\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{l10\_csspace2 (TMVkDFxm7AvsiqKboeb4vCxJQcMAudDLuKy)}
\maketitle
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k18\_csspace : {\iota}$ be given.
Let $ k6\_csspace : {\iota}$ be given.
Let $ v6\_clvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k11\_csspace : {\iota}$ be given.
Let $ k7\_csspace : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\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 $ g1\_csspace : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ g1\_clvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k10\_csspace : {{\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 $ k17\_csspace : {\iota}$ be given.
Let $ v1\_csspace : {{\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 $ v1\_clvect\_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 $ k1\_csspace : {\iota}$ be given.
Let $ k4\_csspace : {\iota}$ be given.
Let $ k5\_csspace : {\iota}$ be given.
Let $ l2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_csspace : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ u1\_csspace : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{{({{{v6\_clvect\_1}~{k11\_csspace}}~{k7\_csspace}})}{\unicdcdcdhd}{({\preoh{{{v1\_xboole\_0}~{k11\_csspace}}}})}}\label{hyp:ehbdcdpfdgdhdhahbgdgfg}
\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~(k2\_zfmisc\_1~\\
X0~X0)~k2\_numbers){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)~k2\_numbers)))))))){\unicdbdjdcd}({\unicdcdadad} X5 .  {\unicdcdadad} X6 .  \\
{\unicdcdadad} X7 .  {\unicdcdadad} X8 .  {\unicdcdadad} X9 .  (g1\_csspace~X0~X1~X2~X3~X4=g1\_csspace~\\
X5~X6~X7~X8~X9){\unicdbdjdcd}((X0=X5){\unicdcdcdhd}((X1=X6){\unicdcdcdhd}((X2=X7){\unicdcdcdhd}((X3=X8){\unicdcdcdhd}(X4=X9))))))\end{array}
\label{hyp:ggchfgfgpfhgbdpfdgdhdhahbgdgfg}
\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}(\preoh v2\_struct\_0~(g1\_csspace~k11\_csspace~(k10\_csspace~k7\_csspace~\\
k11\_csspace)~(k8\_csspace~k7\_csspace~k11\_csspace)~(k9\_csspace~\\
k7\_csspace~k11\_csspace)~k17\_csspace)){\unicdcdcdhd}(v1\_csspace~(g1\_csspace~\\
k11\_csspace~(k10\_csspace~k7\_csspace~k11\_csspace)~(k8\_csspace~\\
k7\_csspace~k11\_csspace)~(k9\_csspace~k7\_csspace~k11\_csspace)~\\
k17\_csspace))\end{array}
\label{hyp:ggdgedpfdgdhdhahbgdgfg}
\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}
\begin{array}{c}(v2\_rlvect\_1~(g1\_clvect\_1~k1\_csspace~k6\_csspace~k4\_csspace~k5\_csspace)){\unicdcdcdhd}\\
(v1\_clvect\_1~(g1\_clvect\_1~k1\_csspace~k6\_csspace~k4\_csspace~k5\_csspace))\end{array}
\label{hyp:ggdgbdpfdgdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l2\_struct\_0}~{X0}})}{\unicdcdcdhd}{({{l1\_algstr\_0}~{X0}})}})}}}\label{hyp:egehpfmgcdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_csspace}~{X0}})}{\unicdbdjdcd}{({{l1\_clvect\_1}~{X0}})}}}\label{hyp:egehpfmgbdpfdgdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_clvect\_1}~{X0}})}{\unicdbdjdcd}{({{l2\_algstr\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfdgmgghfgdgehpfbd}
\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}
{{{m1\_subset\_1}~{k6\_csspace}}~{k1\_csspace}}\label{hyp:egehpflggdpfdgdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k5\_csspace){\unicdcdcdhd}((v1\_funct\_2~k5\_csspace~(k2\_zfmisc\_1~\\
k2\_numbers~k1\_csspace)~k1\_csspace){\unicdcdcdhd}(m1\_subset\_1~k5\_csspace~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~k2\_numbers~k1\_csspace)~\\
k1\_csspace))))\end{array}
\label{hyp:egehpflgfdpfdgdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k4\_csspace){\unicdcdcdhd}((v1\_funct\_2~k4\_csspace~(k2\_zfmisc\_1~\\
k1\_csspace~k1\_csspace)~k1\_csspace){\unicdcdcdhd}(m1\_subset\_1~k4\_csspace~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~k1\_csspace~k1\_csspace)~\\
k1\_csspace))))\end{array}
\label{hyp:egehpflgedpfdgdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v2\_struct\_0}~{k18\_csspace}}}})}{\unicdcdcdhd}{({{l1\_csspace}~{k18\_csspace}})}}\label{hyp:egehpflgbdidpfdgdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k17\_csspace){\unicdcdcdhd}((v1\_funct\_2~k17\_csspace~(k2\_zfmisc\_1~\\
k11\_csspace~k11\_csspace)~k2\_numbers){\unicdcdcdhd}(m1\_subset\_1~k17\_csspace~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~k11\_csspace~k11\_csspace)~\\
k2\_numbers))))\end{array}
\label{hyp:egehpflgbdhdpfdgdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k11\_csspace}}~{({{k1\_zfmisc\_1}~{({{u1\_struct\_0}~{k7\_csspace}})}})}}\label{hyp:egehpflgbdbdpfdgdhdhahbgdgfg}
\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}
{{k7\_csspace}={{{{{g1\_clvect\_1}~{k1\_csspace}}~{k6\_csspace}}~{k4\_csspace}}~{k5\_csspace}}}\label{hyp:eghdpfdgdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{{k4\_struct\_0}~{X0}}={{u2\_struct\_0}~{X0}}})}}}\label{hyp:eggdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k18\_csspace=g1\_csspace~k11\_csspace~(k10\_csspace~k7\_csspace~\\
k11\_csspace)~(k8\_csspace~k7\_csspace~k11\_csspace)~(k9\_csspace~\\
k7\_csspace~k11\_csspace)~k17\_csspace\end{array}
\label{hyp:egbdidpfdgdhdhahbgdgfg}
\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}((v2\_clvect\_1~X0){\unicdcdcdhd}\\
((v3\_clvect\_1~X0){\unicdcdcdhd}((v4\_clvect\_1~X0){\unicdcdcdhd}((v5\_clvect\_1~X0){\unicdcdcdhd}(l1\_clvect\_1~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))){\unicdbdjdcd}((v6\_clvect\_1~X1~X0){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}(k10\_csspace~X0~\\
X1=k4\_struct\_0~X0))))\end{array}
\label{hyp:egbdadpfdgdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_csspace~X0){\unicdbdjdcd}((v1\_csspace~X0){\unicdbdjdcd}(X0=g1\_csspace~\\
(u1\_struct\_0~X0)~(u2\_struct\_0~X0)~(u1\_algstr\_0~X0)~(u1\_clvect\_1~\\
X0)~(u1\_csspace~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpfdgdhdhahbgdgfg}
\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:mgbdadpfdgdhdhahbgdgfgcd}
${{{k4\_struct\_0}~{k18\_csspace}}={k6\_csspace}}$.
\end{theorem}
\end{document}
