\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\_rat\_1 (TMJdEmRdKi52GrjccVgjBcRDBpSWUBPvpvs)}
\maketitle
Let $ v1\_rat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_rat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_rat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_rat\_1~X0){\unicdbdjdcd}((X0=k6\_real\_1~(k2\_rat\_1~X0)~(k1\_rat\_1~\\
X0)){\unicdcdcdhd}((X0=k4\_real\_1~(k2\_rat\_1~X0)~(k2\_real\_1~(k1\_rat\_1~X0))){\unicdcdcdhd}\\
(X0=k8\_real\_1~(k2\_real\_1~(k1\_rat\_1~X0))~(k2\_rat\_1~X0))))\end{array}
\label{hyp:ehbdfdpfchbgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedbdpfchbgehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_rat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_rat\_1~X1){\unicdbdjdcd}(((k1\_rat\_1~\\
X0=k1\_rat\_1~X1){\unicdcdcdhd}(k2\_rat\_1~X0=k2\_rat\_1~X1)){\unicdbdjdcd}(X0=X1)))\end{array}$$
\end{theorem}
\end{document}
