\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{t31\_filter\_2 (TMWCiHoEzm9GZQTBZK9X2DAJ4V5z73XGfa9)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v10\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v14\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_filter\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_filter\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_filter\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r3\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v19\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v20\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v18\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v21\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)){\unicdbdjdcd}(({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~X0){\unicdbdjdcd}(X2 \in X1)){\unicdbdjdcd}(X0=X1))\end{array}
\label{hyp:ehcdidpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}(l3\_lattices~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}((X1 \in k6\_filter\_2~X0~X2){\unicdbdjded}(r3\_lattices~\\
X0~X1~X2))))\end{array}
\label{hyp:ehcdidpfggjgmgehfgchpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}((v14\_lattices~\\
X0){\unicdcdcdhd}(l3\_lattices~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(r3\_lattices~X0~X1~(k6\_lattices~X0)))\end{array}
\label{hyp:ehbdjdpfmgbgehehjgdgfgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}(l3\_lattices~\\
X0))){\unicdbdjdcd}((\preoh v1\_xboole\_0~(u1\_struct\_0~X0)){\unicdcdcdhd}((v19\_lattices~(u1\_struct\_0~\\
X0)~X0){\unicdcdcdhd}((v20\_lattices~(u1\_struct\_0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~(u1\_struct\_0~\\
X0)~(k1\_zfmisc\_1~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:ehbdedpfggjgmgehfgchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}(l3\_lattices~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v19\_lattices~X1~X0){\unicdcdcdhd}\\
((v20\_lattices~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))))){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}((v14\_lattices~\\
X0){\unicdcdcdhd}(l3\_lattices~X0)))){\unicdbdjdcd}(k6\_lattices~X0 \in X1)))\end{array}
\label{hyp:ehbdbdpfggjgmgehfgchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}((r1\_filter\_2~\\
X0~X1~X2){\unicdbdjded}(X1=X2))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchbdpfggjgmgehfgchpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}\\
(l3\_lattices~X0))){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~X0))){\unicdbdjdcd}((\preoh v1\_xboole\_0~\\
(k6\_filter\_2~X0~X1)){\unicdcdcdhd}((v18\_lattices~(k6\_filter\_2~X0~X1)~X0){\unicdcdcdhd}(\\
(v21\_lattices~(k6\_filter\_2~X0~X1)~X0){\unicdcdcdhd}(m1\_subset\_1~(k6\_filter\_2~\\
X0~X1)~(k1\_zfmisc\_1~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egehpflggdpfggjgmgehfgchpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}(l3\_lattices~\\
X0))){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k5\_filter\_2~X0)){\unicdcdcdhd}((v18\_lattices~(k5\_filter\_2~\\
X0)~X0){\unicdcdcdhd}((v21\_lattices~(k5\_filter\_2~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~(k5\_filter\_2~\\
X0)~(k1\_zfmisc\_1~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egehpflgfdpfggjgmgehfgchpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}(l3\_lattices~\\
X0))){\unicdbdjdcd}(k5\_filter\_2~X0=u1\_struct\_0~X0)\end{array}
\label{hyp:eggdpfggjgmgehfgchpfcd}
\end{equation}
\begin{theorem}\label{thm:ehddbdpfggjgmgehfgchpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}(l3\_lattices~\\
X0))){\unicdbdjdcd}((v14\_lattices~X0){\unicdbdjdcd}(r1\_filter\_2~(u1\_struct\_0~X0)~(k5\_filter\_2~\\
X0)~(k6\_filter\_2~X0~(k6\_lattices~X0))))\end{array}$$
\end{theorem}
\end{document}
