\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\begin{document}
\title{t12\_real\_3 (TMPDSoMmhebj94ZkJvHbMdysKh5MQZMHc8m)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k2\_real\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_nat\_d : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_real\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\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 $ k4\_nat\_d : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}(\\
(v1\_funct\_1~(k2\_real\_3~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k2\_real\_3~X0~X1)~\\
k5\_numbers~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~(k2\_real\_3~X0~X1)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k5\_numbers~k5\_numbers)))))\end{array}
\label{hyp:egehpflgcdpfchfgbgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}(\\
(v1\_funct\_1~(k1\_real\_3~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k1\_real\_3~X0~X1)~\\
k5\_numbers~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~(k1\_real\_3~X0~X1)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k5\_numbers~k5\_numbers)))))\end{array}
\label{hyp:egehpflgbdpfchfgbgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~k5\_numbers~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k5\_numbers))))){\unicdbdjdcd}((X2=\\
k2\_real\_3~X0~X1){\unicdbdjded}((k3\_funct\_2~k5\_numbers~k5\_numbers~X2~k6\_numbers=\\
k3\_nat\_d~X0~X1){\unicdcdcdhd}((k3\_funct\_2~k5\_numbers~k5\_numbers~X2~np\_\_1=k3\_nat\_d~\\
X1~(k4\_nat\_d~X0~X1)){\unicdcdcdhd}({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}(k3\_funct\_2~\\
k5\_numbers~k5\_numbers~X2~(k1\_nat\_1~X3~np\_\_2)=k3\_nat\_d~(k1\_seq\_1~\\
(k1\_real\_3~X0~X1)~X3)~(k3\_funct\_2~k5\_numbers~k5\_numbers~(k1\_real\_3~\\
X0~X1)~(k1\_nat\_1~X3~np\_\_1)))))))))\end{array}
\label{hyp:egcdpfchfgbgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~k5\_numbers~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k5\_numbers))))){\unicdbdjdcd}((X2=\\
k1\_real\_3~X0~X1){\unicdbdjded}((k3\_funct\_2~k5\_numbers~k5\_numbers~X2~k6\_numbers=\\
k4\_nat\_d~X0~X1){\unicdcdcdhd}((k3\_funct\_2~k5\_numbers~k5\_numbers~X2~np\_\_1=k4\_nat\_d~\\
X1~(k4\_nat\_d~X0~X1)){\unicdcdcdhd}({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}(k3\_funct\_2~\\
k5\_numbers~k5\_numbers~X2~(k1\_nat\_1~X3~np\_\_2)=k4\_nat\_d~(k1\_seq\_1~\\
X2~X3)~(k3\_funct\_2~k5\_numbers~k5\_numbers~X2~(k1\_nat\_1~X3~np\_\_1)))))))))\end{array}
\label{hyp:egbdpfchfgbgmgpfdd}
\end{equation}
\begin{theorem}\label{thm:ehbdcdpfchfgbgmgpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}(k3\_funct\_2~\\
k5\_numbers~k5\_numbers~(k2\_real\_3~X0~X1)~np\_\_1=k3\_nat\_d~X1~(k3\_funct\_2~\\
k5\_numbers~k5\_numbers~(k1\_real\_3~X0~X1)~k6\_numbers)))\end{array}$$
\end{theorem}
\end{document}
