\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{t45\_relset\_2 (TMXnPFMiMcLczGhCzWtZaxjwzS9G93xzJBe)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k7\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_relset\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (\preoh ({\unicdcdaddd} X5 .  {\unicdcdaddd} X6 .  \\
(X5 \in X3){\unicdcdcdhd}((X6 \in X4){\unicdcdcdhd}(X5 \in k1\_relset\_2~X1~X0~(k3\_relset\_1~X0~X1~X2)~\\
X6))){\unicdcdcdhd}(r1\_xboole\_0~X4~(k7\_relset\_1~X0~X1~X2~X3))){\unicdcdcdhd}(\preoh (\preoh r1\_xboole\_0~\\
X4~(k7\_relset\_1~X0~X1~X2~X3)){\unicdcdcdhd}({\unicdcdadad} X5 .  {\unicdcdadad} X6 .  \preoh (X5 \in X3){\unicdcdcdhd}\\
((X6 \in X4){\unicdcdcdhd}(X5 \in k1\_relset\_2~X1~X0~(k3\_relset\_1~X0~X1~X2)~X6)))))\end{array}
\label{hyp:ehededpfchfgmgdhfgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (\preoh (\preoh r1\_xboole\_0~\\
X3~(k7\_relset\_1~X1~X0~(k3\_relset\_1~X0~X1~X2)~X4)){\unicdcdcdhd}({\unicdcdadad} X5 .  {\unicdcdadad} X6 .  \\
\preoh (X5 \in X3){\unicdcdcdhd}((X6 \in X4){\unicdcdcdhd}(X5 \in k1\_relset\_2~X1~X0~(k3\_relset\_1~X0~X1~X2)~\\
X6)))){\unicdcdcdhd}(\preoh ({\unicdcdaddd} X5 .  {\unicdcdaddd} X6 .  (X5 \in X3){\unicdcdcdhd}((X6 \in X4){\unicdcdcdhd}(X5 \in k1\_relset\_2~\\
X1~X0~(k3\_relset\_1~X0~X1~X2)~X6))){\unicdcdcdhd}(r1\_xboole\_0~X3~(k7\_relset\_1~\\
X1~X0~(k3\_relset\_1~X0~X1~X2)~X4))))\end{array}
\label{hyp:ehedddpfchfgmgdhfgehpfcd}
\end{equation}
\begin{theorem}\label{thm:ehedfdpfchfgmgdhfgehpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}((r1\_xboole\_0~\\
X2~(k7\_relset\_1~X1~X0~(k3\_relset\_1~X0~X1~X4)~X3)){\unicdbdjded}(r1\_xboole\_0~X3~\\
(k7\_relset\_1~X0~X1~X4~X2)))))\end{array}$$
\end{theorem}
\end{document}
