\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{t57\_rewrite3 (TMGTweo8YMicqVVBDjfv3ZMCn4q9gVDafeT)}
\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 $ k8\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_rewrite3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_rewrite3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ m1\_rewrite1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k10\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_flang\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_rewrite3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_catalan2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (v1\_relat\_1~X2){\unicdbdjdcd}((m1\_rewrite1~\\
(k10\_finseq\_1~X0~X1)~X2){\unicdbdjdcd}(k4\_tarski~X0~X1 \in X2))\end{array}
\label{hyp:ehidpfchfghhchjgehfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (k4\_tarski~\\
X1~X2 \in X0){\unicdbdjdcd}(m1\_rewrite1~(k10\_finseq\_1~X1~X2)~X0))\end{array}
\label{hyp:ehhdpfchfghhchjgehfgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (\preoh v1\_xboole\_0~X3){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_zfmisc\_1~(k8\_afinsq\_1~X3))){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  ((\preoh v2\_struct\_0~X5){\unicdcdcdhd}(l1\_rewrite3~X5~X4)){\unicdbdjdcd}((r1\_rewrite3~\\
X4~X5~X0~X1~X2){\unicdbdjded}(k4\_tarski~(k4\_tarski~X0~X1)~(k4\_tarski~X2~(k2\_flang\_1~\\
X3)) \in k1\_rewrite3~X3~X4~X5))))\end{array}
\label{hyp:ehddhdpfchfghhchjgehfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k8\_afinsq\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((\preoh v2\_struct\_0~\\
X3){\unicdcdcdhd}(l1\_rewrite3~X3~X2)){\unicdbdjdcd}(\preoh (X0 \in k1\_rewrite3~X1~X2~X3){\unicdcdcdhd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(u1\_struct\_0~X3)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~\\
(u1\_struct\_0~X3)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(k8\_afinsq\_1~X1)){\unicdbdjdcd}\\
({\unicdcdadad} X7 .  (m1\_subset\_1~X7~(k8\_afinsq\_1~X1)){\unicdbdjdcd}(X0{\unicdcdgdad}k4\_tarski~\\
(k4\_tarski~X4~X6)~(k4\_tarski~X5~X7)))))))))\end{array}
\label{hyp:ehddddpfchfghhchjgehfgdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k3\_catalan2}~{X0}}={{k8\_afinsq\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfdgbgehbgmgbgogcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjded}({\unicdcdadad} X1 .  \preoh (X1 \in X0){\unicdcdcdhd}({\unicdcdadad} X2 .  \\
{\unicdcdadad} X3 .  X1{\unicdcdgdad}k4\_tarski~X2~X3))\end{array}
\label{hyp:egbdpfchfgmgbgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehfdhdpfchfghhchjgehfgdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (\preoh v1\_xboole\_0~X3){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_zfmisc\_1~(k8\_afinsq\_1~X3))){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  ((\preoh v2\_struct\_0~X5){\unicdcdcdhd}(l1\_rewrite3~X5~X4)){\unicdbdjdcd}((r1\_rewrite3~\\
X4~X5~X0~X1~X2){\unicdbdjded}(m1\_rewrite1~(k10\_finseq\_1~(k4\_tarski~X0~X1)~(k4\_tarski~\\
X2~(k2\_flang\_1~X3)))~(k1\_rewrite3~X3~X4~X5)))))\end{array}$$
\end{theorem}
\end{document}
