\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{t15\_card\_fil (TMdkxsn5FtWoBZsqazGzq4h8S7LrhKSBen6)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_card\_fil : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_card\_fil : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 : \iota{\unicdbdjdcd}o .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2 \in ReplSep~(toset~\\
({\uniddcgcg} X3 : \iota .  m1\_subset\_1~X3~X1))~({\uniddcgcg} X3 : \iota .  X0~X3)~({\uniddcgcg} X3 : \iota .  \\
X3)){\unicdbdjdcd}(X0~X2)\end{array}
\label{hyp:dhbdpfdgbgchegpfggjgmg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_card\_fil~X1~X0){\unicdbdjdcd}\\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
X0)))))\end{array}
\label{hyp:egehpfngbdpfdgbgchegpfggjgmg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}(k3\_card\_fil~X0=ReplSep~(toset~\\
({\uniddcgcg} X1 : \iota .  m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~X0))))~\\
({\uniddcgcg} X1 : \iota .  m1\_card\_fil~X1~X0)~({\uniddcgcg} X1 : \iota .  X1))\end{array}
\label{hyp:egjdpfdgbgchegpfggjgmg}
\end{equation}
\begin{theorem}\label{thm:ehbdfdpfdgbgchegpfggjgmg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (X1 \in k3\_card\_fil~X0){\unicdbdjded}\\
(m1\_card\_fil~X1~X0))\end{array}$$
\end{theorem}
\end{document}
