\documentclass{article}
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\newtheorem{conjecture}{Conjecture}
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\begin{document}
\title{t50\_pre\_poly (TMJsnuMT6SG9VYcMWYsuQmZvTn6povP4H8z)}
\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 $ r6\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k11\_pre\_poly : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r3\_pre\_poly : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ 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}(({\unicdcdadad} X3 .  (X3 \in X0){\unicdbdjdcd}(r1\_xxreal\_0~(k1\_funct\_1~X1~X3)~\\
(k1\_funct\_1~X2~X3))){\unicdbdjdcd}(r3\_pre\_poly~X0~X1~X2)))\end{array}
\label{hyp:ehedgdpfahchfgpfahpgmgjh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}(r1\_xxreal\_0~\\
X0~(k2\_xcmplx\_0~X0~X1)))\end{array}
\label{hyp:ehbdbdpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~X0)))){\unicdcdcdhd}((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~X2~X0))))){\unicdbdjdcd}\\
((r6\_pboole~X0~X1~X2){\unicdbdjded}(X1=X2))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchgdpfahcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xcmplx\_0~X0){\unicdcdcdhd}(v1\_xcmplx\_0~X1)){\unicdbdjdcd}(\\
k3\_binop\_2~X0~X1=k2\_xcmplx\_0~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfcgjgogpgahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v4\_valued\_0~\\
X0))){\unicdbdjdcd}(v7\_ordinal1~(k1\_funct\_1~X0~X1))\end{array}
\label{hyp:ggdggdgdpfghbgmgfhfgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_valued\_0~\\
X0))){\unicdbdjdcd}(v1\_xcmplx\_0~(k1\_funct\_1~X0~X1))\end{array}
\label{hyp:ggdggdbdpfghbgmgfhfgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}(v1\_valued\_0~X1))))){\unicdcdcdhd}\\
((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_partfun1~\\
X2~X0){\unicdcdcdhd}(v1\_valued\_0~X2)))))){\unicdbdjdcd}((v1\_relat\_1~(k11\_pre\_poly~X0~X1~\\
X2)){\unicdcdcdhd}((v4\_relat\_1~(k11\_pre\_poly~X0~X1~X2)~X0){\unicdcdcdhd}((v1\_funct\_1~(k11\_pre\_poly~\\
X0~X1~X2)){\unicdcdcdhd}(v1\_partfun1~(k11\_pre\_poly~X0~X1~X2)~X0))))\end{array}
\label{hyp:egehpflgbdbdpfahchfgpfahpgmgjh}
\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}(v1\_valued\_0~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}(v1\_valued\_0~X2))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (\\
(v1\_relat\_1~X3){\unicdcdcdhd}((v4\_relat\_1~X3~X0){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}(v1\_partfun1~\\
X3~X0)))){\unicdbdjdcd}((X3=k11\_pre\_poly~X0~X1~X2){\unicdbdjded}({\unicdcdadad} X4 .  k1\_funct\_1~\\
X3~X4=k3\_binop\_2~(k1\_funct\_1~X1~X4)~(k1\_funct\_1~X2~X4)))))\end{array}
\label{hyp:egfdpfahchfgpfahpgmgjh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v4\_valued\_0~X0)){\unicdbdjdcd}((v1\_relat\_1~\\
X0){\unicdcdcdhd}(v3\_valued\_0~X0))\end{array}
\label{hyp:dgdgidpfghbgmgfhfgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v3\_valued\_0~X0)){\unicdbdjdcd}((v1\_relat\_1~\\
X0){\unicdcdcdhd}(v1\_valued\_0~X0))\end{array}
\label{hyp:dgdggdpfghbgmgfhfgegpfad}
\end{equation}
\begin{theorem}\label{thm:ehfdadpfahchfgpfahpgmgjh}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}((v4\_valued\_0~X1){\unicdcdcdhd}(v2\_pre\_poly~\\
X1)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X2){\unicdcdcdhd}((v1\_partfun1~X2~X0){\unicdcdcdhd}((v4\_valued\_0~X2){\unicdcdcdhd}(v2\_pre\_poly~\\
X2)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}((v4\_relat\_1~X3~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X3){\unicdcdcdhd}((v1\_partfun1~X3~X0){\unicdcdcdhd}((v4\_valued\_0~X3){\unicdcdcdhd}(v2\_pre\_poly~\\
X3)))))){\unicdbdjdcd}((r6\_pboole~X0~X1~(k11\_pre\_poly~X0~X2~X3)){\unicdbdjdcd}(r3\_pre\_poly~\\
X0~X2~X1))))\end{array}$$
\end{theorem}
\end{document}
