\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t27\_funct\_5 (TMKT285yeaXfuMw5vcuB7kYxmBsdz4JVx1s)}
\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\_xboole\_0 : {\iota}$ be given.
Let $ k3\_funct\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\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){\unicdbdjdcd}(((k9\_xtuple\_0~X0=k1\_xboole\_0){\unicdcdcdid}\\
(k10\_xtuple\_0~X0=k1\_xboole\_0)){\unicdbdjdcd}(X0=k1\_xboole\_0))\end{array}
\label{hyp:ehedbdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}(k9\_xtuple\_0~(\\
k3\_funct\_5~X0)=k10\_xtuple\_0~(k9\_xtuple\_0~X0))\end{array}
\label{hyp:ehcdddpfggfhogdgehpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \preoh k4\_tarski~X1~X2 \in X0){\unicdbdjdcd}((k9\_xtuple\_0~\\
X0=k1\_xboole\_0){\unicdcdcdhd}(k10\_xtuple\_0~X0=k1\_xboole\_0))\end{array}
\label{hyp:ehbdedpfggfhogdgehpffd}
\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){\unicdbdjded}({\unicdcdadad} X1 .  \preoh (X1 \in X0){\unicdcdcdhd}({\unicdcdadad} X2 .  \\
{\unicdcdadad} X3 .  X1{\unicdcdgdad}k4\_tarski~X2~X3))\end{array}
\label{hyp:egbdpfchfgmgbgehpfbd}
\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 .  (v1\_funct\_1~X0){\unicdbdjded}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  \\
((k4\_tarski~X1~X2 \in X0){\unicdcdcdhd}(k4\_tarski~X1~X3 \in X0)){\unicdbdjdcd}(X2=X3))\end{array}
\label{hyp:egbdpfggfhogdgehpfbd}
\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:ehcdhdpfggfhogdgehpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}(({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \\
\preoh k4\_tarski~X1~X2 \in k9\_xtuple\_0~X0){\unicdbdjdcd}((k1\_funct\_5~X0=k1\_xboole\_0){\unicdcdcdhd}\\
(k3\_funct\_5~X0=k1\_xboole\_0)))\end{array}$$
\end{theorem}
\end{document}
