\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{t8\_polynom2 (TMHvSg6iwJesmCTYvNWRYVdJZwQAH9B5ZzA)}
\maketitle
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r3\_orders\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_pre\_poly : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k7\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_tarski : {{\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}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_finset\_1~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~X0))){\unicdcdcdhd}((v1\_partfun1~X2~X0){\unicdcdcdhd}((v1\_relat\_2~X2){\unicdcdcdhd}\\
((v4\_relat\_2~X2){\unicdcdcdhd}((v8\_relat\_2~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)))))))){\unicdbdjdcd}(m2\_finseq\_1~(k7\_pre\_poly~X0~X1~X2)~\\
X0)\end{array}
\label{hyp:egehpflghdpfahchfgpfahpgmgjh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_finset\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_partfun1~X2~X0){\unicdcdcdhd}((v1\_relat\_2~X2){\unicdcdcdhd}((v4\_relat\_2~\\
X2){\unicdcdcdhd}((v8\_relat\_2~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0))))))){\unicdbdjdcd}((r3\_orders\_1~X2~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_finseq\_1~X3~\\
X0){\unicdbdjdcd}((X3=k7\_pre\_poly~X0~X1~X2){\unicdbdjded}((k2\_relset\_1~X0~X3=X1){\unicdcdcdhd}({\unicdcdadad} X4 .  \\
(v7\_ordinal1~X4){\unicdbdjdcd}({\unicdcdadad} X5 .  (v7\_ordinal1~X5){\unicdbdjdcd}(((X4 \in k4\_finseq\_1~\\
X3){\unicdcdcdhd}(X5 \in k4\_finseq\_1~X3)){\unicdbdjdcd}((r1\_xxreal\_0~X5~X4){\unicdcdcdid}((k7\_partfun1~\\
X0~X3~X4{\unicdcdgdad}k7\_partfun1~X0~X3~X5){\unicdcdcdhd}(k4\_tarski~(k7\_partfun1~X0~X3~X4)~\\
(k7\_partfun1~X0~X3~X5) \in X2)))))))))))\end{array}
\label{hyp:egcdpfahchfgpfahpgmgjh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\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:ehidpfahpgmgjhogpgngcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_finset\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_partfun1~X2~X0){\unicdcdcdhd}((v1\_relat\_2~X2){\unicdcdcdhd}((v4\_relat\_2~\\
X2){\unicdcdcdhd}((v8\_relat\_2~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0))))))){\unicdbdjdcd}((r3\_orders\_1~X2~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k5\_numbers){\unicdbdjdcd}(((X3 \in \\
k4\_finseq\_1~(k7\_pre\_poly~X0~X1~X2)){\unicdcdcdhd}((X4 \in k4\_finseq\_1~(k7\_pre\_poly~\\
X0~X1~X2)){\unicdcdcdhd}(k7\_partfun1~X0~(k7\_pre\_poly~X0~X1~X2)~X3=k7\_partfun1~\\
X0~(k7\_pre\_poly~X0~X1~X2)~X4))){\unicdbdjdcd}(X3=X4))))))\end{array}$$
\end{theorem}
\end{document}
