\documentclass{article}
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\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\begin{document}
\title{t63\_real\_3 (TMa5K3qQwBHcEBFeTv43aqWXDbqk3Pr9DcP)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k10\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_real\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k6\_real\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_real\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}((v1\_funct\_1~(k6\_real\_3~X0)){\unicdcdcdhd}((v1\_funct\_2~\\
(k6\_real\_3~X0)~k5\_numbers~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~(k6\_real\_3~\\
X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers)))))\end{array}
\label{hyp:egehpflggdpfchfgbgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}((v1\_funct\_1~(k5\_real\_3~X0)){\unicdcdcdhd}((v1\_funct\_2~\\
(k5\_real\_3~X0)~k5\_numbers~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~(k5\_real\_3~\\
X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers)))))\end{array}
\label{hyp:egehpflgfdpfchfgbgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~\\
X1~k5\_numbers~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k5\_numbers~k1\_numbers))))){\unicdbdjdcd}((X1=k6\_real\_3~X0){\unicdbdjded}((k3\_funct\_2~\\
k5\_numbers~k1\_numbers~X1~k6\_numbers=np\_\_1){\unicdcdcdhd}((k3\_funct\_2~k5\_numbers~\\
k1\_numbers~X1~np\_\_1=k3\_funct\_2~k5\_numbers~k1\_numbers~(k4\_real\_3~\\
X0)~np\_\_1){\unicdcdcdhd}({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}(k3\_funct\_2~k5\_numbers~\\
k1\_numbers~X1~(k1\_nat\_1~X2~np\_\_2)=k7\_real\_1~(k8\_real\_1~(k3\_funct\_2~\\
k5\_numbers~k1\_numbers~(k4\_real\_3~X0)~(k1\_nat\_1~X2~np\_\_2))~(k3\_funct\_2~\\
k5\_numbers~k1\_numbers~X1~(k1\_nat\_1~X2~np\_\_1)))~(k1\_seq\_1~X1~X2)))))))\end{array}
\label{hyp:eggdpfchfgbgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~\\
X1~k5\_numbers~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k5\_numbers~k1\_numbers))))){\unicdbdjdcd}((X1=k5\_real\_3~X0){\unicdbdjded}((k3\_funct\_2~\\
k5\_numbers~k1\_numbers~X1~k6\_numbers=k3\_funct\_2~k5\_numbers~k1\_numbers~\\
(k4\_real\_3~X0)~k6\_numbers){\unicdcdcdhd}((k3\_funct\_2~k5\_numbers~k1\_numbers~\\
X1~np\_\_1=k7\_real\_1~(k8\_real\_1~(k3\_funct\_2~k5\_numbers~k1\_numbers~\\
(k4\_real\_3~X0)~np\_\_1)~(k3\_funct\_2~k5\_numbers~k1\_numbers~(k4\_real\_3~\\
X0)~k6\_numbers))~np\_\_1){\unicdcdcdhd}({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}(k3\_funct\_2~\\
k5\_numbers~k1\_numbers~X1~(k1\_nat\_1~X2~np\_\_2)=k7\_real\_1~(k8\_real\_1~\\
(k3\_funct\_2~k5\_numbers~k1\_numbers~(k4\_real\_3~X0)~(k1\_nat\_1~X2~\\
np\_\_2))~(k3\_funct\_2~k5\_numbers~k1\_numbers~X1~(k1\_nat\_1~X2~np\_\_1)))~\\
(k1\_seq\_1~X1~X2)))))))\end{array}
\label{hyp:egfdpfchfgbgmgpfdd}
\end{equation}
\begin{theorem}\label{thm:ehgdddpfchfgbgmgpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}(k10\_real\_1~\\
(k3\_funct\_2~k5\_numbers~k1\_numbers~(k5\_real\_3~X1)~(k1\_nat\_1~X0~\\
np\_\_2))~(k3\_funct\_2~k5\_numbers~k1\_numbers~(k6\_real\_3~X1)~(k1\_nat\_1~\\
X0~np\_\_2))=k10\_real\_1~(k7\_real\_1~(k8\_real\_1~(k3\_funct\_2~k5\_numbers~\\
k1\_numbers~(k4\_real\_3~X1)~(k1\_nat\_1~X0~np\_\_2))~(k3\_funct\_2~k5\_numbers~\\
k1\_numbers~(k5\_real\_3~X1)~(k1\_nat\_1~X0~np\_\_1)))~(k1\_seq\_1~(k5\_real\_3~\\
X1)~X0))~(k7\_real\_1~(k8\_real\_1~(k3\_funct\_2~k5\_numbers~k1\_numbers~\\
(k4\_real\_3~X1)~(k1\_nat\_1~X0~np\_\_2))~(k3\_funct\_2~k5\_numbers~k1\_numbers~\\
(k6\_real\_3~X1)~(k1\_nat\_1~X0~np\_\_1)))~(k1\_seq\_1~(k6\_real\_3~X1)~X0))))\end{array}$$
\end{theorem}
\end{document}
