\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{l2\_limfunc2 (TMPQiA2rCZY2kZ3F2L7oTfgxB7FjDjAgHTB)}
\maketitle
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 $ k1\_numbers : {\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 $ 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 $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k20\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k3\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((r1\_tarski~X0~X1){\unicdcdcdhd}\\
(r1\_tarski~X2~X3)){\unicdbdjdcd}(r1\_tarski~(k3\_xboole\_0~X0~X2)~(k3\_xboole\_0~\\
X1~X3))\end{array}
\label{hyp:ehcdhdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((r1\_tarski~X0~X1){\unicdcdcdhd}(r1\_tarski~\\
X1~X2)){\unicdbdjdcd}(r1\_tarski~X0~X2)\end{array}
\label{hyp:ehbdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{r1\_tarski}~{({{{k3\_xboole\_0}~{X0}}~{X1}})}}~{X0}}}}\label{hyp:ehbdhdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(k9\_subset\_1~X0~X1~X2=k3\_xboole\_0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}((r1\_tarski~\\
(k2\_relset\_1~k1\_numbers~X0)~(k1\_relset\_1~k1\_numbers~(k20\_valued\_1~\\
k1\_numbers~k1\_numbers~k1\_numbers~X1~X2))){\unicdbdjdcd}((k1\_relset\_1~k1\_numbers~\\
(k20\_valued\_1~k1\_numbers~k1\_numbers~k1\_numbers~X1~X2)=k9\_subset\_1~\\
k1\_numbers~(k1\_relset\_1~k1\_numbers~X1)~(k1\_relset\_1~k1\_numbers~\\
X2)){\unicdcdcdhd}((r1\_tarski~(k2\_relset\_1~k1\_numbers~X0)~(k1\_relset\_1~k1\_numbers~\\
X1)){\unicdcdcdhd}(r1\_tarski~(k2\_relset\_1~k1\_numbers~X0)~(k1\_relset\_1~k1\_numbers~\\
X2)))))))\end{array}
\label{hyp:mgddpfmgjgngggfhogdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2=k3\_xboole\_0~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in X2){\unicdbdjded}((X3 \in X0){\unicdcdcdhd}(X3 \in X1)))\end{array}
\label{hyp:egedpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k3\_xboole\_0}~{X0}}~{X1}}={{{k3\_xboole\_0}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgddpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:mgcdpfmgjgngggfhogdgcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~k1\_numbers)){\unicdbdjdcd}((r1\_tarski~(k2\_relset\_1~\\
k1\_numbers~X0)~(k9\_subset\_1~k1\_numbers~(k1\_relset\_1~k1\_numbers~\\
(k20\_valued\_1~k1\_numbers~k1\_numbers~k1\_numbers~X1~X2))~X3)){\unicdbdjdcd}(\\
(r1\_tarski~(k2\_relset\_1~k1\_numbers~X0)~(k1\_relset\_1~k1\_numbers~\\
(k20\_valued\_1~k1\_numbers~k1\_numbers~k1\_numbers~X1~X2))){\unicdcdcdhd}((r1\_tarski~\\
(k2\_relset\_1~k1\_numbers~X0)~X3){\unicdcdcdhd}((k1\_relset\_1~k1\_numbers~(k20\_valued\_1~\\
k1\_numbers~k1\_numbers~k1\_numbers~X1~X2)=k9\_subset\_1~k1\_numbers~\\
(k1\_relset\_1~k1\_numbers~X1)~(k1\_relset\_1~k1\_numbers~X2)){\unicdcdcdhd}((r1\_tarski~\\
(k2\_relset\_1~k1\_numbers~X0)~(k1\_relset\_1~k1\_numbers~X1)){\unicdcdcdhd}((r1\_tarski~\\
(k2\_relset\_1~k1\_numbers~X0)~(k1\_relset\_1~k1\_numbers~X2)){\unicdcdcdhd}((r1\_tarski~\\
(k2\_relset\_1~k1\_numbers~X0)~(k9\_subset\_1~k1\_numbers~(k1\_relset\_1~\\
k1\_numbers~X1)~X3)){\unicdcdcdhd}(r1\_tarski~(k2\_relset\_1~k1\_numbers~X0)~(k9\_subset\_1~\\
k1\_numbers~(k1\_relset\_1~k1\_numbers~X2)~X3))))))))))))\end{array}$$
\end{theorem}
\end{document}
