\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{t54\_rewrite1 (TMKBdoeUDMNqSNL9kCuP2qu7AvxsQSus4vL)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_rewrite1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_rewrite1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r4\_rewrite1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_rewrite1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_relat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r9\_rewrite1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v4\_rewrite1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \\
{\unicdcdadad} X3 .  ((r4\_rewrite1~X0~X1~X2){\unicdcdcdhd}(r4\_rewrite1~X0~X1~X3)){\unicdbdjdcd}(X2=\\
X3))\end{array}
\label{hyp:ehfdddpfchfghhchjgehfgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh X1 \in k1\_relat\_1~X0){\unicdbdjdcd}\\
(r9\_rewrite1~X0~X1))\end{array}
\label{hyp:ehedgdpfchfghhchjgehfgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}((v2\_rewrite1~X0){\unicdbdjded}({\unicdcdadad} X1 .  (X1 \in \\
k1\_relat\_1~X0){\unicdbdjdcd}(r9\_rewrite1~X0~X1)))\end{array}
\label{hyp:egbdedpfchfghhchjgehfgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((r9\_rewrite1~X0~X1){\unicdcdcdhd}\\
({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((r4\_rewrite1~X0~X1~X2){\unicdcdcdhd}(r4\_rewrite1~X0~\\
X1~X3)){\unicdbdjdcd}(X2=X3))){\unicdbdjdcd}({\unicdcdadad} X2 .  (X2=k2\_rewrite1~X0~X1){\unicdbdjded}(r4\_rewrite1~\\
X0~X1~X2)))\end{array}
\label{hyp:egbdcdpfchfghhchjgehfgbd}
\end{equation}
\begin{theorem}\label{thm:ehfdedpfchfghhchjgehfgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v2\_rewrite1~X0){\unicdcdcdhd}(v4\_rewrite1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  r4\_rewrite1~X0~X1~(k2\_rewrite1~X0~X1))\end{array}$$
\end{theorem}
\end{document}
