\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{t14\_cayley (TMGfqhbMmQU9C54fX9xgL1zJCe9eGtdbYT2)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_group\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k10\_group\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_cayley : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_cayley : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 $ v1\_group\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v15\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_monoid\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_group\_1~\\
X1){\unicdcdcdhd}((v3\_group\_1~X1){\unicdcdcdhd}(l3\_algstr\_0~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~X1)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_group\_6~\\
X2~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X1)~(u1\_struct\_0~X0))))))){\unicdbdjdcd}((v2\_funct\_1~X2){\unicdbdjdcd}(r1\_group\_6~X1~(\\
k10\_group\_6~X1~X0~X2)))))\end{array}
\label{hyp:ehgdidpfhgchpgfhahpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdbdjdcd}((v1\_funct\_1~(k4\_cayley~X0)){\unicdcdcdhd}((v2\_funct\_1~\\
(k4\_cayley~X0)){\unicdcdcdhd}(v1\_funct\_2~(k4\_cayley~X0)~(u1\_struct\_0~X0)~(\\
u1\_struct\_0~(k2\_cayley~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:ggdgjdpfdgbgjhmgfgjh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdbdjdcd}((v1\_funct\_1~(k4\_cayley~X0)){\unicdcdcdhd}((v1\_funct\_2~\\
(k4\_cayley~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~(k2\_cayley~(u1\_struct\_0~\\
X0)))){\unicdcdcdhd}(v1\_group\_6~(k4\_cayley~X0)~X0~(k2\_cayley~(u1\_struct\_0~\\
X0)))))\end{array}
\label{hyp:ggdgidpfdgbgjhmgfgjh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v2\_struct\_0~(k2\_cayley~X0)){\unicdcdcdhd}((v15\_algstr\_0~(k2\_cayley~\\
X0)){\unicdcdcdhd}((v2\_group\_1~(k2\_cayley~X0)){\unicdcdcdhd}((v3\_group\_1~(k2\_cayley~X0)){\unicdcdcdhd}\\
(v1\_monoid\_0~(k2\_cayley~X0)))))\end{array}
\label{hyp:ggdgedpfdgbgjhmgfgjh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdbdjdcd}((v1\_funct\_1~(k4\_cayley~X0)){\unicdcdcdhd}((v1\_funct\_2~\\
(k4\_cayley~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~(k2\_cayley~(u1\_struct\_0~\\
X0)))){\unicdcdcdhd}(m1\_subset\_1~(k4\_cayley~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~(k2\_cayley~(u1\_struct\_0~X0))))))))\end{array}
\label{hyp:egehpflgedpfdgbgjhmgfgjh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v15\_algstr\_0~(k2\_cayley~X0)){\unicdcdcdhd}((v1\_monoid\_0~(k2\_cayley~\\
X0)){\unicdcdcdhd}(l3\_algstr\_0~(k2\_cayley~X0)))\end{array}
\label{hyp:egehpflgcdpfdgbgjhmgfgjh}
\end{equation}
\begin{theorem}\label{thm:ehbdedpfdgbgjhmgfgjh}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdbdjdcd}(r1\_group\_6~X0~(k10\_group\_6~X0~(k2\_cayley~\\
(u1\_struct\_0~X0))~(k4\_cayley~X0)))\end{array}$$
\end{theorem}
\end{document}
