\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{t14\_arytm\_2 (TMW8HBgtFJtuCUYVsCenpDrDPXDU74AAmiW)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_arytm\_2 : {\iota}$ be given.
Let $ k11\_arytm\_3 : {\iota}$ be given.
Let $ k8\_arytm\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k12\_arytm\_3 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_arytm\_3 : {\iota}$ be given.
Let $ k5\_arytm\_3 : {\iota}$ be given.
Let $ k1\_arytm\_2 : {\iota}$ be given.
Let $ k6\_arytm\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_arytm\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ c3\_\_arytm\_2 : {\iota}$ be given.
Let $ k4\_arytm\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_arytm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ r3\_arytm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k12\_arytm\_3}={k1\_arytm\_3}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdcdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~(k1\_zfmisc\_1~k5\_arytm\_3)~k1\_arytm\_2){\unicdbdjdcd}\\
(\preoh (X0{\unicdcdgdad}k11\_arytm\_3){\unicdcdcdhd}({\unicdcdadad} X1 .  (m2\_subset\_1~X1~(k1\_zfmisc\_1~\\
k5\_arytm\_3)~k1\_arytm\_2){\unicdbdjdcd}(k6\_arytm\_2~X0~X1{\unicdcdgdad}k3\_arytm\_2~c3\_\_arytm\_2)))\end{array}
\label{hyp:mggdjdpfbgchjhehngpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_arytm\_2){\unicdbdjdcd}(k4\_arytm\_2~(k3\_arytm\_2~\\
X0)=X0)\end{array}
\label{hyp:mgddddpfbgchjhehngpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~(k1\_zfmisc\_1~k5\_arytm\_3)~k1\_arytm\_2){\unicdbdjdcd}\\
(k3\_arytm\_2~(k4\_arytm\_2~X0)=X0)\end{array}
\label{hyp:mgcdbdpfbgchjhehngpfcd}
\end{equation}
Assume the following.
\begin{equation}
\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}
\label{hyp:mgbdjdpfbgchjhehngpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {\preoh{{{v1\_xboole\_0}~{({{k1\_zfmisc\_1}~{X0}})}}}}}\label{hyp:ggdgbdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k1\_arytm\_2}}}}\label{hyp:ggdgbdpfbgchjhehngpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_arytm\_2){\unicdbdjdcd}(m1\_subset\_1~(k4\_arytm\_2~\\
X0)~k2\_arytm\_2)\end{array}
\label{hyp:egehpflgedpfbgchjhehngpfcd}
\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}~{k1\_arytm\_2}}~{({{k1\_zfmisc\_1}~{({{k1\_zfmisc\_1}~{k5\_arytm\_3}})}})}}\label{hyp:egehpflgbdpfbgchjhehngpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{c3\_\_arytm\_2}}~{k2\_arytm\_2}}\label{hyp:egehpfdgddpfpfbgchjhehngpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{c3\_\_arytm\_2}={k12\_arytm\_3}}\label{hyp:egfgpfdgddpfpfbgchjhehngpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_arytm\_2){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k2\_arytm\_2){\unicdbdjdcd}(k8\_arytm\_2~X0~X1=k4\_arytm\_2~(k6\_arytm\_2~(k3\_arytm\_2~\\
X0)~(k3\_arytm\_2~X1))))\end{array}
\label{hyp:egjdpfbgchjhehngpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k5\_arytm\_3=k2\_xboole\_0~(k6\_subset\_1~(ReplSep2~(toset~({\uniddcgcg} X0 : \\
\iota .  m1\_subset\_1~X0~k4\_ordinal1))~({\uniddcgcg} X0 : \iota .  toset~({\uniddcgcg} X1 : \\
\iota .  m1\_subset\_1~X1~k4\_ordinal1))~({\uniddcgcg} X0 : \iota .  {\uniddcgcg} X1 : \iota .  (r1\_arytm\_3~\\
X0~X1){\unicdcdcdhd}(X1{\unicdcdgdad}k1\_xboole\_0))~({\uniddcgcg} X0 : \iota .  {\uniddcgcg} X1 : \iota .  k4\_tarski~\\
X0~X1))~(ReplSep~(toset~({\uniddcgcg} X0 : \iota .  m1\_subset\_1~X0~k4\_ordinal1))~\\
({\uniddcgcg} X0 : \iota .  True)~({\uniddcgcg} X0 : \iota .  k4\_tarski~X0~np\_\_1)))~k4\_ordinal1\end{array}
\label{hyp:eghdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{k1\_arytm\_3}={np\_\_1}}\label{hyp:egbdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k1\_arytm\_2=k6\_subset\_1~(ReplSep~(toset~({\uniddcgcg} X0 : \iota .  m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~k5\_arytm\_3)))~({\uniddcgcg} X0 : \iota .  {\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k5\_arytm\_3){\unicdbdjdcd}((X1 \in X0){\unicdbdjdcd}(({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k5\_arytm\_3){\unicdbdjdcd}\\
((r3\_arytm\_3~X2~X1){\unicdbdjdcd}(X2 \in X0))){\unicdcdcdhd}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~k5\_arytm\_3){\unicdcdcdhd}\\
((X2 \in X0){\unicdcdcdhd}(\preoh r3\_arytm\_3~X2~X1))))))~({\uniddcgcg} X0 : \iota .  X0))~(k1\_tarski~\\
k5\_arytm\_3)\end{array}
\label{hyp:egbdpfbgchjhehngpfcd}
\end{equation}
\begin{theorem}\label{thm:ehbdedpfbgchjhehngpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_arytm\_2){\unicdbdjdcd}(\preoh (X0{\unicdcdgdad}k11\_arytm\_3){\unicdcdcdhd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k2\_arytm\_2){\unicdbdjdcd}(k8\_arytm\_2~X0~X1{\unicdcdgdad}k12\_arytm\_3)))\end{array}$$
\end{theorem}
\end{document}
