\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{l71\_cc0sp2 (TMNSfw47boMZqr24tDbzCQFHhmgTN15ocmq)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_cc0sp2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_normsp\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_clvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k8\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k18\_complex1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k7\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k16\_complex1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k17\_complex1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v7\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xcmplx\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~(k9\_cc0sp2~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~(k9\_cc0sp2~X1))){\unicdbdjdcd}(((k1\_normsp\_0~(k9\_cc0sp2~X1)~\\
X2=k6\_numbers){\unicdbdjdcd}(X2=k4\_struct\_0~(k9\_cc0sp2~X1))){\unicdcdcdhd}(((X2=k4\_struct\_0~\\
(k9\_cc0sp2~X1)){\unicdbdjdcd}(k1\_normsp\_0~(k9\_cc0sp2~X1)~X2=k6\_numbers)){\unicdcdcdhd}\\
((k1\_normsp\_0~(k9\_cc0sp2~X1)~(k1\_clvect\_1~(k9\_cc0sp2~X1)~X2~X0)=\\
k8\_real\_1~(k18\_complex1~X0)~(k1\_normsp\_0~(k9\_cc0sp2~X1)~X2)){\unicdcdcdhd}\\
(r1\_xxreal\_0~(k1\_normsp\_0~(k9\_cc0sp2~X1)~(k1\_algstr\_0~(k9\_cc0sp2~\\
X1)~X2~X3))~(k7\_real\_1~(k1\_normsp\_0~(k9\_cc0sp2~X1)~X2)~(k1\_normsp\_0~\\
(k9\_cc0sp2~X1)~X3)))))))))\end{array}
\label{hyp:ehedgdpfdgdgaddhahcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjdcd}{({{{k18\_complex1}~{X0}}={{k16\_complex1}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdidpfdgpgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjdcd}{({{{k17\_complex1}~{X0}}={{k16\_complex1}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdhdpfdgpgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k9\_cc0sp2~X0)){\unicdcdcdhd}(v7\_clvect\_1~(k9\_cc0sp2~\\
X0)))\end{array}
\label{hyp:ggdgbdedpfdgdgaddhahcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}(l2\_clvect\_1~(k9\_cc0sp2~X0))\end{array}
\label{hyp:egehpflgjdpfdgdgaddhahcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_clvect\_1~X0)){\unicdbdjdcd}((v8\_clvect\_1~\\
X0){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_xcmplx\_0~X3){\unicdbdjdcd}\\
((k1\_normsp\_0~X0~(k1\_clvect\_1~X0~X1~X3)=k8\_real\_1~(k17\_complex1~\\
X3)~(k1\_normsp\_0~X0~X1)){\unicdcdcdhd}(r1\_xxreal\_0~(k1\_normsp\_0~X0~(k1\_algstr\_0~\\
X0~X1~X2))~(k7\_real\_1~(k1\_normsp\_0~X0~X1)~(k1\_normsp\_0~X0~X2))))))))\end{array}
\label{hyp:egbdddpfdgmgghfgdgehpfbd}
\end{equation}
\begin{theorem}\label{thm:mghdbdpfdgdgaddhahcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}(v8\_clvect\_1~(k9\_cc0sp2~X0))\end{array}$$
\end{theorem}
\end{document}
