\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{t37\_euclid\_6 (TMMGfzsPaiPTiu9aMoNDfhqHNxoCvWbExn6)}
\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 $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_jgraph\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_euclid\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k2\_numbers : {\iota}$ be given.
Let $ k4\_complex2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k32\_sin\_cos : {\iota}$ be given.
Let $ k2\_euclid\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ 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}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k2\_numbers){\unicdbdjdcd}(\preoh (X0{\unicdcdgdad}\\
X1){\unicdcdcdhd}((X0{\unicdcdgdad}X2){\unicdcdcdhd}((X1{\unicdcdgdad}X2){\unicdcdcdhd}((k4\_complex2~X0~X1~X2=k6\_numbers){\unicdcdcdhd}(\\
(\preoh (k4\_complex2~X1~X2~X0=k6\_numbers){\unicdcdcdhd}(k4\_complex2~X2~X0~X1=k32\_sin\_cos)){\unicdcdcdhd}\\
(\preoh (k4\_complex2~X1~X2~X0=k32\_sin\_cos){\unicdcdcdhd}(k4\_complex2~X2~X0~X1=k6\_numbers)))))))))\end{array}
\label{hyp:ehidhdpfdgpgngahmgfgihcd}
\end{equation}
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}\\
((k2\_euclid\_3~X0=k2\_euclid\_3~X1){\unicdbdjdcd}(X0=X1)))\end{array}
\label{hyp:ehedpffgfhdgmgjgegpfdd}
\end{equation}
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}\\
({\unicdcdadad} X3 .  (v1\_xreal\_0~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (v1\_xreal\_0~X4){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
(v1\_xreal\_0~X5){\unicdbdjdcd}(\preoh (X0 \in k5\_jgraph\_6~X3~X4~X5){\unicdcdcdhd}((X1 \in k5\_jgraph\_6~\\
X3~X4~X5){\unicdcdcdhd}((X2 \in k5\_jgraph\_6~X3~X4~X5){\unicdcdcdhd}((X0{\unicdcdgdad}X1){\unicdcdcdhd}((X1{\unicdcdgdad}X2){\unicdcdcdhd}(k4\_euclid\_3~\\
X0~X1~X2=k32\_sin\_cos)))))))))))\end{array}
\label{hyp:ehddfdpffgfhdgmgjgegpfgd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
(m1\_subset\_1~(k2\_euclid\_3~X0)~k2\_numbers)\end{array}
\label{hyp:egehpflgcdpffgfhdgmgjgegpfdd}
\end{equation}
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}\\
(k4\_euclid\_3~X0~X1~X2=k4\_complex2~(k2\_euclid\_3~X0)~(k2\_euclid\_3~\\
X1)~(k2\_euclid\_3~X2))))\end{array}
\label{hyp:egedpffgfhdgmgjgegpfdd}
\end{equation}
\begin{theorem}\label{thm:ehddhdpffgfhdgmgjgegpfgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (v1\_xreal\_0~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (v1\_xreal\_0~X4){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
(v1\_xreal\_0~X5){\unicdbdjdcd}(((X0 \in k5\_jgraph\_6~X3~X4~X5){\unicdcdcdhd}((X1 \in k5\_jgraph\_6~\\
X3~X4~X5){\unicdcdcdhd}((X2 \in k5\_jgraph\_6~X3~X4~X5){\unicdcdcdhd}(k4\_euclid\_3~X0~X1~X2=k6\_numbers)))){\unicdbdjdcd}\\
((X0=X1){\unicdcdcdid}((X1=X2){\unicdcdcdid}(X0=X2)))))))))\end{array}$$
\end{theorem}
\end{document}
