\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{t13\_rfunct\_2 (TMHc6cXwt5va4PfxyYJmBLXAJ5RsDR7tp4j)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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 $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k8\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k3\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k47\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ 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 $ k3\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\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}(\\
m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k1\_numbers)))){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~\\
X3~k5\_numbers~X0){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~\\
X0))))){\unicdbdjdcd}((r1\_tarski~(k2\_relset\_1~X0~X3)~(k9\_subset\_1~X0~(k1\_relset\_1~\\
X0~X1)~(k1\_relset\_1~X0~X2))){\unicdbdjdcd}((r2\_relset\_1~k5\_numbers~k1\_numbers~\\
(k8\_funct\_2~k5\_numbers~k1\_numbers~X0~X3~(k3\_valued\_1~X0~k1\_numbers~\\
k1\_numbers~X1~X2))~(k3\_valued\_1~k5\_numbers~k1\_numbers~k1\_numbers~\\
(k8\_funct\_2~k5\_numbers~k1\_numbers~X0~X3~X1)~(k8\_funct\_2~k5\_numbers~\\
k1\_numbers~X0~X3~X2))){\unicdcdcdhd}((r2\_relset\_1~k5\_numbers~k1\_numbers~(k8\_funct\_2~\\
k5\_numbers~k1\_numbers~X0~X3~(k47\_valued\_1~X0~k1\_numbers~k1\_numbers~\\
X1~X2))~(k47\_valued\_1~k5\_numbers~k1\_numbers~k1\_numbers~(k8\_funct\_2~\\
k5\_numbers~k1\_numbers~X0~X3~X1)~(k8\_funct\_2~k5\_numbers~k1\_numbers~\\
X0~X3~X2))){\unicdcdcdhd}(r2\_relset\_1~k5\_numbers~k1\_numbers~(k8\_funct\_2~k5\_numbers~\\
k1\_numbers~X0~X3~(k20\_valued\_1~X0~k1\_numbers~k1\_numbers~X1~X2))~\\
(k20\_valued\_1~k5\_numbers~k1\_numbers~k1\_numbers~(k8\_funct\_2~k5\_numbers~\\
k1\_numbers~X0~X3~X1)~(k8\_funct\_2~k5\_numbers~k1\_numbers~X0~X3~X2)))))))))\end{array}
\label{hyp:ehidpfchggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~X1)){\unicdbdjded}(r1\_tarski~\\
X0~X1)\end{array}
\label{hyp:ehddpfdhfhcgdhfgeh}
\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}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k3\_xboole\_0}~{X0}}~{X0}}={X0}}}}\label{hyp:jgegfgngahpgehfgogdgfgpflgddpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v5\_relat\_1~X1~X0)){\unicdbdjdcd}(\\
m1\_subset\_1~(k2\_relset\_1~X0~X1)~(k1\_zfmisc\_1~X0))\end{array}
\label{hyp:egehpflgcdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v4\_relat\_1~X1~X0)){\unicdbdjdcd}(\\
m1\_subset\_1~(k1\_relset\_1~X0~X1)~(k1\_zfmisc\_1~X0))\end{array}
\label{hyp:egehpflgbdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v4\_relat\_1~X1~X0)){\unicdbdjdcd}(\\
(v1\_partfun1~X1~X0){\unicdbdjded}(k1\_relset\_1~X0~X1=X0))\end{array}
\label{hyp:egcdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}(v5\_relat\_1~X2~X1))\end{array}
\label{hyp:dgdgcdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v1\_relat\_1~X2)\end{array}
\label{hyp:dgdgbdpfchfgmgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdddpfchggfhogdgehpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k1\_numbers)))){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~\\
X3~k5\_numbers~X0){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~\\
X0))))){\unicdbdjdcd}(((v1\_partfun1~X1~X0){\unicdcdcdhd}(v1\_partfun1~X2~X0)){\unicdbdjdcd}((r2\_relset\_1~\\
k5\_numbers~k1\_numbers~(k8\_funct\_2~k5\_numbers~k1\_numbers~X0~X3~\\
(k3\_valued\_1~X0~k1\_numbers~k1\_numbers~X1~X2))~(k3\_valued\_1~k5\_numbers~\\
k1\_numbers~k1\_numbers~(k8\_funct\_2~k5\_numbers~k1\_numbers~X0~X3~\\
X1)~(k8\_funct\_2~k5\_numbers~k1\_numbers~X0~X3~X2))){\unicdcdcdhd}((r2\_relset\_1~\\
k5\_numbers~k1\_numbers~(k8\_funct\_2~k5\_numbers~k1\_numbers~X0~X3~\\
(k47\_valued\_1~X0~k1\_numbers~k1\_numbers~X1~X2))~(k47\_valued\_1~k5\_numbers~\\
k1\_numbers~k1\_numbers~(k8\_funct\_2~k5\_numbers~k1\_numbers~X0~X3~\\
X1)~(k8\_funct\_2~k5\_numbers~k1\_numbers~X0~X3~X2))){\unicdcdcdhd}(r2\_relset\_1~\\
k5\_numbers~k1\_numbers~(k8\_funct\_2~k5\_numbers~k1\_numbers~X0~X3~\\
(k20\_valued\_1~X0~k1\_numbers~k1\_numbers~X1~X2))~(k20\_valued\_1~k5\_numbers~\\
k1\_numbers~k1\_numbers~(k8\_funct\_2~k5\_numbers~k1\_numbers~X0~X3~\\
X1)~(k8\_funct\_2~k5\_numbers~k1\_numbers~X0~X3~X2)))))))))\end{array}$$
\end{theorem}
\end{document}
