\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\_funct\_6 (TMP4DzxKEEjv5UFPDHPa13nubYiM1iatBEt)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k1\_funct\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_funct\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (r1\_tarski~X0~X1){\unicdbdjdcd}(r1\_tarski~\\
(k1\_funct\_2~X2~X0)~(k1\_funct\_2~X2~X1))\end{array}
\label{hyp:ehfdgdpfggfhogdgehpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~\\
X2)){\unicdbdjdcd}((k9\_xtuple\_0~X2=k2\_zfmisc\_1~X0~X1){\unicdbdjdcd}((r1\_tarski~(k10\_xtuple\_0~\\
(k1\_funct\_5~X2))~(k1\_funct\_2~X1~(k10\_xtuple\_0~X2))){\unicdcdcdhd}(r1\_tarski~\\
(k10\_xtuple\_0~(k3\_funct\_5~X2))~(k1\_funct\_2~X0~(k10\_xtuple\_0~X2)))))\end{array}
\label{hyp:ehddfdpfggfhogdgehpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~\\
X2)){\unicdbdjdcd}((k9\_xtuple\_0~X2=k2\_zfmisc\_1~X0~X1){\unicdbdjdcd}((k2\_zfmisc\_1~X0~X1=\\
k1\_xboole\_0){\unicdcdcdid}((k9\_xtuple\_0~(k1\_funct\_5~X2)=X0){\unicdcdcdhd}(k9\_xtuple\_0~\\
(k3\_funct\_5~X2)=X1))))\end{array}
\label{hyp:ehcdedpfggfhogdgehpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((r1\_tarski~X0~X1){\unicdcdcdhd}(r1\_tarski~\\
X1~X2)){\unicdbdjdcd}(r1\_tarski~X0~X2)\end{array}
\label{hyp:ehbdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}((v1\_relat\_1~(\\
k3\_funct\_5~X0)){\unicdcdcdhd}(v1\_funct\_1~(k3\_funct\_5~X0)))\end{array}
\label{hyp:egehpflgddpfggfhogdgehpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}((v1\_relat\_1~(\\
k1\_funct\_5~X0)){\unicdcdcdhd}(v1\_funct\_1~(k1\_funct\_5~X0)))\end{array}
\label{hyp:egehpflgbdpfggfhogdgehpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2=k1\_funct\_2~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in X2){\unicdbdjded}({\unicdcdaddd} X4 .  ((v1\_relat\_1~X4){\unicdcdcdhd}(v1\_funct\_1~X4)){\unicdcdcdhd}((X3=\\
X4){\unicdcdcdhd}((k9\_xtuple\_0~X4=X0){\unicdcdcdhd}(r1\_tarski~(k10\_xtuple\_0~X4)~X1)))))\end{array}
\label{hyp:egcdpfggfhogdgehpfcd}
\end{equation}
\begin{theorem}\label{thm:ehbdadpfggfhogdgehpfgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}\\
(v1\_funct\_1~X3)){\unicdbdjdcd}((X3 \in k1\_funct\_2~(k2\_zfmisc\_1~X0~X1)~X2){\unicdbdjdcd}((k2\_zfmisc\_1~\\
X0~X1=k1\_xboole\_0){\unicdcdcdid}((k1\_funct\_5~X3 \in k1\_funct\_2~X0~(k1\_funct\_2~\\
X1~X2)){\unicdcdcdhd}(k3\_funct\_5~X3 \in k1\_funct\_2~X1~(k1\_funct\_2~X0~X2)))))\end{array}$$
\end{theorem}
\end{document}
