\documentclass{article}
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\newtheorem{conjecture}{Conjecture}
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\begin{document}
\title{t49\_pre\_poly (TMR5ZALin9222F1q6hqJCoCiiEW3ihxZAMw)}
\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 $ r3\_pre\_poly : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r2\_pre\_poly : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r6\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_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.
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 .  ((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}((r2\_pre\_poly~X0~X1~X2){\unicdcdcdid}(r2\_pre\_poly~X0~\\
X2~X1))))\end{array}
\label{hyp:ehedfdpfahchfgpfahpgmgjh}
\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 .  (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}((r1\_pre\_poly~X0~X1~X2){\unicdbdjded}({\unicdcdaddd} X3 .  (v3\_ordinal1~\\
X3){\unicdcdcdhd}((\preoh r1\_xxreal\_0~(k1\_funct\_1~X2~X3)~(k1\_funct\_1~X1~X3)){\unicdcdcdhd}({\unicdcdadad} X4 .  \\
(v3\_ordinal1~X4){\unicdbdjdcd}((X4 \in X3){\unicdbdjdcd}(k1\_funct\_1~X1~X4=k1\_funct\_1~X2~X4))))))))\end{array}
\label{hyp:egjdpfahchfgpfahpgmgjh}
\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}({\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){\unicdbdjded}({\unicdcdadad} X3 .  r1\_xxreal\_0~(k1\_funct\_1~\\
X1~X3)~(k1\_funct\_1~X2~X3))))\end{array}
\label{hyp:egbdbdpfahchfgpfahpgmgjh}
\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 .  ((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}((r2\_pre\_poly~X0~X1~X2){\unicdbdjded}((r1\_pre\_poly~\\
X0~X1~X2){\unicdcdcdid}(r6\_pboole~X0~X1~X2)))))\end{array}
\label{hyp:egbdadpfahchfgpfahpgmgjh}
\end{equation}
\begin{theorem}\label{thm:ehedjdpfahchfgpfahpgmgjh}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((\\
v4\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}((v4\_valued\_0~\\
X1){\unicdcdcdhd}(v2\_pre\_poly~X1)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~\\
X2~X0){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_partfun1~X2~X0){\unicdcdcdhd}((v4\_valued\_0~X2){\unicdcdcdhd}\\
(v2\_pre\_poly~X2)))))){\unicdbdjdcd}((r3\_pre\_poly~X0~X1~X2){\unicdbdjdcd}(r2\_pre\_poly~X0~\\
X1~X2))))\end{array}$$
\end{theorem}
\end{document}
