\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{t80\_filter\_2 (TMHMJGnuTeXbhuY5uzgeZ45T5L4151Kdf9W)}
\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 $ v13\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k10\_filter\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_filter\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v20\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v21\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_filter\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_lattice2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_filter\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v19\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_filter\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v14\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_filter\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_filter\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m2\_nat\_lat : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v18\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
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}((v20\_lattices~X1~X0){\unicdcdcdhd}\\
((v21\_lattices~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))))){\unicdbdjdcd}(k10\_filter\_2~X0~X1=k11\_filter\_2~(k1\_lattice2~X0)~(\\
k10\_filter\_2~(k1\_lattice2~X0)~(k3\_filter\_2~X0~X1))))\end{array}
\label{hyp:ehhdadpfggjgmgehfgchpfcd}
\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}(k6\_filter\_0~X0~X1=k10\_filter\_2~X0~X1))\end{array}
\label{hyp:ehgdjdpfggjgmgehfgchpfcd}
\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}(k6\_lattices~X0=k5\_lattices~(k1\_lattice2~\\
X0))\end{array}
\label{hyp:ehgdcdpfmgbgehehjgdgfgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}((v13\_lattices~\\
X0){\unicdcdcdhd}(l3\_lattices~X0)))){\unicdbdjdcd}(k5\_lattices~X0=k6\_lattices~(k1\_lattice2~\\
X0))\end{array}
\label{hyp:ehgdbdpfmgbgehehjgdgfgcd}
\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}((v14\_lattices~\\
X0){\unicdbdjdcd}(k6\_lattices~(k6\_filter\_0~X0~(k2\_filter\_0~X0~X1))=k6\_lattices~\\
X0)))\end{array}
\label{hyp:ehfdhdpfggjgmgehfgchpfad}
\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}((v14\_lattices~X0){\unicdbdjdcd}(v14\_lattices~(k6\_filter\_0~X0~X1))))\end{array}
\label{hyp:ehfdcdpfggjgmgehfgchpfad}
\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}((v14\_lattices~X0){\unicdbdjded}(v13\_lattices~(k1\_lattice2~X0)))\end{array}
\label{hyp:ehedjdpfmgbgehehjgdgfgcd}
\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}((v13\_lattices~X0){\unicdbdjded}(v14\_lattices~(k1\_lattice2~X0)))\end{array}
\label{hyp:ehedidpfmgbgehehjgdgfgcd}
\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}((k6\_filter\_2~\\
X0~X1=k2\_filter\_0~(k1\_lattice2~X0)~(k1\_filter\_2~X0~X1)){\unicdcdcdhd}(k6\_filter\_2~\\
(k1\_lattice2~X0)~(k1\_filter\_2~X0~X1)=k2\_filter\_0~X0~X1)))\end{array}
\label{hyp:ehcdjdpfggjgmgehfgchpfcd}
\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}(m2\_nat\_lat~X1~X0)){\unicdbdjdcd}(k11\_filter\_2~X0~X1=k1\_lattice2~\\
X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdbdpfggjgmgehfgchpfcd}
\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}((v3\_lattices~(k1\_lattice2~X0)){\unicdcdcdhd}(v10\_lattices~(k1\_lattice2~\\
X0)))\end{array}
\label{hyp:ggdgidpfmgbgehehjgdgfgcd}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}\\
(l3\_lattices~X0))){\unicdcdcdhd}((v20\_lattices~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))))){\unicdbdjdcd}(v21\_lattices~(k3\_filter\_2~X0~X1)~(k1\_lattice2~\\
X0))\end{array}
\label{hyp:ggdgddpfggjgmgehfgchpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l3\_lattices~X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
(k1\_lattice2~X0)){\unicdcdcdhd}(v3\_lattices~(k1\_lattice2~X0)))\end{array}
\label{hyp:ggdgbdpfmgbgehehjgdgfgcd}
\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 .  {\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 .  {\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}((v3\_lattices~(k1\_lattice2~X0)){\unicdcdcdhd}\\
(l3\_lattices~(k1\_lattice2~X0)))\end{array}
\label{hyp:egehpflgbdpfmgbgehehjgdgfgcd}
\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}(m1\_subset\_1~\\
(k1\_filter\_2~X0~X1)~(u1\_struct\_0~(k1\_lattice2~X0)))\end{array}
\label{hyp:egehpflgbdpfggjgmgehfgchpfcd}
\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}((v20\_lattices~X1~X0){\unicdcdcdhd}\\
((v21\_lattices~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))))))){\unicdbdjdcd}(m2\_nat\_lat~(k10\_filter\_2~X0~X1)~X0)\end{array}
\label{hyp:egehpflgbdadpfggjgmgehfgchpfcd}
\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~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))){\unicdbdjdcd}(k3\_filter\_2~X0~X1=X1))\end{array}
\label{hyp:egedpfggjgmgehfgchpfcd}
\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}(k1\_filter\_2~\\
X0~X1=X1))\end{array}
\label{hyp:egcdpfggjgmgehfgchpfcd}
\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~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))){\unicdbdjdcd}((v18\_lattices~X1~X0){\unicdbdjdcd}(v20\_lattices~X1~X0)))\end{array}
\label{hyp:dgdgjdpfmgbgehehjgdgfgdh}
\end{equation}
\begin{theorem}\label{thm:ehidadpfggjgmgehfgchpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}(l3\_lattices~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}((v13\_lattices~\\
X0){\unicdbdjdcd}((v13\_lattices~(k10\_filter\_2~X0~(k6\_filter\_2~X0~X1))){\unicdcdcdhd}(k5\_lattices~\\
(k10\_filter\_2~X0~(k6\_filter\_2~X0~X1))=k5\_lattices~X0))))\end{array}$$
\end{theorem}
\end{document}
