\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{t14\_pencil\_1 (TMcEH2i8qnZkALwGpnQJ29ASytK4rwLd3ej)}
\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 $ v11\_pencil\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_pencil\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ g1\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_pralg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k12\_pralg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_pencil\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_pre\_topc : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (g1\_pre\_topc~X0~X1=g1\_pre\_topc~\\
X2~X3){\unicdbdjdcd}((X0=X2){\unicdcdcdhd}(X1=X3)))\end{array}
\label{hyp:ggchfgfgpfhgbdpfahchfgpfehpgahdg}
\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}((v2\_pralg\_1~X1){\unicdcdcdhd}(v4\_waybel\_3~\\
X1)))))){\unicdbdjdcd}((v1\_relat\_1~(k12\_pralg\_1~X0~X1)){\unicdcdcdhd}((v2\_relat\_1~(k12\_pralg\_1~\\
X0~X1)){\unicdcdcdhd}((v4\_relat\_1~(k12\_pralg\_1~X0~X1)~X0){\unicdcdcdhd}((v1\_funct\_1~(k12\_pralg\_1~\\
X0~X1)){\unicdcdcdhd}(v1\_partfun1~(k12\_pralg\_1~X0~X1)~X0)))))\end{array}
\label{hyp:ggdgfdpfjhfgmgmgpghhpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v2\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0))){\unicdbdjdcd}\\
(\preoh v1\_xboole\_0~(k4\_card\_3~X0))\end{array}
\label{hyp:ggdgfdpfdgbgchegpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\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}(v11\_pencil\_1~X1))))))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k5\_pencil\_1~X0~\\
X1)){\unicdcdcdhd}(l1\_pre\_topc~(k5\_pencil\_1~X0~X1)))\end{array}
\label{hyp:egehpflgfdpfahfgogdgjgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\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}(v11\_pencil\_1~X1))))))){\unicdbdjdcd}(m1\_subset\_1~(k4\_pencil\_1~X0~X1)~\\
(k1\_zfmisc\_1~(k1\_zfmisc\_1~(k4\_card\_3~(k12\_pralg\_1~X0~X1)))))\end{array}
\label{hyp:egehpflgedpfahfgogdgjgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
X0))){\unicdbdjdcd}((v1\_pre\_topc~(g1\_pre\_topc~X0~X1)){\unicdcdcdhd}(l1\_pre\_topc~(g1\_pre\_topc~\\
X0~X1)))\end{array}
\label{hyp:egehpfhgbdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (X1=\\
k4\_card\_3~X0){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}({\unicdcdaddd} X3 .  ((v1\_relat\_1~\\
X3){\unicdcdcdhd}(v1\_funct\_1~X3)){\unicdcdcdhd}((X2=X3){\unicdcdcdhd}((k9\_xtuple\_0~X3=k9\_xtuple\_0~\\
X0){\unicdcdcdhd}({\unicdcdadad} X4 .  (X4 \in k9\_xtuple\_0~X0){\unicdbdjdcd}(k1\_funct\_1~X3~X4 \in k1\_funct\_1~\\
X0~X4)))))))\end{array}
\label{hyp:egfdpfdgbgchegpfdd}
\end{equation}
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}(v11\_pencil\_1~X1)))))){\unicdbdjdcd}(k5\_pencil\_1~X0~X1=g1\_pre\_topc~(\\
k4\_card\_3~(k12\_pralg\_1~X0~X1))~(k4\_pencil\_1~X0~X1)))\end{array}
\label{hyp:egcdddpfahfgogdgjgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v11\_pencil\_1~\\
X0))){\unicdbdjdcd}((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v2\_pralg\_1~X0)))\end{array}
\label{hyp:dgdgbdpfahfgogdgjgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v2\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~X0))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k4\_card\_3~X1)){\unicdbdjdcd}(v1\_partfun1~X2~X0))\end{array}
\label{hyp:dgdgbdddpfdgbgchegpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v2\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~X0){\unicdcdcdhd}(v1\_funct\_1~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k4\_card\_3~\\
X1)){\unicdbdjdcd}(v4\_relat\_1~X2~X0))\end{array}
\label{hyp:dgdgbdadpfdgbgchegpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}((v1\_pre\_topc~X0){\unicdbdjdcd}(X0=g1\_pre\_topc~\\
(u1\_struct\_0~X0)~(u1\_pre\_topc~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpfahchfgpfehpgahdg}
\end{equation}
\begin{theorem}\label{thm:ehbdedpfahfgogdgjgmgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(\\
(v4\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}((v4\_waybel\_3~\\
X1){\unicdcdcdhd}(v11\_pencil\_1~X1)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
(k5\_pencil\_1~X0~X1))){\unicdbdjdcd}((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~X2~X0))))))\end{array}$$
\end{theorem}
\end{document}
