\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{t40\_bspace (TMXRnAQwrkJshxETrEebSroARjUuWPd7RNA)}
\maketitle
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_vectsp\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k9\_bspace : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_bspace : {\iota}$ be given.
Let $ k7\_bspace : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_vectsp\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_vectsp\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v33\_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\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v9\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v10\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v11\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_finset\_1~X0){\unicdbdjdcd}(k1\_vectsp\_7~k2\_bspace~(k7\_bspace~\\
X0)~(k9\_bspace~X0)=k7\_bspace~X0)\end{array}
\label{hyp:ehddjdpfcgdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{{v1\_vectsp\_7}~{({{k9\_bspace}~{X0}})}}~{k2\_bspace}}~{({{k7\_bspace}~{X0}})}}}\label{hyp:ehddgdpfcgdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v33\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}\\
((v4\_rlvect\_1~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v5\_group\_1~X0){\unicdcdcdhd}((v4\_vectsp\_1~\\
X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}(l6\_algstr\_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}((v8\_vectsp\_1~X1~X0){\unicdcdcdhd}((v9\_vectsp\_1~\\
X1~X0){\unicdcdcdhd}((v10\_vectsp\_1~X1~X0){\unicdcdcdhd}((v11\_vectsp\_1~X1~X0){\unicdcdcdhd}(l1\_vectsp\_1~\\
X1~X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X1))){\unicdbdjdcd}((v1\_vectsp\_7~X2~X0~X1){\unicdbdjdcd}(m1\_vectsp\_7~X2~X0~(k1\_vectsp\_7~\\
X0~X1~X2)))))\end{array}
\label{hyp:ehcdadpfchbgoglgogfhmgmg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v2\_struct\_0~(k7\_bspace~X0)){\unicdcdcdhd}((v13\_algstr\_0~(k7\_bspace~\\
X0)){\unicdcdcdhd}((v8\_vectsp\_1~(k7\_bspace~X0)~k2\_bspace){\unicdcdcdhd}((v9\_vectsp\_1~\\
(k7\_bspace~X0)~k2\_bspace){\unicdcdcdhd}((v10\_vectsp\_1~(k7\_bspace~X0)~k2\_bspace){\unicdcdcdhd}\\
((v11\_vectsp\_1~(k7\_bspace~X0)~k2\_bspace){\unicdcdcdhd}((v2\_rlvect\_1~(k7\_bspace~\\
X0)){\unicdcdcdhd}((v3\_rlvect\_1~(k7\_bspace~X0)){\unicdcdcdhd}(v4\_rlvect\_1~(k7\_bspace~\\
X0)))))))))\end{array}
\label{hyp:ggdgbdpfcgdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  m1\_subset\_1~(k9\_bspace~X0)~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k7\_bspace~X0)))\end{array}
\label{hyp:egehpflgjdpfcgdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v2\_struct\_0~(k7\_bspace~X0)){\unicdcdcdhd}(l1\_vectsp\_1~(k7\_bspace~\\
X0)~k2\_bspace)\end{array}
\label{hyp:egehpflghdpfcgdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v2\_struct\_0~k2\_bspace){\unicdcdcdhd}((\preoh v6\_struct\_0~k2\_bspace){\unicdcdcdhd}((v13\_algstr\_0~\\
k2\_bspace){\unicdcdcdhd}((v33\_algstr\_0~k2\_bspace){\unicdcdcdhd}((v3\_group\_1~k2\_bspace){\unicdcdcdhd}\\
((v5\_group\_1~k2\_bspace){\unicdcdcdhd}((v4\_vectsp\_1~k2\_bspace){\unicdcdcdhd}((v5\_vectsp\_1~\\
k2\_bspace){\unicdcdcdhd}((v2\_rlvect\_1~k2\_bspace){\unicdcdcdhd}((v3\_rlvect\_1~k2\_bspace){\unicdcdcdhd}\\
((v4\_rlvect\_1~k2\_bspace){\unicdcdcdhd}(l6\_algstr\_0~k2\_bspace)))))))))))\end{array}
\label{hyp:egehpflgcdpfcgdhahbgdgfg}
\end{equation}
\begin{theorem}\label{thm:ehedadpfcgdhahbgdgfg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_finset\_1~X0){\unicdbdjdcd}(m1\_vectsp\_7~(k9\_bspace~X0)~k2\_bspace~\\
(k7\_bspace~X0))\end{array}$$
\end{theorem}
\end{document}
