\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{t4\_ens\_1 (TMcUaKSWfPByKpyyGjCniaNHqwhUBBcPWrc)}
\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 $ k1\_ens\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({\preoh{{{v1\_xboole\_0}~{X0}}}})}{\unicdbdjdcd}{({\preoh{{{v1\_xboole\_0}~{({{k2\_ens\_1}~{X0}})}}}})}}}\label{hyp:ggdgcdpffgogdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}(k2\_ens\_1~X0=ReplSep3~(toset~({\uniddcgcg} X1 : \\
\iota .  m1\_subset\_1~X1~X0))~({\uniddcgcg} X1 : \iota .  toset~({\uniddcgcg} X2 : \iota .  m1\_subset\_1~\\
X2~X0))~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  toset~({\uniddcgcg} X3 : \iota .  m1\_subset\_1~\\
X3~(k1\_ens\_1~X0)))~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  ((X2=\\
k1\_xboole\_0){\unicdbdjdcd}(X1=k1\_xboole\_0)){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~\\
X3~X1~X2){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~X2))))))~\\
({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  k1\_domain\_1~(k2\_zfmisc\_1~\\
X0~X0)~(k1\_ens\_1~X0)~(k1\_domain\_1~X0~X0~X1~X2)~X3))\end{array}
\label{hyp:egcdpffgogdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((m1\_subset\_1~X1~X0){\unicdbdjded}\\
(X1 \in X0))){\unicdcdcdhd}((v1\_xboole\_0~X0){\unicdbdjdcd}((m1\_subset\_1~X1~X0){\unicdbdjded}(v1\_xboole\_0~\\
X1)))\end{array}
\label{hyp:egbdpfdhfhcgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedpffgogdhpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k2\_ens\_1~\\
X0)){\unicdbdjdcd}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~(k1\_ens\_1~X0)){\unicdcdcdhd}({\unicdcdaddd} X3 .  \\
(m1\_subset\_1~X3~X0){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~X0){\unicdcdcdhd}((X1=k1\_domain\_1~\\
(k2\_zfmisc\_1~X0~X0)~(k1\_ens\_1~X0)~(k1\_domain\_1~X0~X0~X3~X4)~X2){\unicdcdcdhd}(\\
((X4=k1\_xboole\_0){\unicdbdjdcd}(X3=k1\_xboole\_0)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~X3~X4){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X3~X4)))))))))))\end{array}$$
\end{theorem}
\end{document}
