\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{l29\_lp\_space (TMQ7UCv1MkmfkNBiGXGXjCk4hA5gBhX7q78)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\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 $ k5\_numbers : {\iota}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_series\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_lp\_space : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_series\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_power : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_series\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))){\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}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}(((r1\_xxreal\_0~np\_\_1~\\
X2){\unicdcdcdhd}((v1\_series\_1~(k1\_lp\_space~X0~X2)){\unicdcdcdhd}(v1\_series\_1~(k1\_lp\_space~\\
X1~X2)))){\unicdbdjdcd}((v1\_series\_1~(k1\_lp\_space~(k1\_series\_1~k1\_numbers~\\
X0~X1)~X2)){\unicdcdcdhd}(r1\_xxreal\_0~(k4\_power~(k4\_series\_1~(k1\_lp\_space~\\
(k1\_series\_1~k1\_numbers~X0~X1)~X2))~(k10\_real\_1~np\_\_1~X2))~(k7\_real\_1~\\
(k4\_power~(k4\_series\_1~(k1\_lp\_space~X0~X2))~(k10\_real\_1~np\_\_1~\\
X2))~(k4\_power~(k4\_series\_1~(k1\_lp\_space~X1~X2))~(k10\_real\_1~np\_\_1~\\
X2))))))))\end{array}
\label{hyp:ehddpfmgahpfdhahbgdgfg}
\end{equation}
\begin{theorem}\label{thm:mgcdjdpfmgahpfdhahbgdgfg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}((r1\_xxreal\_0~np\_\_1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~k5\_numbers~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~k5\_numbers~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))){\unicdbdjdcd}\\
(((v1\_series\_1~(k1\_lp\_space~X1~X0)){\unicdcdcdhd}(v1\_series\_1~(k1\_lp\_space~\\
X2~X0))){\unicdbdjdcd}(v1\_series\_1~(k1\_lp\_space~(k1\_series\_1~k1\_numbers~X1~\\
X2)~X0))))))\end{array}$$
\end{theorem}
\end{document}
