\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{t15\_tex\_3 (TMbyRAQ1mZuWi9B3P6qwL2DoXJXjYFE6Fhj)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ g1\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_pre\_topc : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_tex\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_pre\_topc~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_pre\_topc~X2~X1){\unicdbdjdcd}(m1\_pre\_topc~\\
X2~X0)))\end{array}
\label{hyp:ehhdpfehdhfgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_pre\_topc~X1){\unicdbdjdcd}((\\
m1\_pre\_topc~X0~X1){\unicdbdjded}(m1\_pre\_topc~X0~(g1\_pre\_topc~(u1\_struct\_0~\\
X1)~(u1\_pre\_topc~X1)))))\end{array}
\label{hyp:ehddfdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_pre\_topc}~{X0}})}{\unicdbdjdcd}{({{{m1\_pre\_topc}~{X0}}~{X0}})}}}\label{hyp:ehcdpfehdhfgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_tex\_3~X1~X0){\unicdcdcdhd}(m1\_pre\_topc~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_pre\_topc~X2~X0){\unicdbdjdcd}((m1\_pre\_topc~X1~X2){\unicdbdjdcd}(v1\_tex\_3~X2~X0))))\end{array}
\label{hyp:ehbdcdpfehfgihpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_pre\_topc~X1~X0){\unicdbdjdcd}\\
((v1\_pre\_topc~(g1\_pre\_topc~(u1\_struct\_0~X1)~(u1\_pre\_topc~X1))){\unicdcdcdhd}\\
(m1\_pre\_topc~(g1\_pre\_topc~(u1\_struct\_0~X1)~(u1\_pre\_topc~X1))~\\
X0)))\end{array}
\label{hyp:mghdpfehdhfgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}(m1\_pre\_topc~(g1\_pre\_topc~(u1\_struct\_0~\\
X0)~(u1\_pre\_topc~X0))~X0)\end{array}
\label{hyp:mgbdbdpfahchfgpfehpgahdg}
\end{equation}
\begin{theorem}\label{thm:ehbdfdpfehfgihpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v2\_pre\_topc~X2){\unicdcdcdhd}(l1\_pre\_topc~\\
X2))){\unicdbdjdcd}((X2=g1\_pre\_topc~(u1\_struct\_0~X1)~(u1\_pre\_topc~X1)){\unicdbdjdcd}(\\
((v1\_tex\_3~X1~X0){\unicdcdcdhd}(m1\_pre\_topc~X1~X0)){\unicdbdjded}((v1\_tex\_3~X2~X0){\unicdcdcdhd}(m1\_pre\_topc~\\
X2~X0))))))\end{array}$$
\end{theorem}
\end{document}
