\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{t24\_csspace4 (TMLouuGf3qb43o6yTS7HjbMw5at15r7ZVWf)}
\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 $ l2\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_csspace4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ 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 $ l1\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ k4\_csspace4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_csspace : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_clopban1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_csspace : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_csspace : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_normsp\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k8\_csspace4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v7\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_lopban\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_lopban\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_clopban1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_normsp\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_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:ehcdpfdgdhdhahbgdgfgdd}
\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}((v4\_normsp\_0~(k9\_csspace4~\\
X0~X1)){\unicdcdcdhd}((v3\_normsp\_0~(k9\_csspace4~X0~X1)){\unicdcdcdhd}(v8\_clvect\_1~(k9\_csspace4~\\
X0~X1)))))\end{array}
\label{hyp:ehcdddpfdgdhdhahbgdgfged}
\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 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\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}((v13\_algstr\_0~(g1\_clvect\_1~\\
(k4\_csspace4~X0~X1)~(k10\_csspace~(k3\_clopban1~X0~X1)~(k4\_csspace4~\\
X0~X1))~(k8\_csspace~(k3\_clopban1~X0~X1)~(k4\_csspace4~X0~X1))~(k9\_csspace~\\
(k3\_clopban1~X0~X1)~(k4\_csspace4~X0~X1)))){\unicdcdcdhd}((v2\_rlvect\_1~(g1\_clvect\_1~\\
(k4\_csspace4~X0~X1)~(k10\_csspace~(k3\_clopban1~X0~X1)~(k4\_csspace4~\\
X0~X1))~(k8\_csspace~(k3\_clopban1~X0~X1)~(k4\_csspace4~X0~X1))~(k9\_csspace~\\
(k3\_clopban1~X0~X1)~(k4\_csspace4~X0~X1)))){\unicdcdcdhd}((v3\_rlvect\_1~(g1\_clvect\_1~\\
(k4\_csspace4~X0~X1)~(k10\_csspace~(k3\_clopban1~X0~X1)~(k4\_csspace4~\\
X0~X1))~(k8\_csspace~(k3\_clopban1~X0~X1)~(k4\_csspace4~X0~X1))~(k9\_csspace~\\
(k3\_clopban1~X0~X1)~(k4\_csspace4~X0~X1)))){\unicdcdcdhd}((v4\_rlvect\_1~(g1\_clvect\_1~\\
(k4\_csspace4~X0~X1)~(k10\_csspace~(k3\_clopban1~X0~X1)~(k4\_csspace4~\\
X0~X1))~(k8\_csspace~(k3\_clopban1~X0~X1)~(k4\_csspace4~X0~X1))~(k9\_csspace~\\
(k3\_clopban1~X0~X1)~(k4\_csspace4~X0~X1)))){\unicdcdcdhd}((v1\_clvect\_1~(g1\_clvect\_1~\\
(k4\_csspace4~X0~X1)~(k10\_csspace~(k3\_clopban1~X0~X1)~(k4\_csspace4~\\
X0~X1))~(k8\_csspace~(k3\_clopban1~X0~X1)~(k4\_csspace4~X0~X1))~(k9\_csspace~\\
(k3\_clopban1~X0~X1)~(k4\_csspace4~X0~X1)))){\unicdcdcdhd}((v2\_clvect\_1~(g1\_clvect\_1~\\
(k4\_csspace4~X0~X1)~(k10\_csspace~(k3\_clopban1~X0~X1)~(k4\_csspace4~\\
X0~X1))~(k8\_csspace~(k3\_clopban1~X0~X1)~(k4\_csspace4~X0~X1))~(k9\_csspace~\\
(k3\_clopban1~X0~X1)~(k4\_csspace4~X0~X1)))){\unicdcdcdhd}((v3\_clvect\_1~(g1\_clvect\_1~\\
(k4\_csspace4~X0~X1)~(k10\_csspace~(k3\_clopban1~X0~X1)~(k4\_csspace4~\\
X0~X1))~(k8\_csspace~(k3\_clopban1~X0~X1)~(k4\_csspace4~X0~X1))~(k9\_csspace~\\
(k3\_clopban1~X0~X1)~(k4\_csspace4~X0~X1)))){\unicdcdcdhd}((v4\_clvect\_1~(g1\_clvect\_1~\\
(k4\_csspace4~X0~X1)~(k10\_csspace~(k3\_clopban1~X0~X1)~(k4\_csspace4~\\
X0~X1))~(k8\_csspace~(k3\_clopban1~X0~X1)~(k4\_csspace4~X0~X1))~(k9\_csspace~\\
(k3\_clopban1~X0~X1)~(k4\_csspace4~X0~X1)))){\unicdcdcdhd}(v5\_clvect\_1~(g1\_clvect\_1~\\
(k4\_csspace4~X0~X1)~(k10\_csspace~(k3\_clopban1~X0~X1)~(k4\_csspace4~\\
X0~X1))~(k8\_csspace~(k3\_clopban1~X0~X1)~(k4\_csspace4~X0~X1))~(k9\_csspace~\\
(k3\_clopban1~X0~X1)~(k4\_csspace4~X0~X1))))))))))))\end{array}
\label{hyp:ggdghdpfdgdhdhahbgdgfged}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\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 v1\_xboole\_0~(k4\_csspace4~\\
X0~X1))\end{array}
\label{hyp:ggdggdpfdgdhdhahbgdgfged}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
((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}((\preoh v2\_struct\_0~(g1\_clvect\_1~\\
X0~X1~X2~X3)){\unicdcdcdhd}(v1\_clvect\_1~(g1\_clvect\_1~X0~X1~X2~X3)))\end{array}
\label{hyp:ggdgbdpfdgmgghfgdgehpfbd}
\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 v1\_xboole\_0~X0){\unicdcdcdhd}((\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}(l2\_clvect\_1~(k9\_csspace4~X0~X1)))\end{array}
\label{hyp:egehpflgjdpfdgdhdhahbgdgfged}
\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 v1\_xboole\_0~X0){\unicdcdcdhd}((\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}((v1\_funct\_1~(k8\_csspace4~\\
X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k8\_csspace4~X0~X1)~(k4\_csspace4~X0~X1)~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~(k8\_csspace4~X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k4\_csspace4~\\
X0~X1)~k1\_numbers)))))\end{array}
\label{hyp:egehpflgidpfdgdhdhahbgdgfged}
\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}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\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}(m1\_subset\_1~(k4\_csspace4~\\
X0~X1)~(k1\_zfmisc\_1~(u1\_struct\_0~(k3\_clopban1~X0~X1))))\end{array}
\label{hyp:egehpflgedpfdgdhdhahbgdgfged}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\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}((v2\_clvect\_1~X1){\unicdcdcdhd}((v3\_clvect\_1~X1){\unicdcdcdhd}((v4\_clvect\_1~X1){\unicdcdcdhd}\\
((v5\_clvect\_1~X1){\unicdcdcdhd}(l1\_clvect\_1~X1))))))))))){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
(k3\_clopban1~X0~X1)){\unicdcdcdhd}((v13\_algstr\_0~(k3\_clopban1~X0~X1)){\unicdcdcdhd}((v2\_rlvect\_1~\\
(k3\_clopban1~X0~X1)){\unicdcdcdhd}((v3\_rlvect\_1~(k3\_clopban1~X0~X1)){\unicdcdcdhd}((v4\_rlvect\_1~\\
(k3\_clopban1~X0~X1)){\unicdcdcdhd}((v2\_clvect\_1~(k3\_clopban1~X0~X1)){\unicdcdcdhd}((v3\_clvect\_1~\\
(k3\_clopban1~X0~X1)){\unicdcdcdhd}((v4\_clvect\_1~(k3\_clopban1~X0~X1)){\unicdcdcdhd}((v5\_clvect\_1~\\
(k3\_clopban1~X0~X1)){\unicdcdcdhd}(l1\_clvect\_1~(k3\_clopban1~X0~X1)))))))))))\end{array}
\label{hyp:egehpflgddpfdgmgpgahcgbgogbd}
\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}{\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}((v1\_clvect\_1~(g1\_clvect\_1~X0~X1~X2~X3)){\unicdcdcdhd}\\
(l1\_clvect\_1~(g1\_clvect\_1~X0~X1~X2~X3)))\end{array}
\label{hyp:egehpfhgbdpfdgmgghfgdgehpfbd}
\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}((v2\_clvect\_1~X1){\unicdcdcdhd}((v3\_clvect\_1~X1){\unicdcdcdhd}((v4\_clvect\_1~X1){\unicdcdcdhd}\\
((v5\_clvect\_1~X1){\unicdcdcdhd}(l1\_clvect\_1~X1)))))))))){\unicdbdjdcd}(k3\_clopban1~X0~\\
X1=g1\_clvect\_1~(k9\_funct\_2~X0~(u1\_struct\_0~X1))~(k4\_lopban\_1~\\
X0~X1)~(k2\_lopban\_1~X0~X1)~(k2\_clopban1~X0~X1)))\end{array}
\label{hyp:egcdpfdgmgpgahcgbgogbd}
\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}(k9\_csspace4~X0~X1=g2\_clvect\_1~\\
(k4\_csspace4~X0~X1)~(k10\_csspace~(k3\_clopban1~X0~X1)~(k4\_csspace4~\\
X0~X1))~(k8\_csspace~(k3\_clopban1~X0~X1)~(k4\_csspace4~X0~X1))~(k9\_csspace~\\
(k3\_clopban1~X0~X1)~(k4\_csspace4~X0~X1))~(k8\_csspace4~X0~X1)))\end{array}
\label{hyp:egbdadpfdgdhdhahbgdgfged}
\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}
\begin{theorem}\label{thm:ehcdedpfdgdhdhahbgdgfged}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v13\_algstr\_0~X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~\\
X1){\unicdcdcdhd}((v3\_normsp\_0~X1){\unicdcdcdhd}((v4\_normsp\_0~X1){\unicdcdcdhd}((v2\_clvect\_1~X1){\unicdcdcdhd}\\
((v3\_clvect\_1~X1){\unicdcdcdhd}((v4\_clvect\_1~X1){\unicdcdcdhd}((v5\_clvect\_1~X1){\unicdcdcdhd}((v8\_clvect\_1~\\
X1){\unicdcdcdhd}(l2\_clvect\_1~X1))))))))))))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k9\_csspace4~\\
X0~X1)){\unicdcdcdhd}((v13\_algstr\_0~(k9\_csspace4~X0~X1)){\unicdcdcdhd}((v2\_rlvect\_1~(k9\_csspace4~\\
X0~X1)){\unicdcdcdhd}((v3\_rlvect\_1~(k9\_csspace4~X0~X1)){\unicdcdcdhd}((v4\_rlvect\_1~(k9\_csspace4~\\
X0~X1)){\unicdcdcdhd}((v3\_normsp\_0~(k9\_csspace4~X0~X1)){\unicdcdcdhd}((v4\_normsp\_0~(k9\_csspace4~\\
X0~X1)){\unicdcdcdhd}((v2\_clvect\_1~(k9\_csspace4~X0~X1)){\unicdcdcdhd}((v3\_clvect\_1~(k9\_csspace4~\\
X0~X1)){\unicdcdcdhd}((v4\_clvect\_1~(k9\_csspace4~X0~X1)){\unicdcdcdhd}((v5\_clvect\_1~(k9\_csspace4~\\
X0~X1)){\unicdcdcdhd}((v8\_clvect\_1~(k9\_csspace4~X0~X1)){\unicdcdcdhd}(l2\_clvect\_1~(k9\_csspace4~\\
X0~X1)))))))))))))))\end{array}$$
\end{theorem}
\end{document}
