\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{t9\_quatern3 (TMUrWdw5ZbKrDMxWtyG9b12Pi6CfDBW5aBe)}
\maketitle
Let $ v1\_quaterni : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k27\_quaterni : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k26\_quaterni : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k23\_quaterni : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_real\_1 : {{\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 $ k18\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k19\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k20\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k25\_quaterni : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xcmplx\_0 : {\iota}$ be given.
Let $ k11\_quaterni : {\iota}$ be given.
Let $ k12\_quaterni : {\iota}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v3\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_quaterni~X1){\unicdbdjdcd}(k27\_quaterni~\\
X0~X1=k26\_quaterni~(k26\_quaterni~(k23\_quaterni~(k9\_real\_1~(k9\_real\_1~\\
(k9\_real\_1~(k8\_real\_1~(k17\_quaterni~X0)~(k17\_quaterni~X1))~(k8\_real\_1~\\
(k18\_quaterni~X0)~(k18\_quaterni~X1)))~(k8\_real\_1~(k19\_quaterni~\\
X0)~(k19\_quaterni~X1)))~(k8\_real\_1~(k20\_quaterni~X0)~(k20\_quaterni~\\
X1)))~(k25\_quaterni~(k9\_real\_1~(k7\_real\_1~(k7\_real\_1~(k8\_real\_1~\\
(k17\_quaterni~X0)~(k18\_quaterni~X1))~(k8\_real\_1~(k18\_quaterni~\\
X0)~(k17\_quaterni~X1)))~(k8\_real\_1~(k19\_quaterni~X0)~(k20\_quaterni~\\
X1)))~(k8\_real\_1~(k20\_quaterni~X0)~(k19\_quaterni~X1)))~k1\_xcmplx\_0))~\\
(k25\_quaterni~(k9\_real\_1~(k7\_real\_1~(k7\_real\_1~(k8\_real\_1~(k17\_quaterni~\\
X0)~(k19\_quaterni~X1))~(k8\_real\_1~(k19\_quaterni~X0)~(k17\_quaterni~\\
X1)))~(k8\_real\_1~(k20\_quaterni~X0)~(k18\_quaterni~X1)))~(k8\_real\_1~\\
(k18\_quaterni~X0)~(k20\_quaterni~X1)))~k11\_quaterni))~(k25\_quaterni~\\
(k9\_real\_1~(k7\_real\_1~(k7\_real\_1~(k8\_real\_1~(k17\_quaterni~X0)~\\
(k20\_quaterni~X1))~(k8\_real\_1~(k20\_quaterni~X0)~(k17\_quaterni~\\
X1)))~(k8\_real\_1~(k18\_quaterni~X0)~(k19\_quaterni~X1)))~(k8\_real\_1~\\
(k19\_quaterni~X0)~(k18\_quaterni~X1)))~k12\_quaterni)))\end{array}
\label{hyp:ehjdddpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjdcd}{({{{{k3\_xcmplx\_0}~{X0}}~{k6\_numbers}}={k6\_numbers}})}}}\label{hyp:ehcdpfbgchjgehigng}
\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}(k8\_real\_1~X0~X1=k3\_xcmplx\_0~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpfchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}((m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}((\\
X0=k17\_quaterni~X0){\unicdcdcdhd}((k18\_quaterni~X0=k6\_numbers){\unicdcdcdhd}((k19\_quaterni~\\
X0=k6\_numbers){\unicdcdcdhd}(k20\_quaterni~X0=k6\_numbers)))))\end{array}
\label{hyp:mgcdpfbhfhbgehfgchogdd}
\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\_xreal\_0~\\
X1)){\unicdbdjdcd}(m1\_subset\_1~(k8\_real\_1~X0~X1)~k1\_numbers)\end{array}
\label{hyp:egehpflgidpfchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(m1\_subset\_1~(k20\_quaterni~X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgcdadpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(m1\_subset\_1~(k19\_quaterni~X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgbdjdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(m1\_subset\_1~(k18\_quaterni~X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgbdidpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(m1\_subset\_1~(k17\_quaterni~X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgbdhdpfbhfhbgehfgchogjg}
\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}(k8\_real\_1~X0~X1=k8\_real\_1~X1~X0)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgidpfchfgbgmgpfbd}
\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}(k7\_real\_1~X0~X1=k7\_real\_1~X1~X0)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflghdpfchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xcmplx\_0~X0){\unicdcdcdhd}(v1\_xcmplx\_0~X1)){\unicdbdjdcd}(\\
k3\_xcmplx\_0~X0~X1=k3\_xcmplx\_0~X1~X0)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgddpfihdgngahmgihpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v3\_membered}~{X0}})}{\unicdbdjdcd}{({{v1\_membered}~{X0}})}}}\label{hyp:dgdgfdpfngfgngcgfgchfgeg}
\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}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
(v1\_xcmplx\_0~X1))\end{array}
\label{hyp:dgdgbdcdpfngfgngcgfgchfgeg}
\end{equation}
\begin{theorem}\label{thm:ehjdpfbhfhbgehfgchogdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_quaterni~X1){\unicdbdjdcd}((\\
m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(k27\_quaterni~X0~X1=k27\_quaterni~\\
X1~X0)))\end{array}$$
\end{theorem}
\end{document}
