\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=}
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\newcommand\unicdcdbdgd{\setminus}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
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\newcommand\unicdcdcdhd{\land}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t19\_funct\_5 (TMEtbrM4nNissYCzz5ttDA9vgFbCEmQ8ozC)}
\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\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ k1\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
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 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}((X1=k1\_funct\_5~X0){\unicdbdjded}((k9\_xtuple\_0~\\
X1=k9\_xtuple\_0~(k9\_xtuple\_0~X0)){\unicdcdcdhd}({\unicdcdadad} X2 .  \preoh (X2 \in k9\_xtuple\_0~\\
(k9\_xtuple\_0~X0)){\unicdcdcdhd}({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}(v1\_funct\_1~\\
X3)){\unicdbdjdcd}(\preoh (k1\_funct\_1~X1~X2=X3){\unicdcdcdhd}((k9\_xtuple\_0~X3=k10\_xtuple\_0~\\
(k3\_xboole\_0~(k9\_xtuple\_0~X0)~(k2\_zfmisc\_1~(k1\_tarski~X2)~(k10\_xtuple\_0~\\
(k9\_xtuple\_0~X0))))){\unicdcdcdhd}({\unicdcdadad} X4 .  (X4 \in k9\_xtuple\_0~X3){\unicdbdjdcd}(k1\_funct\_1~\\
X3~X4=k1\_binop\_1~X0~X2~X4)))))))))\end{array}
\label{hyp:egbdpfggfhogdgehpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (X1=k9\_xtuple\_0~X0){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}\\
({\unicdcdaddd} X3 .  k4\_tarski~X2~X3 \in X0))\end{array}
\label{hyp:egbdcdpfihehfhahmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehbdjdpfggfhogdgehpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~\\
X2)){\unicdbdjdcd}((k4\_tarski~X0~X1 \in k9\_xtuple\_0~X2){\unicdbdjdcd}((X0 \in k9\_xtuple\_0~(k1\_funct\_5~\\
X2)){\unicdcdcdhd}((v1\_relat\_1~(k1\_funct\_1~(k1\_funct\_5~X2)~X0)){\unicdcdcdhd}(v1\_funct\_1~\\
(k1\_funct\_1~(k1\_funct\_5~X2)~X0)))))\end{array}$$
\end{theorem}
\end{document}
