\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{t28\_pcs\_0 (TMcJkDJQ8epA3dpJHx8QBRuNd7NvvaS4zoL)}
\maketitle
Let $ l2\_pcs\_0 : {{\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 $ k19\_pcs\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_pcs\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ l1\_pcs\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ u1\_pcs\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_orders\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v12\_pcs\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pcs\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_pcs\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X1)){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X1)){\unicdbdjdcd}(((r1\_relset\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_pcs\_0~X0)~(u1\_pcs\_0~X1)){\unicdcdcdhd}\\
((X2=X4){\unicdcdcdhd}((X3=X5){\unicdcdcdhd}(r1\_pcs\_0~X0~X2~X3)))){\unicdbdjdcd}(r1\_pcs\_0~X1~X4~X5)))))))\end{array}
\label{hyp:ehjdpfahdgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_pcs\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (r1\_tarski~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~(k19\_pcs\_0~X0~X1))){\unicdcdcdhd}((r1\_relset\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~(u1\_orders\_2~X0)~(u1\_orders\_2~(k19\_pcs\_0~\\
X0~X1))){\unicdcdcdhd}(r1\_relset\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_pcs\_0~\\
X0)~(u1\_pcs\_0~(k19\_pcs\_0~X0~X1)))))\end{array}
\label{hyp:ehcdbdpfahdgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_pcs\_0}~{X0}})}{\unicdbdjdcd}{({{({{l1\_orders\_2}~{X0}})}{\unicdcdcdhd}{({{l1\_pcs\_0}~{X0}})}})}}}\label{hyp:egehpfmgcdpfahdgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (l2\_pcs\_0~X0){\unicdbdjdcd}((v12\_pcs\_0~(k19\_pcs\_0~X0~\\
X1)){\unicdcdcdhd}(l2\_pcs\_0~(k19\_pcs\_0~X0~X1)))\end{array}
\label{hyp:egehpflgbdjdpfahdgdhpfad}
\end{equation}
\begin{theorem}\label{thm:ehcdidpfahdgdhpfad}
$$\begin{array}{c}{\unicdcdadad} X0 .  (l2\_pcs\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~(k19\_pcs\_0~X0~X1))){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~(k19\_pcs\_0~X0~X1))){\unicdbdjdcd}\\
(((X2=X4){\unicdcdcdhd}((X3=X5){\unicdcdcdhd}(r1\_pcs\_0~X0~X2~X3))){\unicdbdjdcd}(r1\_pcs\_0~(k19\_pcs\_0~\\
X0~X1)~X4~X5))))))\end{array}$$
\end{theorem}
\end{document}
