\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{t18\_compos\_1 (TMVY5FZ72usWwJctM5pHL5wUvJQ97WANhcg)}
\maketitle
Let $ l1\_compos\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\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\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k63\_valued\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_compos\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ 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 $ k61\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_compos\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_card\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_compos\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ 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}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_afinsq\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~\\
X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}(r1\_xboole\_0~(k2\_afinsq\_1~X0)~(k9\_xtuple\_0~\\
(k61\_valued\_1~X1~(k5\_card\_1~X0)))))\end{array}
\label{hyp:ehhdcdpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_compos\_1}~{X0}})}{\unicdbdjdcd}{({{{k5\_card\_1}~{({{k4\_compos\_1}~{X0}})}}={np\_\_1}})}}}\label{hyp:ehedpfdgpgngahpgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{k1\_card\_1}~{X0}}={np\_\_1}})}{\unicdbdjded}{({{\unicdcdaddd} X1 .  {{X0}={{k1\_tarski}~{X1}}}})}}}\label{hyp:ehedcdpfdgbgchegpfcd}
\end{equation}
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))))){\unicdbdjdcd}(k5\_card\_1~(k63\_valued\_1~\\
X0)=k6\_xcmplx\_0~(k5\_card\_1~X0)~np\_\_1)\end{array}
\label{hyp:ehddidpfghbgmgfhfgegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finset\_1~X0)){\unicdbdjdcd}(k6\_xcmplx\_0~\\
(k5\_card\_1~X0)~np\_\_1=k1\_xreal\_0~(k5\_card\_1~X0)~np\_\_1)\end{array}
\label{hyp:ehcdadpfahchfgpfdgjgchdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}(\\
k7\_nat\_d~X0~X1=k1\_xreal\_0~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfogbgehpfeg}
\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}
{{\unicdcdaddd} X0 .  {{({{l1\_compos\_1}~{X0}})}{\unicdcdcdhd}{({{v1\_compos\_1}~{X0}})}}}\label{hyp:chdgbdpfdgpgngahpgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_finset\_1~X0){\unicdbdjdcd}((v1\_finset\_1~(k1\_card\_1~X0)){\unicdcdcdhd}(\\
v1\_card\_1~(k1\_card\_1~X0)))\end{array}
\label{hyp:ggdggdpfdgbgchegpfbd}
\end{equation}
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}\\
((v1\_relat\_1~(k63\_valued\_1~X0)){\unicdcdcdhd}((v1\_funct\_1~(k63\_valued\_1~\\
X0)){\unicdcdcdhd}(v1\_afinsq\_1~(k63\_valued\_1~X0))))\end{array}
\label{hyp:ggdgcdddpfbgggjgogdhbhpfbd}
\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\_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:ggdgbdpfdgpgngahpgdhpfbd}
\end{equation}
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))))){\unicdbdjdcd}((v1\_relat\_1~(\\
k63\_valued\_1~X0)){\unicdcdcdhd}((v4\_relat\_1~(k63\_valued\_1~X0)~k5\_numbers){\unicdcdcdhd}\\
((v1\_funct\_1~(k63\_valued\_1~X0)){\unicdcdcdhd}(v1\_finset\_1~(k63\_valued\_1~\\
X0)))))\end{array}
\label{hyp:ggdgbdadjdpfghbgmgfhfgegpfbd}
\end{equation}
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))))){\unicdbdjdcd}((v1\_relat\_1~(\\
k63\_valued\_1~X0)){\unicdcdcdhd}(v1\_funct\_1~(k63\_valued\_1~X0)))\end{array}
\label{hyp:egehpflggdddpfghbgmgfhfgegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((l1\_compos\_1~X0){\unicdcdcdhd}(((v1\_relat\_1~\\
X1){\unicdcdcdhd}((v4\_relat\_1~X1~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X1~(u1\_compos\_1~\\
X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finset\_1~X1))))){\unicdcdcdhd}(v7\_ordinal1~X2))){\unicdbdjdcd}\\
((v1\_relat\_1~(k5\_compos\_1~X0~X1~X2)){\unicdcdcdhd}((v4\_relat\_1~(k5\_compos\_1~\\
X0~X1~X2)~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~(k5\_compos\_1~X0~X1~X2)~(u1\_compos\_1~\\
X0)){\unicdcdcdhd}((v1\_funct\_1~(k5\_compos\_1~X0~X1~X2)){\unicdcdcdhd}(v1\_finset\_1~(k5\_compos\_1~\\
X0~X1~X2))))))\end{array}
\label{hyp:egehpflgfdpfdgpgngahpgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{v1\_card\_1}~{({{k1\_card\_1}~{X0}})}}}\label{hyp:egehpflgbdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_compos\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((\\
v4\_relat\_1~X1~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X1~(u1\_compos\_1~X0)){\unicdcdcdhd}\\
((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finset\_1~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (v7\_ordinal1~\\
X2){\unicdbdjdcd}(k6\_compos\_1~X0~X1~X2=k61\_valued\_1~(k5\_compos\_1~X0~X1~X2)~X2)))\end{array}
\label{hyp:egcdcdpfdgpgngahpgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{({{v3\_ordinal1}~{X0}})}{\unicdcdcdhd}{({{v1\_finset\_1}~{X0}})}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdggdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_card\_1}~{X0}})}{\unicdbdjdcd}{({{v3\_ordinal1}~{X0}})}}}\label{hyp:dgdgbdpfdgbgchegpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdidpfdgpgngahpgdhpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (l1\_compos\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X1~\\
(u1\_compos\_1~X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_finset\_1~X1){\unicdcdcdhd}(v1\_afinsq\_1~\\
X1))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((v1\_relat\_1~X2){\unicdcdcdhd}\\
((v4\_relat\_1~X2~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X2~(u1\_compos\_1~X0)){\unicdcdcdhd}\\
((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_finset\_1~X2)))))){\unicdbdjdcd}(r1\_xboole\_0~(k2\_afinsq\_1~\\
(k63\_valued\_1~X1))~(k9\_xtuple\_0~(k6\_compos\_1~X0~X2~(k7\_nat\_d~(\\
k5\_card\_1~X1)~np\_\_1))))))\end{array}$$
\end{theorem}
\end{document}
