\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{t6\_catalg\_1 (TMNMryo62AiWY5RHQHZk9XspSfBZZzhtcB6)}
\maketitle
Let $ v3\_catalg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_catalg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_msualg\_1~X0){\unicdbdjdcd}((v3\_catalg\_1~X0){\unicdbdjded}({\unicdcdaddd} X1 .  (\\
(v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~k5\_numbers~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k5\_numbers))))){\unicdcdcdhd}(({\unicdcdadad} X2 .  \\
\preoh (X2 \in u1\_struct\_0~X0){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k5\_numbers){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  ((v1\_relat\_1~X4){\unicdcdcdhd}((v1\_funct\_1~X4){\unicdcdcdhd}(v1\_finseq\_1~\\
X4))){\unicdbdjdcd}(\preoh (X2=k4\_tarski~X3~X4){\unicdcdcdhd}((k3\_finseq\_1~X4=k3\_funct\_2~k5\_numbers~\\
k5\_numbers~X1~X3){\unicdcdcdhd}(r1\_tarski~(k2\_zfmisc\_1~(k1\_tarski~X3)~(k4\_finseq\_2~\\
(k3\_funct\_2~k5\_numbers~k5\_numbers~X1~X3)~(k4\_catalg\_1~X0)))~(u1\_struct\_0~\\
X0))))))){\unicdcdcdhd}({\unicdcdadad} X2 .  \preoh (X2 \in u4\_struct\_0~X0){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_relat\_1~X4){\unicdcdcdhd}((v1\_funct\_1~X4){\unicdcdcdhd}\\
(v1\_finseq\_1~X4))){\unicdbdjdcd}(\preoh (X2=k4\_tarski~X3~X4){\unicdcdcdhd}((k3\_finseq\_1~X4=\\
k3\_funct\_2~k5\_numbers~k5\_numbers~X1~X3){\unicdcdcdhd}(r1\_tarski~(k2\_zfmisc\_1~\\
(k1\_tarski~X3)~(k4\_finseq\_2~(k3\_funct\_2~k5\_numbers~k5\_numbers~\\
X1~X3)~(k4\_catalg\_1~X0)))~(u4\_struct\_0~X0))))))))))\end{array}
\label{hyp:eghdpfdgbgehbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_msualg\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (X1=k4\_catalg\_1~X0){\unicdbdjded}\\
({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}({\unicdcdaddd} X3 .  {\unicdcdaddd} X4 .  ((v1\_relat\_1~X4){\unicdcdcdhd}\\
(v1\_funct\_1~X4)){\unicdcdcdhd}((k4\_tarski~X3~X4 \in k2\_xboole\_0~(u1\_struct\_0~\\
X0)~(u4\_struct\_0~X0)){\unicdcdcdhd}(X2 \in k10\_xtuple\_0~X4)))))\end{array}
\label{hyp:eggdpfdgbgehbgmghgpfbd}
\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 .  (r1\_tarski~X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X0){\unicdbdjdcd}\\
(X2 \in X1))\end{array}
\label{hyp:egddpfehbgchdhlgjg}
\end{equation}
\begin{theorem}\label{thm:ehgdpfdgbgehbgmghgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_catalg\_1~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
\preoh ((X1 \in u1\_struct\_0~X0){\unicdcdcdid}(X1 \in u4\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}\\
(v1\_finseq\_1~X3))){\unicdbdjdcd}(\preoh (X1=k4\_tarski~X2~X3){\unicdcdcdhd}(r1\_tarski~(k10\_xtuple\_0~\\
X3)~(k4\_catalg\_1~X0))))))\end{array}$$
\end{theorem}
\end{document}
