\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{l36\_poset\_1 (TMQByqgRjEYvQ23CHTcKp31rCPfkjisRUcw)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_poset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_relat\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_poset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_poset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ 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 $ r1\_yellow\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k9\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_poset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_orders\_2~X0){\unicdcdcdhd}((v3\_orders\_2~\\
X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_poset\_1~X0){\unicdcdcdhd}(\\
l1\_orders\_2~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v1\_orders\_2~\\
X1){\unicdcdcdhd}((v3\_orders\_2~X1){\unicdcdcdhd}((v4\_orders\_2~X1){\unicdcdcdhd}((v5\_orders\_2~X1){\unicdcdcdhd}\\
((v1\_poset\_1~X1){\unicdcdcdhd}(l1\_orders\_2~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}\\
(r1\_yellow\_2~(u1\_struct\_0~X0)~X1~X2~X2)))\end{array}
\label{hyp:mgddbdpfahpgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(u1\_struct\_0~X0))\end{array}
\label{hyp:ggdgcdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_funct\_2~\\
X2~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_funct\_2~X3~X0~X1~X2){\unicdbdjdcd}((v1\_funct\_1~X3){\unicdcdcdhd}\\
((v1\_funct\_2~X3~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1))))))\end{array}
\label{hyp:egehpfngcdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_orders\_2}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfpgchegfgchdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}(m1\_funct\_2~(k9\_funct\_2~\\
X0~X1)~X0~X1)\end{array}
\label{hyp:egehpflgjdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_orders\_2~X0){\unicdcdcdhd}\\
((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_poset\_1~\\
X0){\unicdcdcdhd}(l1\_orders\_2~X0))))))){\unicdcdcdhd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v1\_orders\_2~\\
X1){\unicdcdcdhd}((v3\_orders\_2~X1){\unicdcdcdhd}((v4\_orders\_2~X1){\unicdcdcdhd}((v5\_orders\_2~X1){\unicdcdcdhd}\\
((v1\_poset\_1~X1){\unicdcdcdhd}(l1\_orders\_2~X1)))))))){\unicdbdjdcd}(m1\_subset\_1~(k5\_poset\_1~\\
X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k4\_poset\_1~X0~X1)~(k4\_poset\_1~\\
X0~X1))))\end{array}
\label{hyp:egehpflgfdpfahpgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_orders\_2~X0){\unicdcdcdhd}((v3\_orders\_2~\\
X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_poset\_1~X0){\unicdcdcdhd}(\\
l1\_orders\_2~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v1\_orders\_2~\\
X1){\unicdcdcdhd}((v3\_orders\_2~X1){\unicdcdcdhd}((v4\_orders\_2~X1){\unicdcdcdhd}((v5\_orders\_2~X1){\unicdcdcdhd}\\
((v1\_poset\_1~X1){\unicdcdcdhd}(l1\_orders\_2~X1))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k4\_poset\_1~X0~X1)~(k4\_poset\_1~X0~\\
X1)))){\unicdbdjdcd}((X2=k5\_poset\_1~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (k4\_tarski~\\
X3~X4 \in X2){\unicdbdjded}((X3 \in k4\_poset\_1~X0~X1){\unicdcdcdhd}((X4 \in k4\_poset\_1~X0~X1){\unicdcdcdhd}({\unicdcdaddd} X5 .  \\
((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~X5~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1)){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1)))))){\unicdcdcdhd}({\unicdcdaddd} X6 .  ((v1\_funct\_1~X6){\unicdcdcdhd}((v1\_funct\_2~\\
X6~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X6~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))){\unicdcdcdhd}((X3=X5){\unicdcdcdhd}\\
((X4=X6){\unicdcdcdhd}(r1\_yellow\_2~(u1\_struct\_0~X0)~X1~X5~X6)))))))))))\end{array}
\label{hyp:eghdpfahpgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_orders\_2~X0){\unicdcdcdhd}((v3\_orders\_2~\\
X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_poset\_1~X0){\unicdcdcdhd}(\\
l1\_orders\_2~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v1\_orders\_2~\\
X1){\unicdcdcdhd}((v3\_orders\_2~X1){\unicdcdcdhd}((v4\_orders\_2~X1){\unicdcdcdhd}((v5\_orders\_2~X1){\unicdcdcdhd}\\
((v1\_poset\_1~X1){\unicdcdcdhd}(l1\_orders\_2~X1))))))){\unicdbdjdcd}(k4\_poset\_1~X0~X1=ReplSep~\\
(toset~({\uniddcgcg} X2 : \iota .  m2\_funct\_2~X2~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1)~(k9\_funct\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1))))~({\uniddcgcg} X2 : \\
\iota .  {\unicdcdaddd} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}((v2\_poset\_1~X3~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X3~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1))))))){\unicdcdcdhd}\\
(r2\_funct\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~X3~X2))~({\uniddcgcg} X2 : \\
\iota .  X2)))\end{array}
\label{hyp:eggdpfahpgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (r1\_relat\_2~X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  \\
(X2 \in X1){\unicdbdjdcd}(k4\_tarski~X2~X2 \in X0)))\end{array}
\label{hyp:egbdpfchfgmgbgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v1\_relat\_1~X2)\end{array}
\label{hyp:dgdgbdpfchfgmgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:mgddgdpfahpgdhfgehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_orders\_2~X0){\unicdcdcdhd}((v3\_orders\_2~\\
X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_poset\_1~X0){\unicdcdcdhd}(\\
l1\_orders\_2~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v1\_orders\_2~\\
X1){\unicdcdcdhd}((v3\_orders\_2~X1){\unicdcdcdhd}((v4\_orders\_2~X1){\unicdcdcdhd}((v5\_orders\_2~X1){\unicdcdcdhd}\\
((v1\_poset\_1~X1){\unicdcdcdhd}(l1\_orders\_2~X1))))))){\unicdbdjdcd}(r1\_relat\_2~(k5\_poset\_1~\\
X0~X1)~(k4\_poset\_1~X0~X1)))\end{array}$$
\end{theorem}
\end{document}
