\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{t23\_funct\_6 (TMHe8BWp7p3FYZmtm3KsQdr1RXmSVTojk9g)}
\maketitle
Let $ k2\_funct\_6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k3\_funct\_6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k8\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{\preoh{{({{X0} \in {X1}})}}}{\unicdcdcdhd}{({{v1\_xboole\_0}~{X1}})}}}}\label{hyp:ehhdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(k9\_xtuple\_0~k1\_xboole\_0=k1\_xboole\_0){\unicdcdcdhd}(k10\_xtuple\_0~k1\_xboole\_0=\\
k1\_xboole\_0)\end{array}
\label{hyp:ehddidpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{k1\_xboole\_0}}\label{hyp:ggdgbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \\
(X2=k8\_relat\_1~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  (X3 \in X2){\unicdbdjded}((X3 \in k9\_xtuple\_0~\\
X0){\unicdcdcdhd}(k1\_funct\_1~X0~X3 \in X1))))\end{array}
\label{hyp:eghdpfggfhogdgehpfbd}
\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=k3\_funct\_6~X0){\unicdbdjded}((k9\_xtuple\_0~\\
X1=k8\_relat\_1~X0~(k1\_funct\_6~(k10\_xtuple\_0~X0))){\unicdcdcdhd}({\unicdcdadad} X2 .  \\
(X2 \in k8\_relat\_1~X0~(k1\_funct\_6~(k10\_xtuple\_0~X0))){\unicdbdjdcd}(k1\_funct\_1~\\
X1~X2=k10\_xtuple\_0~(k1\_funct\_1~X0~X2))))))\end{array}
\label{hyp:egddpfggfhogdgehpfgd}
\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=k2\_funct\_6~X0){\unicdbdjded}((k9\_xtuple\_0~\\
X1=k8\_relat\_1~X0~(k1\_funct\_6~(k10\_xtuple\_0~X0))){\unicdcdcdhd}({\unicdcdadad} X2 .  \\
(X2 \in k8\_relat\_1~X0~(k1\_funct\_6~(k10\_xtuple\_0~X0))){\unicdbdjdcd}(k1\_funct\_1~\\
X1~X2=k9\_xtuple\_0~(k1\_funct\_1~X0~X2))))))\end{array}
\label{hyp:egcdpfggfhogdgehpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (X1=k1\_funct\_6~X0){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}\\
((X2 \in X0){\unicdcdcdhd}((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~X2))))\end{array}
\label{hyp:egbdpfggfhogdgehpfgd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_relat\_1}~{X0}})}}}\label{hyp:dgdgbdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_funct\_1}~{X0}})}}}\label{hyp:dgdgbdpfggfhogdgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdddpfggfhogdgehpfgd}
$$\begin{array}{c}(k2\_funct\_6~k1\_xboole\_0=k1\_xboole\_0){\unicdcdcdhd}(k3\_funct\_6~k1\_xboole\_0=\\
k1\_xboole\_0)\end{array}$$
\end{theorem}
\end{document}
