\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{l16\_euclid\_6 (TMVmRQkurXmjxTsC96TU9ZrvTpHmJi3ZKMx)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_numbers : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_comptrig : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_complex2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k32\_sin\_cos : {\iota}$ be given.
Let $ k2\_complex2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k2\_numbers){\unicdbdjdcd}(\preoh (X1{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}((\preoh r1\_xxreal\_0~k6\_numbers~\\
(k9\_real\_1~(k1\_comptrig~X1)~(k1\_comptrig~X0))){\unicdcdcdhd}(k1\_comptrig~\\
(k2\_complex2~X1~(k1\_real\_1~(k1\_comptrig~X0))){\unicdcdgdad}k7\_real\_1~(k9\_real\_1~\\
(k8\_real\_1~np\_\_2~k32\_sin\_cos)~(k1\_comptrig~X0))~(k1\_comptrig~\\
X1)))))\end{array}
\label{hyp:mgbdfdpffgfhdgmgjgegpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xcmplx\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xcmplx\_0~X1){\unicdbdjdcd}((\\
(\preoh (k1\_comptrig~X0{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}(X1=k6\_numbers)){\unicdbdjdcd}(k3\_complex2~\\
X0~X1=k1\_comptrig~(k2\_complex2~X1~(k1\_real\_1~(k1\_comptrig~X0))))){\unicdcdcdhd}\\
(\preoh (k1\_comptrig~X0{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}((X1=k6\_numbers){\unicdcdcdhd}(k3\_complex2~\\
X0~X1{\unicdcdgdad}k9\_real\_1~(k8\_real\_1~np\_\_2~k32\_sin\_cos)~(k1\_comptrig~X0))))))\end{array}
\label{hyp:egddpfdgpgngahmgfgihcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k2\_numbers}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{X0}})}}}\label{hyp:dgdgddpfihdgngahmgihpfad}
\end{equation}
\begin{theorem}\label{thm:mgbdgdpffgfhdgmgjgegpfgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k2\_numbers){\unicdbdjdcd}(\preoh (X1{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}((\preoh r1\_xxreal\_0~k6\_numbers~\\
(k9\_real\_1~(k1\_comptrig~X1)~(k1\_comptrig~X0))){\unicdcdcdhd}(k3\_complex2~\\
X0~X1{\unicdcdgdad}k7\_real\_1~(k9\_real\_1~(k8\_real\_1~np\_\_2~k32\_sin\_cos)~(k1\_comptrig~\\
X0))~(k1\_comptrig~X1)))))\end{array}$$
\end{theorem}
\end{document}
