\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{t12\_waybel\_0 (TMSWtvWv5yHqcD96mNixhrD9xi2hCDJHvZ6)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v11\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\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 $ r1\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r1\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 : \iota{\unicdbdjdcd}o .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X2){\unicdcdcdhd}\\
(l1\_orders\_2~X2)){\unicdcdcdhd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_waybel\_0~X1~X2))){\unicdbdjdcd}\\
((r1\_waybel\_0~X2~X1~(ReplSep~(toset~({\uniddcgcg} X3 : \iota .  m1\_subset\_1~X3~\\
(u1\_struct\_0~X1)))~({\uniddcgcg} X3 : \iota .  X0~(k2\_waybel\_0~X2~X1~X3))~({\uniddcgcg} X3 : \\
\iota .  k2\_waybel\_0~X2~X1~X3))){\unicdbdjded}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
X1)){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X1)){\unicdbdjdcd}((r1\_orders\_2~\\
X1~X3~X4){\unicdbdjdcd}(X0~(k2\_waybel\_0~X2~X1~X4))))))\end{array}
\label{hyp:dhbdpfhhbgjhcgfgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_waybel\_0~X1~X0)){\unicdbdjdcd}((v11\_waybel\_0~X1~X0){\unicdbdjded}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X1)){\unicdbdjdcd}(r1\_waybel\_0~X0~\\
X1~(ReplSep~(toset~({\uniddcgcg} X3 : \iota .  m1\_subset\_1~X3~(u1\_struct\_0~X1)))~\\
({\uniddcgcg} X3 : \iota .  r1\_orders\_2~X0~(k2\_waybel\_0~X0~X1~X3)~(k2\_waybel\_0~\\
X0~X1~X2))~({\uniddcgcg} X3 : \iota .  k2\_waybel\_0~X0~X1~X3))))))\end{array}
\label{hyp:egbdedpfhhbgjhcgfgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehbdcdpfhhbgjhcgfgmgpfad}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_waybel\_0~X1~X0)){\unicdbdjdcd}((v11\_waybel\_0~X1~X0){\unicdbdjded}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdaddd} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X1)){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~\\
X1)){\unicdbdjdcd}((r1\_orders\_2~X1~X3~X4){\unicdbdjdcd}(r1\_orders\_2~X0~(k2\_waybel\_0~X0~X1~\\
X4)~(k2\_waybel\_0~X0~X1~X2))))))))\end{array}$$
\end{theorem}
\end{document}
