\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{t26\_altcat\_2 (TMGrZVZh9Foo5k6KT6Je7KxuZZQPK1JnzuC)}
\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\_altcat\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ g2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r2\_altcat\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\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 .  (m1\_altcat\_2~X1~X0){\unicdbdjdcd}(((u1\_struct\_0~X1=u1\_struct\_0~\\
X0){\unicdcdcdhd}(u1\_altcat\_1~X1=u1\_altcat\_1~X0)){\unicdbdjdcd}(g2\_altcat\_1~(u1\_struct\_0~\\
X1)~(u1\_altcat\_1~X1)~(u2\_altcat\_1~X1)=g2\_altcat\_1~(u1\_struct\_0~\\
X0)~(u1\_altcat\_1~X0)~(u2\_altcat\_1~X0))))\end{array}
\label{hyp:ehcdfdpfbgmgehdgbgehpfcd}
\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 .  ((\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}(((r1\_tarski~(u1\_struct\_0~X1)~(u1\_struct\_0~\\
X2)){\unicdcdcdhd}(r2\_altcat\_2~(k2\_zfmisc\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~\\
X1))~(k2\_zfmisc\_1~(u1\_struct\_0~X2)~(u1\_struct\_0~X2))~(u1\_altcat\_1~\\
X1)~(u1\_altcat\_1~X2))){\unicdbdjdcd}(m1\_altcat\_2~X1~X2))))\end{array}
\label{hyp:ehcdedpfbgmgehdgbgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_altcat\_1}~{X0}})}{\unicdbdjdcd}{({{{m1\_altcat\_2}~{X0}}~{X0}})}}}\label{hyp:ehcdadpfbgmgehdgbgehpfcd}
\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}\\
(l2\_altcat\_1~X1))\end{array}
\label{hyp:egehpfngbdpfbgmgehdgbgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_altcat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l2\_altcat\_1~X1){\unicdbdjdcd}((\\
m1\_altcat\_2~X1~X0){\unicdbdjded}((r1\_tarski~(u1\_struct\_0~X1)~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((r2\_altcat\_2~(k2\_zfmisc\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~\\
X1))~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~(u1\_altcat\_1~\\
X1)~(u1\_altcat\_1~X0)){\unicdcdcdhd}(r2\_altcat\_2~(k3\_zfmisc\_1~(u1\_struct\_0~\\
X1)~(u1\_struct\_0~X1)~(u1\_struct\_0~X1))~(k3\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~(u2\_altcat\_1~X1)~(u2\_altcat\_1~\\
X0))))))\end{array}
\label{hyp:egbdbdpfbgmgehdgbgehpfcd}
\end{equation}
\begin{theorem}\label{thm:ehcdgdpfbgmgehdgbgehpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}(m1\_altcat\_2~\\
X1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v2\_altcat\_1~X2){\unicdcdcdhd}(\\
m1\_altcat\_2~X2~X0))){\unicdbdjdcd}(((u1\_struct\_0~X1=u1\_struct\_0~X2){\unicdcdcdhd}(u1\_altcat\_1~\\
X1=u1\_altcat\_1~X2)){\unicdbdjdcd}(g2\_altcat\_1~(u1\_struct\_0~X1)~(u1\_altcat\_1~\\
X1)~(u2\_altcat\_1~X1)=g2\_altcat\_1~(u1\_struct\_0~X2)~(u1\_altcat\_1~\\
X2)~(u2\_altcat\_1~X2)))))\end{array}$$
\end{theorem}
\end{document}
