\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{t82\_afinsq\_2 (TMYbzGWrc1F6ojHrZJjeX47szQ5DTApxcPZ)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k8\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 $ k8\_afinsq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_ordinal4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k15\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(\\
(v5\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v5\_ordinal1~X1){\unicdcdcdhd}(v1\_finset\_1~\\
X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v5\_relat\_1~X2~X0){\unicdcdcdhd}((\\
v1\_funct\_1~X2){\unicdcdcdhd}((v5\_ordinal1~X2){\unicdcdcdhd}(v1\_finset\_1~X2))))){\unicdbdjdcd}(\preoh (r1\_tarski~\\
X1~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}((v5\_relat\_1~X3~X0){\unicdcdcdhd}((v1\_funct\_1~\\
X3){\unicdcdcdhd}((v5\_ordinal1~X3){\unicdcdcdhd}(v1\_finset\_1~X3))))){\unicdbdjdcd}(k1\_ordinal4~X1~\\
X3{\unicdcdgdad}X2)))))\end{array}
\label{hyp:ehidadpfbgggjgogdhbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v5\_relat\_1~X1~(k8\_afinsq\_1~\\
X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v5\_ordinal1~X1){\unicdcdcdhd}(v1\_finset\_1~X1))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v5\_relat\_1~X2~(k8\_afinsq\_1~X0)){\unicdcdcdhd}\\
((v1\_funct\_1~X2){\unicdcdcdhd}((v5\_ordinal1~X2){\unicdcdcdhd}(v1\_finset\_1~X2))))){\unicdbdjdcd}(k8\_afinsq\_2~\\
X0~(k1\_ordinal4~X1~X2)=k15\_afinsq\_1~X0~(k8\_afinsq\_2~X0~X1)~(k8\_afinsq\_2~\\
X0~X2)))\end{array}
\label{hyp:ehhdfdpfbgggjgogdhbhpfcd}
\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 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_subset\_1~X1~(k8\_afinsq\_1~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k8\_afinsq\_1~X0))){\unicdbdjdcd}(k15\_afinsq\_1~X0~X1~X2=\\
k1\_ordinal4~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdfdpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{v4\_funct\_1}~{({{k8\_afinsq\_1}~{X0}})}}}\label{hyp:ggdgcdedpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {\preoh{{{v1\_xboole\_0}~{({{k8\_afinsq\_1}~{X0}})}}}}}\label{hyp:ggdgcdadpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v5\_relat\_1~X1~(k8\_afinsq\_1~\\
X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v5\_ordinal1~X1){\unicdcdcdhd}(v1\_finset\_1~X1))))){\unicdbdjdcd}\\
(m1\_subset\_1~(k8\_afinsq\_2~X0~X1)~(k8\_afinsq\_1~X0))\end{array}
\label{hyp:egehpflgidpfbgggjgogdhbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v4\_funct\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}(\\
(v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)))\end{array}
\label{hyp:dgdgidpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k8\_afinsq\_1~X0)){\unicdbdjdcd}((v5\_ordinal1~\\
X1){\unicdcdcdhd}(v1\_finset\_1~X1))\end{array}
\label{hyp:dgdgbdadpfbgggjgogdhbhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehidcdpfbgggjgogdhbhpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v5\_relat\_1~X1~(k8\_afinsq\_1~\\
X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v5\_ordinal1~X1){\unicdcdcdhd}(v1\_finset\_1~X1))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v5\_relat\_1~X2~(k8\_afinsq\_1~X0)){\unicdcdcdhd}\\
((v1\_funct\_1~X2){\unicdcdcdhd}((v5\_ordinal1~X2){\unicdcdcdhd}(v1\_finset\_1~X2))))){\unicdbdjdcd}((\\
r1\_tarski~X1~X2){\unicdbdjdcd}(r1\_tarski~(k8\_afinsq\_2~X0~X1)~(k8\_afinsq\_2~X0~\\
X2))))\end{array}$$
\end{theorem}
\end{document}
