\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{t88\_quatern3 (TMYJ7Hw3tZTZTQinU98WrPB2dt8JtPK5Kxt)}
\maketitle
Let $ k4\_quatern3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k28\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_quatern2 : {\iota}$ be given.
Let $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k6\_quaterni : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k5\_arytm\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_quatern3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_quaterni : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_quatern3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k21\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k32\_sin\_cos : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k18\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_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 $ k31\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xcmplx\_0 : {\iota}$ be given.
Let $ k22\_quaterni : {\iota}$ be given.
Let $ k27\_quaterni : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k1\_quaterni : {\iota}$ be given.
Let $ k3\_quatern3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_funct\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_numbers){\unicdbdjdcd}(k6\_quaterni~X0~X1~k6\_numbers~k6\_numbers=k5\_arytm\_0~\\
X0~X1))\end{array}
\label{hyp:ehjdbdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{{k2\_quatern3}~{({{k28\_quaterni}~{k2\_quatern2}})}}={np\_\_1}}\label{hyp:ehidhdpfbhfhbgehfgchogdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(k1\_quatern3~X0=k2\_quatern3~(k28\_quaterni~\\
X0))\end{array}
\label{hyp:ehidbdpfbhfhbgehfgchogdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(k21\_sin\_cos~(k10\_real\_1~k32\_sin\_cos~np\_\_2)=k6\_numbers){\unicdcdcdhd}((\\
k18\_sin\_cos~(k10\_real\_1~k32\_sin\_cos~np\_\_2)=np\_\_1){\unicdcdcdhd}((k21\_sin\_cos~\\
k32\_sin\_cos=k1\_real\_1~np\_\_1){\unicdcdcdhd}((k18\_sin\_cos~k32\_sin\_cos=k6\_numbers){\unicdcdcdhd}\\
((k21\_sin\_cos~(k7\_real\_1~k32\_sin\_cos~(k10\_real\_1~k32\_sin\_cos~\\
np\_\_2))=k6\_numbers){\unicdcdcdhd}((k18\_sin\_cos~(k7\_real\_1~k32\_sin\_cos~(\\
k10\_real\_1~k32\_sin\_cos~np\_\_2))=k1\_real\_1~np\_\_1){\unicdcdcdhd}((k21\_sin\_cos~\\
(k8\_real\_1~np\_\_2~k32\_sin\_cos)=np\_\_1){\unicdcdcdhd}(k18\_sin\_cos~(k8\_real\_1~\\
np\_\_2~k32\_sin\_cos)=k6\_numbers)))))))\end{array}
\label{hyp:ehhdhdpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(k28\_quaterni~X0=k6\_quaterni~(k1\_real\_1~\\
(k17\_quaterni~X0))~(k1\_real\_1~(k18\_quaterni~X0))~(k1\_real\_1~(\\
k19\_quaterni~X0))~(k1\_real\_1~(k20\_quaterni~X0)))\end{array}
\label{hyp:ehgdcdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{{k31\_quaterni}~{k1\_xcmplx\_0}}={{k28\_quaterni}~{k1\_xcmplx\_0}}}\label{hyp:ehfdbdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}((k17\_quaterni~(k31\_quaterni~X0)=\\
k17\_quaterni~X0){\unicdcdcdhd}((k18\_quaterni~(k31\_quaterni~X0)=k1\_real\_1~\\
(k18\_quaterni~X0)){\unicdcdcdhd}((k19\_quaterni~(k31\_quaterni~X0)=k1\_real\_1~\\
(k19\_quaterni~X0)){\unicdcdcdhd}(k20\_quaterni~(k31\_quaterni~X0)=k1\_real\_1~\\
(k20\_quaterni~X0)))))\end{array}
\label{hyp:ehededpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}((k17\_quaterni~(k28\_quaterni~X0)=\\
k1\_real\_1~(k17\_quaterni~X0)){\unicdcdcdhd}((k18\_quaterni~(k28\_quaterni~X0)=\\
k1\_real\_1~(k18\_quaterni~X0)){\unicdcdcdhd}((k19\_quaterni~(k28\_quaterni~X0)=\\
k1\_real\_1~(k19\_quaterni~X0)){\unicdcdcdhd}(k20\_quaterni~(k28\_quaterni~X0)=\\
k1\_real\_1~(k20\_quaterni~X0)))))\end{array}
\label{hyp:ehedbdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(k17\_quaterni~k1\_xcmplx\_0=k6\_numbers){\unicdcdcdhd}((k18\_quaterni~k1\_xcmplx\_0=\\
np\_\_1){\unicdcdcdhd}((k19\_quaterni~k1\_xcmplx\_0=k6\_numbers){\unicdcdcdhd}(k20\_quaterni~\\
k1\_xcmplx\_0=k6\_numbers)))\end{array}
\label{hyp:ehddadpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(k17\_quaterni~k22\_quaterni=np\_\_1){\unicdcdcdhd}((k18\_quaterni~k22\_quaterni=\\
k6\_numbers){\unicdcdcdhd}((k19\_quaterni~k22\_quaterni=k6\_numbers){\unicdcdcdhd}(k20\_quaterni~\\
k22\_quaterni=k6\_numbers)))\end{array}
\label{hyp:ehcdjdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_quaterni~X1){\unicdbdjdcd}(k27\_quaterni~\\
(k28\_quaterni~X0)~(k28\_quaterni~X1)=k27\_quaterni~X0~X1))\end{array}
\label{hyp:ehcdcdpfbhfhbgehfgchogcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(k28\_quaterni~X0=k27\_quaterni~(\\
k28\_quaterni~k2\_quatern2)~X0)\end{array}
\label{hyp:ehbdjdpfbhfhbgehfgchogcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_quaterni}~{X0}})}{\unicdbdjdcd}{({{{{k27\_quaterni}~{k2\_quatern2}}~{X0}}={X0}})}}}\label{hyp:ehbdfdpfbhfhbgehfgchogcd}
\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 .  (m1\_subset\_1~X0~k1\_quaterni){\unicdbdjdcd}(k4\_quatern3~X0=k3\_quatern3~\\
X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfbhfhbgehfgchogdd}
\end{equation}
Assume the following.
\begin{equation}
{{k2\_quatern2}={k22\_quaterni}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfbhfhbgehfgchogcd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_quaterni}~{k1\_xcmplx\_0}}\label{hyp:ggdgddpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{k1\_xboole\_0}}\label{hyp:ggdgbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}\\
((v1\_xreal\_0~X1){\unicdcdcdhd}((v1\_xreal\_0~X2){\unicdcdcdhd}(v1\_xreal\_0~X3)))){\unicdbdjdcd}(m1\_subset\_1~\\
(k6\_quaterni~X0~X1~X2~X3)~k1\_quaterni)\end{array}
\label{hyp:egehpflggdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k32\_sin\_cos}}~{k1\_numbers}}\label{hyp:egehpflgddcdpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(m1\_subset\_1~(k28\_quaterni~X0)~k1\_quaterni)\end{array}
\label{hyp:egehpflgcdidpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_quaterni~X0){\unicdcdcdhd}(v1\_quaterni~X1)){\unicdbdjdcd}(\\
m1\_subset\_1~(k27\_quaterni~X0~X1)~k1\_quaterni)\end{array}
\label{hyp:egehpflgcdhdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_quaterni}~{k22\_quaterni}}\label{hyp:egehpflgcdcdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(m1\_subset\_1~(k21\_sin\_cos~\\
X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgcdbdpfdhjgogpfdgpgdh}
\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 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_numbers){\unicdbdjdcd}(((X1=k6\_numbers){\unicdbdjdcd}(k5\_arytm\_0~X0~X1=X0)){\unicdcdcdhd}((\\
X1{\unicdcdgdad}k6\_numbers){\unicdbdjdcd}(k5\_arytm\_0~X0~X1=k5\_funct\_4~k1\_numbers~k6\_numbers~\\
np\_\_1~X0~X1))))\end{array}
\label{hyp:egfdpfbgchjhehngpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(k3\_quatern3~X0=k27\_quaterni~(k27\_quaterni~\\
X0~X0)~X0)\end{array}
\label{hyp:egcdpfbhfhbgehfgchogdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_quaterni}~{X0}})}{\unicdbdjdcd}{({{{k1\_quatern3}~{X0}}={{{k27\_quaterni}~{X0}}~{X0}}})}}}\label{hyp:egbdpfbhfhbgehfgchogdd}
\end{equation}
Assume the following.
\begin{equation}
{{k22\_quaterni}={np\_\_1}}\label{hyp:egbdidpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdghdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgcdpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgbdpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_quaterni}})}{\unicdbdjdcd}{({{v1\_quaterni}~{X0}})}}}\label{hyp:dgdgbdpfbhfhbgehfgchogjg}
\end{equation}
\begin{theorem}\label{thm:ehididpfbhfhbgehfgchogdd}
${{{k4\_quatern3}~{({{k28\_quaterni}~{k2\_quatern2}})}}={{k1\_real\_1}~{np\_\_1}}}$.
\end{theorem}
\end{document}
