\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{l60\_funct\_6 (TMQXvKPUMkkZnjqPZdjnTqB4ta4eyvPJGVL)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_xboole\_0 : {{\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 $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~X2)){\unicdbdjdcd}(((X0 \in k9\_xtuple\_0~(k1\_funct\_5~\\
X1)){\unicdcdcdhd}(X2=k1\_funct\_1~(k1\_funct\_5~X1)~X0)){\unicdbdjdcd}((k9\_xtuple\_0~X2=k10\_xtuple\_0~\\
(k3\_xboole\_0~(k9\_xtuple\_0~X1)~(k2\_zfmisc\_1~(k1\_tarski~X0)~(k10\_xtuple\_0~\\
(k9\_xtuple\_0~X1))))){\unicdcdcdhd}((r1\_tarski~(k9\_xtuple\_0~X2)~(k10\_xtuple\_0~\\
(k9\_xtuple\_0~X1))){\unicdcdcdhd}((r1\_tarski~(k10\_xtuple\_0~X2)~(k10\_xtuple\_0~\\
X1)){\unicdcdcdhd}({\unicdcdadad} X3 .  (X3 \in k9\_xtuple\_0~X2){\unicdbdjdcd}((k1\_funct\_1~X2~X3=k1\_binop\_1~\\
X1~X0~X3){\unicdcdcdhd}(k4\_tarski~X0~X3 \in k9\_xtuple\_0~X1))))))))\end{array}
\label{hyp:ehddbdpfggfhogdgehpffd}
\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}((k4\_tarski~X0~X1 \in k9\_xtuple\_0~X2){\unicdbdjdcd}((X0 \in k9\_xtuple\_0~(k1\_funct\_5~\\
X2)){\unicdcdcdhd}((v1\_relat\_1~(k1\_funct\_1~(k1\_funct\_5~X2)~X0)){\unicdcdcdhd}(v1\_funct\_1~\\
(k1\_funct\_1~(k1\_funct\_5~X2)~X0)))))\end{array}
\label{hyp:ehbdjdpfggfhogdgehpffd}
\end{equation}
\begin{theorem}\label{thm:mggdadpfggfhogdgehpfgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}\\
(v1\_funct\_1~X3)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_relat\_1~X4){\unicdcdcdhd}(v1\_funct\_1~X4)){\unicdbdjdcd}\\
(((k4\_tarski~X0~X1 \in k9\_xtuple\_0~X3){\unicdcdcdhd}((X4=k1\_funct\_1~(k1\_funct\_5~\\
X3)~X0){\unicdcdcdhd}(X2 \in k9\_xtuple\_0~X4))){\unicdbdjdcd}(k4\_tarski~X0~X2 \in k9\_xtuple\_0~X3)))\end{array}$$
\end{theorem}
\end{document}
