\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{t35\_c0sp2 (TMTsvBYEtgq9vuK8QAjQ7bBwhvFV7EpAopF)}
\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 $ v2\_normsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_c0sp2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ 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\_rlvect\_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 $ l1\_normsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\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\_c0sp2~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(\\
u1\_struct\_0~(k9\_c0sp2~X1))){\unicdbdjdcd}(((k1\_normsp\_0~(k9\_c0sp2~X1)~X2=\\
k6\_numbers){\unicdbdjdcd}(X2=k4\_struct\_0~(k9\_c0sp2~X1))){\unicdcdcdhd}(((X2=k4\_struct\_0~\\
(k9\_c0sp2~X1)){\unicdbdjdcd}(k1\_normsp\_0~(k9\_c0sp2~X1)~X2=k6\_numbers)){\unicdcdcdhd}(\\
(k1\_normsp\_0~(k9\_c0sp2~X1)~(k1\_rlvect\_1~(k9\_c0sp2~X1)~X2~X0)=k8\_real\_1~\\
(k18\_complex1~X0)~(k1\_normsp\_0~(k9\_c0sp2~X1)~X2)){\unicdcdcdhd}(r1\_xxreal\_0~\\
(k1\_normsp\_0~(k9\_c0sp2~X1)~(k1\_algstr\_0~(k9\_c0sp2~X1)~X2~X3))~(\\
k7\_real\_1~(k1\_normsp\_0~(k9\_c0sp2~X1)~X2)~(k1\_normsp\_0~(k9\_c0sp2~\\
X1)~X3)))))))))\end{array}
\label{hyp:ehddedpfdgaddhahcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdaddd} X1 .  {{{m1\_subset\_1}~{X1}}~{X0}}}}\label{hyp:fgihjgdhehfgogdgfgpfngbdpfdhfhcgdhfgehpfbd}
\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\_c0sp2~X0)){\unicdcdcdhd}(l1\_normsp\_1~(k9\_c0sp2~\\
X0)))\end{array}
\label{hyp:egehpflgjdpfdgaddhahcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_normsp\_1~X0)){\unicdbdjdcd}((v2\_normsp\_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 .  (m1\_subset\_1~X3~\\
k1\_numbers){\unicdbdjdcd}((k1\_normsp\_0~X0~(k1\_rlvect\_1~X0~X1~X3)=k8\_real\_1~\\
(k18\_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:egbdpfogpgchngdhahpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddfdpfdgaddhahcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}(v2\_normsp\_1~(k9\_c0sp2~X0))\end{array}$$
\end{theorem}
\end{document}
