\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{l69\_waybel11 (TMJeM8NDE18wLEQYKNaN1TmRneN3Kbj4yr9)}
\maketitle
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 $ v3\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ g1\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_orders\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_waybel11 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~\\
X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}((v3\_lattice3~X0){\unicdcdcdhd}\\
(l1\_orders\_2~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}\\
((v3\_lattice3~X1){\unicdcdcdhd}(l1\_orders\_2~X1))))))){\unicdbdjdcd}((g1\_orders\_2~(u1\_struct\_0~\\
X0)~(u1\_orders\_2~X0)=g1\_orders\_2~(u1\_struct\_0~X1)~(u1\_orders\_2~\\
X1)){\unicdbdjdcd}(r1\_tarski~(k2\_waybel11~X0)~(k2\_waybel11~X1))))\end{array}
\label{hyp:mggdidpfhhbgjhcgfgmgbdbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0}={X1}})}{\unicdbdjded}{({{({{{r1\_tarski}~{X0}}~{X1}})}{\unicdcdcdhd}{({{{r1\_tarski}~{X1}}~{X0}})}})}}}}\label{hyp:egbdadpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:mggdjdpfhhbgjhcgfgmgbdbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~\\
X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}((v3\_lattice3~X0){\unicdcdcdhd}\\
(l1\_orders\_2~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v3\_orders\_2~X1){\unicdcdcdhd}((v4\_orders\_2~\\
X1){\unicdcdcdhd}((v5\_orders\_2~X1){\unicdcdcdhd}((v1\_lattice3~X1){\unicdcdcdhd}((v2\_lattice3~X1){\unicdcdcdhd}\\
((v3\_lattice3~X1){\unicdcdcdhd}(l1\_orders\_2~X1))))))){\unicdbdjdcd}((g1\_orders\_2~(u1\_struct\_0~\\
X0)~(u1\_orders\_2~X0)=g1\_orders\_2~(u1\_struct\_0~X1)~(u1\_orders\_2~\\
X1)){\unicdbdjdcd}(k2\_waybel11~X0=k2\_waybel11~X1)))\end{array}$$
\end{theorem}
\end{document}
