\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{t48\_monoid\_0 (TMUfSTaWEQa4q5A84Hu56m6wuVZvKKX2bwq)}
\maketitle
Let $ r3\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k47\_binop\_2 : {\iota}$ be given.
Let $ v9\_monoid\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_monoid\_0 : {\iota}$ be given.
Let $ g3\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ 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 $ m5\_monoid\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_monoid\_0 : {\iota}$ be given.
Let $ k3\_monoid\_0 : {\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l3\_algstr\_0 : {{\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}
{{k4\_monoid\_0}={{{g3\_algstr\_0}~{k5\_numbers}}~{k47\_binop\_2}}}\label{hyp:ehedddpfngpgogpgjgegpfad}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{{{r3\_binop\_1}~{k5\_numbers}}~{k6\_numbers}}~{k47\_binop\_2}}\label{hyp:mgddddpfcgjgogpgahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v2\_struct\_0~k4\_monoid\_0){\unicdcdcdhd}((v15\_algstr\_0~k4\_monoid\_0){\unicdcdcdhd}((\\
v1\_group\_1~k4\_monoid\_0){\unicdcdcdhd}((v17\_monoid\_0~k4\_monoid\_0){\unicdcdcdhd}(m5\_monoid\_0~\\
k4\_monoid\_0~k2\_monoid\_0~k3\_monoid\_0))))\end{array}
\label{hyp:egehpflgedpfngpgogpgjgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k47\_binop\_2){\unicdcdcdhd}((v1\_funct\_2~k47\_binop\_2~(k2\_zfmisc\_1~\\
k5\_numbers~k5\_numbers)~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~k47\_binop\_2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k5\_numbers)~\\
k5\_numbers))))\end{array}
\label{hyp:egehpflgedhdpfcgjgogpgahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k2\_zfmisc\_1~\\
X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0)~X0))))){\unicdbdjdcd}((v15\_algstr\_0~(g3\_algstr\_0~X0~X1)){\unicdcdcdhd}(l3\_algstr\_0~\\
(g3\_algstr\_0~X0~X1)))\end{array}
\label{hyp:egehpfhgddpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{k47\_binop\_2}={{u2\_algstr\_0}~{k4\_monoid\_0}}}\label{hyp:egcdjdpfngpgogpgjgegpfad}
\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}(m5\_monoid\_0~X0~k2\_monoid\_0~k3\_monoid\_0))))){\unicdbdjdcd}\\
((X0=k4\_monoid\_0){\unicdbdjded}(u1\_struct\_0~X0=k5\_numbers))\end{array}
\label{hyp:egcdhdpfngpgogpgjgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l3\_algstr\_0~X0)){\unicdbdjdcd}((v17\_monoid\_0~\\
X0){\unicdbdjded}(v9\_monoid\_0~(u2\_algstr\_0~X0)~(u1\_struct\_0~X0)))\end{array}
\label{hyp:egcdadpfngpgogpgjgegpfad}
\end{equation}
\begin{theorem}\label{thm:ehedidpfngpgogpgjgegpfad}
$$\begin{array}{c}(r3\_binop\_1~k5\_numbers~k6\_numbers~k47\_binop\_2){\unicdcdcdhd}(v9\_monoid\_0~\\
k47\_binop\_2~k5\_numbers)\end{array}$$
\end{theorem}
\end{document}
