\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{t16\_yellow17 (TMS6JqkfpzXveYgrau7fRGgCp5YWnDfiEUA)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_waybel\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_waybel18 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_waybel18 : {{\iota}{\unicdbdjdcd}{{\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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_waybel18 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v3\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k8\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_waybel18 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_waybel18 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_funct\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k12\_pralg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(\\
(v4\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}((v4\_waybel\_3~\\
X1){\unicdcdcdhd}(v1\_waybel18~X1)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X0){\unicdbdjdcd}(\\
{\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~(k4\_waybel18~\\
X0~X1~X2)))){\unicdbdjdcd}(k8\_relset\_1~(u1\_struct\_0~(k3\_waybel18~X0~X1))~(u1\_struct\_0~\\
(k4\_waybel18~X0~X1~X2))~(k6\_waybel18~X0~X1~X2)~X3=k4\_card\_3~(k2\_funct\_7~\\
(k12\_pralg\_1~X0~X1)~X2~X3)))))\end{array}
\label{hyp:ehedpfhhbgjhcgfgmgbdid}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0 \in X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~X0~X2)\end{array}
\label{hyp:ehedpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((v1\_relat\_1~\\
X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}\\
((v4\_waybel\_3~X1){\unicdcdcdhd}(v1\_waybel18~X1)))))){\unicdcdcdhd}(m1\_subset\_1~X2~X0))){\unicdbdjdcd}\\
(k4\_waybel18~X0~X1~X2=k1\_funct\_1~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfhhbgjhcgfgmgbdid}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}(v1\_waybel18~X1))))){\unicdbdjdcd}(\\
m1\_subset\_1~(k2\_waybel18~X0~X1)~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(k4\_card\_3~\\
(k12\_pralg\_1~X0~X1)))))\end{array}
\label{hyp:egehpflgcdpfhhbgjhcgfgmgbdid}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}(v1\_waybel18~X1))))){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(k4\_card\_3~\\
(k12\_pralg\_1~X0~X1))))){\unicdbdjdcd}((X2=k2\_waybel18~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k4\_card\_3~(k12\_pralg\_1~X0~X1)))){\unicdbdjdcd}\\
((X3 \in X2){\unicdbdjded}({\unicdcdaddd} X4 .  {\unicdcdaddd} X5 .  (l1\_pre\_topc~X5){\unicdcdcdhd}({\unicdcdaddd} X6 .  \\
(m1\_subset\_1~X6~(k1\_zfmisc\_1~(u1\_struct\_0~X5))){\unicdcdcdhd}((X4 \in X0){\unicdcdcdhd}((\\
v3\_pre\_topc~X6~X5){\unicdcdcdhd}((X5=k1\_funct\_1~X1~X4){\unicdcdcdhd}(X3=k4\_card\_3~(k2\_funct\_7~\\
(k12\_pralg\_1~X0~X1)~X4~X6)))))))))))\end{array}
\label{hyp:egcdpfhhbgjhcgfgmgbdid}
\end{equation}
\begin{theorem}\label{thm:ehbdgdpfjhfgmgmgpghhbdhd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(\\
(v4\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}((v4\_waybel\_3~\\
X1){\unicdcdcdhd}(v1\_waybel18~X1)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \preoh (X2 \in k2\_waybel18~X0~X1){\unicdcdcdhd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~X0){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(\\
k1\_zfmisc\_1~(u1\_struct\_0~(k4\_waybel18~X0~X1~X3)))){\unicdbdjdcd}(\preoh (v3\_pre\_topc~\\
X4~(k4\_waybel18~X0~X1~X3)){\unicdcdcdhd}(k8\_relset\_1~(u1\_struct\_0~(k3\_waybel18~\\
X0~X1))~(u1\_struct\_0~(k4\_waybel18~X0~X1~X3))~(k6\_waybel18~X0~X1~X3)~\\
X4=X2))))))\end{array}$$
\end{theorem}
\end{document}
