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\begin{document}
\title{t52\_pre\_poly (TMcQgqfWknSHcf1wJkACRZMHadL4JoLRfmf)}
\maketitle
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k16\_pre\_poly : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k2\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k8\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\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 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X1 \in X0){\unicdbdjdcd}(k1\_funct\_1~(k2\_funcop\_1~\\
X0~X2)~X1=X2)\end{array}
\label{hyp:ehhdpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k1\_xboole\_0}}~{k4\_ordinal1}}\label{hyp:ehbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (k9\_xtuple\_0~(k2\_funcop\_1~X0~X1)=X0){\unicdcdcdhd}(\\
r1\_tarski~(k10\_xtuple\_0~(k2\_funcop\_1~X0~X1))~(k1\_tarski~X1))\end{array}
\label{hyp:ehbdddpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X2~X0)){\unicdbdjdcd}(k8\_funcop\_1~X0~X1~X2=k2\_funcop\_1~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k4\_ordinal1}}}})}{\unicdcdcdhd}{({{v3\_ordinal1}~{k4\_ordinal1}})}}\label{hyp:ggdggdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_relat\_1~(k2\_funcop\_1~X0~X1)){\unicdcdcdhd}(v1\_funct\_1~\\
(k2\_funcop\_1~X0~X1))\end{array}
\label{hyp:ggdgbdpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \\
((X1 \in k9\_xtuple\_0~X0){\unicdbdjdcd}((X2=k1\_funct\_1~X0~X1){\unicdbdjded}(k4\_tarski~X1~X2 \in \\
X0))){\unicdcdcdhd}((\preoh X1 \in k9\_xtuple\_0~X0){\unicdbdjdcd}((X2=k1\_funct\_1~X0~X1){\unicdbdjded}(X2=k1\_xboole\_0))))\end{array}
\label{hyp:egcdpfggfhogdgehpfbd}
\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:ehfdcdpfahchfgpfahpgmgjh}
${{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k1\_funct\_1}~{({{k16\_pre\_poly}~{X0}})}}~{X1}}={k6\_numbers}}}}$.
\end{theorem}
\end{document}
