\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{t25\_altcat\_1 (TMLfTRtPTuepK8KoCceu3PKmHCajYWK4fh3)}
\maketitle
Let $ v1\_xboole\_0 : {{\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 $ k9\_altcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_altcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ k17\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_relat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v6\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~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}\\
((v1\_funct\_1~(k4\_altcat\_1~(u1\_struct\_0~X0)~(u1\_altcat\_1~X0)~(\\
u2\_altcat\_1~X0)~X1~X2~X3)){\unicdcdcdhd}((v1\_funct\_2~(k4\_altcat\_1~(u1\_struct\_0~\\
X0)~(u1\_altcat\_1~X0)~(u2\_altcat\_1~X0)~X1~X2~X3)~(k2\_zfmisc\_1~(k1\_altcat\_1~\\
X0~X2~X3)~(k1\_altcat\_1~X0~X1~X2))~(k1\_altcat\_1~X0~X1~X3)){\unicdcdcdhd}(m1\_subset\_1~\\
(k4\_altcat\_1~(u1\_struct\_0~X0)~(u1\_altcat\_1~X0)~(u2\_altcat\_1~X0)~\\
X1~X2~X3)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_altcat\_1~\\
X0~X2~X3)~(k1\_altcat\_1~X0~X1~X2))~(k1\_altcat\_1~X0~X1~X3)))))))))\end{array}
\label{hyp:ehbdfdpfbgmgehdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k9\_altcat\_1~X0)){\unicdcdcdhd}\\
((v6\_altcat\_1~(k9\_altcat\_1~X0)){\unicdcdcdhd}((v13\_altcat\_1~(k9\_altcat\_1~\\
X0)){\unicdcdcdhd}(l2\_altcat\_1~(k9\_altcat\_1~X0)))))\end{array}
\label{hyp:egehpflgjdpfbgmgehdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v6\_altcat\_1~X1){\unicdcdcdhd}((v13\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1)))){\unicdbdjdcd}(\\
(X1=k9\_altcat\_1~X0){\unicdbdjded}((u1\_struct\_0~X1=X0){\unicdcdcdhd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X1)){\unicdbdjdcd}(k1\_altcat\_1~X1~X2~X2=k1\_tarski~(k4\_relat\_1~\\
X2))))))\end{array}
\label{hyp:egcdadpfbgmgehdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}\\
((v1\_funct\_2~X3~(k2\_zfmisc\_1~(k1\_tarski~X0)~(k1\_tarski~X1))~(k1\_tarski~\\
X2)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k1\_tarski~X0)~(k1\_tarski~X1))~(k1\_tarski~X2)))))){\unicdbdjdcd}(X3=k17\_funcop\_1~\\
X0~X1~X2)\end{array}
\label{hyp:egbdadpfggfhogdgpgahpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdfdpfbgmgehdgbgehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
(k9\_altcat\_1~X0))){\unicdbdjdcd}(k4\_altcat\_1~(u1\_struct\_0~(k9\_altcat\_1~X0))~\\
(u1\_altcat\_1~(k9\_altcat\_1~X0))~(u2\_altcat\_1~(k9\_altcat\_1~X0))~\\
X1~X1~X1=k17\_funcop\_1~(k4\_relat\_1~X1)~(k4\_relat\_1~X1)~(k4\_relat\_1~\\
X1)))\end{array}$$
\end{theorem}
\end{document}
