\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
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\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{t7\_hilbasis (TMThdSFDkugJKmc339GCtnHV544MHEqdaKg)}
\maketitle
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_poly : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k15\_pre\_poly : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k20\_pre\_poly : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r3\_pre\_poly : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r3\_orders\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_orders\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_relat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 $ k17\_pre\_poly : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_pre\_poly : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k7\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~X1)){\unicdbdjded}(r1\_tarski~\\
X0~X1)\end{array}
\label{hyp:ehddpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((r3\_orders\_1~\\
X0~X1){\unicdcdcdhd}(r1\_tarski~X2~X1)){\unicdbdjdcd}(r3\_orders\_1~X0~X2))\end{array}
\label{hyp:ehddidpfpgchegfgchdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}((v3\_orders\_1~X0){\unicdbdjdcd}(r3\_orders\_1~X0~\\
(k1\_relat\_1~X0)))\end{array}
\label{hyp:ehddhdpfpgchegfgchdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_2~X1){\unicdcdcdhd}((v4\_relat\_2~X1){\unicdcdcdhd}((v8\_relat\_2~\\
X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0))))))){\unicdbdjdcd}(k1\_relat\_1~X1=X0)\end{array}
\label{hyp:ehbdfdpfpgchegfgchdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}((v1\_partfun1~(k17\_pre\_poly~X0)~\\
(k15\_pre\_poly~X0)){\unicdcdcdhd}((v1\_relat\_2~(k17\_pre\_poly~X0)){\unicdcdcdhd}((v4\_relat\_2~\\
(k17\_pre\_poly~X0)){\unicdcdcdhd}((v8\_relat\_2~(k17\_pre\_poly~X0)){\unicdcdcdhd}(v3\_orders\_1~\\
(k17\_pre\_poly~X0))))))\end{array}
\label{hyp:ggdgcdfdpfahchfgpfahpgmgjh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v3\_ordinal1~X0){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((\\
v4\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}((v4\_valued\_0~\\
X1){\unicdcdcdhd}(v2\_pre\_poly~X1))))))){\unicdbdjdcd}(m2\_finseq\_1~(k20\_pre\_poly~X0~X1)~\\
(k15\_pre\_poly~X0))\end{array}
\label{hyp:egehpflgcdadpfahchfgpfahpgmgjh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}((v1\_partfun1~(k17\_pre\_poly~X0)~\\
(k15\_pre\_poly~X0)){\unicdcdcdhd}((v1\_relat\_2~(k17\_pre\_poly~X0)){\unicdcdcdhd}((v4\_relat\_2~\\
(k17\_pre\_poly~X0)){\unicdcdcdhd}((v8\_relat\_2~(k17\_pre\_poly~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
(k17\_pre\_poly~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k15\_pre\_poly~X0)~\\
(k15\_pre\_poly~X0))))))))\end{array}
\label{hyp:egehpflgbdhdpfahchfgpfahpgmgjh}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((\\
v4\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}((v4\_valued\_0~\\
X1){\unicdcdcdhd}(v2\_pre\_poly~X1)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~(k15\_pre\_poly~\\
X0)){\unicdbdjdcd}((X2=k20\_pre\_poly~X0~X1){\unicdbdjded}({\unicdcdaddd} X3 .  ((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}\\
((v1\_finset\_1~X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k15\_pre\_poly~\\
X0))))){\unicdcdcdhd}((X2=k7\_pre\_poly~(k15\_pre\_poly~X0)~X3~(k17\_pre\_poly~\\
X0)){\unicdcdcdhd}({\unicdcdadad} X4 .  ((v1\_relat\_1~X4){\unicdcdcdhd}((v4\_relat\_1~X4~X0){\unicdcdcdhd}((v1\_funct\_1~\\
X4){\unicdcdcdhd}((v1\_partfun1~X4~X0){\unicdcdcdhd}((v4\_valued\_0~X4){\unicdcdcdhd}(v2\_pre\_poly~X4)))))){\unicdbdjdcd}\\
((X4 \in X3){\unicdbdjded}(r3\_pre\_poly~X0~X4~X1))))))))\end{array}
\label{hyp:egbdgdpfahchfgpfahpgmgjh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v1\_relat\_1~X2)\end{array}
\label{hyp:dgdgbdpfchfgmgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehhdpfigjgmgcgbgdhjgdh}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((\\
v4\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}((v4\_valued\_0~\\
X1){\unicdcdcdhd}(v2\_pre\_poly~X1)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~\\
X2~X0){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_partfun1~X2~X0){\unicdcdcdhd}((v4\_valued\_0~X2){\unicdcdcdhd}\\
(v2\_pre\_poly~X2)))))){\unicdbdjdcd}((X2 \in k2\_relset\_1~(k15\_pre\_poly~X0)~(k20\_pre\_poly~\\
X0~X1)){\unicdbdjded}(r3\_pre\_poly~X0~X2~X1))))\end{array}$$
\end{theorem}
\end{document}
