\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{l23\_jgraph\_4 (TMMNK5ThDW9Sk7xJxVxBab7Wr2VV8bfoHiN)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_pscomp\_1 : {\iota}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_topmetr : {\iota}$ be given.
Let $ v5\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\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 $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(\\
u1\_struct\_0~(k15\_euclid~np\_\_2))))){\unicdbdjdcd}((v1\_funct\_1~(k3\_pscomp\_1~\\
(k15\_euclid~np\_\_2)~k4\_pscomp\_1~X0)){\unicdcdcdhd}((v1\_funct\_2~(k3\_pscomp\_1~\\
(k15\_euclid~np\_\_2)~k4\_pscomp\_1~X0)~(u1\_struct\_0~(k1\_pre\_topc~\\
(k15\_euclid~np\_\_2)~X0))~(u1\_struct\_0~k3\_topmetr)){\unicdcdcdhd}((v5\_pre\_topc~\\
(k3\_pscomp\_1~(k15\_euclid~np\_\_2)~k4\_pscomp\_1~X0)~(k1\_pre\_topc~\\
(k15\_euclid~np\_\_2)~X0)~k3\_topmetr){\unicdcdcdhd}(m1\_subset\_1~(k3\_pscomp\_1~\\
(k15\_euclid~np\_\_2)~k4\_pscomp\_1~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~(k1\_pre\_topc~(k15\_euclid~np\_\_2)~X0))~(u1\_struct\_0~\\
k3\_topmetr)))))))\end{array}
\label{hyp:mgbdidpfkghgchbgahigpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(\\
u1\_struct\_0~(k15\_euclid~np\_\_2))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~(k1\_pre\_topc~(k15\_euclid~np\_\_2)~X0))){\unicdbdjdcd}(k3\_funct\_2~\\
(u1\_struct\_0~(k1\_pre\_topc~(k15\_euclid~np\_\_2)~X0))~k1\_numbers~\\
(k3\_pscomp\_1~(k15\_euclid~np\_\_2)~k4\_pscomp\_1~X0)~X1=k1\_funct\_1~\\
k4\_pscomp\_1~X1))\end{array}
\label{hyp:mgbdhdpfkghgchbgahigpfdd}
\end{equation}
\begin{theorem}\label{thm:mgcdddpfkghgchbgahigpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(\\
u1\_struct\_0~(k15\_euclid~np\_\_2))))){\unicdbdjdcd}(((v1\_funct\_1~(k3\_pscomp\_1~\\
(k15\_euclid~np\_\_2)~k4\_pscomp\_1~X0)){\unicdcdcdhd}((v1\_funct\_2~(k3\_pscomp\_1~\\
(k15\_euclid~np\_\_2)~k4\_pscomp\_1~X0)~(u1\_struct\_0~(k1\_pre\_topc~\\
(k15\_euclid~np\_\_2)~X0))~(u1\_struct\_0~k3\_topmetr)){\unicdcdcdhd}((v5\_pre\_topc~\\
(k3\_pscomp\_1~(k15\_euclid~np\_\_2)~k4\_pscomp\_1~X0)~(k1\_pre\_topc~\\
(k15\_euclid~np\_\_2)~X0)~k3\_topmetr){\unicdcdcdhd}(m1\_subset\_1~(k3\_pscomp\_1~\\
(k15\_euclid~np\_\_2)~k4\_pscomp\_1~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~(k1\_pre\_topc~(k15\_euclid~np\_\_2)~X0))~(u1\_struct\_0~\\
k3\_topmetr))))))){\unicdcdcdhd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
(k1\_pre\_topc~(k15\_euclid~np\_\_2)~X0))){\unicdbdjdcd}(k3\_funct\_2~(u1\_struct\_0~\\
(k1\_pre\_topc~(k15\_euclid~np\_\_2)~X0))~k1\_numbers~(k3\_pscomp\_1~\\
(k15\_euclid~np\_\_2)~k4\_pscomp\_1~X0)~X1=k1\_funct\_1~k4\_pscomp\_1~\\
X1)))\end{array}$$
\end{theorem}
\end{document}
