\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{t27\_csspace4 (TMHBNY14PzSEbbBhLVY7qWcFJJEmbfDi8Ga)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_normsp\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_normsp\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_clopban1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_csspace4 : {{\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 $ k5\_numbers : {\iota}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 $ v1\_csspace3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v9\_clvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v13\_algstr\_0~X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~\\
X1){\unicdcdcdhd}((v3\_normsp\_0~X1){\unicdcdcdhd}((v4\_normsp\_0~X1){\unicdcdcdhd}((v2\_clvect\_1~X1){\unicdcdcdhd}\\
((v3\_clvect\_1~X1){\unicdcdcdhd}((v4\_clvect\_1~X1){\unicdcdcdhd}((v5\_clvect\_1~X1){\unicdcdcdhd}((v8\_clvect\_1~\\
X1){\unicdcdcdhd}(l2\_clvect\_1~X1))))))))))))){\unicdbdjdcd}((v3\_clopban1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~k5\_numbers~(u1\_struct\_0~(k9\_csspace4~\\
X0~X1))){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~\\
(u1\_struct\_0~(k9\_csspace4~X0~X1))))))){\unicdbdjdcd}((v1\_csspace3~X2~(k9\_csspace4~\\
X0~X1)){\unicdbdjdcd}(v9\_clvect\_1~X2~(k9\_csspace4~X0~X1))))))\end{array}
\label{hyp:ehcdgdpfdgdhdhahbgdgfged}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v13\_algstr\_0~X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~\\
X1){\unicdcdcdhd}((v3\_normsp\_0~X1){\unicdcdcdhd}((v4\_normsp\_0~X1){\unicdcdcdhd}((v2\_clvect\_1~X1){\unicdcdcdhd}\\
((v3\_clvect\_1~X1){\unicdcdcdhd}((v4\_clvect\_1~X1){\unicdcdcdhd}((v5\_clvect\_1~X1){\unicdcdcdhd}((v8\_clvect\_1~\\
X1){\unicdcdcdhd}(l2\_clvect\_1~X1))))))))))))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k9\_csspace4~\\
X0~X1)){\unicdcdcdhd}((v13\_algstr\_0~(k9\_csspace4~X0~X1)){\unicdcdcdhd}((v2\_rlvect\_1~(k9\_csspace4~\\
X0~X1)){\unicdcdcdhd}((v3\_rlvect\_1~(k9\_csspace4~X0~X1)){\unicdcdcdhd}((v4\_rlvect\_1~(k9\_csspace4~\\
X0~X1)){\unicdcdcdhd}((v3\_normsp\_0~(k9\_csspace4~X0~X1)){\unicdcdcdhd}((v4\_normsp\_0~(k9\_csspace4~\\
X0~X1)){\unicdcdcdhd}((v2\_clvect\_1~(k9\_csspace4~X0~X1)){\unicdcdcdhd}((v3\_clvect\_1~(k9\_csspace4~\\
X0~X1)){\unicdcdcdhd}((v4\_clvect\_1~(k9\_csspace4~X0~X1)){\unicdcdcdhd}((v5\_clvect\_1~(k9\_csspace4~\\
X0~X1)){\unicdcdcdhd}((v8\_clvect\_1~(k9\_csspace4~X0~X1)){\unicdcdcdhd}(l2\_clvect\_1~(k9\_csspace4~\\
X0~X1)))))))))))))))\end{array}
\label{hyp:ehcdedpfdgdhdhahbgdgfged}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v3\_normsp\_0~X0){\unicdcdcdhd}\\
((v4\_normsp\_0~X0){\unicdcdcdhd}((v2\_clvect\_1~X0){\unicdcdcdhd}((v3\_clvect\_1~X0){\unicdcdcdhd}((v4\_clvect\_1~\\
X0){\unicdcdcdhd}((v5\_clvect\_1~X0){\unicdcdcdhd}((v8\_clvect\_1~X0){\unicdcdcdhd}(l2\_clvect\_1~X0))))))))))))){\unicdbdjdcd}\\
((v3\_clopban1~X0){\unicdbdjded}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~\\
X1~k5\_numbers~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k5\_numbers~(u1\_struct\_0~X0)))))){\unicdbdjdcd}((v1\_csspace3~\\
X1~X0){\unicdbdjdcd}(v9\_clvect\_1~X1~X0))))\end{array}
\label{hyp:egbdddpfdgmgpgahcgbgogbd}
\end{equation}
\begin{theorem}\label{thm:ehcdhdpfdgdhdhahbgdgfged}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v13\_algstr\_0~X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~\\
X1){\unicdcdcdhd}((v3\_normsp\_0~X1){\unicdcdcdhd}((v4\_normsp\_0~X1){\unicdcdcdhd}((v2\_clvect\_1~X1){\unicdcdcdhd}\\
((v3\_clvect\_1~X1){\unicdcdcdhd}((v4\_clvect\_1~X1){\unicdcdcdhd}((v5\_clvect\_1~X1){\unicdcdcdhd}((v8\_clvect\_1~\\
X1){\unicdcdcdhd}((v3\_clopban1~X1){\unicdcdcdhd}(l2\_clvect\_1~X1)))))))))))))){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
(k9\_csspace4~X0~X1)){\unicdcdcdhd}((v13\_algstr\_0~(k9\_csspace4~X0~X1)){\unicdcdcdhd}((v2\_rlvect\_1~\\
(k9\_csspace4~X0~X1)){\unicdcdcdhd}((v3\_rlvect\_1~(k9\_csspace4~X0~X1)){\unicdcdcdhd}((v4\_rlvect\_1~\\
(k9\_csspace4~X0~X1)){\unicdcdcdhd}((v3\_normsp\_0~(k9\_csspace4~X0~X1)){\unicdcdcdhd}((v4\_normsp\_0~\\
(k9\_csspace4~X0~X1)){\unicdcdcdhd}((v2\_clvect\_1~(k9\_csspace4~X0~X1)){\unicdcdcdhd}((v3\_clvect\_1~\\
(k9\_csspace4~X0~X1)){\unicdcdcdhd}((v4\_clvect\_1~(k9\_csspace4~X0~X1)){\unicdcdcdhd}((v5\_clvect\_1~\\
(k9\_csspace4~X0~X1)){\unicdcdcdhd}((v8\_clvect\_1~(k9\_csspace4~X0~X1)){\unicdcdcdhd}((v3\_clopban1~\\
(k9\_csspace4~X0~X1)){\unicdcdcdhd}(l2\_clvect\_1~(k9\_csspace4~X0~X1))))))))))))))))\end{array}$$
\end{theorem}
\end{document}
