\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{t47\_filter\_2 (TMXGzu1XuGZPc6qT8zHAVCgkFGuDCCuENJ3)}
\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 $ v1\_xboole\_0 : {{\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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_filter\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k8\_filter\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v18\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v19\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \preoh (X0 \in X1){\unicdcdcdhd}((m1\_subset\_1~X1~(\\
k1\_zfmisc\_1~X2)){\unicdcdcdhd}(v1\_xboole\_0~X2))\end{array}
\label{hyp:ehfdpfdhfhcgdhfgeh}
\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 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~\\
X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}(\preoh (X1 \in \\
k8\_filter\_2~X0~X2~X3){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (X1=k3\_lattices~\\
X0~X4~X5){\unicdcdcdhd}((X4 \in X2){\unicdcdcdhd}(X5 \in X3))))))))\end{array}
\label{hyp:ehedgdpfggjgmgehfgchpfcd}
\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}({\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~\\
X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
((\preoh v1\_xboole\_0~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}(((X1 \in X3){\unicdcdcdhd}(X2 \in X4)){\unicdbdjdcd}((k3\_lattices~X0~X1~X2 \in k8\_filter\_2~\\
X0~X3~X4){\unicdcdcdhd}(k3\_lattices~X0~X2~X1 \in k8\_filter\_2~X0~X3~X4)))))))\end{array}
\label{hyp:ehedfdpfggjgmgehfgchpfcd}
\end{equation}
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~(k1\_zfmisc\_1~X0)){\unicdbdjdcd}(({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~X0){\unicdbdjdcd}((X3 \in X1){\unicdbdjded}(X3 \in X2))){\unicdbdjdcd}(X1=X2)))\end{array}
\label{hyp:ehddpfdhfhcgdhfgehpfbd}
\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 .  {\unicdcdaddd} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)){\unicdcdcdhd}(v1\_xboole\_0~\\
X1)\end{array}
\label{hyp:chdgcdpfdhfhcgdhfgehpfbd}
\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}({\unicdcdaddd} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v18\_lattices~X1~X0){\unicdcdcdhd}(v19\_lattices~\\
X1~X0))))\end{array}
\label{hyp:chdgbdedpfmgbgehehjgdgfgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~\\
X0){\unicdcdcdhd}(l3\_lattices~X0))){\unicdcdcdhd}(((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_subset\_1~X1~\\
(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdcdcdhd}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))))){\unicdbdjdcd}(m1\_subset\_1~(k8\_filter\_2~\\
X0~X1~X2)~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))\end{array}
\label{hyp:egehpflgidpfggjgmgehfgchpfcd}
\end{equation}
\begin{theorem}\label{thm:ehedhdpfggjgmgehfgchpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}(l3\_lattices~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}(r1\_filter\_2~(u1\_struct\_0~\\
X0)~(k8\_filter\_2~X0~X1~X2)~(k8\_filter\_2~X0~X2~X1))))\end{array}$$
\end{theorem}
\end{document}
