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\begin{document}
\title{t58\_pre\_poly (TMWG3pKyb8HEuw13zafnxuYbVRtMNDsfrdF)}
\maketitle
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 $ r3\_pre\_poly : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k16\_pre\_poly : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r6\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k12\_pre\_poly : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k8\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\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}(((r3\_pre\_poly~X0~X1~X2){\unicdcdcdhd}(r6\_pboole~X0~(k12\_pre\_poly~\\
X0~X2~X1)~(k16\_pre\_poly~X0))){\unicdbdjdcd}(r6\_pboole~X0~X2~X1)))\end{array}
\label{hyp:ehfdhdpfahchfgpfahpgmgjh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\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}(r6\_pboole~X0~(k12\_pre\_poly~X0~(k16\_pre\_poly~X0)~X1)~\\
(k16\_pre\_poly~X0))\end{array}
\label{hyp:ehfdfdpfahchfgpfahpgmgjh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~(k8\_funcop\_1~k5\_numbers~X0~k6\_numbers)){\unicdcdcdhd}\\
((v4\_relat\_1~(k8\_funcop\_1~k5\_numbers~X0~k6\_numbers)~X0){\unicdcdcdhd}((v1\_funct\_1~\\
(k8\_funcop\_1~k5\_numbers~X0~k6\_numbers)){\unicdcdcdhd}((v1\_partfun1~(k8\_funcop\_1~\\
k5\_numbers~X0~k6\_numbers)~X0){\unicdcdcdhd}((v4\_valued\_0~(k8\_funcop\_1~k5\_numbers~\\
X0~k6\_numbers)){\unicdcdcdhd}(v2\_pre\_poly~(k8\_funcop\_1~k5\_numbers~X0~k6\_numbers))))))\end{array}
\label{hyp:ehedadpfahchfgpfahpgmgjh}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k16\_pre\_poly}~{X0}}={{{{k8\_funcop\_1}~{k5\_numbers}}~{X0}}~{k6\_numbers}}}}\label{hyp:egbdddpfahchfgpfahpgmgjh}
\end{equation}
\begin{theorem}\label{thm:ehfdidpfahchfgpfahpgmgjh}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}((v4\_valued\_0~X1){\unicdcdcdhd}(v2\_pre\_poly~\\
X1)))))){\unicdbdjdcd}((r3\_pre\_poly~X0~X1~(k16\_pre\_poly~X0)){\unicdbdjdcd}(r6\_pboole~X0~\\
(k16\_pre\_poly~X0)~X1))\end{array}$$
\end{theorem}
\end{document}
