\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{t56\_rewrite3 (TMGuCb4mCYmTpmbJRKpR3iT6rVSLycFCoMi)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k8\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_zfmisc\_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 $ m1\_rewrite1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_rewrite3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_rewrite3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ k1\_flang\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
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~\\
(k8\_afinsq\_1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}(l1\_rewrite3~\\
X2~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_rewrite1~X3~(k1\_rewrite3~X0~X1~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(v7\_ordinal1~X4){\unicdbdjdcd}(\preoh (X4 \in k4\_finseq\_1~X3){\unicdcdcdhd}((k2\_xcmplx\_0~X4~np\_\_1 \in \\
k4\_finseq\_1~X3){\unicdcdcdhd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(k8\_afinsq\_1~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(k8\_afinsq\_1~X0)){\unicdbdjdcd}(\preoh (X5=k2\_xtuple\_0~\\
(k1\_funct\_1~X3~(k2\_xcmplx\_0~X4~np\_\_1))){\unicdcdcdhd}((r1\_rewrite3~X1~X2~(k1\_xtuple\_0~\\
(k1\_funct\_1~X3~X4))~X6~(k1\_xtuple\_0~(k1\_funct\_1~X3~(k2\_xcmplx\_0~\\
X4~np\_\_1)))){\unicdcdcdhd}(k2\_xtuple\_0~(k1\_funct\_1~X3~X4)=k1\_flang\_1~X0~X6~\\
X5)))))))))))\end{array}
\label{hyp:ehfdfdpfchfghhchjgehfgdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{k2\_xtuple\_0}~{({{{k4\_tarski}~{X0}}~{X1}})}}={X1}}}}\label{hyp:chegcdpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{k1\_xtuple\_0}~{({{{k4\_tarski}~{X0}}~{X1}})}}={X0}}}}\label{hyp:chegbdpfihehfhahmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehfdgdpfchfghhchjgehfgdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(k8\_afinsq\_1~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(k8\_afinsq\_1~X2)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(k1\_zfmisc\_1~(\\
k8\_afinsq\_1~X2))){\unicdbdjdcd}({\unicdcdadad} X6 .  ((\preoh v2\_struct\_0~X6){\unicdcdcdhd}(l1\_rewrite3~\\
X6~X5)){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_rewrite1~X7~(k1\_rewrite3~X2~X5~X6)){\unicdbdjdcd}({\unicdcdadad} X8 .  \\
(v7\_ordinal1~X8){\unicdbdjdcd}(\preoh (X8 \in k4\_finseq\_1~X7){\unicdcdcdhd}((k2\_xcmplx\_0~X8~np\_\_1 \in \\
k4\_finseq\_1~X7){\unicdcdcdhd}((k1\_funct\_1~X7~X8=k4\_tarski~X0~X3){\unicdcdcdhd}((k1\_funct\_1~\\
X7~(k2\_xcmplx\_0~X8~np\_\_1)=k4\_tarski~X1~X4){\unicdcdcdhd}({\unicdcdadad} X9 .  (m1\_subset\_1~\\
X9~(k8\_afinsq\_1~X2)){\unicdbdjdcd}(\preoh (r1\_rewrite3~X5~X6~X0~X9~X1){\unicdcdcdhd}(X3=k1\_flang\_1~\\
X2~X9~X4)))))))))))))\end{array}$$
\end{theorem}
\end{document}
