\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{t69\_bvfunc14 (TMdoV4PrYrxHVxuLmP1hGtR3ibcnzd4Bx6G)}
\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 $ k1\_bvfunc\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_eqrel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k7\_enumset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}}}}$ be given.
Let $ k5\_bvfunc\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_partit1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_enumset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_enumset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  {\unicdcdadad} X7 .  {\unicdcdadad} X8 .  k7\_enumset1~X0~X1~X2~X3~X4~X5~X6~\\
X7~X8=k2\_xboole\_0~(k1\_enumset1~X0~X1~X2)~(k4\_enumset1~X3~X4~X5~X6~\\
X7~X8)\end{array}
\label{hyp:ehhdjdpffgogfhngdhfgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_bvfunc\_2~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_eqrel\_1~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_eqrel\_1~X3~X0){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_eqrel\_1~X4~X0){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
(m1\_eqrel\_1~X5~X0){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_eqrel\_1~X6~X0){\unicdbdjdcd}({\unicdcdadad} X7 .  \\
(m1\_eqrel\_1~X7~X0){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_eqrel\_1~X8~X0){\unicdbdjdcd}({\unicdcdadad} X9 .  \\
(m1\_eqrel\_1~X9~X0){\unicdbdjdcd}({\unicdcdadad} X10 .  (m1\_eqrel\_1~X10~X0){\unicdbdjdcd}((X1=k7\_enumset1~\\
X2~X3~X4~X5~X6~X7~X8~X9~X10){\unicdbdjdcd}((X2=X3){\unicdcdcdid}((X2=X4){\unicdcdcdid}((X2=X5){\unicdcdcdid}((X2=X6){\unicdcdcdid}\\
((X2=X7){\unicdcdcdid}((X2=X8){\unicdcdcdid}((X2=X9){\unicdcdcdid}((X2=X10){\unicdcdcdid}((X3=X4){\unicdcdcdid}((X3=X5){\unicdcdcdid}\\
((X3=X6){\unicdcdcdid}((X3=X7){\unicdcdcdid}((X3=X8){\unicdcdcdid}((X3=X9){\unicdcdcdid}((X3=X10){\unicdcdcdid}((X4=X5){\unicdcdcdid}\\
((X4=X6){\unicdcdcdid}((X4=X7){\unicdcdcdid}((X4=X8){\unicdcdcdid}((X4=X9){\unicdcdcdid}((X4=X10){\unicdcdcdid}((X5=X6){\unicdcdcdid}\\
((X5=X7){\unicdcdcdid}((X5=X8){\unicdcdcdid}((X5=X9){\unicdcdcdid}((X5=X10){\unicdcdcdid}((X6=X7){\unicdcdcdid}((X6=X8){\unicdcdcdid}\\
((X6=X9){\unicdcdcdid}((X6=X10){\unicdcdcdid}((X7=X8){\unicdcdcdid}((X7=X9){\unicdcdcdid}((X7=X10){\unicdcdcdid}((X8=X9){\unicdcdcdid}\\
((X8=X10){\unicdcdcdid}((X9=X10){\unicdcdcdid}(k5\_bvfunc\_2~X0~X3~X1=k2\_partit1~X0~(k2\_partit1~\\
X0~(k2\_partit1~X0~(k2\_partit1~X0~(k2\_partit1~X0~(k2\_partit1~X0~(\\
k2\_partit1~X0~X2~X4)~X5)~X6)~X7)~X8)~X9)~X10))))))))))))))))))))))))))))))))))))))))))))))))\end{array}
\label{hyp:ehgdidpfcgghggfhogdgbded}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k1\_enumset1~X0~X1~X2=k2\_xboole\_0~\\
(k1\_tarski~X0)~(k2\_tarski~X1~X2)\end{array}
\label{hyp:ehcdpffgogfhngdhfgehbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_tarski}~{X0}}~{X1}}={{{k2\_tarski}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfehbgchdhlgjg}
\end{equation}
\begin{theorem}\label{thm:ehgdjdpfcgghggfhogdgbded}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_bvfunc\_2~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_eqrel\_1~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_eqrel\_1~X3~X0){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_eqrel\_1~X4~X0){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
(m1\_eqrel\_1~X5~X0){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_eqrel\_1~X6~X0){\unicdbdjdcd}({\unicdcdadad} X7 .  \\
(m1\_eqrel\_1~X7~X0){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_eqrel\_1~X8~X0){\unicdbdjdcd}({\unicdcdadad} X9 .  \\
(m1\_eqrel\_1~X9~X0){\unicdbdjdcd}({\unicdcdadad} X10 .  (m1\_eqrel\_1~X10~X0){\unicdbdjdcd}((X1=k7\_enumset1~\\
X2~X3~X4~X5~X6~X7~X8~X9~X10){\unicdbdjdcd}((X2=X3){\unicdcdcdid}((X2=X4){\unicdcdcdid}((X2=X5){\unicdcdcdid}((X2=X6){\unicdcdcdid}\\
((X2=X7){\unicdcdcdid}((X2=X8){\unicdcdcdid}((X2=X9){\unicdcdcdid}((X2=X10){\unicdcdcdid}((X3=X4){\unicdcdcdid}((X3=X5){\unicdcdcdid}\\
((X3=X6){\unicdcdcdid}((X3=X7){\unicdcdcdid}((X3=X8){\unicdcdcdid}((X3=X9){\unicdcdcdid}((X3=X10){\unicdcdcdid}((X4=X5){\unicdcdcdid}\\
((X4=X6){\unicdcdcdid}((X4=X7){\unicdcdcdid}((X4=X8){\unicdcdcdid}((X4=X9){\unicdcdcdid}((X4=X10){\unicdcdcdid}((X5=X6){\unicdcdcdid}\\
((X5=X7){\unicdcdcdid}((X5=X8){\unicdcdcdid}((X5=X9){\unicdcdcdid}((X5=X10){\unicdcdcdid}((X6=X7){\unicdcdcdid}((X6=X8){\unicdcdcdid}\\
((X6=X9){\unicdcdcdid}((X6=X10){\unicdcdcdid}((X7=X8){\unicdcdcdid}((X7=X9){\unicdcdcdid}((X7=X10){\unicdcdcdid}((X8=X9){\unicdcdcdid}\\
((X8=X10){\unicdcdcdid}((X9=X10){\unicdcdcdid}(k5\_bvfunc\_2~X0~X4~X1=k2\_partit1~X0~(k2\_partit1~\\
X0~(k2\_partit1~X0~(k2\_partit1~X0~(k2\_partit1~X0~(k2\_partit1~X0~(\\
k2\_partit1~X0~X2~X3)~X5)~X6)~X7)~X8)~X9)~X10))))))))))))))))))))))))))))))))))))))))))))))))\end{array}$$
\end{theorem}
\end{document}
