\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{t29\_monoid\_0 (TMJktR1pz221MeoeDLpeBzTFENEfAsQQXjy)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l4\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m3\_monoid\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m7\_monoid\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ l3\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_monoid\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m5\_monoid\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ l3\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l3\_algstr\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(m2\_monoid\_0~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~\\
X2){\unicdcdcdhd}(m2\_monoid\_0~X2~X0)){\unicdbdjdcd}((r1\_tarski~(u1\_struct\_0~X1)~(u1\_struct\_0~\\
X2)){\unicdbdjdcd}(m5\_monoid\_0~X1~X0~X2))))\end{array}
\label{hyp:ehcdidpfngpgogpgjgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l3\_algstr\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m3\_monoid\_0~X1~X0){\unicdbdjdcd}\\
(m2\_monoid\_0~X1~X0))\end{array}
\label{hyp:ehcdbdpfngpgogpgjgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l3\_algstr\_0~X0){\unicdcdcdhd}(m3\_monoid\_0~X1~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m7\_monoid\_0~X2~X0~X1){\unicdbdjded}(m3\_monoid\_0~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfnghdpfngpgogpgjgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l3\_algstr\_0~X0){\unicdcdcdhd}(m2\_monoid\_0~X1~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m5\_monoid\_0~X2~X0~X1){\unicdbdjded}(m2\_monoid\_0~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngfdpfngpgogpgjgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l3\_algstr\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m3\_monoid\_0~X1~X0){\unicdbdjdcd}\\
(l4\_algstr\_0~X1))\end{array}
\label{hyp:egehpfngddpfngpgogpgjgegpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l4\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l3\_struct\_0}~{X0}})}{\unicdcdcdhd}{({{l3\_algstr\_0}~{X0}})}})}}}\label{hyp:egehpfmgedpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l4\_algstr\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l4\_algstr\_0~X1){\unicdbdjdcd}((\\
m3\_monoid\_0~X1~X0){\unicdbdjded}((r1\_tarski~(u2\_algstr\_0~X1)~(u2\_algstr\_0~\\
X0)){\unicdcdcdhd}(k5\_struct\_0~X1=k5\_struct\_0~X0))))\end{array}
\label{hyp:egcdfdpfngpgogpgjgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l3\_algstr\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l3\_algstr\_0~X1){\unicdbdjdcd}((\\
m2\_monoid\_0~X1~X0){\unicdbdjded}(r1\_tarski~(u2\_algstr\_0~X1)~(u2\_algstr\_0~X0))))\end{array}
\label{hyp:egcdddpfngpgogpgjgegpfad}
\end{equation}
\begin{theorem}\label{thm:ehcdjdpfngpgogpgjgegpfad}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l4\_algstr\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(m3\_monoid\_0~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~\\
X2){\unicdcdcdhd}(m3\_monoid\_0~X2~X0)){\unicdbdjdcd}((r1\_tarski~(u1\_struct\_0~X1)~(u1\_struct\_0~\\
X2)){\unicdbdjdcd}(m7\_monoid\_0~X1~X0~X2))))\end{array}$$
\end{theorem}
\end{document}
