\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{t19\_filter\_2 (TMX47z3RCfFZvbBLxkS4a6SyjCUfJ5xQnMX)}
\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 $ k1\_lattice2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r3\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_filter\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_filter\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u2\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~(k1\_lattice2~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u1\_struct\_0~(k1\_lattice2~X0))){\unicdbdjdcd}(((r3\_lattices~(k1\_lattice2~\\
X0)~X3~X4){\unicdcdcdhd}((X1=X3){\unicdcdcdhd}(X2=X4))){\unicdbdjdcd}(r3\_lattices~X0~X2~X1))))))\end{array}
\label{hyp:ehddjdpfmgbgehehjgdgfgcd}
\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}((r3\_lattices~X0~X1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~(k1\_lattice2~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(u1\_struct\_0~(k1\_lattice2~X0))){\unicdbdjdcd}(((X1=X3){\unicdcdcdhd}(\\
X2=X4)){\unicdbdjdcd}(r3\_lattices~(k1\_lattice2~X0)~X4~X3)))))))\end{array}
\label{hyp:ehddidpfmgbgehehjgdgfgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l3\_lattices~X0)){\unicdbdjdcd}((u1\_struct\_0~\\
X0=u1\_struct\_0~(k1\_lattice2~X0)){\unicdcdcdhd}((r1\_funct\_2~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~(u1\_struct\_0~X0)~(k2\_zfmisc\_1~\\
(u1\_struct\_0~(k1\_lattice2~X0))~(u1\_struct\_0~(k1\_lattice2~X0)))~\\
(u1\_struct\_0~(k1\_lattice2~X0))~(u2\_lattices~X0)~(u1\_lattices~\\
(k1\_lattice2~X0))){\unicdcdcdhd}(r1\_funct\_2~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~\\
(u1\_struct\_0~X0))~(u1\_struct\_0~X0)~(k2\_zfmisc\_1~(u1\_struct\_0~\\
(k1\_lattice2~X0))~(u1\_struct\_0~(k1\_lattice2~X0)))~(u1\_struct\_0~\\
(k1\_lattice2~X0))~(u1\_lattices~X0)~(u2\_lattices~(k1\_lattice2~\\
X0)))))\end{array}
\label{hyp:ehbdcdpfmgbgehehjgdgfgcd}
\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~(k1\_lattice2~\\
X0))){\unicdbdjdcd}(k2\_filter\_2~X0~X1=X1))\end{array}
\label{hyp:egddpfggjgmgehfgchpfcd}
\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}
\begin{theorem}\label{thm:ehbdjdpfggjgmgehfgchpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}(l3\_lattices~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~(k1\_lattice2~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u1\_struct\_0~(k1\_lattice2~X0))){\unicdbdjdcd}(((r3\_lattices~X0~X1~X2){\unicdbdjdcd}(r3\_lattices~\\
(k1\_lattice2~X0)~(k1\_filter\_2~X0~X2)~(k1\_filter\_2~X0~X1))){\unicdcdcdhd}(((\\
r3\_lattices~(k1\_lattice2~X0)~(k1\_filter\_2~X0~X2)~(k1\_filter\_2~\\
X0~X1)){\unicdbdjdcd}(r3\_lattices~X0~X1~X2)){\unicdcdcdhd}(((r3\_lattices~(k1\_lattice2~X0)~\\
X3~X4){\unicdbdjdcd}(r3\_lattices~X0~(k2\_filter\_2~X0~X4)~(k2\_filter\_2~X0~X3))){\unicdcdcdhd}\\
((r3\_lattices~X0~(k2\_filter\_2~X0~X4)~(k2\_filter\_2~X0~X3)){\unicdbdjdcd}(r3\_lattices~\\
(k1\_lattice2~X0)~X3~X4)))))))))\end{array}$$
\end{theorem}
\end{document}
