\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\_catalg\_1 (TMcZZV4L4jyYruTTyw6xVkuiC1MGRgwEWEn)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_catalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_catalg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_catalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_catalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ k11\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k10\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k9\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_instalg1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_instalg1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_catalg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ u2\_msualg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 .  (X1 \in k4\_finseq\_2~np\_\_3~X0){\unicdbdjded}({\unicdcdaddd} X2 .  \\
{\unicdcdaddd} X3 .  {\unicdcdaddd} X4 .  (X2 \in X0){\unicdcdcdhd}((X3 \in X0){\unicdcdcdhd}((X4 \in X0){\unicdcdcdhd}(X1=k11\_finseq\_1~\\
X2~X3~X4))))\end{array}
\label{hyp:ehbdddjdpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (X1 \in k4\_finseq\_2~np\_\_2~X0){\unicdbdjded}({\unicdcdaddd} X2 .  \\
{\unicdcdaddd} X3 .  (X2 \in X0){\unicdcdcdhd}((X3 \in X0){\unicdcdcdhd}(X1=k10\_finseq\_1~X2~X3)))\end{array}
\label{hyp:ehbdddhdpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (X1 \in k4\_finseq\_2~np\_\_1~X0){\unicdbdjded}({\unicdcdaddd} X2 .  \\
(X2 \in X0){\unicdcdcdhd}(X1=k9\_finseq\_1~X2))\end{array}
\label{hyp:ehbdddfdpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_instalg1~X1~X0){\unicdbdjdcd}((r1\_tarski~(u1\_struct\_0~X1)~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}(r1\_tarski~(u4\_struct\_0~X1)~(u4\_struct\_0~X0))))\end{array}
\label{hyp:ehbdadpfjgogdhehbgmghgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (k4\_tarski~X0~X1 \in \\
k2\_zfmisc\_1~(k1\_tarski~X2)~X3){\unicdbdjded}((X0=X2){\unicdcdcdhd}(X1 \in X3))\end{array}
\label{hyp:ehbdadfdpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_catalg\_1~X1~X0){\unicdbdjdcd}((v1\_instalg1~X1){\unicdcdcdhd}\\
(l1\_msualg\_1~X1))\end{array}
\label{hyp:egehpfngbdpfdgbgehbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_msualg\_1~(k2\_catalg\_1~X0)){\unicdcdcdhd}(l1\_msualg\_1~(k2\_catalg\_1~\\
X0))\end{array}
\label{hyp:egehpflgcdpfdgbgehbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k6\_catalg\_1~X0~X1=k4\_tarski~k6\_numbers~\\
(k10\_finseq\_1~X0~X1)\end{array}
\label{hyp:egjdpfdgbgehbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k5\_catalg\_1}~{X0}}={{{k4\_tarski}~{np\_\_1}}~{({{k9\_finseq\_1}~{X0}})}}}}\label{hyp:egidpfdgbgehbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k4\_tarski~X0~X1=k2\_tarski~(k2\_tarski~X0~\\
X1)~(k1\_tarski~X0)\end{array}
\label{hyp:egfdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_instalg1~X1){\unicdcdcdhd}(l1\_msualg\_1~X1)){\unicdbdjdcd}(\\
(m1\_catalg\_1~X1~X0){\unicdbdjded}((m1\_instalg1~(k2\_catalg\_1~X0)~X1){\unicdcdcdhd}(u1\_struct\_0~\\
X1=k2\_zfmisc\_1~(k1\_tarski~k6\_numbers)~(k4\_finseq\_2~np\_\_2~X0))))\end{array}
\label{hyp:egfdpfdgbgehbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2=k2\_xboole\_0~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in X2){\unicdbdjded}((X3 \in X0){\unicdcdcdid}(X3 \in X1)))\end{array}
\label{hyp:egddpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_msualg\_1~X1){\unicdcdcdhd}(l1\_msualg\_1~X1)){\unicdbdjdcd}(\\
(X1=k2\_catalg\_1~X0){\unicdbdjded}((u1\_struct\_0~X1=k2\_zfmisc\_1~(k1\_tarski~\\
k6\_numbers)~(k4\_finseq\_2~np\_\_2~X0)){\unicdcdcdhd}((u4\_struct\_0~X1=k2\_xboole\_0~\\
(k2\_zfmisc\_1~(k1\_tarski~np\_\_1)~(k4\_finseq\_2~np\_\_1~X0))~(k2\_zfmisc\_1~\\
(k1\_tarski~np\_\_2)~(k4\_finseq\_2~np\_\_3~X0))){\unicdcdcdhd}(({\unicdcdadad} X2 .  (X2 \in \\
X0){\unicdbdjdcd}((k1\_funct\_1~(u1\_msualg\_1~X1)~(k4\_tarski~np\_\_1~(k9\_finseq\_1~\\
X2))=k1\_xboole\_0){\unicdcdcdhd}(k1\_funct\_1~(u2\_msualg\_1~X1)~(k4\_tarski~np\_\_1~\\
(k9\_finseq\_1~X2))=k4\_tarski~k6\_numbers~(k10\_finseq\_1~X2~X2)))){\unicdcdcdhd}\\
({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((X2 \in X0){\unicdcdcdhd}((X3 \in X0){\unicdcdcdhd}(X4 \in X0))){\unicdbdjdcd}\\
((k1\_funct\_1~(u1\_msualg\_1~X1)~(k4\_tarski~np\_\_2~(k11\_finseq\_1~\\
X2~X3~X4))=k10\_finseq\_1~(k4\_tarski~k6\_numbers~(k10\_finseq\_1~X3~\\
X4))~(k4\_tarski~k6\_numbers~(k10\_finseq\_1~X2~X3))){\unicdcdcdhd}(k1\_funct\_1~\\
(u2\_msualg\_1~X1)~(k4\_tarski~np\_\_2~(k11\_finseq\_1~X2~X3~X4))=k4\_tarski~\\
k6\_numbers~(k10\_finseq\_1~X2~X4))))))))\end{array}
\label{hyp:egddpfdgbgehbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k7\_catalg\_1~X0~X1~X2=k4\_tarski~\\
np\_\_2~(k11\_finseq\_1~X0~X1~X2)\end{array}
\label{hyp:egbdadpfdgbgehbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_tarski}~{X0}}~{X1}}={{{k2\_tarski}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfehbgchdhlgjg}
\end{equation}
\begin{theorem}\label{thm:ehbdadpfdgbgehbgmghgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_catalg\_1~X1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X0){\unicdbdjdcd}((k5\_catalg\_1~X2 \in u4\_struct\_0~\\
X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~X0){\unicdbdjdcd}((k6\_catalg\_1~X2~X3 \in u1\_struct\_0~\\
X1){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~X0){\unicdbdjdcd}(k7\_catalg\_1~X2~X3~X4 \in u4\_struct\_0~\\
X1)))))))\end{array}$$
\end{theorem}
\end{document}
