\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{t33\_afinsq\_2 (TMYjr34sP7SyL47KqHgAsAhCgPuaP3gmRV7)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_afinsq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_recdef\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_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 $ v2\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}((\\
(r1\_xxreal\_0~X0~X1){\unicdcdcdhd}(r1\_xxreal\_0~X1~X0)){\unicdbdjdcd}(X0=X1)))\end{array}
\label{hyp:ehbdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_finset\_1~X0){\unicdcdcdhd}(v6\_membered~X0)){\unicdbdjdcd}((v1\_relat\_1~\\
(k4\_afinsq\_2~X0)){\unicdcdcdhd}((v5\_relat\_1~(k4\_afinsq\_2~X0)~k5\_numbers){\unicdcdcdhd}\\
((v1\_funct\_1~(k4\_afinsq\_2~X0)){\unicdcdcdhd}((v2\_funct\_1~(k4\_afinsq\_2~X0)){\unicdcdcdhd}\\
((v5\_ordinal1~(k4\_afinsq\_2~X0)){\unicdcdcdhd}(v1\_finset\_1~(k4\_afinsq\_2~X0)))))))\end{array}
\label{hyp:ggdgcdidpfbgggjgogdhbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_finset\_1~X0){\unicdcdcdhd}(v6\_membered~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_relat\_1~X1){\unicdcdcdhd}((v5\_relat\_1~X1~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}\\
((v5\_ordinal1~X1){\unicdcdcdhd}(v1\_finset\_1~X1))))){\unicdbdjdcd}((X1=k4\_afinsq\_2~X0){\unicdbdjded}\\
((k2\_relset\_1~k5\_numbers~X1=X0){\unicdcdcdhd}({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (v7\_ordinal1~X4){\unicdbdjdcd}(\\
{\unicdcdadad} X5 .  (v7\_ordinal1~X5){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X3~X2){\unicdcdcdhd}((\preoh r1\_xxreal\_0~\\
(k1\_afinsq\_1~X1)~X3){\unicdcdcdhd}((X4=k1\_recdef\_1~X1~X2){\unicdcdcdhd}((X5=k1\_recdef\_1~\\
X1~X3){\unicdcdcdhd}(r1\_xxreal\_0~X5~X4))))))))))))\end{array}
\label{hyp:egedpfbgggjgogdhbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v1\_xxreal\_0~X1)){\unicdbdjdcd}(\\
(r1\_xxreal\_0~X0~X1){\unicdcdcdid}(r1\_xxreal\_0~X1~X0))\end{array}
\label{hyp:dgpgogogfgdgehfgegogfgdhdhpfchbdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgcdpfihihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehddddpfbgggjgogdhbhpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v7\_ordinal1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (\\
(v1\_finset\_1~X4){\unicdcdcdhd}(v6\_membered~X4)){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X0~X3){\unicdcdcdhd}(\\
(\preoh r1\_xxreal\_0~(k1\_afinsq\_1~(k4\_afinsq\_2~X4))~X1){\unicdcdcdhd}((k1\_recdef\_1~\\
(k4\_afinsq\_2~X4)~X1=X3){\unicdcdcdhd}((k1\_recdef\_1~(k4\_afinsq\_2~X4)~X2=X0){\unicdcdcdhd}\\
(r1\_xxreal\_0~X2~X1)))))))))\end{array}$$
\end{theorem}
\end{document}
