\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{t3\_fdiff\_6 (TMNuvyE2s6LrxRmcXxuatxE7nmS5nuDasNF)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ v3\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k47\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_square\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_taylor\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ r2\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v3\_rcomp\_1~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~k1\_numbers))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~\\
k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}(m1\_subset\_1~X3~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}(((r1\_tarski~\\
X1~(k9\_xtuple\_0~(k47\_valued\_1~k1\_numbers~k1\_numbers~k1\_numbers~\\
X2~X3))){\unicdcdcdhd}(({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k1\_numbers){\unicdbdjdcd}((X4 \in X1){\unicdbdjdcd}\\
(k1\_seq\_1~X2~X4=X0))){\unicdcdcdhd}(X3=k1\_taylor\_1~np\_\_2))){\unicdbdjdcd}((r2\_fdiff\_1~\\
(k47\_valued\_1~k1\_numbers~k1\_numbers~k1\_numbers~X2~X3)~X1){\unicdcdcdhd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~k1\_numbers){\unicdbdjdcd}((X4 \in X1){\unicdbdjdcd}(k1\_seq\_1~(k2\_fdiff\_1~\\
(k47\_valued\_1~k1\_numbers~k1\_numbers~k1\_numbers~X2~X3)~X1)~X4=k1\_real\_1~\\
(k8\_real\_1~np\_\_2~X4)))))))))\end{array}
\label{hyp:mgcdpfggegjgggggpffd}
\end{equation}
Assume the following.
\begin{equation}
{{v3\_membered}~{k1\_numbers}}\label{hyp:ggdgddpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v3\_valued\_0~\\
X0))){\unicdbdjdcd}(m1\_subset\_1~(k1\_seq\_1~X0~X1)~k1\_numbers)\end{array}
\label{hyp:egehpflgbdpfdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v1\_relat\_1~X2)\end{array}
\label{hyp:dgdgbdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v3\_membered~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v3\_valued\_0~X2))\end{array}
\label{hyp:dgdgbdidpfghbgmgfhfgegpfad}
\end{equation}
\begin{theorem}\label{thm:ehddpfggegjgggggpfgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v3\_rcomp\_1~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~k1\_numbers))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~\\
k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}(m1\_subset\_1~X3~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}(((r1\_tarski~\\
X1~(k9\_xtuple\_0~(k47\_valued\_1~k1\_numbers~k1\_numbers~k1\_numbers~\\
X2~X3))){\unicdcdcdhd}(({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k1\_numbers){\unicdbdjdcd}((X4 \in X1){\unicdbdjdcd}\\
(k1\_seq\_1~X2~X4=k5\_square\_1~X0))){\unicdcdcdhd}(X3=k1\_taylor\_1~np\_\_2))){\unicdbdjdcd}\\
((r2\_fdiff\_1~(k47\_valued\_1~k1\_numbers~k1\_numbers~k1\_numbers~\\
X2~X3)~X1){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k1\_numbers){\unicdbdjdcd}((X4 \in X1){\unicdbdjdcd}\\
(k1\_seq\_1~(k2\_fdiff\_1~(k47\_valued\_1~k1\_numbers~k1\_numbers~k1\_numbers~\\
X2~X3)~X1)~X4=k1\_real\_1~(k8\_real\_1~np\_\_2~X4)))))))))\end{array}$$
\end{theorem}
\end{document}
