\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\_quofield (TMN8KGQWsquLhwxmEypDA7R8UxMT7RR8Yae)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_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 $ v5\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_vectsp\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_quofield : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_quofield : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k15\_quofield : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k17\_quofield : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_quofield : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_quofield : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k13\_quofield : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l5\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}\\
((v3\_group\_1~X0){\unicdcdcdhd}((v5\_group\_1~X0){\unicdcdcdhd}((v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~\\
X0){\unicdcdcdhd}((v1\_vectsp\_2~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_quofield~X0))~(k7\_quofield~X0)){\unicdbdjdcd}\\
((k8\_quofield~X0~X1~(k13\_quofield~X0~X1)=k11\_quofield~X0){\unicdcdcdhd}(k8\_quofield~\\
X0~(k13\_quofield~X0~X1)~X1=k11\_quofield~X0)))\end{array}
\label{hyp:ehbdhdpfbhfhpgggjgfgmgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}(l5\_algstr\_0~\\
X0))){\unicdbdjdcd}(\preoh v1\_xboole\_0~(k7\_quofield~X0))\end{array}
\label{hyp:ggdgddpfbhfhpgggjgfgmgeg}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}(l5\_algstr\_0~\\
X0))){\unicdbdjdcd}(m1\_subset\_1~(k7\_quofield~X0)~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
(k1\_quofield~X0))))\end{array}
\label{hyp:egehpflghdpfbhfhpgggjgfgmgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}\\
((v3\_group\_1~X0){\unicdcdcdhd}((v5\_group\_1~X0){\unicdcdcdhd}((v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~\\
X0){\unicdcdcdhd}((v1\_vectsp\_2~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)))))))))))){\unicdbdjdcd}((v1\_funct\_1~\\
(k17\_quofield~X0)){\unicdcdcdhd}((v1\_funct\_2~(k17\_quofield~X0)~(k7\_quofield~\\
X0)~(k7\_quofield~X0)){\unicdcdcdhd}(m1\_subset\_1~(k17\_quofield~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k7\_quofield~X0)~(k7\_quofield~X0))))))\end{array}
\label{hyp:egehpflgbdhdpfbhfhpgggjgfgmgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}\\
((v3\_group\_1~X0){\unicdcdcdhd}((v5\_group\_1~X0){\unicdcdcdhd}((v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~\\
X0){\unicdcdcdhd}((v1\_vectsp\_2~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)))))))))))){\unicdbdjdcd}((v1\_funct\_1~\\
(k15\_quofield~X0)){\unicdcdcdhd}((v1\_funct\_2~(k15\_quofield~X0)~(k2\_zfmisc\_1~\\
(k7\_quofield~X0)~(k7\_quofield~X0))~(k7\_quofield~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
(k15\_quofield~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k7\_quofield~\\
X0)~(k7\_quofield~X0))~(k7\_quofield~X0))))))\end{array}
\label{hyp:egehpflgbdfdpfbhfhpgggjgfgmgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}\\
((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v5\_group\_1~X0){\unicdcdcdhd}((v4\_vectsp\_1~X0){\unicdcdcdhd}((\\
v5\_vectsp\_1~X0){\unicdcdcdhd}((v1\_vectsp\_2~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)))))))))))){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k7\_quofield~X0))){\unicdbdjdcd}(m2\_subset\_1~(k13\_quofield~\\
X0~X1)~(k1\_zfmisc\_1~(k1\_quofield~X0))~(k7\_quofield~X0))\end{array}
\label{hyp:egehpflgbdddpfbhfhpgggjgfgmgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}\\
((v3\_group\_1~X0){\unicdcdcdhd}((v5\_group\_1~X0){\unicdcdcdhd}((v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~\\
X0){\unicdcdcdhd}((v1\_vectsp\_2~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k7\_quofield~X0)~(k7\_quofield~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k7\_quofield~\\
X0)~(k7\_quofield~X0)))))){\unicdbdjdcd}((X1=k17\_quofield~X0){\unicdbdjded}({\unicdcdadad} X2 .  \\
(m2\_subset\_1~X2~(k1\_zfmisc\_1~(k1\_quofield~X0))~(k7\_quofield~X0)){\unicdbdjdcd}\\
(k3\_funct\_2~(k7\_quofield~X0)~(k7\_quofield~X0)~X1~X2=k13\_quofield~\\
X0~X2))))\end{array}
\label{hyp:egbdedpfbhfhpgggjgfgmgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}\\
((v3\_group\_1~X0){\unicdcdcdhd}((v5\_group\_1~X0){\unicdcdcdhd}((v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~\\
X0){\unicdcdcdhd}((v1\_vectsp\_2~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k2\_zfmisc\_1~(k7\_quofield~X0)~\\
(k7\_quofield~X0))~(k7\_quofield~X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k7\_quofield~X0)~(k7\_quofield~X0))~\\
(k7\_quofield~X0)))))){\unicdbdjdcd}((X1=k15\_quofield~X0){\unicdbdjded}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k1\_quofield~X0))~(k7\_quofield~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m2\_subset\_1~X3~(k1\_zfmisc\_1~(k1\_quofield~X0))~(k7\_quofield~X0)){\unicdbdjdcd}\\
(k5\_binop\_1~(k7\_quofield~X0)~X1~X2~X3=k8\_quofield~X0~X2~X3)))))\end{array}
\label{hyp:egbdcdpfbhfhpgggjgfgmgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_xboole\_0~X1))\end{array}
\label{hyp:dgdgbdpfdhfhcgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdidpfbhfhpgggjgfgmgeg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}\\
((v3\_group\_1~X0){\unicdcdcdhd}((v5\_group\_1~X0){\unicdcdcdhd}((v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~\\
X0){\unicdcdcdhd}((v1\_vectsp\_2~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_quofield~X0))~(k7\_quofield~X0)){\unicdbdjdcd}\\
((k5\_binop\_1~(k7\_quofield~X0)~(k15\_quofield~X0)~X1~(k3\_funct\_2~\\
(k7\_quofield~X0)~(k7\_quofield~X0)~(k17\_quofield~X0)~X1)=k11\_quofield~\\
X0){\unicdcdcdhd}(k5\_binop\_1~(k7\_quofield~X0)~(k15\_quofield~X0)~(k3\_funct\_2~\\
(k7\_quofield~X0)~(k7\_quofield~X0)~(k17\_quofield~X0)~X1)~X1=k11\_quofield~\\
X0)))\end{array}$$
\end{theorem}
\end{document}
