\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{t4\_modal\_1 (TMMotZyjcCmLkCrhW1FgEWBghTB3Sp64A32)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k12\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r3\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~k5\_numbers){\unicdbdjdcd}(\preoh (X0{\unicdcdgdad}\\
X1){\unicdcdcdhd}(r2\_xboole\_0~(k12\_finseq\_1~k5\_numbers~X0)~(k8\_finseq\_1~k5\_numbers~\\
(k12\_finseq\_1~k5\_numbers~X1)~X2)))))\end{array}
\label{hyp:ehddpfngpgegbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~k5\_numbers){\unicdbdjdcd}(\preoh (X0{\unicdcdgdad}\\
X1){\unicdcdcdhd}(r3\_xboole\_0~(k12\_finseq\_1~k5\_numbers~X0)~(k8\_finseq\_1~k5\_numbers~\\
(k12\_finseq\_1~k5\_numbers~X1)~X2)))))\end{array}
\label{hyp:ehbdpfngpgegbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (\preoh (\preoh r2\_xboole\_0~X0~X1){\unicdcdcdhd}((X0{\unicdcdgdad}X1){\unicdcdcdhd}(\preoh r2\_xboole\_0~\\
X1~X0))){\unicdbdjded}(r3\_xboole\_0~X0~X1)\end{array}
\label{hyp:ehbdadedpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r2\_xboole\_0~X0~X1){\unicdbdjded}((r1\_tarski~X0~X1){\unicdcdcdhd}\\
(X0{\unicdcdgdad}X1))\end{array}
\label{hyp:egidpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehedpfngpgegbgmgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~k5\_numbers){\unicdbdjdcd}(\preoh (X0{\unicdcdgdad}\\
X1){\unicdcdcdhd}(r1\_tarski~(k12\_finseq\_1~k5\_numbers~X0)~(k8\_finseq\_1~k5\_numbers~\\
(k12\_finseq\_1~k5\_numbers~X1)~X2)))))\end{array}$$
\end{theorem}
\end{document}
