\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{t63\_compos\_1 (TMHFJwJigHrrXuimeBmVySWPbUcdeCQWiFh)}
\maketitle
Let $ l1\_compos\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\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 $ k2\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_compos\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v5\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_ordinal4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
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 .  {\unicdcdadad} X1 .  ((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}(v1\_afinsq\_1~X1))))))){\unicdbdjdcd}\\
((\preoh v1\_xboole\_0~(k10\_compos\_1~X0~X1)){\unicdcdcdhd}((v1\_relat\_1~(k10\_compos\_1~\\
X0~X1)){\unicdcdcdhd}((v4\_relat\_1~(k10\_compos\_1~X0~X1)~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~\\
(k10\_compos\_1~X0~X1)~(u1\_compos\_1~X0)){\unicdcdcdhd}((v1\_funct\_1~(k10\_compos\_1~\\
X0~X1)){\unicdcdcdhd}((v1\_finset\_1~(k10\_compos\_1~X0~X1)){\unicdcdcdhd}(v1\_afinsq\_1~(k10\_compos\_1~\\
X0~X1))))))))\end{array}
\label{hyp:ggdgbdddpfdgpgngahpgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v5\_ordinal1~X0){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}(v1\_finset\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v5\_ordinal1~\\
X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finset\_1~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v5\_ordinal1~X2){\unicdcdcdhd}(v1\_funct\_1~X2))){\unicdbdjdcd}((X2=k1\_ordinal4~X0~\\
X1){\unicdbdjded}((k9\_xtuple\_0~X2=k2\_nat\_1~(k1\_afinsq\_1~X0)~(k1\_afinsq\_1~\\
X1)){\unicdcdcdhd}(({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}((X3 \in k2\_afinsq\_1~X0){\unicdbdjdcd}(k1\_funct\_1~\\
X2~X3=k1\_funct\_1~X0~X3))){\unicdcdcdhd}({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}((X3 \in \\
k2\_afinsq\_1~X1){\unicdbdjdcd}(k1\_funct\_1~X2~(k2\_nat\_1~(k1\_afinsq\_1~X0)~X3)=\\
k1\_funct\_1~X1~X3))))))))\end{array}
\label{hyp:egddpfbgggjgogdhbhpfbd}
\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){\unicdcdcdhd}(v1\_afinsq\_1~X1)))))){\unicdbdjdcd}(\\
k10\_compos\_1~X0~X1=k1\_ordinal4~X1~(k4\_compos\_1~X0)))\end{array}
\label{hyp:egcdedpfdgpgngahpgdhpfbd}
\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}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_afinsq\_1~X0))))){\unicdbdjdcd}((v1\_relat\_1~X0){\unicdcdcdhd}\\
((v5\_ordinal1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)))\end{array}
\label{hyp:dgdgjdpfbgggjgogdhbhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehgdddpfdgpgngahpgdhpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (l1\_compos\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X2~\\
(u1\_compos\_1~X0)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_finset\_1~X2){\unicdcdcdhd}(v1\_afinsq\_1~\\
X2)))))){\unicdbdjdcd}((X1 \in k2\_afinsq\_1~X2){\unicdbdjdcd}(k1\_funct\_1~(k10\_compos\_1~X0~\\
X2)~X1=k1\_funct\_1~X2~X1))))\end{array}$$
\end{theorem}
\end{document}
