\documentclass{article}
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\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t43\_ndiff\_5 (TMWf85Y2yS2mm4XF91A3B1QwQJ9qxc3m4hJ)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_prvect\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_ndiff\_5 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_prvect\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_card\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_prvect\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(k4\_card\_3~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k4\_card\_3~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  m1\_subset\_1~(k1\_funct\_4~X1~(k5\_relat\_1~X2~X3))~(k4\_card\_3~\\
X0))))\end{array}
\label{hyp:ehhdjdpfdgbgchegpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v2\_relat\_1~\\
X0){\unicdcdcdhd}(v1\_funct\_1~X0))){\unicdcdcdhd}(m1\_subset\_1~X1~(k4\_card\_3~X0))){\unicdbdjdcd}(k11\_card\_3~\\
X0~X1~X2=k5\_relat\_1~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdbdpfdgbgchegpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((v1\_finseq\_1~X0){\unicdcdcdhd}(v1\_prvect\_2~X0))))){\unicdbdjdcd}((v1\_relat\_1~(k4\_prvect\_2~\\
X0)){\unicdcdcdhd}((v2\_relat\_1~(k4\_prvect\_2~X0)){\unicdcdcdhd}((v1\_funct\_1~(k4\_prvect\_2~\\
X0)){\unicdcdcdhd}((\preoh v1\_xboole\_0~(k4\_prvect\_2~X0)){\unicdcdcdhd}(v1\_finseq\_1~(k4\_prvect\_2~\\
X0))))))\end{array}
\label{hyp:egehpflgedpfahchghfgdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_finseq\_1~\\
X0){\unicdcdcdhd}(v2\_prvect\_2~X0)))){\unicdbdjdcd}((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}\\
((v1\_finseq\_1~X0){\unicdcdcdhd}(v1\_prvect\_2~X0))))\end{array}
\label{hyp:dgdgcdpfahchghfgdgehpfcd}
\end{equation}
\begin{theorem}\label{thm:ehedddpfogegjgggggpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finseq\_1~X0){\unicdcdcdhd}((v2\_prvect\_2~X0){\unicdcdcdhd}(v1\_ndiff\_5~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k4\_card\_3~(k4\_prvect\_2~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k4\_card\_3~(k4\_prvect\_2~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  m1\_subset\_1~\\
(k1\_funct\_4~X1~(k11\_card\_3~(k4\_prvect\_2~X0)~X2~X3))~(k4\_card\_3~\\
(k4\_prvect\_2~X0)))))\end{array}$$
\end{theorem}
\end{document}
