\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{t8\_jgraph\_2 (TMPus7XsVbVeCrQgizRgNN1hQFGVsif4CXN)}
\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 $ k19\_euclid : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k4\_pscomp\_1 : {\iota}$ be given.
Let $ k5\_pscomp\_1 : {\iota}$ be given.
Let $ k17\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k18\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ np\_\_1 : {\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}\\
(X0=k19\_euclid~(k17\_euclid~X0)~(k18\_euclid~X0))\end{array}
\label{hyp:ehfdddpffgfhdgmgjgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
((k7\_partfun1~k1\_numbers~X0~np\_\_1=k3\_funct\_2~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~k1\_numbers~k4\_pscomp\_1~X0){\unicdcdcdhd}(k7\_partfun1~k1\_numbers~X0~\\
np\_\_2=k3\_funct\_2~(u1\_struct\_0~(k15\_euclid~np\_\_2))~k1\_numbers~\\
k5\_pscomp\_1~X0))\end{array}
\label{hyp:ehddadpfkgpgchegbgogcdcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
((k7\_partfun1~k1\_numbers~X0~np\_\_1=k17\_euclid~X0){\unicdcdcdhd}(k7\_partfun1~\\
k1\_numbers~X0~np\_\_2=k18\_euclid~X0))\end{array}
\label{hyp:ehcdjdpfkgpgchegbgogcdcg}
\end{equation}
\begin{theorem}\label{thm:ehidpfkghgchbgahigpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
(X0=k19\_euclid~(k3\_funct\_2~(u1\_struct\_0~(k15\_euclid~np\_\_2))~\\
k1\_numbers~k4\_pscomp\_1~X0)~(k3\_funct\_2~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~k1\_numbers~k5\_pscomp\_1~X0))\end{array}$$
\end{theorem}
\end{document}
