\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{t21\_msualg\_5 (TMHKuWSMWNWAjWMqgBmACkmGoPzc3y5U9yp)}
\maketitle
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_msualg\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v10\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u1\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_eqrel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u2\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_eqrel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v2\_struct\_0~(k2\_msualg\_5~X0)){\unicdcdcdhd}((v3\_lattices~(k2\_msualg\_5~\\
X0)){\unicdcdcdhd}((v10\_lattices~(k2\_msualg\_5~X0)){\unicdcdcdhd}(l3\_lattices~(k2\_msualg\_5~\\
X0))))\end{array}
\label{hyp:egehpflgcdpfngdhfhbgmghgpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v3\_lattices~X1){\unicdcdcdhd}\\
((v10\_lattices~X1){\unicdcdcdhd}(l3\_lattices~X1)))){\unicdbdjdcd}((X1=k2\_msualg\_5~X0){\unicdbdjded}\\
((u1\_struct\_0~X1=ReplSep~(toset~({\uniddcgcg} X2 : \iota .  m1\_subset\_1~X2~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0))))~({\uniddcgcg} X2 : \iota .  (v1\_partfun1~\\
X2~X0){\unicdcdcdhd}((v3\_relat\_2~X2){\unicdcdcdhd}((v8\_relat\_2~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0))))))~({\uniddcgcg} X2 : \iota .  X2)){\unicdcdcdhd}({\unicdcdadad} X2 .  ((v1\_partfun1~\\
X2~X0){\unicdcdcdhd}((v3\_relat\_2~X2){\unicdcdcdhd}((v8\_relat\_2~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_partfun1~X3~X0){\unicdcdcdhd}((\\
v3\_relat\_2~X3){\unicdcdcdhd}((v8\_relat\_2~X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)))))){\unicdbdjdcd}((k1\_binop\_1~(u1\_lattices~X1)~X2~X3=\\
k4\_eqrel\_1~X0~X2~X3){\unicdcdcdhd}(k1\_binop\_1~(u2\_lattices~X1)~X2~X3=k5\_eqrel\_1~\\
X0~X2~X3))))))\end{array}
\label{hyp:egcdpfngdhfhbgmghgpffd}
\end{equation}
\begin{theorem}\label{thm:ehcdbdpfngdhfhbgmghgpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (X0 \in u1\_struct\_0~(k2\_msualg\_5~X1)){\unicdbdjded}((v1\_partfun1~\\
X0~X1){\unicdcdcdhd}((v3\_relat\_2~X0){\unicdcdcdhd}((v8\_relat\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X1~X1))))))\end{array}$$
\end{theorem}
\end{document}
