\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{l15\_quaterni (TMGpHfYM26AVf7zv4Z1NYMxcvprJoMahNpT)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k6\_quaterni : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k5\_arytm\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_quaterni : {\iota}$ be given.
Let $ k2\_quaterni : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k6\_numbers}}~{k1\_numbers}}\label{hyp:mgbdjdpfbgchjhehngpfad}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k1\_numbers}}}}\label{hyp:ggdgbdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}\\
((v1\_xreal\_0~X1){\unicdcdcdhd}((v1\_xreal\_0~X2){\unicdcdcdhd}(v1\_xreal\_0~X3)))){\unicdbdjdcd}(m1\_subset\_1~\\
(k6\_quaterni~X0~X1~X2~X3)~k1\_quaterni)\end{array}
\label{hyp:egehpflggdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_xreal\_0~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~k1\_quaterni){\unicdbdjdcd}((((X2=k6\_numbers){\unicdcdcdhd}(X3=k6\_numbers)){\unicdbdjdcd}((X4=\\
k6\_quaterni~X0~X1~X2~X3){\unicdbdjded}({\unicdcdaddd} X5 .  (m1\_subset\_1~X5~k1\_numbers){\unicdcdcdhd}\\
({\unicdcdaddd} X6 .  (m1\_subset\_1~X6~k1\_numbers){\unicdcdcdhd}((X5=X0){\unicdcdcdhd}((X6=X1){\unicdcdcdhd}\\
(X4=k5\_arytm\_0~X5~X6))))))){\unicdcdcdhd}((\preoh (X2=k6\_numbers){\unicdcdcdhd}(X3=k6\_numbers)){\unicdbdjdcd}\\
((X4=k6\_quaterni~X0~X1~X2~X3){\unicdbdjded}(X4=k2\_quaterni~k6\_numbers~np\_\_1~\\
np\_\_2~np\_\_3~X0~X1~X2~X3))))))))\end{array}
\label{hyp:eggdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjded}{({{X0} \in {k1\_numbers}})}}}\label{hyp:egbdpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:mgbdfdpfbhfhbgehfgchogjg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_numbers){\unicdbdjdcd}(k6\_quaterni~X0~X1~k6\_numbers~k6\_numbers=k5\_arytm\_0~\\
X0~X1))\end{array}$$
\end{theorem}
\end{document}
