\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{t74\_monoid\_0 (TMPgrtDsYSsjDKVdRJJ1JbfvpSiXNsAQpu4)}
\maketitle
Let $ u2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k15\_monoid\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_realset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k14\_monoid\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_struct\_0 : {{\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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v15\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k12\_monoid\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_monoid\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\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}(u2\_algstr\_0~X1=k1\_realset1~\\
(u2\_algstr\_0~X0)~(u1\_struct\_0~X1)))\end{array}
\label{hyp:ehcdedpfngpgogpgjgegpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k1\_funct\_2}~{X0}}~{X1}}={{k4\_card\_3}~{({{{k7\_funcop\_1}~{X0}}~{X1}})}}}}}\label{hyp:ehbdbdpfdgbgchegpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k7\_funcop\_1}~{X0}}~{X1}}={{{k2\_funcop\_1}~{X0}}~{X1}}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v2\_struct\_0~(k15\_monoid\_0~X0)){\unicdcdcdhd}((v15\_algstr\_0~\\
(k15\_monoid\_0~X0)){\unicdcdcdhd}(v1\_group\_1~(k15\_monoid\_0~X0)))\end{array}
\label{hyp:ggdgddpfngpgogpgjgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v2\_struct\_0~(k12\_monoid\_0~X0)){\unicdcdcdhd}((v15\_algstr\_0~\\
(k12\_monoid\_0~X0)){\unicdcdcdhd}((v1\_group\_1~(k12\_monoid\_0~X0)){\unicdcdcdhd}((v3\_group\_1~\\
(k12\_monoid\_0~X0)){\unicdcdcdhd}(v1\_monoid\_0~(k12\_monoid\_0~X0)))))\end{array}
\label{hyp:ggdgcdpfngpgogpgjgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v15\_algstr\_0~(k15\_monoid\_0~X0)){\unicdcdcdhd}(m2\_monoid\_0~(k15\_monoid\_0~\\
X0)~(k12\_monoid\_0~X0))\end{array}
\label{hyp:egehpflgbdfdpfngpgogpgjgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v15\_algstr\_0~(k12\_monoid\_0~X0)){\unicdcdcdhd}((v1\_monoid\_0~(\\
k12\_monoid\_0~X0)){\unicdcdcdhd}(l3\_algstr\_0~(k12\_monoid\_0~X0)))\end{array}
\label{hyp:egehpflgbdcdpfngpgogpgjgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v15\_algstr\_0~X1){\unicdcdcdhd}(m2\_monoid\_0~X1~(k12\_monoid\_0~\\
X0))){\unicdbdjdcd}((X1=k15\_monoid\_0~X0){\unicdbdjded}(u1\_struct\_0~X1=k1\_funct\_2~X0~X0))\end{array}
\label{hyp:egedadpfngpgogpgjgegpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k14\_monoid\_0}~{X0}}={{u2\_algstr\_0}~{({{k12\_monoid\_0}~{X0}})}}}}\label{hyp:egddjdpfngpgogpgjgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k2\_funcop\_1~X0~X1=k2\_zfmisc\_1~X0~(k1\_tarski~\\
X1)\end{array}
\label{hyp:egcdpfggfhogdgpgahpfbd}
\end{equation}
\begin{theorem}\label{thm:ehhdedpfngpgogpgjgegpfad}
$$\begin{array}{c}{\unicdcdadad} X0 .  u2\_algstr\_0~(k15\_monoid\_0~X0)=k1\_realset1~(k14\_monoid\_0~\\
X0)~(k1\_funct\_2~X0~X0)\end{array}$$
\end{theorem}
\end{document}
