\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{l21\_compos\_1 (TMMUhucTo3WVKNwZPAb7NqbagyrMK5EnCPZ)}
\maketitle
Let $ l1\_compos\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k62\_valued\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ 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 $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_nat\_d : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_afinsq\_1~X0)))))){\unicdbdjdcd}\\
(k62\_valued\_1~X0=k7\_nat\_d~(k5\_card\_1~X0)~np\_\_1)\end{array}
\label{hyp:ehhdadpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_compos\_1~X0){\unicdbdjdcd}(k7\_nat\_d~(k5\_card\_1~(k4\_compos\_1~\\
X0))~np\_\_1=k6\_numbers)\end{array}
\label{hyp:mgcdadpfdgpgngahpgdhpfbd}
\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:mgcdbdpfdgpgngahpgdhpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (l1\_compos\_1~X0){\unicdbdjdcd}(k62\_valued\_1~(k4\_compos\_1~X0)=\\
k6\_numbers)\end{array}$$
\end{theorem}
\end{document}
