\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{t13\_ens\_1 (TMZHqTJr7wC89Ku7fwVxG9KVM287bcZFHkx)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_ens\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_ens\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_ens\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_ens\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_relat\_1~X2){\unicdbdjdcd}(k3\_relat\_1~(k3\_relat\_1~X0~X1)~X2=k3\_relat\_1~\\
X0~(k3\_relat\_1~X1~X2))))\end{array}
\label{hyp:ehddgdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k2\_ens\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k2\_ens\_1~X0)){\unicdbdjdcd}((k3\_ens\_1~X0~\\
X1=k4\_ens\_1~X0~X2){\unicdbdjdcd}((k2\_xtuple\_0~(k6\_ens\_1~X0~X2~X1)=k3\_relat\_1~\\
(k2\_xtuple\_0~X2)~(k2\_xtuple\_0~X1)){\unicdcdcdhd}((k3\_ens\_1~X0~(k6\_ens\_1~X0~\\
X2~X1)=k3\_ens\_1~X0~X2){\unicdcdcdhd}(k4\_ens\_1~X0~(k6\_ens\_1~X0~X2~X1)=k4\_ens\_1~\\
X0~X1))))))\end{array}
\label{hyp:ehbdcdpffgogdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k2\_ens\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k2\_ens\_1~X0)){\unicdbdjdcd}(((k2\_xtuple\_0~\\
X1=k2\_xtuple\_0~X2){\unicdcdcdhd}((k3\_ens\_1~X0~X1=k3\_ens\_1~X0~X2){\unicdcdcdhd}(k4\_ens\_1~\\
X0~X1=k4\_ens\_1~X0~X2))){\unicdbdjdcd}(X1=X2))))\end{array}
\label{hyp:mgbdedpffgogdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k2\_ens\_1~\\
X0))){\unicdbdjdcd}((v1\_relat\_1~(k2\_xtuple\_0~X1)){\unicdcdcdhd}(v1\_funct\_1~(k2\_xtuple\_0~\\
X1)))\end{array}
\label{hyp:ggdgddpffgogdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~(k2\_ens\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k2\_ens\_1~X0)))){\unicdbdjdcd}(m1\_subset\_1~\\
(k6\_ens\_1~X0~X1~X2)~(k2\_ens\_1~X0))\end{array}
\label{hyp:egehpflggdpffgogdhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdddpffgogdhpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k2\_ens\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k2\_ens\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(k2\_ens\_1~X0)){\unicdbdjdcd}(((k3\_ens\_1~X0~X1=k4\_ens\_1~X0~X2){\unicdcdcdhd}\\
(k3\_ens\_1~X0~X3=k4\_ens\_1~X0~X1)){\unicdbdjdcd}(k6\_ens\_1~X0~(k6\_ens\_1~X0~X2~X1)~\\
X3=k6\_ens\_1~X0~X2~(k6\_ens\_1~X0~X1~X3))))))\end{array}$$
\end{theorem}
\end{document}
