\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{t81\_afinsq\_2 (TMKuUAFHQm55uCArg7ktMa3hS5pLDFeX9KV)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_ordinal4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((v5\_ordinal1~\\
X0){\unicdcdcdhd}(v1\_finset\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v5\_ordinal1~X1){\unicdcdcdhd}(v1\_finset\_1~X1)))){\unicdbdjdcd}(\preoh (r1\_tarski~X0~X1){\unicdcdcdhd}\\
({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v5\_ordinal1~\\
X2){\unicdcdcdhd}(v1\_finset\_1~X2)))){\unicdbdjdcd}(k1\_ordinal4~X0~X2{\unicdcdgdad}X1))))\end{array}
\label{hyp:ehhdjdpfbgggjgogdhbhpfcd}
\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}(r1\_tarski~X0~(k1\_ordinal4~\\
X0~X1)))\end{array}
\label{hyp:ehhdedpfbgggjgogdhbhpfbd}
\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){\unicdcdcdhd}(v1\_finset\_1~X2)))){\unicdbdjdcd}\\
(k1\_ordinal4~(k1\_ordinal4~X0~X1)~X2=k1\_ordinal4~X0~(k1\_ordinal4~\\
X1~X2))))\end{array}
\label{hyp:ehcdhdpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v5\_ordinal1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finset\_1~X0)))){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v5\_ordinal1~\\
X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finset\_1~X1))))){\unicdbdjdcd}((v1\_relat\_1~(k1\_ordinal4~\\
X0~X1)){\unicdcdcdhd}((v5\_ordinal1~(k1\_ordinal4~X0~X1)){\unicdcdcdhd}((v1\_funct\_1~(k1\_ordinal4~\\
X0~X1)){\unicdcdcdhd}(v1\_finset\_1~(k1\_ordinal4~X0~X1)))))\end{array}
\label{hyp:ggdgfdpfbgggjgogdhbhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehidbdpfbgggjgogdhbhpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((v5\_ordinal1~\\
X0){\unicdcdcdhd}(v1\_finset\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v5\_ordinal1~X1){\unicdcdcdhd}(v1\_finset\_1~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v5\_ordinal1~X2){\unicdcdcdhd}(v1\_finset\_1~X2)))){\unicdbdjdcd}\\
((r1\_tarski~X0~X2){\unicdbdjdcd}(r1\_tarski~(k1\_ordinal4~X1~X0)~(k1\_ordinal4~\\
X1~X2)))))\end{array}$$
\end{theorem}
\end{document}
