\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\_classes2 (TMZ94HuWhYaxd4nnKhnEx2k8QhpnZpHr25o)}
\maketitle
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_classes1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_ordinal1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_classes1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k1\_ordinal1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v4\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 : \iota{\unicdbdjdcd}o .  ((X0~k1\_xboole\_0){\unicdcdcdhd}(({\unicdcdadad} X1 .  (v3\_ordinal1~\\
X1){\unicdbdjdcd}((X0~X1){\unicdbdjdcd}(X0~(k1\_ordinal1~X1)))){\unicdcdcdhd}({\unicdcdadad} X1 .  (v3\_ordinal1~\\
X1){\unicdbdjdcd}(((v4\_ordinal1~X1){\unicdcdcdhd}({\unicdcdadad} X2 .  (v3\_ordinal1~X2){\unicdbdjdcd}((X2 \in X1){\unicdbdjdcd}\\
(X0~X2)))){\unicdbdjdcd}((X1=k1\_xboole\_0){\unicdcdcdid}(X0~X1)))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (v3\_ordinal1~\\
X1){\unicdbdjdcd}(X0~X1))\end{array}
\label{hyp:dhbdpfpgchegjgogbgmgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}(((v4\_ordinal1~X0){\unicdcdcdhd}({\unicdcdadad} X1 .  \\
(v3\_ordinal1~X1){\unicdbdjdcd}((X1 \in X0){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v2\_classes1~X2){\unicdcdcdhd}(X1 \in \\
k2\_ordinal1~X2)){\unicdbdjdcd}((k1\_card\_1~(k4\_classes1~X1) \in k1\_card\_1~X2){\unicdcdcdhd}\\
(k4\_classes1~X1 \in X2)))))){\unicdbdjdcd}((X0=k1\_xboole\_0){\unicdcdcdid}({\unicdcdadad} X1 .  ((\\
v2\_classes1~X1){\unicdcdcdhd}(X0 \in k2\_ordinal1~X1)){\unicdbdjdcd}((k1\_card\_1~(k4\_classes1~\\
X0) \in k1\_card\_1~X1){\unicdcdcdhd}(k4\_classes1~X0 \in X1)))))\end{array}
\label{hyp:mgcdidpfdgmgbgdhdhfgdhcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}(({\unicdcdadad} X1 .  ((v2\_classes1~X1){\unicdcdcdhd}\\
(X0 \in k2\_ordinal1~X1)){\unicdbdjdcd}((k1\_card\_1~(k4\_classes1~X0) \in k1\_card\_1~\\
X1){\unicdcdcdhd}(k4\_classes1~X0 \in X1))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v2\_classes1~X1){\unicdcdcdhd}(k1\_ordinal1~\\
X0 \in k2\_ordinal1~X1)){\unicdbdjdcd}((k1\_card\_1~(k4\_classes1~(k1\_ordinal1~X0)) \in \\
k1\_card\_1~X1){\unicdcdcdhd}(k4\_classes1~(k1\_ordinal1~X0) \in X1))))\end{array}
\label{hyp:mgcdhdpfdgmgbgdhdhfgdhcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_classes1~X0){\unicdcdcdhd}(k1\_xboole\_0 \in k2\_ordinal1~X0)){\unicdbdjdcd}\\
((k1\_card\_1~(k4\_classes1~k1\_xboole\_0) \in k1\_card\_1~X0){\unicdcdcdhd}(k4\_classes1~\\
k1\_xboole\_0 \in X0))\end{array}
\label{hyp:mgcdgdpfdgmgbgdhdhfgdhcd}
\end{equation}
\begin{theorem}\label{thm:ehcdfdpfdgmgbgdhdhfgdhcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v2\_classes1~X1){\unicdcdcdhd}(\\
X0 \in k2\_ordinal1~X1)){\unicdbdjdcd}((k1\_card\_1~(k4\_classes1~X0) \in k1\_card\_1~\\
X1){\unicdcdcdhd}(k4\_classes1~X0 \in X1)))\end{array}$$
\end{theorem}
\end{document}
