\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{l7\_csspace4 (TMLhryosVHDnxdzYAykbQV4wvKVQNkHuqWM)}
\maketitle
Let $ v2\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ g1\_clvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_csspace4 : {\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 $ v3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_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 $ v1\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}(v13\_algstr\_0~(g1\_clvect\_1~k1\_csspace4~(k10\_csspace~k7\_csspace~\\
k1\_csspace4)~(k8\_csspace~k7\_csspace~k1\_csspace4)~(k9\_csspace~\\
k7\_csspace~k1\_csspace4))){\unicdcdcdhd}((v2\_rlvect\_1~(g1\_clvect\_1~k1\_csspace4~\\
(k10\_csspace~k7\_csspace~k1\_csspace4)~(k8\_csspace~k7\_csspace~\\
k1\_csspace4)~(k9\_csspace~k7\_csspace~k1\_csspace4))){\unicdcdcdhd}((v3\_rlvect\_1~\\
(g1\_clvect\_1~k1\_csspace4~(k10\_csspace~k7\_csspace~k1\_csspace4)~\\
(k8\_csspace~k7\_csspace~k1\_csspace4)~(k9\_csspace~k7\_csspace~k1\_csspace4))){\unicdcdcdhd}\\
((v4\_rlvect\_1~(g1\_clvect\_1~k1\_csspace4~(k10\_csspace~k7\_csspace~\\
k1\_csspace4)~(k8\_csspace~k7\_csspace~k1\_csspace4)~(k9\_csspace~\\
k7\_csspace~k1\_csspace4))){\unicdcdcdhd}((v1\_clvect\_1~(g1\_clvect\_1~k1\_csspace4~\\
(k10\_csspace~k7\_csspace~k1\_csspace4)~(k8\_csspace~k7\_csspace~\\
k1\_csspace4)~(k9\_csspace~k7\_csspace~k1\_csspace4))){\unicdcdcdhd}((v2\_clvect\_1~\\
(g1\_clvect\_1~k1\_csspace4~(k10\_csspace~k7\_csspace~k1\_csspace4)~\\
(k8\_csspace~k7\_csspace~k1\_csspace4)~(k9\_csspace~k7\_csspace~k1\_csspace4))){\unicdcdcdhd}\\
((v3\_clvect\_1~(g1\_clvect\_1~k1\_csspace4~(k10\_csspace~k7\_csspace~\\
k1\_csspace4)~(k8\_csspace~k7\_csspace~k1\_csspace4)~(k9\_csspace~\\
k7\_csspace~k1\_csspace4))){\unicdcdcdhd}((v4\_clvect\_1~(g1\_clvect\_1~k1\_csspace4~\\
(k10\_csspace~k7\_csspace~k1\_csspace4)~(k8\_csspace~k7\_csspace~\\
k1\_csspace4)~(k9\_csspace~k7\_csspace~k1\_csspace4))){\unicdcdcdhd}(v5\_clvect\_1~\\
(g1\_clvect\_1~k1\_csspace4~(k10\_csspace~k7\_csspace~k1\_csspace4)~\\
(k8\_csspace~k7\_csspace~k1\_csspace4)~(k9\_csspace~k7\_csspace~k1\_csspace4))))))))))\end{array}
\label{hyp:ggdgddpfdgdhdhahbgdgfged}
\end{equation}
\begin{theorem}\label{thm:mghdpfdgdhdhahbgdgfged}
$$\begin{array}{c}(v2\_rlvect\_1~(g1\_clvect\_1~k1\_csspace4~(k10\_csspace~k7\_csspace~\\
k1\_csspace4)~(k8\_csspace~k7\_csspace~k1\_csspace4)~(k9\_csspace~\\
k7\_csspace~k1\_csspace4))){\unicdcdcdhd}((v3\_rlvect\_1~(g1\_clvect\_1~k1\_csspace4~\\
(k10\_csspace~k7\_csspace~k1\_csspace4)~(k8\_csspace~k7\_csspace~\\
k1\_csspace4)~(k9\_csspace~k7\_csspace~k1\_csspace4))){\unicdcdcdhd}((v4\_rlvect\_1~\\
(g1\_clvect\_1~k1\_csspace4~(k10\_csspace~k7\_csspace~k1\_csspace4)~\\
(k8\_csspace~k7\_csspace~k1\_csspace4)~(k9\_csspace~k7\_csspace~k1\_csspace4))){\unicdcdcdhd}\\
((v13\_algstr\_0~(g1\_clvect\_1~k1\_csspace4~(k10\_csspace~k7\_csspace~\\
k1\_csspace4)~(k8\_csspace~k7\_csspace~k1\_csspace4)~(k9\_csspace~\\
k7\_csspace~k1\_csspace4))){\unicdcdcdhd}((v2\_clvect\_1~(g1\_clvect\_1~k1\_csspace4~\\
(k10\_csspace~k7\_csspace~k1\_csspace4)~(k8\_csspace~k7\_csspace~\\
k1\_csspace4)~(k9\_csspace~k7\_csspace~k1\_csspace4))){\unicdcdcdhd}((v3\_clvect\_1~\\
(g1\_clvect\_1~k1\_csspace4~(k10\_csspace~k7\_csspace~k1\_csspace4)~\\
(k8\_csspace~k7\_csspace~k1\_csspace4)~(k9\_csspace~k7\_csspace~k1\_csspace4))){\unicdcdcdhd}\\
((v4\_clvect\_1~(g1\_clvect\_1~k1\_csspace4~(k10\_csspace~k7\_csspace~\\
k1\_csspace4)~(k8\_csspace~k7\_csspace~k1\_csspace4)~(k9\_csspace~\\
k7\_csspace~k1\_csspace4))){\unicdcdcdhd}(v5\_clvect\_1~(g1\_clvect\_1~k1\_csspace4~\\
(k10\_csspace~k7\_csspace~k1\_csspace4)~(k8\_csspace~k7\_csspace~\\
k1\_csspace4)~(k9\_csspace~k7\_csspace~k1\_csspace4)))))))))\end{array}$$
\end{theorem}
\end{document}
