\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{t36\_c0sp1 (TMFAKvgBm2bdSGEmoG5HrGN6Szrma48fmzW)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k11\_c0sp1 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 $ v5\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_normsp\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_normsp\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_normsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_lopban\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_normsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_rsspace3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_normsp\_1 : {{\iota}{\unicdbdjdcd}{{\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 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~k5\_numbers~(u1\_struct\_0~(k11\_c0sp1~X0))){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(u1\_struct\_0~(k11\_c0sp1~\\
X0))))))){\unicdbdjdcd}((v1\_rsspace3~X1~(k11\_c0sp1~X0)){\unicdbdjdcd}(v3\_normsp\_1~X1~(\\
k11\_c0sp1~X0))))\end{array}
\label{hyp:ehddfdpfdgaddhahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((v13\_algstr\_0~(k11\_c0sp1~X0)){\unicdcdcdhd}\\
((v2\_rlvect\_1~(k11\_c0sp1~X0)){\unicdcdcdhd}((v3\_rlvect\_1~(k11\_c0sp1~X0)){\unicdcdcdhd}\\
((v4\_rlvect\_1~(k11\_c0sp1~X0)){\unicdcdcdhd}((v5\_rlvect\_1~(k11\_c0sp1~X0)){\unicdcdcdhd}\\
((v6\_rlvect\_1~(k11\_c0sp1~X0)){\unicdcdcdhd}((v7\_rlvect\_1~(k11\_c0sp1~X0)){\unicdcdcdhd}\\
((v8\_rlvect\_1~(k11\_c0sp1~X0)){\unicdcdcdhd}((v3\_normsp\_0~(k11\_c0sp1~X0)){\unicdcdcdhd}\\
((v4\_normsp\_0~(k11\_c0sp1~X0)){\unicdcdcdhd}(v2\_normsp\_1~(k11\_c0sp1~X0))))))))))))\end{array}
\label{hyp:ggdggdpfdgaddhahbd}
\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 .  {{({{l1\_lopban\_2}~{X0}})}{\unicdbdjdcd}{({{({{l1\_funcsdom}~{X0}})}{\unicdcdcdhd}{({{l1\_normsp\_1}~{X0}})}})}}}\label{hyp:egehpfmgbdpfmgpgahcgbgogpfcd}
\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}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v5\_rlvect\_1~X0){\unicdcdcdhd}\\
((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~X0){\unicdcdcdhd}((v3\_normsp\_0~\\
X0){\unicdcdcdhd}((v4\_normsp\_0~X0){\unicdcdcdhd}((v2\_normsp\_1~X0){\unicdcdcdhd}(l1\_normsp\_1~X0))))))))))))){\unicdbdjdcd}\\
((v3\_lopban\_1~X0){\unicdbdjded}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~\\
X1~k5\_numbers~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k5\_numbers~(u1\_struct\_0~X0)))))){\unicdbdjdcd}((v1\_rsspace3~\\
X1~X0){\unicdbdjdcd}(v3\_normsp\_1~X1~X0))))\end{array}
\label{hyp:egbdfdpfmgpgahcgbgogpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddgdpfdgaddhahbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k11\_c0sp1~X0)){\unicdcdcdhd}\\
((v13\_algstr\_0~(k11\_c0sp1~X0)){\unicdcdcdhd}((v2\_rlvect\_1~(k11\_c0sp1~X0)){\unicdcdcdhd}\\
((v3\_rlvect\_1~(k11\_c0sp1~X0)){\unicdcdcdhd}((v4\_rlvect\_1~(k11\_c0sp1~X0)){\unicdcdcdhd}\\
((v5\_rlvect\_1~(k11\_c0sp1~X0)){\unicdcdcdhd}((v6\_rlvect\_1~(k11\_c0sp1~X0)){\unicdcdcdhd}\\
((v7\_rlvect\_1~(k11\_c0sp1~X0)){\unicdcdcdhd}((v8\_rlvect\_1~(k11\_c0sp1~X0)){\unicdcdcdhd}\\
((v3\_normsp\_0~(k11\_c0sp1~X0)){\unicdcdcdhd}((v4\_normsp\_0~(k11\_c0sp1~X0)){\unicdcdcdhd}\\
((v2\_normsp\_1~(k11\_c0sp1~X0)){\unicdcdcdhd}((v3\_lopban\_1~(k11\_c0sp1~X0)){\unicdcdcdhd}\\
(l1\_normsp\_1~(k11\_c0sp1~X0)))))))))))))))\end{array}$$
\end{theorem}
\end{document}
