\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{l19\_arytm\_2 (TMWFv7pJgrUsrwppRziDYNmLXtPmPxgjKPw)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_arytm\_2 : {\iota}$ be given.
Let $ k3\_arytm\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_arytm\_3 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k5\_arytm\_3 : {\iota}$ be given.
Let $ r3\_arytm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_arytm\_2 : {\iota}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_arytm\_3){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k5\_arytm\_3){\unicdbdjdcd}((\preoh r3\_arytm\_3~X1~X0){\unicdbdjded}((r3\_arytm\_3~X0~X1){\unicdcdcdhd}(X0{\unicdcdgdad}\\
X1))))\end{array}
\label{hyp:ehgdidpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k5\_arytm\_3}})}{\unicdbdjdcd}{({{{r3\_arytm\_3}~{k11\_arytm\_3}}~{X0}})}}}\label{hyp:ehgdedpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{k11\_arytm\_3}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdbdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_arytm\_2){\unicdbdjdcd}(m2\_subset\_1~(k3\_arytm\_2~\\
X0)~(k1\_zfmisc\_1~k5\_arytm\_3)~k1\_arytm\_2)\end{array}
\label{hyp:egehpflgddpfbgchjhehngpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k11\_arytm\_3}}~{k5\_arytm\_3}}\label{hyp:egehpflgbdbdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_arytm\_2){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~\\
X1~(k1\_zfmisc\_1~k5\_arytm\_3)~k1\_arytm\_2){\unicdbdjdcd}(((X0 \in k5\_arytm\_3){\unicdbdjdcd}\\
((X1=k3\_arytm\_2~X0){\unicdbdjded}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~k5\_arytm\_3){\unicdcdcdhd}\\
((X0=X2){\unicdcdcdhd}(X1=ReplSep~(toset~({\uniddcgcg} X3 : \iota .  m1\_subset\_1~X3~k5\_arytm\_3))~\\
({\uniddcgcg} X3 : \iota .  \preoh r3\_arytm\_3~X2~X3)~({\uniddcgcg} X3 : \iota .  X3)))))){\unicdcdcdhd}((\preoh X0 \in \\
k5\_arytm\_3){\unicdbdjdcd}((X1=k3\_arytm\_2~X0){\unicdbdjded}(X1=X0)))))\end{array}
\label{hyp:egddpfbgchjhehngpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjded}{({{\unicdcdadad} X1 .  {\preoh{{{X1} \in {X0}}}}})}}}\label{hyp:egbdpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:mgbdjdpfbgchjhehngpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_arytm\_2){\unicdbdjdcd}((k3\_arytm\_2~X0=k11\_arytm\_3){\unicdbdjded}\\
(X0=k11\_arytm\_3))\end{array}$$
\end{theorem}
\end{document}
