\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{t72\_mcart\_1 (TMU7WptrRRtb4YqvhjNYpcW2Qy7agvcNqRr)}
\maketitle
Let $ v1\_xboole\_0 : {{\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 $ k3\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  \preoh (X0 \in k3\_zfmisc\_1~\\
X1~X2~X3){\unicdcdcdhd}({\unicdcdadad} X4 .  {\unicdcdadad} X5 .  {\unicdcdadad} X6 .  \preoh (X4 \in X1){\unicdcdcdhd}((X5 \in X2){\unicdcdcdhd}\\
((X6 \in X3){\unicdcdcdhd}(X0=k3\_xtuple\_0~X4~X5~X6))))\end{array}
\label{hyp:ehgdidpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k3\_zfmisc\_1~\\
X0~X1~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  {\unicdcdadad} X5 .  {\unicdcdadad} X6 .  (X3=k3\_xtuple\_0~\\
X4~X5~X6){\unicdbdjdcd}((k1\_mcart\_1~X0~X1~X2~X3=X4){\unicdcdcdhd}((k2\_mcart\_1~X0~X1~X2~X3=X5){\unicdcdcdhd}\\
(k3\_mcart\_1~X0~X1~X2~X3=X6)))))))\end{array}
\label{hyp:ehgdedpfngdgbgchehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehhdcdpfngdgbgchehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~\\
X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((\preoh v1\_xboole\_0~\\
X5){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~X2))){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~\\
X6~(k3\_zfmisc\_1~X0~X1~X2)){\unicdbdjdcd}((X6 \in k3\_zfmisc\_1~X3~X4~X5){\unicdbdjdcd}((k1\_mcart\_1~\\
X0~X1~X2~X6 \in X3){\unicdcdcdhd}((k2\_mcart\_1~X0~X1~X2~X6 \in X4){\unicdcdcdhd}(k3\_mcart\_1~X0~X1~X2~\\
X6 \in X5))))))))))\end{array}$$
\end{theorem}
\end{document}
