\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{t5\_csspace3 (TMRf8z4x2QtJGc6xLZSpwSWVYVQrW8SsUT4)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_csspace3 : {\iota}$ 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 $ 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 $ l1\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ g1\_clvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_clvect\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_csspace3 : {\iota}$ be given.
Let $ k10\_csspace : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_csspace : {\iota}$ be given.
Let $ k8\_csspace : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_csspace : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ 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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_numbers : {\iota}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ g2\_clvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ v1\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_normsp\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_csspace3 : {\iota}$ be given.
Let $ v7\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_normsp\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_clvect\_1~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~(g1\_clvect\_1~(u1\_struct\_0~\\
X0)~(u2\_struct\_0~X0)~(u1\_algstr\_0~X0)~(u1\_clvect\_1~X0))){\unicdcdcdhd}((v13\_algstr\_0~\\
(g1\_clvect\_1~(u1\_struct\_0~X0)~(u2\_struct\_0~X0)~(u1\_algstr\_0~X0)~\\
(u1\_clvect\_1~X0))){\unicdcdcdhd}((v2\_rlvect\_1~(g1\_clvect\_1~(u1\_struct\_0~\\
X0)~(u2\_struct\_0~X0)~(u1\_algstr\_0~X0)~(u1\_clvect\_1~X0))){\unicdcdcdhd}((v3\_rlvect\_1~\\
(g1\_clvect\_1~(u1\_struct\_0~X0)~(u2\_struct\_0~X0)~(u1\_algstr\_0~X0)~\\
(u1\_clvect\_1~X0))){\unicdcdcdhd}((v4\_rlvect\_1~(g1\_clvect\_1~(u1\_struct\_0~\\
X0)~(u2\_struct\_0~X0)~(u1\_algstr\_0~X0)~(u1\_clvect\_1~X0))){\unicdcdcdhd}((v2\_clvect\_1~\\
(g1\_clvect\_1~(u1\_struct\_0~X0)~(u2\_struct\_0~X0)~(u1\_algstr\_0~X0)~\\
(u1\_clvect\_1~X0))){\unicdcdcdhd}((v3\_clvect\_1~(g1\_clvect\_1~(u1\_struct\_0~\\
X0)~(u2\_struct\_0~X0)~(u1\_algstr\_0~X0)~(u1\_clvect\_1~X0))){\unicdcdcdhd}((v4\_clvect\_1~\\
(g1\_clvect\_1~(u1\_struct\_0~X0)~(u2\_struct\_0~X0)~(u1\_algstr\_0~X0)~\\
(u1\_clvect\_1~X0))){\unicdcdcdhd}((v5\_clvect\_1~(g1\_clvect\_1~(u1\_struct\_0~\\
X0)~(u2\_struct\_0~X0)~(u1\_algstr\_0~X0)~(u1\_clvect\_1~X0))){\unicdcdcdhd}(l1\_clvect\_1~\\
(g1\_clvect\_1~(u1\_struct\_0~X0)~(u2\_struct\_0~X0)~(u1\_algstr\_0~X0)~\\
(u1\_clvect\_1~X0)))))))))))){\unicdbdjdcd}((\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}\\
((v2\_clvect\_1~X0){\unicdcdcdhd}((v3\_clvect\_1~X0){\unicdcdcdhd}((v4\_clvect\_1~X0){\unicdcdcdhd}((v5\_clvect\_1~\\
X0){\unicdcdcdhd}(l1\_clvect\_1~X0)))))))))))\end{array}
\label{hyp:ehhdjdpfdgdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v2\_struct\_0~(g1\_clvect\_1~k1\_csspace3~(k10\_csspace~k7\_csspace~\\
k1\_csspace3)~(k8\_csspace~k7\_csspace~k1\_csspace3)~(k9\_csspace~\\
k7\_csspace~k1\_csspace3))){\unicdcdcdhd}((v13\_algstr\_0~(g1\_clvect\_1~k1\_csspace3~\\
(k10\_csspace~k7\_csspace~k1\_csspace3)~(k8\_csspace~k7\_csspace~\\
k1\_csspace3)~(k9\_csspace~k7\_csspace~k1\_csspace3))){\unicdcdcdhd}((v2\_rlvect\_1~\\
(g1\_clvect\_1~k1\_csspace3~(k10\_csspace~k7\_csspace~k1\_csspace3)~\\
(k8\_csspace~k7\_csspace~k1\_csspace3)~(k9\_csspace~k7\_csspace~k1\_csspace3))){\unicdcdcdhd}\\
((v3\_rlvect\_1~(g1\_clvect\_1~k1\_csspace3~(k10\_csspace~k7\_csspace~\\
k1\_csspace3)~(k8\_csspace~k7\_csspace~k1\_csspace3)~(k9\_csspace~\\
k7\_csspace~k1\_csspace3))){\unicdcdcdhd}((v4\_rlvect\_1~(g1\_clvect\_1~k1\_csspace3~\\
(k10\_csspace~k7\_csspace~k1\_csspace3)~(k8\_csspace~k7\_csspace~\\
k1\_csspace3)~(k9\_csspace~k7\_csspace~k1\_csspace3))){\unicdcdcdhd}((v2\_clvect\_1~\\
(g1\_clvect\_1~k1\_csspace3~(k10\_csspace~k7\_csspace~k1\_csspace3)~\\
(k8\_csspace~k7\_csspace~k1\_csspace3)~(k9\_csspace~k7\_csspace~k1\_csspace3))){\unicdcdcdhd}\\
((v3\_clvect\_1~(g1\_clvect\_1~k1\_csspace3~(k10\_csspace~k7\_csspace~\\
k1\_csspace3)~(k8\_csspace~k7\_csspace~k1\_csspace3)~(k9\_csspace~\\
k7\_csspace~k1\_csspace3))){\unicdcdcdhd}((v4\_clvect\_1~(g1\_clvect\_1~k1\_csspace3~\\
(k10\_csspace~k7\_csspace~k1\_csspace3)~(k8\_csspace~k7\_csspace~\\
k1\_csspace3)~(k9\_csspace~k7\_csspace~k1\_csspace3))){\unicdcdcdhd}((v5\_clvect\_1~\\
(g1\_clvect\_1~k1\_csspace3~(k10\_csspace~k7\_csspace~k1\_csspace3)~\\
(k8\_csspace~k7\_csspace~k1\_csspace3)~(k9\_csspace~k7\_csspace~k1\_csspace3))){\unicdcdcdhd}\\
(l1\_clvect\_1~(g1\_clvect\_1~k1\_csspace3~(k10\_csspace~k7\_csspace~\\
k1\_csspace3)~(k8\_csspace~k7\_csspace~k1\_csspace3)~(k9\_csspace~\\
k7\_csspace~k1\_csspace3)))))))))))\end{array}
\label{hyp:mgidpfdgdhdhahbgdgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((m1\_subset\_1~\\
X1~X0){\unicdcdcdhd}(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~\\
X0))))){\unicdcdcdhd}(((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k2\_zfmisc\_1~k2\_numbers~\\
X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
k2\_numbers~X0)~X0))))){\unicdcdcdhd}((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~X0~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k1\_numbers)))))))){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  {\unicdcdadad} X6 .  {\unicdcdadad} X7 .  {\unicdcdadad} X8 .  {\unicdcdadad} X9 .  (g2\_clvect\_1~\\
X0~X1~X2~X3~X4=g2\_clvect\_1~X5~X6~X7~X8~X9){\unicdbdjdcd}((X0=X5){\unicdcdcdhd}((X1=X6){\unicdcdcdhd}((X2=\\
X7){\unicdcdcdhd}((X3=X8){\unicdcdcdhd}(X4=X9))))))\end{array}
\label{hyp:ggchfgfgpfhgcdpfdgmgghfgdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((m1\_subset\_1~X1~\\
X0){\unicdcdcdhd}(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~\\
X0))))){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k2\_zfmisc\_1~k2\_numbers~\\
X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
k2\_numbers~X0)~X0))))))){\unicdbdjdcd}({\unicdcdadad} X4 .  {\unicdcdadad} X5 .  {\unicdcdadad} X6 .  {\unicdcdadad} X7 .  \\
(g1\_clvect\_1~X0~X1~X2~X3=g1\_clvect\_1~X4~X5~X6~X7){\unicdbdjdcd}((X0=X4){\unicdcdcdhd}((X1=\\
X5){\unicdcdcdhd}((X2=X6){\unicdcdcdhd}(X3=X7)))))\end{array}
\label{hyp:ggchfgfgpfhgbdpfdgmgghfgdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v13\_algstr\_0~(g1\_clvect\_1~k1\_csspace3~(k10\_csspace~k7\_csspace~\\
k1\_csspace3)~(k8\_csspace~k7\_csspace~k1\_csspace3)~(k9\_csspace~\\
k7\_csspace~k1\_csspace3))){\unicdcdcdhd}((v2\_rlvect\_1~(g1\_clvect\_1~k1\_csspace3~\\
(k10\_csspace~k7\_csspace~k1\_csspace3)~(k8\_csspace~k7\_csspace~\\
k1\_csspace3)~(k9\_csspace~k7\_csspace~k1\_csspace3))){\unicdcdcdhd}((v3\_rlvect\_1~\\
(g1\_clvect\_1~k1\_csspace3~(k10\_csspace~k7\_csspace~k1\_csspace3)~\\
(k8\_csspace~k7\_csspace~k1\_csspace3)~(k9\_csspace~k7\_csspace~k1\_csspace3))){\unicdcdcdhd}\\
((v4\_rlvect\_1~(g1\_clvect\_1~k1\_csspace3~(k10\_csspace~k7\_csspace~\\
k1\_csspace3)~(k8\_csspace~k7\_csspace~k1\_csspace3)~(k9\_csspace~\\
k7\_csspace~k1\_csspace3))){\unicdcdcdhd}((v1\_clvect\_1~(g1\_clvect\_1~k1\_csspace3~\\
(k10\_csspace~k7\_csspace~k1\_csspace3)~(k8\_csspace~k7\_csspace~\\
k1\_csspace3)~(k9\_csspace~k7\_csspace~k1\_csspace3))){\unicdcdcdhd}((v2\_clvect\_1~\\
(g1\_clvect\_1~k1\_csspace3~(k10\_csspace~k7\_csspace~k1\_csspace3)~\\
(k8\_csspace~k7\_csspace~k1\_csspace3)~(k9\_csspace~k7\_csspace~k1\_csspace3))){\unicdcdcdhd}\\
((v3\_clvect\_1~(g1\_clvect\_1~k1\_csspace3~(k10\_csspace~k7\_csspace~\\
k1\_csspace3)~(k8\_csspace~k7\_csspace~k1\_csspace3)~(k9\_csspace~\\
k7\_csspace~k1\_csspace3))){\unicdcdcdhd}((v4\_clvect\_1~(g1\_clvect\_1~k1\_csspace3~\\
(k10\_csspace~k7\_csspace~k1\_csspace3)~(k8\_csspace~k7\_csspace~\\
k1\_csspace3)~(k9\_csspace~k7\_csspace~k1\_csspace3))){\unicdcdcdhd}(v5\_clvect\_1~\\
(g1\_clvect\_1~k1\_csspace3~(k10\_csspace~k7\_csspace~k1\_csspace3)~\\
(k8\_csspace~k7\_csspace~k1\_csspace3)~(k9\_csspace~k7\_csspace~k1\_csspace3))))))))))\end{array}
\label{hyp:ggdgddpfdgdhdhahbgdgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v2\_struct\_0~k7\_csspace){\unicdcdcdhd}((v13\_algstr\_0~k7\_csspace){\unicdcdcdhd}((v2\_rlvect\_1~\\
k7\_csspace){\unicdcdcdhd}((v3\_rlvect\_1~k7\_csspace){\unicdcdcdhd}((v4\_rlvect\_1~k7\_csspace){\unicdcdcdhd}\\
((v1\_clvect\_1~k7\_csspace){\unicdcdcdhd}((v2\_clvect\_1~k7\_csspace){\unicdcdcdhd}((v3\_clvect\_1~\\
k7\_csspace){\unicdcdcdhd}((v4\_clvect\_1~k7\_csspace){\unicdcdcdhd}(v5\_clvect\_1~k7\_csspace)))))))))\end{array}
\label{hyp:ggdgcdpfdgdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_clvect\_1}~{X0}})}{\unicdbdjdcd}{({{({{l1\_clvect\_1}~{X0}})}{\unicdcdcdhd}{({{l2\_normsp\_0}~{X0}})}})}}}\label{hyp:egehpfmgcdpfdgmgghfgdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\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}((v2\_clvect\_1~\\
X0){\unicdcdcdhd}((v3\_clvect\_1~X0){\unicdcdcdhd}((v4\_clvect\_1~X0){\unicdcdcdhd}((v5\_clvect\_1~X0){\unicdcdcdhd}\\
(l1\_clvect\_1~X0)))))))))){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}((v1\_funct\_1~(k9\_csspace~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k9\_csspace~\\
X0~X1)~(k2\_zfmisc\_1~k2\_numbers~X1)~X1){\unicdcdcdhd}(m1\_subset\_1~(k9\_csspace~\\
X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~k2\_numbers~X1)~X1)))))\end{array}
\label{hyp:egehpflgjdpfdgdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\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}((v2\_clvect\_1~\\
X0){\unicdcdcdhd}((v3\_clvect\_1~X0){\unicdcdcdhd}((v4\_clvect\_1~X0){\unicdcdcdhd}((v5\_clvect\_1~X0){\unicdcdcdhd}\\
(l1\_clvect\_1~X0)))))))))){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}((v1\_funct\_1~(k8\_csspace~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k8\_csspace~\\
X0~X1)~(k2\_zfmisc\_1~X1~X1)~X1){\unicdcdcdhd}(m1\_subset\_1~(k8\_csspace~X0~X1)~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X1~X1)~X1)))))\end{array}
\label{hyp:egehpflgidpfdgdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v2\_struct\_0~k7\_csspace){\unicdcdcdhd}((v1\_clvect\_1~k7\_csspace){\unicdcdcdhd}(l1\_clvect\_1~\\
k7\_csspace))\end{array}
\label{hyp:egehpflghdpfdgdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v2\_struct\_0}~{k3\_csspace3}}}})}{\unicdcdcdhd}{({{l2\_clvect\_1}~{k3\_csspace3}})}}\label{hyp:egehpflgddpfdgdhdhahbgdgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k2\_csspace3){\unicdcdcdhd}((v1\_funct\_2~k2\_csspace3~k1\_csspace3~\\
k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~k2\_csspace3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_csspace3~k1\_numbers))))\end{array}
\label{hyp:egehpflgcdpfdgdhdhahbgdgfgdd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k1\_csspace3}}~{({{k1\_zfmisc\_1}~{({{u1\_struct\_0}~{k7\_csspace}})}})}}\label{hyp:egehpflgbdpfdgdhdhahbgdgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\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}((v2\_clvect\_1~\\
X0){\unicdcdcdhd}((v3\_clvect\_1~X0){\unicdcdcdhd}((v4\_clvect\_1~X0){\unicdcdcdhd}((v5\_clvect\_1~X0){\unicdcdcdhd}\\
(l1\_clvect\_1~X0)))))))))){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}(m1\_subset\_1~(k10\_csspace~X0~X1)~X1)\end{array}
\label{hyp:egehpflgbdadpfdgdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((m1\_subset\_1~\\
X1~X0){\unicdcdcdhd}(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~\\
X0))))){\unicdcdcdhd}(((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k2\_zfmisc\_1~k2\_numbers~\\
X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
k2\_numbers~X0)~X0))))){\unicdcdcdhd}((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~X0~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k1\_numbers)))))))){\unicdbdjdcd}\\
((v7\_clvect\_1~(g2\_clvect\_1~X0~X1~X2~X3~X4)){\unicdcdcdhd}(l2\_clvect\_1~(g2\_clvect\_1~\\
X0~X1~X2~X3~X4)))\end{array}
\label{hyp:egehpfhgcdpfdgmgghfgdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k3\_csspace3=g2\_clvect\_1~k1\_csspace3~(k10\_csspace~k7\_csspace~\\
k1\_csspace3)~(k8\_csspace~k7\_csspace~k1\_csspace3)~(k9\_csspace~\\
k7\_csspace~k1\_csspace3)~k2\_csspace3\end{array}
\label{hyp:egddpfdgdhdhahbgdgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_clvect\_1~X0){\unicdbdjdcd}((v7\_clvect\_1~X0){\unicdbdjdcd}(X0=g2\_clvect\_1~\\
(u1\_struct\_0~X0)~(u2\_struct\_0~X0)~(u1\_algstr\_0~X0)~(u1\_clvect\_1~\\
X0)~(u1\_normsp\_0~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghhdpfdgmgghfgdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_clvect\_1~X0){\unicdbdjdcd}((v1\_clvect\_1~X0){\unicdbdjdcd}(X0=g1\_clvect\_1~\\
(u1\_struct\_0~X0)~(u2\_struct\_0~X0)~(u1\_algstr\_0~X0)~(u1\_clvect\_1~\\
X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpfdgmgghfgdgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehfdpfdgdhdhahbgdgfgdd}
$$\begin{array}{c}(\preoh v2\_struct\_0~k3\_csspace3){\unicdcdcdhd}((v13\_algstr\_0~k3\_csspace3){\unicdcdcdhd}((\\
v2\_rlvect\_1~k3\_csspace3){\unicdcdcdhd}((v3\_rlvect\_1~k3\_csspace3){\unicdcdcdhd}((v4\_rlvect\_1~\\
k3\_csspace3){\unicdcdcdhd}((v2\_clvect\_1~k3\_csspace3){\unicdcdcdhd}((v3\_clvect\_1~k3\_csspace3){\unicdcdcdhd}\\
((v4\_clvect\_1~k3\_csspace3){\unicdcdcdhd}((v5\_clvect\_1~k3\_csspace3){\unicdcdcdhd}(l1\_clvect\_1~\\
k3\_csspace3)))))))))\end{array}$$
\end{theorem}
\end{document}
