\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}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t52\_monoid\_0 (TMKWXakbHanQ1fT6nS9FaSaPkcJNv9FynDL)}
\maketitle
Let $ k7\_monoid\_0 : {\iota}$ be given.
Let $ g3\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k48\_binop\_2 : {\iota}$ be given.
Let $ l3\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_monoid\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v15\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v17\_monoid\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_monoid\_0 : {\iota}$ be given.
Let $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l3\_algstr\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_monoid\_0~X1~X0){\unicdbdjdcd}\\
(l3\_algstr\_0~X1))\end{array}
\label{hyp:egehpfngcdpfngpgogpgjgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v2\_struct\_0~k7\_monoid\_0){\unicdcdcdhd}((v15\_algstr\_0~k7\_monoid\_0){\unicdcdcdhd}((\\
v1\_group\_1~k7\_monoid\_0){\unicdcdcdhd}((v17\_monoid\_0~k7\_monoid\_0){\unicdcdcdhd}(m2\_monoid\_0~\\
k7\_monoid\_0~k6\_monoid\_0))))\end{array}
\label{hyp:egehpflghdpfngpgogpgjgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v2\_struct\_0~k6\_monoid\_0){\unicdcdcdhd}((v15\_algstr\_0~k6\_monoid\_0){\unicdcdcdhd}((\\
v1\_group\_1~k6\_monoid\_0){\unicdcdcdhd}((v3\_group\_1~k6\_monoid\_0){\unicdcdcdhd}((v5\_group\_1~\\
k6\_monoid\_0){\unicdcdcdhd}(l3\_algstr\_0~k6\_monoid\_0)))))\end{array}
\label{hyp:egehpflggdpfngpgogpgjgegpfad}
\end{equation}
Assume the following.
\begin{equation}
{{k48\_binop\_2}={{u2\_algstr\_0}~{k7\_monoid\_0}}}\label{hyp:egddddpfngpgogpgjgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v15\_algstr\_0~X0){\unicdcdcdhd}((v1\_group\_1~\\
X0){\unicdcdcdhd}((v17\_monoid\_0~X0){\unicdcdcdhd}(m2\_monoid\_0~X0~k6\_monoid\_0))))){\unicdbdjdcd}((\\
X0=k7\_monoid\_0){\unicdbdjded}(u1\_struct\_0~X0=k5\_numbers))\end{array}
\label{hyp:egddbdpfngpgogpgjgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l3\_algstr\_0~X0){\unicdbdjdcd}((v15\_algstr\_0~X0){\unicdbdjdcd}(X0=g3\_algstr\_0~\\
(u1\_struct\_0~X0)~(u2\_algstr\_0~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdfdpfbgmghgdhehchpfad}
\end{equation}
\begin{theorem}\label{thm:ehfdcdpfngpgogpgjgegpfad}
${{k7\_monoid\_0}={{{g3\_algstr\_0}~{k5\_numbers}}~{k48\_binop\_2}}}$.
\end{theorem}
\end{document}
