\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{t70\_filter\_2 (TMc1X6VJhUuWFa9XUGZYtKMZZLALfQadh6p)}
\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 $ v20\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v21\_lattices : {{\iota}{\unicdbdjdcd}{{\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 $ k10\_filter\_2 : {{\iota}{\unicdbdjdcd}{{\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 $ m2\_nat\_lat : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ g3\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u2\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l1\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_realset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
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 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~\\
X1~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)~X0))))){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~\\
(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)~X0)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
(g3\_lattices~X0~X1~X2=g3\_lattices~X3~X4~X5){\unicdbdjdcd}((X0=X3){\unicdcdcdhd}((X1=X4){\unicdcdcdhd}\\
(X2=X5))))\end{array}
\label{hyp:ggchfgfgpfhgddpfmgbgehehjgdgfgdh}
\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}((v21\_lattices~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))))){\unicdbdjdcd}(v20\_lattices~(k3\_filter\_2~X0~X1)~(k1\_lattice2~\\
X0))\end{array}
\label{hyp:ggdgedpfggjgmgehfgchpfcd}
\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 .  (l2\_lattices~X0){\unicdbdjdcd}((v1\_funct\_1~(u2\_lattices~X0)){\unicdcdcdhd}\\
((v1\_funct\_2~(u2\_lattices~X0)~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(\\
u1\_struct\_0~X0))~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~(u2\_lattices~\\
X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(\\
u1\_struct\_0~X0))~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egehpffhcdpfmgbgehehjgdgfgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_lattices~X0){\unicdbdjdcd}((v1\_funct\_1~(u1\_lattices~X0)){\unicdcdcdhd}\\
((v1\_funct\_2~(u1\_lattices~X0)~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(\\
u1\_struct\_0~X0))~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~(u1\_lattices~\\
X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(\\
u1\_struct\_0~X0))~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egehpffhbdpfmgbgehehjgdgfgdh}
\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}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}(m1\_subset\_1~(k3\_filter\_2~X0~X1)~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k1\_lattice2~X0))))\end{array}
\label{hyp:egehpflgddpfggjgmgehfgchpfcd}
\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}((\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 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~\\
X1~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)~X0))))){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~\\
(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)~X0)))))){\unicdbdjdcd}((v3\_lattices~(g3\_lattices~X0~X1~\\
X2)){\unicdcdcdhd}(l3\_lattices~(g3\_lattices~X0~X1~X2)))\end{array}
\label{hyp:egehpfhgddpfmgbgehehjgdgfgdh}
\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 .  (l3\_lattices~X0){\unicdbdjdcd}(k1\_lattice2~X0=g3\_lattices~(u1\_struct\_0~\\
X0)~(u1\_lattices~X0)~(u2\_lattices~X0))\end{array}
\label{hyp:egcdpfmgbgehehjgdgfgcd}
\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}((v20\_lattices~X1~X0){\unicdcdcdhd}\\
((v21\_lattices~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_nat\_lat~X2~X0){\unicdbdjdcd}((X2=k10\_filter\_2~X0~\\
X1){\unicdbdjded}({\unicdcdaddd} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k2\_zfmisc\_1~\\
X1~X1)~X1){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
X1~X1)~X1))))){\unicdcdcdhd}({\unicdcdaddd} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~(\\
k2\_zfmisc\_1~X1~X1)~X1){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~X1~X1)~X1))))){\unicdcdcdhd}((X3=k1\_realset1~(u2\_lattices~X0)~\\
X1){\unicdcdcdhd}((X4=k1\_realset1~(u1\_lattices~X0)~X1){\unicdcdcdhd}(X2=g3\_lattices~X1~\\
X3~X4))))))))\end{array}
\label{hyp:egbdedpfggjgmgehfgchpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l3\_lattices~X0){\unicdbdjdcd}((v3\_lattices~X0){\unicdbdjdcd}(X0=g3\_lattices~\\
(u1\_struct\_0~X0)~(u2\_lattices~X0)~(u1\_lattices~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghddpfmgbgehehjgdgfgdh}
\end{equation}
\begin{theorem}\label{thm:ehhdadpfggjgmgehfgchpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}(l3\_lattices~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v20\_lattices~X1~X0){\unicdcdcdhd}\\
((v21\_lattices~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))))){\unicdbdjdcd}(k10\_filter\_2~X0~X1=k11\_filter\_2~(k1\_lattice2~X0)~(\\
k10\_filter\_2~(k1\_lattice2~X0)~(k3\_filter\_2~X0~X1))))\end{array}$$
\end{theorem}
\end{document}
