\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{t15\_waybel34 (TMaRwCPT7EXJCY7ZL67iq9ehU4pDzb1HAtH)}
\maketitle
Let $ v2\_setfam\_1 : {{\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\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\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 $ k5\_waybel34 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v12\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_yellow21 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_altcat\_1 : {{\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 $ k3\_yellow21 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v5\_orders\_3 : {{\iota}{\unicdbdjdcd}{{\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 $ k1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v18\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v2\_setfam\_1~X0){\unicdbdjdcd}({\unicdcdaddd} X1 .  (m1\_subset\_1~X1~X0){\unicdcdcdhd}\\
(\preoh v1\_xboole\_0~X1))\end{array}
\label{hyp:chdgddpfdhfgehggbgngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k5\_waybel34~X0)){\unicdcdcdhd}\\
((v2\_altcat\_1~(k5\_waybel34~X0)){\unicdcdcdhd}((v6\_altcat\_1~(k5\_waybel34~\\
X0)){\unicdcdcdhd}((v11\_altcat\_1~(k5\_waybel34~X0)){\unicdcdcdhd}((v12\_altcat\_1~(k5\_waybel34~\\
X0)){\unicdcdcdhd}((v2\_yellow21~(k5\_waybel34~X0)){\unicdcdcdhd}(l2\_altcat\_1~(k5\_waybel34~\\
X0))))))))\end{array}
\label{hyp:egehpflgfdpfhhbgjhcgfgmgdded}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh {\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
(v1\_xboole\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~\\
X1){\unicdcdcdhd}((v6\_altcat\_1~X1){\unicdcdcdhd}((v11\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}\\
((v2\_yellow21~X1){\unicdcdcdhd}(l2\_altcat\_1~X1))))))){\unicdbdjdcd}((X1=k5\_waybel34~\\
X0){\unicdbdjded}(({\unicdcdadad} X2 .  ((v3\_orders\_2~X2){\unicdcdcdhd}((v4\_orders\_2~X2){\unicdcdcdhd}((v5\_orders\_2~\\
X2){\unicdcdcdhd}((v1\_lattice3~X2){\unicdcdcdhd}((v2\_lattice3~X2){\unicdcdcdhd}(l1\_orders\_2~X2)))))){\unicdbdjdcd}\\
((m1\_subset\_1~X2~(u1\_struct\_0~X1)){\unicdbdjded}((v1\_orders\_2~X2){\unicdcdcdhd}((v3\_lattice3~\\
X2){\unicdcdcdhd}(u1\_struct\_0~X2 \in X0))))){\unicdcdcdhd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~(u1\_struct\_0~(k3\_yellow21~X1~\\
X2))~(u1\_struct\_0~(k3\_yellow21~X1~X3))){\unicdcdcdhd}((v5\_orders\_3~X4~(k3\_yellow21~\\
X1~X2)~(k3\_yellow21~X1~X3)){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~(k3\_yellow21~X1~X2))~(u1\_struct\_0~(k3\_yellow21~X1~\\
X3)))))))){\unicdbdjdcd}((X4 \in k1\_altcat\_1~X1~X2~X3){\unicdbdjded}(v18\_waybel\_0~X4~(k3\_yellow21~\\
X1~X2)~(k3\_yellow21~X1~X3))))))))))\end{array}
\label{hyp:egfdpfhhbgjhcgfgmgdded}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((m1\_subset\_1~X1~X0){\unicdbdjded}\\
(X1 \in X0))){\unicdcdcdhd}((v1\_xboole\_0~X0){\unicdbdjdcd}((m1\_subset\_1~X1~X0){\unicdbdjded}(v1\_xboole\_0~\\
X1)))\end{array}
\label{hyp:egbdpfdhfhcgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdfdpfhhbgjhcgfgmgdded}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v2\_setfam\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v3\_orders\_2~X1){\unicdcdcdhd}\\
((v4\_orders\_2~X1){\unicdcdcdhd}((v5\_orders\_2~X1){\unicdcdcdhd}((v1\_lattice3~X1){\unicdcdcdhd}((v2\_lattice3~\\
X1){\unicdcdcdhd}(l1\_orders\_2~X1)))))){\unicdbdjdcd}((m1\_subset\_1~X1~(u1\_struct\_0~(k5\_waybel34~\\
X0))){\unicdbdjded}((v1\_orders\_2~X1){\unicdcdcdhd}((v3\_lattice3~X1){\unicdcdcdhd}(u1\_struct\_0~X1 \in \\
X0)))))\end{array}$$
\end{theorem}
\end{document}
