\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{t33\_c0sp1 (TMWHppNdeM6uFofhie4vLHawyNvhbfCvFaq)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_normsp\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k11\_c0sp1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_normsp\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_normsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_normsp\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_normsp\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_normsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_lopban\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_funcsdom : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k1\_numbers){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k11\_c0sp1~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~(k11\_c0sp1~X0))){\unicdbdjdcd}(((k1\_normsp\_0~\\
(k11\_c0sp1~X0)~X2=k6\_numbers){\unicdbdjdcd}(X2=k4\_struct\_0~(k11\_c0sp1~X0))){\unicdcdcdhd}\\
(((X2=k4\_struct\_0~(k11\_c0sp1~X0)){\unicdbdjdcd}(k1\_normsp\_0~(k11\_c0sp1~X0)~\\
X2=k6\_numbers)){\unicdcdcdhd}((k1\_normsp\_0~(k11\_c0sp1~X0)~(k1\_rlvect\_1~(\\
k11\_c0sp1~X0)~X2~X1)=k8\_real\_1~(k18\_complex1~X1)~(k1\_normsp\_0~\\
(k11\_c0sp1~X0)~X2)){\unicdcdcdhd}(r1\_xxreal\_0~(k1\_normsp\_0~(k11\_c0sp1~X0)~\\
(k1\_algstr\_0~(k11\_c0sp1~X0)~X2~X3))~(k7\_real\_1~(k1\_normsp\_0~(k11\_c0sp1~\\
X0)~X2)~(k1\_normsp\_0~(k11\_c0sp1~X0)~X3)))))))))\end{array}
\label{hyp:ehddcdpfdgaddhahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_1){\unicdcdcdhd}(m2\_subset\_1~np\_\_1~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_1~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_1~k1\_numbers))\end{array}
\label{hyp:dhahdgbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({\preoh{{{v1\_xboole\_0}~{X0}}}})}{\unicdbdjdcd}{({\preoh{{{v2\_struct\_0}~{({{k11\_c0sp1}~{X0}})}}}})}}}\label{hyp:ggdgedpfdgaddhahbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_normsp\_0}~{X0}})}{\unicdbdjdcd}{({{({{l1\_normsp\_0}~{X0}})}{\unicdcdcdhd}{({{l2\_struct\_0}~{X0}})}})}}}\label{hyp:egehpfmgcdpfogpgchngdhahpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_normsp\_1}~{X0}})}{\unicdbdjdcd}{({{({{l1\_rlvect\_1}~{X0}})}{\unicdcdcdhd}{({{l2\_normsp\_0}~{X0}})}})}}}\label{hyp:egehpfmgbdpfogpgchngdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_lopban\_2}~{X0}})}{\unicdbdjdcd}{({{({{l1\_funcsdom}~{X0}})}{\unicdcdcdhd}{({{l1\_normsp\_1}~{X0}})}})}}}\label{hyp:egehpfmgbdpfmgpgahcgbgogpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_struct\_0~X0){\unicdbdjdcd}(m1\_subset\_1~(k4\_struct\_0~X0)~(u1\_struct\_0~\\
X0))\end{array}
\label{hyp:egehpflgedpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({\preoh{{{v1\_xboole\_0}~{X0}}}})}{\unicdbdjdcd}{({{l1\_lopban\_2}~{({{k11\_c0sp1}~{X0}})}})}}}\label{hyp:egehpflgbdbdpfdgaddhahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_normsp\_0~X0)){\unicdbdjdcd}((v4\_normsp\_0~\\
X0){\unicdbdjded}(k1\_normsp\_0~X0~(k4\_struct\_0~X0)=k6\_numbers))\end{array}
\label{hyp:eggdpfogpgchngdhahpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_normsp\_0~X0)){\unicdbdjdcd}((v3\_normsp\_0~\\
X0){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}((k1\_normsp\_0~\\
X0~X1=k6\_numbers){\unicdbdjdcd}(X1=k4\_struct\_0~X0))))\end{array}
\label{hyp:egfdpfogpgchngdhahpfad}
\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:ehddddpfdgaddhahbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((v4\_normsp\_0~(k11\_c0sp1~X0)){\unicdcdcdhd}\\
((v3\_normsp\_0~(k11\_c0sp1~X0)){\unicdcdcdhd}(v2\_normsp\_1~(k11\_c0sp1~X0))))\end{array}$$
\end{theorem}
\end{document}
