\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{t22\_decomp\_1 (TML4qLippvEvLi9YvfLd6kyfHmeUmeTYWDZ)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\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 $ 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 $ v6\_decomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v8\_decomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v17\_decomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k9\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k10\_decomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k19\_decomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_decomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k8\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdbdjdcd}(k9\_subset\_1~\\
(k1\_zfmisc\_1~(u1\_struct\_0~X0))~(k10\_decomp\_1~X0)~(k19\_decomp\_1~\\
X0)=k8\_decomp\_1~X0)\end{array}
\label{hyp:ehbdfdpfegfgdgpgngahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(k9\_subset\_1~X0~X1~X2=k3\_xboole\_0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (m1\_subset\_1~X2~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(k8\_relset\_1~X0~X1~X2~X3=k8\_relat\_1~\\
X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdbdjdcd}(m1\_subset\_1~\\
(k19\_decomp\_1~X0)~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))))\end{array}
\label{hyp:egehpflgbdjdpfegfgdgpgngahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2=k3\_xboole\_0~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in X2){\unicdbdjded}((X3 \in X0){\unicdcdcdhd}(X3 \in X1)))\end{array}
\label{hyp:egedpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))){\unicdbdjdcd}((v17\_decomp\_1~X2~X0~X1){\unicdbdjded}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~X1))){\unicdbdjdcd}\\
((v3\_pre\_topc~X3~X1){\unicdbdjdcd}(k8\_relset\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1)~X2~X3 \in k19\_decomp\_1~X0))))))\end{array}
\label{hyp:egddidpfegfgdgpgngahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))){\unicdbdjdcd}((v8\_decomp\_1~X2~X0~X1){\unicdbdjded}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~X1))){\unicdbdjdcd}\\
((v3\_pre\_topc~X3~X1){\unicdbdjdcd}(k8\_relset\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1)~X2~X3 \in k10\_decomp\_1~X0))))))\end{array}
\label{hyp:egcdjdpfegfgdgpgngahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))){\unicdbdjdcd}((v6\_decomp\_1~X2~X0~X1){\unicdbdjded}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~X1))){\unicdbdjdcd}\\
((v3\_pre\_topc~X3~X1){\unicdbdjdcd}(k8\_relset\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1)~X2~X3 \in k8\_decomp\_1~X0))))))\end{array}
\label{hyp:egcdhdpfegfgdgpgngahpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdcdpfegfgdgpgngahpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))){\unicdbdjdcd}((v6\_decomp\_1~X2~X0~X1){\unicdbdjded}\\
((v8\_decomp\_1~X2~X0~X1){\unicdcdcdhd}(v17\_decomp\_1~X2~X0~X1)))))\end{array}$$
\end{theorem}
\end{document}
