\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{l84\_partfun1 (TMPvtycZmLcHqLHiowbdCo7iYk2qC9rd4JE)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_relat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~(k4\_relat\_1~X0)){\unicdcdcdhd}((v3\_relat\_2~(k4\_relat\_1~\\
X0)){\unicdcdcdhd}((v4\_relat\_2~(k4\_relat\_1~X0)){\unicdcdcdhd}(v8\_relat\_2~(k4\_relat\_1~\\
X0))))\end{array}
\label{hyp:ggdgbdpfchfgmgbgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v3\_relat\_2~X0){\unicdcdcdhd}(v8\_relat\_2~X0))){\unicdbdjdcd}\\
((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_relat\_2~X0))\end{array}
\label{hyp:dgdgcdpfchfgmgbgehpfcd}
\end{equation}
\begin{theorem}\label{thm:mgidedpfahbgchehggfhogbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}((X1=k4\_relat\_1~X0){\unicdbdjdcd}(\\
(v1\_relat\_2~X1){\unicdcdcdhd}((v3\_relat\_2~X1){\unicdcdcdhd}((v4\_relat\_2~X1){\unicdcdcdhd}(v8\_relat\_2~\\
X1)))))\end{array}$$
\end{theorem}
\end{document}
