\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{t18\_latsum\_1 (TMHZ6ELQx7V1n2FasZJnW3b5cQxRaVMEhU7)}
\maketitle
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_latsum\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v13\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_orders\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_orders\_2~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
{\unicdcdadad} X3 .  (((v13\_waybel\_0~(k3\_xboole\_0~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1))~X0){\unicdcdcdhd}(m1\_subset\_1~(k3\_xboole\_0~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1))~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdcdcdhd}((k4\_tarski~X2~X3 \in u1\_orders\_2~\\
(k1\_latsum\_1~X0~X1)){\unicdcdcdhd}(X2 \in u1\_struct\_0~X1))){\unicdbdjdcd}(X3 \in u1\_struct\_0~\\
X1)))\end{array}
\label{hyp:ehbdhdpfmgbgehdhfhngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l1\_orders\_2~X0){\unicdcdcdhd}(l1\_orders\_2~X1)){\unicdbdjdcd}(\\
(v1\_orders\_2~(k1\_latsum\_1~X0~X1)){\unicdcdcdhd}(l1\_orders\_2~(k1\_latsum\_1~\\
X0~X1)))\end{array}
\label{hyp:egehpflgbdpfmgbgehdhfhngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}((r1\_orders\_2~\\
X0~X1~X2){\unicdbdjded}(k4\_tarski~X1~X2 \in u1\_orders\_2~X0))))\end{array}
\label{hyp:egfdpfpgchegfgchdhpfcd}
\end{equation}
\begin{theorem}\label{thm:ehbdidpfmgbgehdhfhngpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_orders\_2~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~(k1\_latsum\_1~X0~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~(k1\_latsum\_1~X0~X1))){\unicdbdjdcd}((((v13\_waybel\_0~\\
(k3\_xboole\_0~(u1\_struct\_0~X0)~(u1\_struct\_0~X1))~X0){\unicdcdcdhd}(m1\_subset\_1~\\
(k3\_xboole\_0~(u1\_struct\_0~X0)~(u1\_struct\_0~X1))~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0)))){\unicdcdcdhd}((r1\_orders\_2~(k1\_latsum\_1~X0~X1)~X2~X3){\unicdcdcdhd}\\
(X2 \in u1\_struct\_0~X1))){\unicdbdjdcd}(X3 \in u1\_struct\_0~X1)))))\end{array}$$
\end{theorem}
\end{document}
