\documentclass{article}
\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{l11\_csspace2 (TMPjWghixADrNxPExLnc63pF6HK9dsn9HUQ)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k18\_csspace : {\iota}$ be given.
Let $ k2\_csspace : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_csspace : {\iota}$ be given.
Let $ k1\_csspace : {\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 $ k2\_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 $ k3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_series\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_clvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k25\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v1\_series\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k20\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k55\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}(u1\_struct\_0~k7\_csspace=k1\_csspace){\unicdcdcdhd}(({\unicdcdadad} X0 .  (m1\_subset\_1~\\
X0~(u1\_struct\_0~k7\_csspace)){\unicdbdjded}((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~\\
X0~k5\_numbers~k2\_numbers){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k5\_numbers~k2\_numbers)))))){\unicdcdcdhd}(({\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~\\
k7\_csspace)){\unicdbdjded}((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k2\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k2\_numbers)))))){\unicdcdcdhd}\\
(({\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~k7\_csspace)){\unicdbdjdcd}(X0=\\
k2\_csspace~X0)){\unicdcdcdhd}(({\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~k7\_csspace)){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~k7\_csspace)){\unicdbdjdcd}(k3\_rlvect\_1~\\
k7\_csspace~X0~X1=k1\_series\_1~k2\_numbers~(k2\_csspace~X0)~(k2\_csspace~\\
X1)))){\unicdcdcdhd}({\unicdcdadad} X0 .  (v1\_xcmplx\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~k7\_csspace)){\unicdbdjdcd}(k1\_clvect\_1~k7\_csspace~X1~X0=k25\_valued\_1~\\
k5\_numbers~k2\_numbers~(k2\_csspace~X1)~X0)))))))\end{array}
\label{hyp:ehbdfdpfdgdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~k18\_csspace)){\unicdbdjded}(((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k2\_numbers){\unicdcdcdhd}(m1\_subset\_1~X0~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k2\_numbers))))){\unicdcdcdhd}(v1\_series\_1~\\
(k20\_valued\_1~k5\_numbers~k1\_numbers~k1\_numbers~(k55\_valued\_1~\\
k5\_numbers~k2\_numbers~(k2\_csspace~X0))~(k55\_valued\_1~k5\_numbers~\\
k2\_numbers~(k2\_csspace~X0)))))\end{array}
\label{hyp:mgjdpfdgdhdhahbgdgfgcd}
\end{equation}
\begin{theorem}\label{thm:mgbdbdpfdgdhdhahbgdgfgcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~k18\_csspace)){\unicdbdjdcd}(X0=k2\_csspace~\\
X0)\end{array}$$
\end{theorem}
\end{document}
