\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{t41\_rewrite3 (TMaZY9TJpAuu5Dt4TsEmBAuhwoUQnLu8Uom)}
\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 $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_rewrite3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_rewrite3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r2\_rewrite3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k8\_afinsq\_1~X2))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
((\preoh v2\_struct\_0~X4){\unicdcdcdhd}(l1\_rewrite3~X4~X3)){\unicdbdjdcd}(\preoh (k4\_tarski~X0~X1 \in k1\_rewrite3~\\
X2~X3~X4){\unicdcdcdhd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X4)){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(m1\_subset\_1~X6~(k8\_afinsq\_1~X2)){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~\\
(u1\_struct\_0~X4)){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~X8~(k8\_afinsq\_1~X2)){\unicdbdjdcd}\\
(\preoh (X0=k4\_tarski~X5~X6){\unicdcdcdhd}(X1=k4\_tarski~X7~X8)))))))))\end{array}
\label{hyp:ehddbdpfchfghhchjgehfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
(\preoh v1\_xboole\_0~X5){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(k1\_zfmisc\_1~(\\
k8\_afinsq\_1~X5))){\unicdbdjdcd}({\unicdcdadad} X7 .  (l1\_rewrite3~X7~X6){\unicdbdjdcd}((((v1\_relat\_1~\\
(u1\_rewrite3~X6~X7)){\unicdcdcdhd}(v1\_funct\_1~(u1\_rewrite3~X6~X7))){\unicdcdcdhd}((r2\_rewrite3~\\
X5~X6~X7~X0~X1~X2~X3){\unicdcdcdhd}(r2\_rewrite3~X5~X6~X7~X0~X1~X4~X3))){\unicdbdjdcd}(X2=X4))))\end{array}
\label{hyp:ehcdhdpfchfghhchjgehfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k8\_afinsq\_1~X0))){\unicdcdcdhd}((\preoh v2\_struct\_0~X2){\unicdcdcdhd}(l1\_rewrite3~\\
X2~X1)))){\unicdbdjdcd}(m1\_subset\_1~(k1\_rewrite3~X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X2)~(k8\_afinsq\_1~X0))~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X2)~(k8\_afinsq\_1~X0)))))\end{array}
\label{hyp:egehpflgbdpfchfghhchjgehfgdd}
\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 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}(l1\_rewrite3~\\
X2~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X2)~(k8\_afinsq\_1~X0))~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X2)~(k8\_afinsq\_1~X0))))){\unicdbdjdcd}((X3=k1\_rewrite3~X0~X1~\\
X2){\unicdbdjded}({\unicdcdadad} X4 .  {\unicdcdadad} X5 .  {\unicdcdadad} X6 .  {\unicdcdadad} X7 .  (k4\_tarski~\\
(k4\_tarski~X4~X5)~(k4\_tarski~X6~X7) \in X3){\unicdbdjded}(r2\_rewrite3~X0~X1~X2~X4~\\
X5~X6~X7))))))\end{array}
\label{hyp:egedpfchfghhchjgehfgdd}
\end{equation}
\begin{theorem}\label{thm:ehedbdpfchfghhchjgehfgdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (\preoh v1\_xboole\_0~\\
X4){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(k1\_zfmisc\_1~(k8\_afinsq\_1~X4))){\unicdbdjdcd}\\
({\unicdcdadad} X6 .  ((\preoh v2\_struct\_0~X6){\unicdcdcdhd}(l1\_rewrite3~X6~X5)){\unicdbdjdcd}((((v1\_relat\_1~\\
(u1\_rewrite3~X5~X6)){\unicdcdcdhd}(v1\_funct\_1~(u1\_rewrite3~X5~X6))){\unicdcdcdhd}((k4\_tarski~\\
X0~(k4\_tarski~X1~X2) \in k1\_rewrite3~X4~X5~X6){\unicdcdcdhd}(k4\_tarski~X0~(k4\_tarski~\\
X3~X2) \in k1\_rewrite3~X4~X5~X6))){\unicdbdjdcd}(X1=X3))))\end{array}$$
\end{theorem}
\end{document}
