\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{t10\_pencil\_3 (TMdTtUGbKh5onHAyo5UamCiKpt8WEr3mNh5)}
\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 $ v11\_pencil\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v14\_pencil\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_pencil\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v16\_pencil\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m3\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k12\_pralg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_pencil\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_pencil\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_pencil\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v2\_relat\_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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_pencil\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_pralg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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}\\
({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v2\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1))){\unicdbdjdcd}\\
((k4\_card\_3~X0=k4\_card\_3~X1){\unicdbdjdcd}(X0=X1)))\end{array}
\label{hyp:ehcdpfahfhbgcdngdhdhbd}
\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)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m3\_pboole~\\
X2~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}
\label{hyp:egehpfngddpfahcgpgpgmgfg}
\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}((v11\_pencil\_1~\\
X1){\unicdcdcdhd}(v14\_pencil\_1~X1))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_pencil\_2~X2~X0~X1){\unicdbdjdcd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~(k5\_pencil\_1~X0~X1)))))\end{array}
\label{hyp:egehpfngbdpfahfgogdgjgmgpfcd}
\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))))){\unicdbdjdcd}((\\
v1\_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:egehpflgbdcdpfahchbgmghgpfbd}
\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}((v11\_pencil\_1~\\
X1){\unicdcdcdhd}(v14\_pencil\_1~X1)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k5\_pencil\_1~X0~X1)))){\unicdbdjdcd}((m1\_pencil\_2~X2~X0~X1){\unicdbdjded}(\\
{\unicdcdaddd} X3 .  ((\preoh v13\_pencil\_1~X3){\unicdcdcdhd}((v16\_pencil\_1~X3~X0){\unicdcdcdhd}(m3\_pboole~\\
X3~X0~(k12\_pralg\_1~X0~X1)))){\unicdcdcdhd}((X2=k4\_card\_3~X3){\unicdcdcdhd}(k1\_funct\_1~X3~\\
(k3\_pencil\_1~X0~X3)=k2\_struct\_0~(k1\_pencil\_1~X0~X1~(k3\_pencil\_1~\\
X0~X3))))))))\end{array}
\label{hyp:egcdpfahfgogdgjgmgpfcd}
\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}((\preoh \\
v13\_pencil\_1~X1){\unicdcdcdhd}(v16\_pencil\_1~X1~X0)))))){\unicdbdjdcd}((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))))))\end{array}
\label{hyp:dgdggdpfahfgogdgjgmgpfbd}
\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}
\begin{theorem}\label{thm:ehbdadpfahfgogdgjgmgpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(\\
(v4\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}((v11\_pencil\_1~\\
X1){\unicdcdcdhd}(v14\_pencil\_1~X1)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v13\_pencil\_1~X2){\unicdcdcdhd}\\
((v16\_pencil\_1~X2~X0){\unicdcdcdhd}(m3\_pboole~X2~X0~(k12\_pralg\_1~X0~X1)))){\unicdbdjdcd}\\
((m1\_pencil\_2~(k4\_card\_3~X2)~X0~X1){\unicdbdjdcd}(k1\_funct\_1~X2~(k3\_pencil\_1~\\
X0~X2)=k2\_struct\_0~(k1\_pencil\_1~X0~X1~(k3\_pencil\_1~X0~X2))))))\end{array}$$
\end{theorem}
\end{document}
