\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{t73\_setlim\_1 (TMGectVX1bMPCV2TiP4ESMjeSFdzEGs5uS3)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_prob\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_prob\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ k9\_setfam\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k6\_prob\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_kurato\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~k5\_numbers~\\
(k9\_setfam\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k5\_numbers~(k9\_setfam\_1~X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}\\
((v1\_funct\_2~X2~k5\_numbers~(k9\_setfam\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k9\_setfam\_1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~k5\_numbers~(k9\_setfam\_1~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k9\_setfam\_1~\\
X0)))))){\unicdbdjdcd}(({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k5\_numbers){\unicdbdjdcd}(k3\_funct\_2~\\
k5\_numbers~(k9\_setfam\_1~X0)~X3~X4=k4\_subset\_1~X0~(k3\_funct\_2~k5\_numbers~\\
(k9\_setfam\_1~X0)~X1~X4)~(k3\_funct\_2~k5\_numbers~(k9\_setfam\_1~X0)~\\
X2~X4))){\unicdbdjdcd}(r1\_tarski~(k4\_subset\_1~X0~(k3\_kurato\_0~X0~X1)~(k3\_kurato\_0~\\
X0~X2))~(k3\_kurato\_0~X0~X3)))))\end{array}
\label{hyp:ehbdcdpflgfhchbgehpgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k9\_setfam\_1}~{X0}}={{k1\_zfmisc\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfdhfgehggbgngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v1\_xboole\_0~\\
X1){\unicdcdcdhd}((v1\_prob\_1~X1~X0){\unicdcdcdhd}((v4\_prob\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~X0)))))){\unicdcdcdhd}((m1\_subset\_1~X2~X1){\unicdcdcdhd}(m1\_subset\_1~X3~X1))){\unicdbdjdcd}\\
(k6\_prob\_1~X0~X1~X2~X3=k2\_xboole\_0~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfahchpgcgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~X0))){\unicdbdjdcd}(k4\_subset\_1~X0~X1~X2=\\
k2\_xboole\_0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k4\_ordinal1}}}})}{\unicdcdcdhd}{({{v3\_ordinal1}~{k4\_ordinal1}})}}\label{hyp:ggdggdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{v4\_prob\_1}~{({{k1\_zfmisc\_1}~{X0}})}}~{X0}}}\label{hyp:ggdgedpfahchpgcgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{v1\_prob\_1}~{({{k1\_zfmisc\_1}~{X0}})}}~{X0}}}\label{hyp:ggdgcdpfahchpgcgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {\preoh{{{v1\_xboole\_0}~{({{k1\_zfmisc\_1}~{X0}})}}}}}\label{hyp:ggdgbdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  m1\_subset\_1~(k9\_setfam\_1~X0)~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
X0))\end{array}
\label{hyp:egehpflgjdpfdhfgehggbgngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))))){\unicdcdcdhd}(m1\_subset\_1~X3~X0))){\unicdbdjdcd}(m1\_subset\_1~(\\
k3\_funct\_2~X0~X1~X2~X3)~X1)\end{array}
\label{hyp:egehpflgddpfggfhogdgehpfcd}
\end{equation}
\begin{theorem}\label{thm:ehhdddpfdhfgehmgjgngpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_prob\_1~X1~X0){\unicdcdcdhd}\\
((v4\_prob\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v5\_relat\_1~X2~X1){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(\\
(v1\_funct\_2~X2~k5\_numbers~(k9\_setfam\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k9\_setfam\_1~X0))))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v5\_relat\_1~X3~X1){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~\\
X3~k5\_numbers~(k9\_setfam\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k5\_numbers~(k9\_setfam\_1~X0))))))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
((v5\_relat\_1~X4~X1){\unicdcdcdhd}((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~k5\_numbers~\\
(k9\_setfam\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k5\_numbers~(k9\_setfam\_1~X0))))))){\unicdbdjdcd}(({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~k5\_numbers){\unicdbdjdcd}(k3\_funct\_2~k5\_numbers~(k9\_setfam\_1~X0)~X2~X5=\\
k6\_prob\_1~X0~(k9\_setfam\_1~X0)~(k3\_funct\_2~k5\_numbers~(k9\_setfam\_1~\\
X0)~X3~X5)~(k3\_funct\_2~k5\_numbers~(k9\_setfam\_1~X0)~X4~X5))){\unicdbdjdcd}(r1\_tarski~\\
(k4\_subset\_1~X0~(k3\_kurato\_0~X0~X3)~(k3\_kurato\_0~X0~X4))~(k3\_kurato\_0~\\
X0~X2))))))\end{array}$$
\end{theorem}
\end{document}
