\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{t46\_cat\_4 (TMUCpPLhPzdU8yEHmBHtbnbWryh1H8r8Rkn)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k23\_cat\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k18\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k16\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ g2\_cat\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v5\_cat\_4 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_cat\_4 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_algstr\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k17\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_graph\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_graph\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_cat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u5\_cat\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u6\_cat\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u7\_cat\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u8\_cat\_4 : {{\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}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k7\_funcop\_1}~{X0}}~{X1}}={{{k2\_funcop\_1}~{X0}}~{X1}}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k18\_funcop\_1}~{X0}}~{X1}}={{{k16\_funcop\_1}~{X0}}~{X1}}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdidpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  {\unicdcdadad} X7 .  {\unicdcdadad} X8 .  (((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~X0))))){\unicdcdcdhd}\\
(((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X1~X0))))){\unicdcdcdhd}(((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X1~X1)~X1)))){\unicdcdcdhd}((m1\_subset\_1~X5~X0){\unicdcdcdhd}\\
(((v1\_funct\_1~X6){\unicdcdcdhd}((v1\_funct\_2~X6~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X6~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~X0))))){\unicdcdcdhd}(((v1\_funct\_1~\\
X7){\unicdcdcdhd}((v1\_funct\_2~X7~(k2\_zfmisc\_1~X0~X0)~X1){\unicdcdcdhd}(m1\_subset\_1~X7~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~X1))))){\unicdcdcdhd}((v1\_funct\_1~X8){\unicdcdcdhd}((\\
v1\_funct\_2~X8~(k2\_zfmisc\_1~X0~X0)~X1){\unicdcdcdhd}(m1\_subset\_1~X8~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~X1))))))))))){\unicdbdjdcd}({\unicdcdadad} X9 .  {\unicdcdadad} X10 .  \\
{\unicdcdadad} X11 .  {\unicdcdadad} X12 .  {\unicdcdadad} X13 .  {\unicdcdadad} X14 .  {\unicdcdadad} X15 .  \\
{\unicdcdadad} X16 .  {\unicdcdadad} X17 .  (g2\_cat\_4~X0~X1~X2~X3~X4~X5~X6~X7~X8=g2\_cat\_4~\\
X9~X10~X11~X12~X13~X14~X15~X16~X17){\unicdbdjdcd}((X0=X9){\unicdcdcdhd}((X1=X10){\unicdcdcdhd}((X2=X11){\unicdcdcdhd}\\
((X3=X12){\unicdcdcdhd}((X4=X13){\unicdcdcdhd}((X5=X14){\unicdcdcdhd}((X6=X15){\unicdcdcdhd}((X7=X16){\unicdcdcdhd}(X8=X17))))))))))\end{array}
\label{hyp:ggchfgfgpfhgcdpfdgbgehpfed}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {\preoh{{{v1\_xboole\_0}~{({{k1\_tarski}~{X0}})}}}}}\label{hyp:ggdgcdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v5\_cat\_4~(k23\_cat\_4~X0~X1)){\unicdcdcdhd}(l2\_cat\_4~\\
(k23\_cat\_4~X0~X1))\end{array}
\label{hyp:egehpflgcdddpfdgbgehpfed}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{m1\_subset\_1}~{({{k1\_algstr\_1}~{X0}})}}~{({{k1\_tarski}~{X0}})}}}\label{hyp:egehpflgbdpfbgmghgdhehchpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_funct\_1~(k18\_funcop\_1~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~\\
(k18\_funcop\_1~X0~X1)~(k1\_tarski~X0)~(k1\_tarski~X1)){\unicdcdcdhd}(m1\_subset\_1~\\
(k18\_funcop\_1~X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_tarski~X0)~\\
(k1\_tarski~X1)))))\end{array}
\label{hyp:egehpflgbdidpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (v1\_funct\_1~(k17\_funcop\_1~X0~\\
X1~X2)){\unicdcdcdhd}((v1\_funct\_2~(k17\_funcop\_1~X0~X1~X2)~(k2\_zfmisc\_1~(k1\_tarski~\\
X0)~(k1\_tarski~X1))~(k1\_tarski~X2)){\unicdcdcdhd}(m1\_subset\_1~(k17\_funcop\_1~\\
X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_tarski~X0)~\\
(k1\_tarski~X1))~(k1\_tarski~X2)))))\end{array}
\label{hyp:egehpflgbdhdpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k16\_funcop\_1~X0~X1=k7\_funcop\_1~(k1\_tarski~\\
X0)~X1\end{array}
\label{hyp:egjdpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k2\_funcop\_1~X0~X1=k2\_zfmisc\_1~X0~(k1\_tarski~\\
X1)\end{array}
\label{hyp:egcdpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k23\_cat\_4~X0~X1=g2\_cat\_4~(k1\_tarski~X0)~\\
(k1\_tarski~X1)~(k18\_funcop\_1~X1~X0)~(k18\_funcop\_1~X1~X0)~(k17\_funcop\_1~\\
X1~X1~X1)~(k1\_algstr\_1~X0)~(k17\_funcop\_1~X0~X0~X0)~(k17\_funcop\_1~\\
X0~X0~X1)~(k17\_funcop\_1~X0~X0~X1)\end{array}
\label{hyp:egcdfdpfdgbgehpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (X1=k1\_tarski~X0){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}\\
(X2=X0))\end{array}
\label{hyp:egbdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_cat\_4~X0){\unicdbdjdcd}((v5\_cat\_4~X0){\unicdbdjdcd}(X0=g2\_cat\_4~(u1\_struct\_0~\\
X0)~(u4\_struct\_0~X0)~(u1\_graph\_1~X0)~(u2\_graph\_1~X0)~(u1\_cat\_1~\\
X0)~(u5\_cat\_4~X0)~(u6\_cat\_4~X0)~(u7\_cat\_4~X0)~(u8\_cat\_4~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghfdpfdgbgehpfed}
\end{equation}
\begin{theorem}\label{thm:ehedgdpfdgbgehpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
(k23\_cat\_4~X0~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
(k23\_cat\_4~X0~X1))){\unicdbdjdcd}(X2=X3))\end{array}$$
\end{theorem}
\end{document}
