\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{t42\_monoid\_0 (TMaAnCLR1hZ1KoqcmxZcLeRsJ9m7M4tarGg)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_monoid\_0 : {\iota}$ be given.
Let $ v1\_int\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v15\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_monoid\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_monoid\_0 : {\iota}$ be given.
Let $ k4\_numbers : {\iota}$ be given.
Let $ k2\_gr\_cy\_1 : {\iota}$ be given.
Let $ k5\_gr\_cy\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v15\_algstr\_0~X0){\unicdcdcdhd}(m2\_monoid\_0~\\
X0~k2\_monoid\_0))){\unicdbdjdcd}((X0=k3\_monoid\_0){\unicdbdjded}(u1\_struct\_0~X0=k4\_numbers))\end{array}
\label{hyp:ehedbdpfngpgogpgjgegpfad}
\end{equation}
Assume the following.
\begin{equation}
{{k3\_monoid\_0}={k2\_gr\_cy\_1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfngpgogpgjgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_int\_1~X0){\unicdbdjdcd}(m1\_subset\_1~(k5\_gr\_cy\_1~X0)~(u1\_struct\_0~\\
k2\_gr\_cy\_1))\end{array}
\label{hyp:egehpflgfdpfhgchpfdgjhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v2\_struct\_0~k3\_monoid\_0){\unicdcdcdhd}((v15\_algstr\_0~k3\_monoid\_0){\unicdcdcdhd}(m2\_monoid\_0~\\
k3\_monoid\_0~k2\_monoid\_0))\end{array}
\label{hyp:egehpflgddpfngpgogpgjgegpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_int\_1}~{X0}})}{\unicdbdjdcd}{({{{k5\_gr\_cy\_1}~{X0}}={X0}})}}}\label{hyp:eggdpfhgchpfdgjhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_numbers}})}{\unicdbdjdcd}{({{v1\_int\_1}~{X0}})}}}\label{hyp:dgdgbdpfjgogehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedcdpfngpgogpgjgegpfad}
${{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{({{u1\_struct\_0}~{k3\_monoid\_0}})}})}{\unicdbdjded}{({{v1\_int\_1}~{X0}})}}}$.
\end{theorem}
\end{document}
