\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{t24\_euclid\_6 (TMdCwkTMR4swfkSqn4FhvsUYpYsLAc24kEb)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k15\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ r1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_euclid\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k32\_sin\_cos : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
(((r1\_zfmisc\_1~X0~X1~X2){\unicdcdcdhd}(r1\_xxreal\_0~(k4\_euclid\_3~X0~X1~X2)~k32\_sin\_cos)){\unicdbdjdcd}\\
((r1\_xxreal\_0~(k4\_euclid\_3~X1~X2~X0)~k32\_sin\_cos){\unicdcdcdhd}(r1\_xxreal\_0~\\
(k4\_euclid\_3~X2~X0~X1)~k32\_sin\_cos)))))\end{array}
\label{hyp:ehcdddpffgfhdgmgjgegpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (r1\_zfmisc\_1~X0~X1~X2){\unicdbdjded}((X0{\unicdcdgdad}\\
X1){\unicdcdcdhd}((X0{\unicdcdgdad}X2){\unicdcdcdhd}(X1{\unicdcdgdad}X2)))\end{array}
\label{hyp:egfdpfkhggngjgdhdgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdedpffgfhdgmgjgegpfgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
((r1\_zfmisc\_1~X0~X1~X2){\unicdbdjdcd}((r1\_xxreal\_0~(k4\_euclid\_3~X0~X1~X2)~k32\_sin\_cos){\unicdcdcdid}\\
((\preoh r1\_xxreal\_0~(k4\_euclid\_3~X1~X2~X0)~k32\_sin\_cos){\unicdcdcdhd}(\preoh r1\_xxreal\_0~\\
(k4\_euclid\_3~X2~X0~X1)~k32\_sin\_cos))))))\end{array}$$
\end{theorem}
\end{document}
