\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{t33\_quatern3 (TMHCn1dUfbxRdfXtrQuJEQWa1YuyaL3a4zq)}
\maketitle
Let $ v1\_quaterni : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_quatern2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k27\_quaterni : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k31\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_square\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k32\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k17\_quaterni : {{\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 $ k10\_quaterni : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(k32\_quaterni~(k27\_quaterni~X0~X0)=\\
k7\_real\_1~(k7\_real\_1~(k7\_real\_1~(k5\_square\_1~(k17\_quaterni~X0))~\\
(k5\_square\_1~(k18\_quaterni~X0)))~(k5\_square\_1~(k19\_quaterni~\\
X0)))~(k5\_square\_1~(k20\_quaterni~X0)))\end{array}
\label{hyp:ehididpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(k3\_quatern2~(k27\_quaterni~X0~X0)=\\
k3\_quatern2~(k27\_quaterni~(k31\_quaterni~X0)~(k31\_quaterni~X0)))\end{array}
\label{hyp:ehddcdpfbhfhbgehfgchogdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(k5\_square\_1~(k3\_quatern2~X0)=k7\_real\_1~\\
(k7\_real\_1~(k7\_real\_1~(k5\_square\_1~(k17\_quaterni~X0))~(k5\_square\_1~\\
(k18\_quaterni~X0)))~(k5\_square\_1~(k19\_quaterni~X0)))~(k5\_square\_1~\\
(k20\_quaterni~X0)))\end{array}
\label{hyp:ehbdbdpfbhfhbgehfgchogdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_quaterni}~{X0}})}{\unicdbdjdcd}{({{{k3\_quatern2}~{X0}}={{k32\_quaterni}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfbhfhbgehfgchogcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_quaterni~X0){\unicdcdcdhd}(v1\_quaterni~X1)){\unicdbdjdcd}(\\
k27\_quaterni~X0~X1=k10\_quaterni~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdhdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_quaterni~X0){\unicdcdcdhd}(v1\_quaterni~X1)){\unicdbdjdcd}(\\
v1\_quaterni~(k10\_quaterni~X0~X1))\end{array}
\label{hyp:ggdghdpfbhfhbgehfgchogjg}
\end{equation}
\begin{theorem}\label{thm:ehddddpfbhfhbgehfgchogdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(k3\_quatern2~(k27\_quaterni~(k31\_quaterni~\\
X0)~(k31\_quaterni~X0))=k5\_square\_1~(k3\_quatern2~X0))\end{array}$$
\end{theorem}
\end{document}
