\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{t56\_filter\_0 (TMbgqu9wvn4hL5U888gtuuHcNLdK4EMDy3X)}
\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 $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_filter\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_filter\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v4\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_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 $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r3\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v8\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v9\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u2\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_realset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v6\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v13\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v4\_lattices~X0){\unicdcdcdhd}(l2\_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}(((r1\_lattices~X0~X1~X2){\unicdcdcdhd}(r1\_lattices~\\
X0~X2~X1)){\unicdbdjdcd}(X1=X2))))\end{array}
\label{hyp:ehidpfmgbgehehjgdgfgdh}
\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}((v19\_lattices~X3~X0){\unicdcdcdhd}((v20\_lattices~X3~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~(k6\_filter\_0~X0~X3))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~(u1\_struct\_0~(k6\_filter\_0~X0~X3))){\unicdbdjdcd}(((X1=X4){\unicdcdcdhd}(X2=X5)){\unicdbdjdcd}((\\
r3\_lattices~X0~X1~X2){\unicdbdjded}(r3\_lattices~(k6\_filter\_0~X0~X3)~X4~X5))))))))\end{array}
\label{hyp:ehfdbdpfggjgmgehfgchpfad}
\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}((v8\_lattices~X0){\unicdcdcdhd}((v9\_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}((r1\_lattices~\\
X0~X1~X2){\unicdbdjded}(k2\_lattices~X0~X1~X2=X1))))\end{array}
\label{hyp:ehedpfmgbgehehjgdgfgdh}
\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}((u1\_struct\_0~(k6\_filter\_0~X0~X1)=X1){\unicdcdcdhd}((u2\_lattices~\\
(k6\_filter\_0~X0~X1)=k1\_realset1~(u2\_lattices~X0)~X1){\unicdcdcdhd}(u1\_lattices~\\
(k6\_filter\_0~X0~X1)=k1\_realset1~(u1\_lattices~X0)~X1))))\end{array}
\label{hyp:ehedjdpfggjgmgehfgchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\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}(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 k2\_filter\_0~X0~X1){\unicdcdcdhd}((\\
k3\_lattices~X0~X1~X2 \in k2\_filter\_0~X0~X1){\unicdcdcdhd}(k3\_lattices~X0~X2~X1 \in k2\_filter\_0~\\
X0~X1)))))\end{array}
\label{hyp:ehbdgdpfggjgmgehfgchpfad}
\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 k2\_filter\_0~X0~X2){\unicdbdjded}(r3\_lattices~\\
X0~X2~X1))))\end{array}
\label{hyp:ehbdfdpfggjgmgehfgchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v6\_lattices~\\
X0){\unicdcdcdhd}((v8\_lattices~X0){\unicdcdcdhd}((v9\_lattices~X0){\unicdcdcdhd}(l3\_lattices~X0))))){\unicdcdcdhd}\\
((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}((r3\_lattices~X0~X1~X2){\unicdbdjded}(r1\_lattices~X0~X1~X2))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchddpfmgbgehehjgdgfgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v6\_lattices~\\
X0){\unicdcdcdhd}(l1\_lattices~X0))){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(\\
m1\_subset\_1~X2~(u1\_struct\_0~X0)))){\unicdbdjdcd}(k4\_lattices~X0~X1~X2=k2\_lattices~\\
X0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfmgbgehehjgdgfgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}\\
((v13\_lattices~X0){\unicdcdcdhd}(l3\_lattices~X0)))){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~\\
X0))){\unicdbdjdcd}(k4\_lattices~X0~(k5\_lattices~X0)~X1=k5\_lattices~X0)\end{array}
\label{hyp:chegedpfmgbgehehjgdgfgdh}
\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 v2\_struct\_0~\\
(k6\_filter\_0~X0~(k2\_filter\_0~X0~X1))){\unicdcdcdhd}((v10\_lattices~(k6\_filter\_0~\\
X0~(k2\_filter\_0~X0~X1))){\unicdcdcdhd}(v13\_lattices~(k6\_filter\_0~X0~(k2\_filter\_0~\\
X0~X1)))))\end{array}
\label{hyp:ggdgedpfggjgmgehfgchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l3\_lattices}~{X0}})}{\unicdbdjdcd}{({{({{l1\_lattices}~{X0}})}{\unicdcdcdhd}{({{l2\_lattices}~{X0}})}})}}}\label{hyp:egehpfmgddpfmgbgehehjgdgfgdh}
\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}((\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~(k6\_filter\_0~X0~X1)){\unicdcdcdhd}((v10\_lattices~\\
(k6\_filter\_0~X0~X1)){\unicdcdcdhd}(l3\_lattices~(k6\_filter\_0~X0~X1))))\end{array}
\label{hyp:egehpflggdpfggjgmgehfgchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_lattices~X0)){\unicdbdjdcd}(m1\_subset\_1~\\
(k5\_lattices~X0)~(u1\_struct\_0~X0))\end{array}
\label{hyp:egehpflgfdpfmgbgehehjgdgfgdh}
\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~\\
(k2\_filter\_0~X0~X1)){\unicdcdcdhd}((v19\_lattices~(k2\_filter\_0~X0~X1)~X0){\unicdcdcdhd}(\\
(v20\_lattices~(k2\_filter\_0~X0~X1)~X0){\unicdcdcdhd}(m1\_subset\_1~(k2\_filter\_0~\\
X0~X1)~(k1\_zfmisc\_1~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egehpflgcdpfggjgmgehfgchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l3\_lattices~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v10\_lattices~\\
X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v4\_lattices~X0){\unicdcdcdhd}((v5\_lattices~X0){\unicdcdcdhd}\\
((v6\_lattices~X0){\unicdcdcdhd}((v7\_lattices~X0){\unicdcdcdhd}((v8\_lattices~X0){\unicdcdcdhd}(v9\_lattices~\\
X0))))))))\end{array}
\label{hyp:dgdgbdpfmgbgehehjgdgfgdh}
\end{equation}
\begin{theorem}\label{thm:ehfdgdpfggjgmgehfgchpfad}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}(l3\_lattices~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k5\_lattices~\\
(k6\_filter\_0~X0~(k2\_filter\_0~X0~X1))=X1))\end{array}$$
\end{theorem}
\end{document}
