\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{t78\_rewrite3 (TMPaWJpibqZhR84BoYuA4UdHrYxP1m7AyTH)}
\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 $ r1\_rewrite1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_rewrite3 : {{\iota}{\unicdbdjdcd}{{\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 $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_rewrite3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_afinsq\_1 : {{\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~(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}(\preoh (\preoh k2\_flang\_1~X2 \in k10\_xtuple\_0~(k9\_xtuple\_0~(u1\_rewrite3~\\
X5~X6))){\unicdcdcdhd}((r1\_rewrite1~(k1\_rewrite3~X2~X5~X6)~(k4\_tarski~X0~X3)~\\
(k4\_tarski~X1~X4)){\unicdcdcdhd}((r1\_xxreal\_0~(k1\_afinsq\_1~X3)~(k1\_afinsq\_1~\\
X4)){\unicdcdcdhd}(\preoh (X0=X1){\unicdcdcdhd}(X3=X4)))))))))\end{array}
\label{hyp:ehhdhdpfchfghhchjgehfgdd}
\end{equation}
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~(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}((r1\_rewrite1~(k1\_rewrite3~X2~X5~X6)~(k4\_tarski~X0~X3)~(\\
k4\_tarski~X1~X4)){\unicdbdjdcd}(r1\_xxreal\_0~(k1\_afinsq\_1~X4)~(k1\_afinsq\_1~\\
X3)))))))\end{array}
\label{hyp:ehhdfdpfchfghhchjgehfgdd}
\end{equation}
\begin{theorem}\label{thm:ehhdidpfchfghhchjgehfgdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(k8\_afinsq\_1~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(k1\_zfmisc\_1~(k8\_afinsq\_1~X2))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((\preoh v2\_struct\_0~\\
X5){\unicdcdcdhd}(l1\_rewrite3~X5~X4)){\unicdbdjdcd}((r1\_rewrite1~(k1\_rewrite3~X2~X4~X5)~\\
(k4\_tarski~X0~X3)~(k4\_tarski~X1~X3)){\unicdbdjdcd}((k2\_flang\_1~X2 \in k10\_xtuple\_0~\\
(k9\_xtuple\_0~(u1\_rewrite3~X4~X5))){\unicdcdcdid}(X0=X1))))))\end{array}$$
\end{theorem}
\end{document}
