\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{t7\_msualg\_8 (TMJ51xx3ihBNkJmXYmkp1WFr3dmvC7A5wUj)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_msualg\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k15\_lattice3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r3\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v10\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k16\_lattice3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ({\unicdcdadad} X2 .  (X2 \in X0){\unicdbdjdcd}(r1\_tarski~X2~X1)){\unicdbdjdcd}\\
(r1\_tarski~(k3\_tarski~X0)~X1)\end{array}
\label{hyp:ehhdgdpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k2\_msualg\_5~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k2\_msualg\_5~\\
X0))){\unicdbdjdcd}((r3\_lattices~(k2\_msualg\_5~X0)~X1~X2){\unicdbdjded}(r1\_tarski~X1~X2)))\end{array}
\label{hyp:ehfdpfmgbgehehjgdgfgfd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0 \in X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~X0~X2)\end{array}
\label{hyp:ehedpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}((v4\_lattice3~\\
X0){\unicdcdcdhd}(l3\_lattices~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (X1 \in X2){\unicdbdjdcd}((r3\_lattices~X0~X1~(k15\_lattice3~X0~\\
X2)){\unicdcdcdhd}(r3\_lattices~X0~(k16\_lattice3~X0~X2)~X1))))\end{array}
\label{hyp:ehddidpfmgbgehehjgdgfgdd}
\end{equation}
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}(v4\_lattice3~(k2\_msualg\_5~\\
X0))))\end{array}
\label{hyp:ggdgcdpfngdhfhbgmghgpfid}
\end{equation}
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~X0){\unicdcdcdhd}(l3\_lattices~X0)){\unicdbdjdcd}\\
(m1\_subset\_1~(k15\_lattice3~X0~X1)~(u1\_struct\_0~X0))\end{array}
\label{hyp:egehpflgbdfdpfmgbgehehjgdgfgdd}
\end{equation}
\begin{theorem}\label{thm:ehhdpfngdhfhbgmghgpfid}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k2\_msualg\_5~X0)))){\unicdbdjdcd}(r1\_tarski~(k3\_tarski~X1)~(k15\_lattice3~\\
(k2\_msualg\_5~X0)~X1))\end{array}$$
\end{theorem}
\end{document}
