\documentclass{article}
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\newtheorem{lemma}{Lemma}
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\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
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\begin{document}
\title{t37\_afinsq\_1 (TMSgjJ5KCnFudZ1uL5eC3eHGa9Br3cNWvpM)}
\maketitle
Let $ k7\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_ordinal4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k5\_afinsq\_1}~{X0}}={{k1\_tarski}~{({{{k4\_tarski}~{k6\_numbers}}~{X0}})}}}}\label{hyp:ehddcdpfbgggjgogdhbhpfbd}
\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}
{{\unicdcdadad} X0 .  {{{k5\_afinsq\_1}~{X0}}={{k3\_afinsq\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v5\_ordinal1~(k3\_afinsq\_1~X0)){\unicdcdcdhd}(v1\_finset\_1~(k3\_afinsq\_1~\\
X0))\end{array}
\label{hyp:ggdgidpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~(k5\_afinsq\_1~X0)){\unicdcdcdhd}(v1\_funct\_1~(k5\_afinsq\_1~\\
X0))\end{array}
\label{hyp:egehpflgfdpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k7\_afinsq\_1~X0~X1~X2=k1\_ordinal4~\\
(k1\_ordinal4~(k5\_afinsq\_1~X0)~(k5\_afinsq\_1~X1))~(k5\_afinsq\_1~\\
X2)\end{array}
\label{hyp:eggdpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k6\_afinsq\_1~X0~X1=k1\_ordinal4~(k5\_afinsq\_1~\\
X0)~(k5\_afinsq\_1~X1)\end{array}
\label{hyp:egfdpfbgggjgogdhbhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddhdpfbgggjgogdhbhpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (k7\_afinsq\_1~X0~X1~X2=k1\_ordinal4~\\
(k5\_afinsq\_1~X0)~(k6\_afinsq\_1~X1~X2)){\unicdcdcdhd}(k7\_afinsq\_1~X0~X1~X2=k1\_ordinal4~\\
(k6\_afinsq\_1~X0~X1)~(k5\_afinsq\_1~X2))\end{array}$$
\end{theorem}
\end{document}
