\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{t30\_altcat\_2 (TMbN4tqraSbj5pQjgmQPqkNux6MgVqnsBBq)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_altcat\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_altcat\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ g2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_realset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}(m1\_altcat\_2~\\
X1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v2\_altcat\_1~X2){\unicdcdcdhd}(\\
m1\_altcat\_2~X2~X0))){\unicdbdjdcd}(((u1\_struct\_0~X1=u1\_struct\_0~X2){\unicdcdcdhd}(u1\_altcat\_1~\\
X1=u1\_altcat\_1~X2)){\unicdbdjdcd}(g2\_altcat\_1~(u1\_struct\_0~X1)~(u1\_altcat\_1~\\
X1)~(u2\_altcat\_1~X1)=g2\_altcat\_1~(u1\_struct\_0~X2)~(u1\_altcat\_1~\\
X2)~(u2\_altcat\_1~X2)))))\end{array}
\label{hyp:ehcdgdpfbgmgehdgbgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_altcat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_altcat\_2~X1~X0){\unicdbdjdcd}\\
((v2\_altcat\_2~X1~X0){\unicdbdjded}(u1\_altcat\_1~X1=k1\_realset1~(u1\_altcat\_1~\\
X0)~(u1\_struct\_0~X1))))\end{array}
\label{hyp:egbdddpfbgmgehdgbgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_altcat\_2~X1~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(\\
v2\_altcat\_2~X1~X0)){\unicdbdjdcd}(v2\_altcat\_1~X1)))\end{array}
\label{hyp:dgdgcdpfbgmgehdgbgehpfcd}
\end{equation}
\begin{theorem}\label{thm:ehddadpfbgmgehdgbgehpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_2~X1~X0){\unicdcdcdhd}(\\
m1\_altcat\_2~X1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v2\_altcat\_2~\\
X2~X0){\unicdcdcdhd}(m1\_altcat\_2~X2~X0))){\unicdbdjdcd}((u1\_struct\_0~X1=u1\_struct\_0~X2){\unicdbdjdcd}\\
(g2\_altcat\_1~(u1\_struct\_0~X1)~(u1\_altcat\_1~X1)~(u2\_altcat\_1~X1)=\\
g2\_altcat\_1~(u1\_struct\_0~X2)~(u1\_altcat\_1~X2)~(u2\_altcat\_1~X2)))))\end{array}$$
\end{theorem}
\end{document}
