\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{t10\_csspace (TMRVuhjGcT1U9tbmMrYyREGHuTm7GQvPVLS)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ g1\_clvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_csspace : {\iota}$ be given.
Let $ k6\_csspace : {\iota}$ be given.
Let $ k4\_csspace : {\iota}$ be given.
Let $ k5\_csspace : {\iota}$ be given.
Let $ k1\_clvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_complex1 : {\iota}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k25\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k2\_numbers : {\iota}$ be given.
Let $ k2\_csspace : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\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 $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v1\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ 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.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xcmplx\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
(g1\_clvect\_1~k1\_csspace~k6\_csspace~k4\_csspace~k5\_csspace))){\unicdbdjdcd}\\
(k1\_clvect\_1~(g1\_clvect\_1~k1\_csspace~k6\_csspace~k4\_csspace~k5\_csspace)~\\
X1~X0=k25\_valued\_1~k5\_numbers~k2\_numbers~(k2\_csspace~X1)~X0))\end{array}
\label{hyp:ehddpfdgdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((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))))){\unicdbdjdcd}\\
(r2\_relset\_1~k5\_numbers~k2\_numbers~(k25\_valued\_1~k5\_numbers~\\
k2\_numbers~X0~k6\_complex1)~X0)\end{array}
\label{hyp:ehcdbdpfdgpgngdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}((r2\_relset\_1~X0~X1~X2~X3){\unicdbdjded}(X2=X3))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchcdpfchfgmgdhfgehpfbd}
\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}
{{v1\_membered}~{k2\_numbers}}\label{hyp:ggdgbdpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k6\_csspace}}~{k1\_csspace}}\label{hyp:egehpflggdpfdgdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k6\_complex1}}~{k2\_numbers}}\label{hyp:egehpflggdpfdgpgngahmgfgihbd}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_funct\_1~(k2\_csspace~X0)){\unicdcdcdhd}((v1\_funct\_2~(k2\_csspace~\\
X0)~k5\_numbers~k2\_numbers){\unicdcdcdhd}(m1\_subset\_1~(k2\_csspace~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k5\_numbers~k2\_numbers))))\end{array}
\label{hyp:egehpflgcdpfdgdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_membered~X1){\unicdcdcdhd}\\
(((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1)))){\unicdcdcdhd}(v1\_xcmplx\_0~X3))){\unicdbdjdcd}((v1\_funct\_1~(k25\_valued\_1~X0~X1~\\
X2~X3)){\unicdcdcdhd}(m1\_subset\_1~(k25\_valued\_1~X0~X1~X2~X3)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~k2\_numbers))))\end{array}
\label{hyp:egehpflgcdfdpfghbgmgfhfgegpfbd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k1\_csspace}}}}\label{hyp:egehpflgbdpfdgdhdhahbgdgfg}
\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}
{{\unicdcdadad} X0 .  {{({{X0} \in {k1\_csspace}})}{\unicdbdjdcd}{({{{k2\_csspace}~{X0}}={X0}})}}}\label{hyp:egcdpfdgdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k2\_numbers}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{X0}})}}}\label{hyp:dgdgddpfihdgngahmgihpfad}
\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:ehbdadpfdgdhdhahbgdgfg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(g1\_clvect\_1~k1\_csspace~\\
k6\_csspace~k4\_csspace~k5\_csspace))){\unicdbdjdcd}(k1\_clvect\_1~(g1\_clvect\_1~\\
k1\_csspace~k6\_csspace~k4\_csspace~k5\_csspace)~X0~k6\_complex1=\\
X0)\end{array}$$
\end{theorem}
\end{document}
