\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\_fcont\_2 (TMaWsGSpwyUCpToGn8oV8Fqg4nCZQXzh38P)}
\maketitle
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_fcont\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_seq\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k5\_seq\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_fcont\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}(((r1\_tarski~X0~(k1\_relset\_1~\\
k1\_numbers~X1)){\unicdcdcdhd}(v1\_fcont\_2~(k2\_partfun1~k1\_numbers~k1\_numbers~\\
X1~X0))){\unicdbdjdcd}(v1\_fcont\_1~(k2\_partfun1~k1\_numbers~k1\_numbers~X1~X0)))\end{array}
\label{hyp:ehjdpfggdgpgogehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0 \in X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~X0~X2)\end{array}
\label{hyp:ehedpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
k1\_numbers)){\unicdbdjdcd}(\preoh (X1{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}((r1\_tarski~X1~(k1\_relset\_1~\\
k1\_numbers~X0)){\unicdcdcdhd}((v1\_rcomp\_1~X1){\unicdcdcdhd}((v1\_fcont\_1~(k2\_partfun1~\\
k1\_numbers~k1\_numbers~X0~X1)){\unicdcdcdhd}({\unicdcdadad} X2 .  (v1\_xreal\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(v1\_xreal\_0~X3){\unicdbdjdcd}(\preoh (X2 \in X1){\unicdcdcdhd}((X3 \in X1){\unicdcdcdhd}((k1\_seq\_1~X0~X2=k4\_seq\_4~\\
(k7\_relset\_1~k1\_numbers~k1\_numbers~X0~X1)){\unicdcdcdhd}(k1\_seq\_1~X0~X3=k5\_seq\_4~\\
(k7\_relset\_1~k1\_numbers~k1\_numbers~X0~X1))))))))))))\end{array}
\label{hyp:ehddbdpfggdgpgogehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdddpfggdgpgogehpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
k1\_numbers)){\unicdbdjdcd}(\preoh (X1{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}((r1\_tarski~X1~(k1\_relset\_1~\\
k1\_numbers~X0)){\unicdcdcdhd}((v1\_rcomp\_1~X1){\unicdcdcdhd}((v1\_fcont\_2~(k2\_partfun1~\\
k1\_numbers~k1\_numbers~X0~X1)){\unicdcdcdhd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k1\_numbers){\unicdbdjdcd}(\preoh (X2 \in X1){\unicdcdcdhd}((X3 \in X1){\unicdcdcdhd}\\
((k1\_seq\_1~X0~X2=k4\_seq\_4~(k7\_relset\_1~k1\_numbers~k1\_numbers~\\
X0~X1)){\unicdcdcdhd}(k1\_seq\_1~X0~X3=k5\_seq\_4~(k7\_relset\_1~k1\_numbers~k1\_numbers~\\
X0~X1))))))))))))\end{array}$$
\end{theorem}
\end{document}
