\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{t39\_knaster (TMag6mHFmkxMKcozZqnM9MGCiqwryRqNFws)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v10\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_lattices : {{\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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v14\_quantal1 : {{\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_knaster : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r3\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_knaster : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_knaster : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r2\_abian : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k7\_knaster : {{\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}\\
((v4\_lattice3~X0){\unicdcdcdhd}(l3\_lattices~X0)))){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~\\
X1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))))))){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
(k8\_knaster~X0~X1)){\unicdcdcdhd}((v3\_lattices~(k8\_knaster~X0~X1)){\unicdcdcdhd}((v10\_lattices~\\
(k8\_knaster~X0~X1)){\unicdcdcdhd}(l3\_lattices~(k8\_knaster~X0~X1)))))\end{array}
\label{hyp:egehpflgidpflgogbgdhehfgch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}((v4\_lattice3~\\
X0){\unicdcdcdhd}(l3\_lattices~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~\\
X1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)))))){\unicdbdjdcd}((v14\_quantal1~\\
X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v3\_lattices~X2){\unicdcdcdhd}((v10\_lattices~\\
X2){\unicdcdcdhd}(l3\_lattices~X2)))){\unicdbdjdcd}((X2=k8\_knaster~X0~X1){\unicdbdjded}({\unicdcdaddd} X3 .  \\
((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}((v2\_knaster~X3~X0){\unicdcdcdhd}((v3\_knaster~X3~X0){\unicdcdcdhd}(\\
m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))))){\unicdcdcdhd}((X3=ReplSep~\\
(toset~({\uniddcgcg} X4 : \iota .  m1\_subset\_1~X4~(u1\_struct\_0~X0)))~({\uniddcgcg} X4 : \\
\iota .  r2\_abian~(u1\_struct\_0~X0)~X4~X1)~({\uniddcgcg} X4 : \iota .  X4)){\unicdcdcdhd}(X2=k7\_knaster~\\
X0~X3)))))))\end{array}
\label{hyp:egjdpflgogbgdhehfgch}
\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}((v2\_knaster~X1~X0){\unicdcdcdhd}((\\
v3\_knaster~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v3\_lattices~X2){\unicdcdcdhd}((v10\_lattices~\\
X2){\unicdcdcdhd}(l3\_lattices~X2)))){\unicdbdjdcd}((X2=k7\_knaster~X0~X1){\unicdbdjded}((u1\_struct\_0~\\
X2=X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(u1\_struct\_0~X2)){\unicdbdjdcd}({\unicdcdaddd} X5 .  (m1\_subset\_1~X5~\\
(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~X0)){\unicdcdcdhd}\\
((X3=X5){\unicdcdcdhd}((X4=X6){\unicdcdcdhd}(((r3\_lattices~X2~X3~X4){\unicdbdjdcd}(r3\_lattices~X0~X5~\\
X6)){\unicdcdcdhd}((r3\_lattices~X0~X5~X6){\unicdbdjdcd}(r3\_lattices~X2~X3~X4)))))))))))))\end{array}
\label{hyp:egidpflgogbgdhehfgch}
\end{equation}
\begin{theorem}\label{thm:ehddjdpflgogbgdhehfgch}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}((v4\_lattice3~\\
X0){\unicdcdcdhd}(l3\_lattices~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~\\
X1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v14\_quantal1~X1~X0){\unicdcdcdhd}(\\
m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k8\_knaster~\\
X0~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(k8\_knaster~\\
X0~X1))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}(((X2=X4){\unicdcdcdhd}(X3=X5)){\unicdbdjdcd}((r3\_lattices~\\
(k8\_knaster~X0~X1)~X2~X3){\unicdbdjded}(r3\_lattices~X0~X4~X5))))))))\end{array}$$
\end{theorem}
\end{document}
