\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t2\_group\_12 (TMHTQKmZ3rWHpRriYAt8PU6DpcobMgSTsgD)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_group\_7 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_group\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_group\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_group\_12 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_group\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_group\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_funct\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_group\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v15\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_monoid\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0 \in X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~X0~X2)\end{array}
\label{hyp:ehedpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(\\
(v4\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}((v1\_group\_7~\\
X1){\unicdcdcdhd}((v2\_group\_7~X1~X0){\unicdcdcdhd}(v3\_group\_7~X1~X0))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}(v1\_funct\_1~\\
X3)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~(k1\_group\_7~X0~\\
X1~X2))){\unicdbdjdcd}(((k9\_xtuple\_0~X3=X0){\unicdcdcdhd}((k1\_funct\_1~X3~X2=X4){\unicdcdcdhd}({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~X0){\unicdbdjdcd}((X5{\unicdcdgdad}X2){\unicdbdjdcd}(k1\_funct\_1~X3~X5=k1\_group\_1~(k1\_group\_7~\\
X0~X1~X5)))))){\unicdbdjded}(X3=k2\_funct\_7~(k1\_group\_1~(k2\_group\_7~X0~X1))~\\
X2~X4))))))\end{array}
\label{hyp:ehbdpfhgchpgfhahpfbdcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}(v1\_group\_7~X1))))){\unicdbdjdcd}((\\
\preoh v2\_struct\_0~(k2\_group\_7~X0~X1)){\unicdcdcdhd}((v15\_algstr\_0~(k2\_group\_7~\\
X0~X1)){\unicdcdcdhd}(v1\_monoid\_0~(k2\_group\_7~X0~X1))))\end{array}
\label{hyp:ggdgcdpfhgchpgfhahpfhd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l3\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgddpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}(v1\_group\_7~X1))))){\unicdbdjdcd}((\\
v15\_algstr\_0~(k2\_group\_7~X0~X1)){\unicdcdcdhd}(l3\_algstr\_0~(k2\_group\_7~X0~\\
X1)))\end{array}
\label{hyp:egehpflgcdpfhgchpgfhahpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((v1\_relat\_1~\\
X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}\\
((v1\_group\_7~X1){\unicdcdcdhd}((v2\_group\_7~X1~X0){\unicdcdcdhd}(v3\_group\_7~X1~X0))))))){\unicdcdcdhd}\\
(m1\_subset\_1~X2~X0))){\unicdbdjdcd}(m1\_subset\_1~(k1\_group\_12~X0~X1~X2)~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k2\_group\_7~X0~X1))))\end{array}
\label{hyp:egehpflgbdpfhgchpgfhahpfbdcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(\\
(v4\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}((v1\_group\_7~\\
X1){\unicdcdcdhd}((v2\_group\_7~X1~X0){\unicdcdcdhd}(v3\_group\_7~X1~X0))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k2\_group\_7~X0~X1)))){\unicdbdjdcd}((X3=k1\_group\_12~X0~X1~X2){\unicdbdjded}\\
({\unicdcdadad} X4 .  (X4 \in X3){\unicdbdjded}({\unicdcdaddd} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~\\
(k1\_group\_7~X0~X1~X2))){\unicdcdcdhd}(X4=k2\_funct\_7~(k1\_group\_1~(k2\_group\_7~\\
X0~X1))~X2~X5)))))))\end{array}
\label{hyp:egbdpfhgchpgfhahpfbdcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_monoid\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~\\
X1)))\end{array}
\label{hyp:dgdgbdpfngpgogpgjgegpfad}
\end{equation}
\begin{theorem}\label{thm:ehcdpfhgchpgfhahpfbdcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(\\
(v4\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}((v1\_group\_7~\\
X1){\unicdcdcdhd}((v2\_group\_7~X1~X0){\unicdcdcdhd}(v3\_group\_7~X1~X0))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (X3 \in k1\_group\_12~X0~X1~X2){\unicdbdjded}({\unicdcdaddd} X4 .  \\
((v1\_relat\_1~X4){\unicdcdcdhd}(v1\_funct\_1~X4)){\unicdcdcdhd}({\unicdcdaddd} X5 .  (m1\_subset\_1~\\
X5~(u1\_struct\_0~(k1\_group\_7~X0~X1~X2))){\unicdcdcdhd}((X4=X3){\unicdcdcdhd}((k9\_xtuple\_0~\\
X4=X0){\unicdcdcdhd}((k1\_funct\_1~X4~X2=X5){\unicdcdcdhd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~X0){\unicdbdjdcd}\\
((X6{\unicdcdgdad}X2){\unicdbdjdcd}(k1\_funct\_1~X4~X6=k1\_group\_1~(k1\_group\_7~X0~X1~X6))))))))))))\end{array}$$
\end{theorem}
\end{document}
