\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{t19\_rewrite3 (TMauSY8MmRjtj3YYc7Ev1a1bAf3tN34jUXF)}
\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\_rewrite3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ k1\_flang\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r1\_struct\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_rewrite3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_flang\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (l1\_rewrite3~\\
X4~X0){\unicdbdjdcd}((r1\_rewrite3~X0~X4~X1~X2~X3){\unicdbdjdcd}((r1\_struct\_0~X4~X1){\unicdcdcdhd}((X2 \in \\
X0){\unicdcdcdhd}((r1\_struct\_0~X4~X3){\unicdcdcdhd}((X1 \in k9\_xtuple\_0~(k9\_xtuple\_0~(u1\_rewrite3~\\
X0~X4))){\unicdcdcdhd}((X2 \in k10\_xtuple\_0~(k9\_xtuple\_0~(u1\_rewrite3~X0~X4))){\unicdcdcdhd}\\
(X3 \in k10\_xtuple\_0~(u1\_rewrite3~X0~X4))))))))\end{array}
\label{hyp:ehbdfdpfchfghhchjgehfgdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{l1\_rewrite3}~{X1}}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X1}})}}}}\label{hyp:egehpfmgbdpfchfghhchjgehfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_struct\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (r1\_struct\_0~X0~X1){\unicdbdjded}\\
(X1 \in u1\_struct\_0~X0))\end{array}
\label{hyp:egfdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (l1\_rewrite3~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  \\
{\unicdcdadad} X4 .  (r1\_rewrite3~X0~X1~X2~X3~X4){\unicdbdjded}(k4\_tarski~(k4\_tarski~X2~\\
X3)~X4 \in u1\_rewrite3~X0~X1))\end{array}
\label{hyp:egcdpfchfghhchjgehfgdd}
\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~\\
(k8\_afinsq\_1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (l1\_rewrite3~X2~X1){\unicdbdjdcd}((v2\_rewrite3~\\
X2~X0~X1){\unicdbdjded}(((v1\_relat\_1~(u1\_rewrite3~X1~X2)){\unicdcdcdhd}(v1\_funct\_1~(u1\_rewrite3~\\
X1~X2))){\unicdcdcdhd}((\preoh k2\_flang\_1~X0 \in k10\_xtuple\_0~(k9\_xtuple\_0~(u1\_rewrite3~\\
X1~X2))){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(k8\_afinsq\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~\\
(k8\_afinsq\_1~X0)){\unicdbdjdcd}(((k4\_tarski~X3~X4 \in k9\_xtuple\_0~(u1\_rewrite3~\\
X1~X2)){\unicdcdcdhd}(k4\_tarski~X3~X5 \in k9\_xtuple\_0~(u1\_rewrite3~X1~X2))){\unicdbdjdcd}((\\
X4=X5){\unicdcdcdid}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(k8\_afinsq\_1~X0)){\unicdbdjdcd}((k1\_flang\_1~\\
X0~X4~X6{\unicdcdgdad}X5){\unicdcdcdhd}(k1\_flang\_1~X0~X5~X6{\unicdcdgdad}X4)))))))))))))\end{array}
\label{hyp:egbdpfchfghhchjgehfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (X1=k9\_xtuple\_0~X0){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}\\
({\unicdcdaddd} X3 .  k4\_tarski~X2~X3 \in X0))\end{array}
\label{hyp:egbdcdpfihehfhahmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehbdjdpfchfghhchjgehfgdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (\preoh v1\_xboole\_0~X3){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k8\_afinsq\_1~X3)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~(k8\_afinsq\_1~X3)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(k1\_zfmisc\_1~\\
(k8\_afinsq\_1~X3))){\unicdbdjdcd}({\unicdcdadad} X7 .  ((v2\_rewrite3~X7~X3~X6){\unicdcdcdhd}(l1\_rewrite3~\\
X7~X6)){\unicdbdjdcd}(((r1\_rewrite3~X6~X7~X0~X4~X1){\unicdcdcdhd}(r1\_rewrite3~X6~X7~X0~X5~X2)){\unicdbdjdcd}\\
((X4=X5){\unicdcdcdid}({\unicdcdadad} X8 .  (m1\_subset\_1~X8~(k8\_afinsq\_1~X3)){\unicdbdjdcd}((k1\_flang\_1~\\
X3~X4~X8{\unicdcdgdad}X5){\unicdcdcdhd}(k1\_flang\_1~X3~X5~X8{\unicdcdgdad}X4)))))))))\end{array}$$
\end{theorem}
\end{document}
