\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{t1\_lattice3 (TMQuQLL73LrUEo4xqAhDL3CMDnF9X6KcBgf)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_lattice3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((m1\_subset\_1~\\
X1~(u1\_struct\_0~(k1\_lattice3~X0))){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~\\
(k1\_lattice3~X0)))){\unicdbdjdcd}(((X1=X3){\unicdcdcdhd}(X2=X4)){\unicdbdjdcd}(k2\_lattices~(k1\_lattice3~\\
X0)~X1~X2=k3\_xboole\_0~X3~X4))\end{array}
\label{hyp:jgfgcdpfmgbgehehjgdgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((m1\_subset\_1~\\
X1~(u1\_struct\_0~(k1\_lattice3~X0))){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~\\
(k1\_lattice3~X0)))){\unicdbdjdcd}(((X1=X3){\unicdcdcdhd}(X2=X4)){\unicdbdjdcd}(k1\_lattices~(k1\_lattice3~\\
X0)~X1~X2=k2\_xboole\_0~X3~X4))\end{array}
\label{hyp:jgfgbdpfmgbgehehjgdgfgdd}
\end{equation}
\begin{theorem}\label{thm:ehbdpfmgbgehehjgdgfgdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k1\_lattice3~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k1\_lattice3~\\
X0))){\unicdbdjdcd}((k1\_lattices~(k1\_lattice3~X0)~X1~X2=k2\_xboole\_0~X1~X2){\unicdcdcdhd}\\
(k2\_lattices~(k1\_lattice3~X0)~X1~X2=k3\_xboole\_0~X1~X2)))\end{array}$$
\end{theorem}
\end{document}
