\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{l34\_altcat\_4 (TMRP1uZ4mnvkwB3x4pnRZ3vqdnzSj8x9nDS)}
\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 $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ l1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (k2\_zfmisc\_1~X0~X1=k1\_xboole\_0){\unicdbdjded}((X0=\\
k1\_xboole\_0){\unicdcdcdid}(X1=k1\_xboole\_0))\end{array}
\label{hyp:ehjdadpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_altcat\_1}~{X0}})}{\unicdbdjdcd}{({{l1\_altcat\_1}~{X0}})}}}\label{hyp:egehpfmgcdpfbgmgehdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_altcat\_1~X0){\unicdbdjdcd}((v2\_altcat\_1~X0){\unicdbdjded}({\unicdcdadad} X1 .  (\\
m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
(\preoh (k1\_altcat\_1~X0~X1~X2{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}((k1\_altcat\_1~X0~X2~X3{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}\\
(k1\_altcat\_1~X0~X1~X3=k1\_xboole\_0)))))))\end{array}
\label{hyp:egcdpfbgmgehdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_altcat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}(k1\_altcat\_1~\\
X0~X1~X2=k1\_binop\_1~(u1\_altcat\_1~X0)~X1~X2)))\end{array}
\label{hyp:egbdpfbgmgehdgbgehpfbd}
\end{equation}
\begin{theorem}\label{thm:mgddedpfbgmgehdgbgehpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}((k1\_binop\_1~(u1\_altcat\_1~X0)~X1~X3=k1\_xboole\_0){\unicdbdjdcd}\\
(k2\_zfmisc\_1~(k1\_binop\_1~(u1\_altcat\_1~X0)~X2~X3)~(k1\_binop\_1~(\\
u1\_altcat\_1~X0)~X1~X2)=k1\_xboole\_0)))))\end{array}$$
\end{theorem}
\end{document}
