\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{t9\_pencil\_2 (TML98DrJEYKnsCcDLFcC4rKJpkYLFEJCj12)}
\maketitle
Let $ l1\_pre\_topc : {{\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 $ r1\_pencil\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v2\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_pencil\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_pencil\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k1\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{\preoh{{({{X0} \in {X1}})}}}{\unicdcdcdhd}{({{v1\_xboole\_0}~{X1}})}}}}\label{hyp:ehhdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \preoh (X0 \in X1){\unicdcdcdhd}((m1\_subset\_1~X1~(\\
k1\_zfmisc\_1~X2)){\unicdcdcdhd}(v1\_xboole\_0~X2))\end{array}
\label{hyp:ehfdpfdhfhcgdhfgeh}
\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}
\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 .  (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 : \iota{\unicdbdjdcd}\iota{\unicdbdjdcd}o .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  \\
(((X4=k1\_funct\_1~X3~np\_\_1){\unicdcdcdhd}(X2=k1\_funct\_1~X3~(k3\_finseq\_1~X3))){\unicdcdcdhd}\\
({\unicdcdadad} X5 .  (m1\_subset\_1~X5~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X6 .  {\unicdcdadad} X7 .  \\
((r1\_xxreal\_0~np\_\_1~X5){\unicdcdcdhd}((X6=k1\_funct\_1~X3~X5){\unicdcdcdhd}(X7=k1\_funct\_1~\\
X3~(k2\_nat\_1~X5~np\_\_1)))){\unicdbdjdcd}((r1\_xxreal\_0~(k3\_finseq\_1~X3)~X5){\unicdcdcdid}\\
(X1~X6~X7))))){\unicdbdjdcd}({\unicdcdaddd} X5 .  ((v2\_funct\_1~X5){\unicdcdcdhd}(m2\_finseq\_1~X5~X0)){\unicdcdcdhd}\\
((X4=k1\_funct\_1~X5~np\_\_1){\unicdcdcdhd}((X2=k1\_funct\_1~X5~(k3\_finseq\_1~X5)){\unicdcdcdhd}\\
((r1\_tarski~(k2\_relset\_1~X0~X5)~(k2\_relset\_1~X0~X3)){\unicdcdcdhd}({\unicdcdadad} X6 .  \\
(m1\_subset\_1~X6~k5\_numbers){\unicdbdjdcd}((r1\_xxreal\_0~np\_\_1~X6){\unicdbdjdcd}((r1\_xxreal\_0~\\
(k3\_finseq\_1~X5)~X6){\unicdcdcdid}(X1~(k1\_funct\_1~X5~X6)~(k1\_funct\_1~X5~(k2\_nat\_1~\\
X6~np\_\_1))))))))))\end{array}
\label{hyp:dhbdpfahfgogdgjgmgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{r1\_tarski}~{X0}}~{X0}}}}\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}((r1\_pencil\_2~X0~X1~X2){\unicdbdjded}({\unicdcdaddd} X3 .  (m2\_finseq\_1~\\
X3~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdcdcdhd}((X1=k1\_funct\_1~X3~np\_\_1){\unicdcdcdhd}\\
((X2=k1\_funct\_1~X3~(k3\_finseq\_1~X3)){\unicdcdcdhd}(({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}((X4 \in k2\_relset\_1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))~X3){\unicdbdjdcd}((v1\_pencil\_1~X4~X0){\unicdcdcdhd}(v2\_pencil\_1~X4~X0)))){\unicdcdcdhd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k5\_numbers){\unicdbdjdcd}((r1\_xxreal\_0~np\_\_1~\\
X4){\unicdbdjdcd}((r1\_xxreal\_0~(k3\_finseq\_1~X3)~X4){\unicdcdcdid}(r1\_tarski~np\_\_2~(k1\_card\_1~\\
(k3\_xboole\_0~(k1\_funct\_1~X3~X4)~(k1\_funct\_1~X3~(k2\_nat\_1~X4~np\_\_1)))))))))))))))\end{array}
\label{hyp:egddpfahfgogdgjgmgpfcd}
\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:ehjdpfahfgogdgjgmgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}(\preoh (r1\_pencil\_2~X0~X1~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  ((v2\_funct\_1~\\
X3){\unicdcdcdhd}(m2\_finseq\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}(\preoh (X1=\\
k1\_funct\_1~X3~np\_\_1){\unicdcdcdhd}((X2=k1\_funct\_1~X3~(k3\_finseq\_1~X3)){\unicdcdcdhd}((\\
{\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}(\\
(X4 \in k2\_relset\_1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))~X3){\unicdbdjdcd}((v1\_pencil\_1~\\
X4~X0){\unicdcdcdhd}(v2\_pencil\_1~X4~X0)))){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k5\_numbers){\unicdbdjdcd}\\
((r1\_xxreal\_0~np\_\_1~X4){\unicdbdjdcd}((r1\_xxreal\_0~(k3\_finseq\_1~X3)~X4){\unicdcdcdid}(\\
r1\_tarski~np\_\_2~(k1\_card\_1~(k3\_xboole\_0~(k1\_funct\_1~X3~X4)~(k1\_funct\_1~\\
X3~(k2\_nat\_1~X4~np\_\_1)))))))))))))))\end{array}$$
\end{theorem}
\end{document}
