\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{t2\_l\_hospit (TMGUmD8MQisAzBxN2jNuBZzfRGoZfXYxkrw)}
\maketitle
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ k1\_numbers : {\iota}$ be given.
Let $ r4\_limfunc2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_limfunc2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v2\_comseq\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_seq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_limfunc1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k1\_numbers){\unicdbdjdcd}\\
((r4\_limfunc2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}\\
((X2=k2\_limfunc2~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~\\
X3~k5\_numbers~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k5\_numbers~k1\_numbers))))){\unicdbdjdcd}(((v2\_comseq\_2~X3){\unicdcdcdhd}((k2\_seq\_2~X3=\\
X1){\unicdcdcdhd}(r1\_tarski~(k2\_relset\_1~k1\_numbers~X3)~(k9\_subset\_1~k1\_numbers~\\
(k1\_relset\_1~k1\_numbers~X0)~(k3\_limfunc1~X1))))){\unicdbdjdcd}((v2\_comseq\_2~\\
(k8\_funct\_2~k5\_numbers~k1\_numbers~k1\_numbers~X3~X0)){\unicdcdcdhd}(k2\_seq\_2~\\
(k8\_funct\_2~k5\_numbers~k1\_numbers~k1\_numbers~X3~X0)=X2))))))))\end{array}
\label{hyp:egidpfmgjgngggfhogdgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k1\_numbers){\unicdbdjdcd}\\
((r4\_limfunc2~X0~X1){\unicdbdjded}(({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}\\
(\preoh (\preoh r1\_xxreal\_0~X2~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k1\_numbers){\unicdbdjdcd}\\
(\preoh (\preoh r1\_xxreal\_0~X2~X3){\unicdcdcdhd}((\preoh r1\_xxreal\_0~X3~X1){\unicdcdcdhd}(X3 \in k1\_relset\_1~\\
k1\_numbers~X0)))))){\unicdcdcdhd}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdcdcdhd}\\
({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~k5\_numbers~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))){\unicdbdjdcd}\\
(((v2\_comseq\_2~X3){\unicdcdcdhd}((k2\_seq\_2~X3=X1){\unicdcdcdhd}(r1\_tarski~(k2\_relset\_1~\\
k1\_numbers~X3)~(k9\_subset\_1~k1\_numbers~(k1\_relset\_1~k1\_numbers~\\
X0)~(k3\_limfunc1~X1))))){\unicdbdjdcd}((v2\_comseq\_2~(k8\_funct\_2~k5\_numbers~\\
k1\_numbers~k1\_numbers~X3~X0)){\unicdcdcdhd}(k2\_seq\_2~(k8\_funct\_2~k5\_numbers~\\
k1\_numbers~k1\_numbers~X3~X0)=X2))))))))\end{array}
\label{hyp:egedpfmgjgngggfhogdgcd}
\end{equation}
\begin{theorem}\label{thm:ehcdpfmgpfigpgdhahjgeh}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k1\_numbers){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}((((r4\_limfunc2~X0~X1){\unicdcdcdhd}\\
(k2\_limfunc2~X0~X1=X2)){\unicdbdjdcd}(({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k1\_numbers){\unicdbdjdcd}\\
(\preoh (\preoh r1\_xxreal\_0~X3~X1){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k1\_numbers){\unicdbdjdcd}\\
(\preoh (\preoh r1\_xxreal\_0~X3~X4){\unicdcdcdhd}((\preoh r1\_xxreal\_0~X4~X1){\unicdcdcdhd}(X4 \in k1\_relset\_1~\\
k1\_numbers~X0)))))){\unicdcdcdhd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~\\
X3~k5\_numbers~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k5\_numbers~k1\_numbers))))){\unicdbdjdcd}(((v2\_comseq\_2~X3){\unicdcdcdhd}((k2\_seq\_2~X3=\\
X1){\unicdcdcdhd}(r1\_tarski~(k2\_relset\_1~k1\_numbers~X3)~(k9\_subset\_1~k1\_numbers~\\
(k1\_relset\_1~k1\_numbers~X0)~(k3\_limfunc1~X1))))){\unicdbdjdcd}((v2\_comseq\_2~\\
(k8\_funct\_2~k5\_numbers~k1\_numbers~k1\_numbers~X3~X0)){\unicdcdcdhd}(k2\_seq\_2~\\
(k8\_funct\_2~k5\_numbers~k1\_numbers~k1\_numbers~X3~X0)=X2)))))){\unicdcdcdhd}\\
((({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k1\_numbers){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X3~\\
X1){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k1\_numbers){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~\\
X3~X4){\unicdcdcdhd}((\preoh r1\_xxreal\_0~X4~X1){\unicdcdcdhd}(X4 \in k1\_relset\_1~k1\_numbers~X0)))))){\unicdcdcdhd}\\
({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~k5\_numbers~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))){\unicdbdjdcd}\\
(((v2\_comseq\_2~X3){\unicdcdcdhd}((k2\_seq\_2~X3=X1){\unicdcdcdhd}(r1\_tarski~(k2\_relset\_1~\\
k1\_numbers~X3)~(k9\_subset\_1~k1\_numbers~(k1\_relset\_1~k1\_numbers~\\
X0)~(k3\_limfunc1~X1))))){\unicdbdjdcd}((v2\_comseq\_2~(k8\_funct\_2~k5\_numbers~\\
k1\_numbers~k1\_numbers~X3~X0)){\unicdcdcdhd}(k2\_seq\_2~(k8\_funct\_2~k5\_numbers~\\
k1\_numbers~k1\_numbers~X3~X0)=X2))))){\unicdbdjdcd}((r4\_limfunc2~X0~X1){\unicdcdcdhd}(k2\_limfunc2~\\
X0~X1=X2))))))\end{array}$$
\end{theorem}
\end{document}
