\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\_compos\_1 (TMF3TZ6D89kvbHnAkJquimGGGXi9nmEXBkT)}
\maketitle
Let $ l1\_compos\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_zfmisc\_1~X0)){\unicdbdjdcd}({\unicdcdaddd} X1 .  \\
(m1\_subset\_1~X1~X0){\unicdcdcdhd}(X0=k1\_tarski~X1))\end{array}
\label{hyp:ehedgdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k1\_card\_1}~{({{k1\_tarski}~{X0}})}}={np\_\_1}}}\label{hyp:ehddadpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_finset\_1}~{X0}})}{\unicdbdjdcd}{({{{k5\_card\_1}~{X0}}={{k1\_card\_1}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_compos\_1~X0){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k4\_compos\_1~X0)){\unicdcdcdhd}\\
((v1\_zfmisc\_1~(k4\_compos\_1~X0)){\unicdcdcdhd}((v1\_relat\_1~(k4\_compos\_1~X0)){\unicdcdcdhd}\\
((v4\_relat\_1~(k4\_compos\_1~X0)~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~(k4\_compos\_1~\\
X0)~(u1\_compos\_1~X0)){\unicdcdcdhd}((v1\_funct\_1~(k4\_compos\_1~X0)){\unicdcdcdhd}((v1\_finset\_1~\\
(k4\_compos\_1~X0)){\unicdcdcdhd}(v1\_afinsq\_1~(k4\_compos\_1~X0)))))))))\end{array}
\label{hyp:ggdgcdpfdgpgngahpgdhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedpfdgpgngahpgdhpfbd}
${{\unicdcdadad} X0 .  {{({{l1\_compos\_1}~{X0}})}{\unicdbdjdcd}{({{{k5\_card\_1}~{({{k4\_compos\_1}~{X0}})}}={np\_\_1}})}}}$.
\end{theorem}
\end{document}
