\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{l33\_csspace (TMdodKXmjD1RAcFFo6NXSpy8DzPGKp7pwNG)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_clvect\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 $ 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 $ l1\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k3\_complex1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_numbers : {\iota}$ be given.
Let $ c2\_\_csspace : {\iota}$ be given.
Let $ k1\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_complex1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k17\_complex1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k5\_complex1 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}(k3\_complex1~k6\_numbers=k6\_numbers){\unicdcdcdhd}(k4\_complex1~k6\_numbers=\\
k6\_numbers)\end{array}
\label{hyp:ehedpfdgpgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xcmplx\_0~X0){\unicdbdjdcd}(r1\_xxreal\_0~k6\_numbers~(k17\_complex1~\\
X0))\end{array}
\label{hyp:ehedgdpfdgpgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
{{{k17\_complex1}~{k6\_numbers}}={k6\_numbers}}\label{hyp:ehededpfdgpgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_complex1}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfdgpgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k3\_clvect\_1~(the~({\uniddcgcg} X1 : \\
\iota .  (\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}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k3\_clvect\_1~(the~({\uniddcgcg} X2 : \\
\iota .  (\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v13\_algstr\_0~X2){\unicdcdcdhd}((v2\_rlvect\_1~X2){\unicdcdcdhd}\\
((v3\_rlvect\_1~X2){\unicdcdcdhd}((v4\_rlvect\_1~X2){\unicdcdcdhd}((v2\_clvect\_1~X2){\unicdcdcdhd}((v3\_clvect\_1~\\
X2){\unicdcdcdhd}((v4\_clvect\_1~X2){\unicdcdcdhd}((v5\_clvect\_1~X2){\unicdcdcdhd}(l1\_clvect\_1~X2)))))))))))))){\unicdbdjdcd}\\
(k3\_funct\_2~(k2\_zfmisc\_1~(u1\_struct\_0~(k3\_clvect\_1~(the~({\uniddcgcg} X2 : \\
\iota .  (\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v13\_algstr\_0~X2){\unicdcdcdhd}((v2\_rlvect\_1~X2){\unicdcdcdhd}\\
((v3\_rlvect\_1~X2){\unicdcdcdhd}((v4\_rlvect\_1~X2){\unicdcdcdhd}((v2\_clvect\_1~X2){\unicdcdcdhd}((v3\_clvect\_1~\\
X2){\unicdcdcdhd}((v4\_clvect\_1~X2){\unicdcdcdhd}((v5\_clvect\_1~X2){\unicdcdcdhd}(l1\_clvect\_1~X2)))))))))))))~\\
(u1\_struct\_0~(k3\_clvect\_1~(the~({\uniddcgcg} X2 : \iota .  (\preoh v2\_struct\_0~X2){\unicdcdcdhd}\\
((v13\_algstr\_0~X2){\unicdcdcdhd}((v2\_rlvect\_1~X2){\unicdcdcdhd}((v3\_rlvect\_1~X2){\unicdcdcdhd}((v4\_rlvect\_1~\\
X2){\unicdcdcdhd}((v2\_clvect\_1~X2){\unicdcdcdhd}((v3\_clvect\_1~X2){\unicdcdcdhd}((v4\_clvect\_1~X2){\unicdcdcdhd}\\
((v5\_clvect\_1~X2){\unicdcdcdhd}(l1\_clvect\_1~X2))))))))))))))~k2\_numbers~\\
c2\_\_csspace~(k1\_domain\_1~(u1\_struct\_0~(k3\_clvect\_1~(the~({\uniddcgcg} X2 : \\
\iota .  (\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v13\_algstr\_0~X2){\unicdcdcdhd}((v2\_rlvect\_1~X2){\unicdcdcdhd}\\
((v3\_rlvect\_1~X2){\unicdcdcdhd}((v4\_rlvect\_1~X2){\unicdcdcdhd}((v2\_clvect\_1~X2){\unicdcdcdhd}((v3\_clvect\_1~\\
X2){\unicdcdcdhd}((v4\_clvect\_1~X2){\unicdcdcdhd}((v5\_clvect\_1~X2){\unicdcdcdhd}(l1\_clvect\_1~X2)))))))))))))~\\
(u1\_struct\_0~(k3\_clvect\_1~(the~({\uniddcgcg} X2 : \iota .  (\preoh v2\_struct\_0~X2){\unicdcdcdhd}\\
((v13\_algstr\_0~X2){\unicdcdcdhd}((v2\_rlvect\_1~X2){\unicdcdcdhd}((v3\_rlvect\_1~X2){\unicdcdcdhd}((v4\_rlvect\_1~\\
X2){\unicdcdcdhd}((v2\_clvect\_1~X2){\unicdcdcdhd}((v3\_clvect\_1~X2){\unicdcdcdhd}((v4\_clvect\_1~X2){\unicdcdcdhd}\\
((v5\_clvect\_1~X2){\unicdcdcdhd}(l1\_clvect\_1~X2)))))))))))))~X0~X1)=k5\_complex1))\end{array}
\label{hyp:mgddadpfdgdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k6\_numbers}}~{k2\_numbers}}\label{hyp:mgcdgdpfcgjgogpgahpfcd}
\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}
\begin{theorem}\label{thm:mgddddpfdgdhdhahbgdgfg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k3\_clvect\_1~(the~({\uniddcgcg} X1 : \\
\iota .  (\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}\\
((r1\_xxreal\_0~k6\_numbers~(k3\_complex1~(k3\_funct\_2~(k2\_zfmisc\_1~\\
(u1\_struct\_0~(k3\_clvect\_1~(the~({\uniddcgcg} X1 : \iota .  (\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)))))))))))))~(u1\_struct\_0~\\
(k3\_clvect\_1~(the~({\uniddcgcg} X1 : \iota .  (\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))))))))))))))~k2\_numbers~c2\_\_csspace~(k1\_domain\_1~\\
(u1\_struct\_0~(k3\_clvect\_1~(the~({\uniddcgcg} X1 : \iota .  (\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)))))))))))))~(u1\_struct\_0~\\
(k3\_clvect\_1~(the~({\uniddcgcg} X1 : \iota .  (\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)))))))))))))~X0~X0)))){\unicdcdcdhd}(k4\_complex1~(k3\_funct\_2~\\
(k2\_zfmisc\_1~(u1\_struct\_0~(k3\_clvect\_1~(the~({\uniddcgcg} X1 : \iota .  (\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)))))))))))))~(u1\_struct\_0~\\
(k3\_clvect\_1~(the~({\uniddcgcg} X1 : \iota .  (\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))))))))))))))~k2\_numbers~c2\_\_csspace~(k1\_domain\_1~\\
(u1\_struct\_0~(k3\_clvect\_1~(the~({\uniddcgcg} X1 : \iota .  (\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)))))))))))))~(u1\_struct\_0~\\
(k3\_clvect\_1~(the~({\uniddcgcg} X1 : \iota .  (\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)))))))))))))~X0~X0))=k6\_numbers))\end{array}$$
\end{theorem}
\end{document}
