\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{l50\_jgraph\_2 (TMUXtVgme65Lzj8FLjXtggxju7NYthBwSFC)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k15\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k18\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k9\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k17\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
((k1\_real\_1~(k17\_euclid~(k5\_algstr\_0~(k15\_euclid~np\_\_2)~X0~X1))=\\
k9\_real\_1~(k1\_real\_1~(k17\_euclid~X0))~(k1\_real\_1~(k17\_euclid~\\
X1))){\unicdcdcdhd}(k18\_euclid~(k5\_algstr\_0~(k15\_euclid~np\_\_2)~X0~X1)=k9\_real\_1~\\
(k18\_euclid~X0)~(k18\_euclid~X1))))\end{array}
\label{hyp:mgedhdpfkghgchbgahigpfcd}
\end{equation}
\begin{theorem}\label{thm:mgfdadpfkghgchbgahigpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
((k18\_euclid~(k5\_algstr\_0~(k15\_euclid~np\_\_2)~X0~X1)=k9\_real\_1~\\
(k18\_euclid~X0)~(k18\_euclid~X1)){\unicdcdcdhd}(k1\_real\_1~(k17\_euclid~(k5\_algstr\_0~\\
(k15\_euclid~np\_\_2)~X0~X1))=k9\_real\_1~(k1\_real\_1~(k17\_euclid~X0))~\\
(k1\_real\_1~(k17\_euclid~X1)))))\end{array}$$
\end{theorem}
\end{document}
