\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{t42\_arytm\_3 (TMYPyvRTmCq4X9AKU5VJKsLrvuud1a3ejKs)}
\maketitle
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k6\_arytm\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_arytm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_arytm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_arytm\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_arytm\_3 : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {\preoh{{{{{k4\_tarski}~{X0}}~{X1}} \in {k4\_ordinal1}}}}}}\label{hyp:ehddcdpfbgchjhehngpfdd}
\end{equation}
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}
{{({\preoh{{{v1\_xboole\_0}~{k4\_ordinal1}}}})}{\unicdcdcdhd}{({{v3\_ordinal1}~{k4\_ordinal1}})}}\label{hyp:ggdggdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v3\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X0)){\unicdcdcdhd}\\
((v3\_ordinal1~X1){\unicdcdcdhd}(v7\_ordinal1~X1))){\unicdbdjdcd}(m1\_subset\_1~(k8\_arytm\_3~\\
X0~X1)~k5\_arytm\_3)\end{array}
\label{hyp:egehpflgidpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_arytm\_3){\unicdbdjdcd}(m1\_subset\_1~(k7\_arytm\_3~\\
X0)~k4\_ordinal1)\end{array}
\label{hyp:egehpflghdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_arytm\_3){\unicdbdjdcd}(m1\_subset\_1~(k6\_arytm\_3~\\
X0)~k4\_ordinal1)\end{array}
\label{hyp:egehpflggdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v3\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X0)){\unicdcdcdhd}\\
((v3\_ordinal1~X1){\unicdcdcdhd}(v7\_ordinal1~X1))){\unicdbdjdcd}(m1\_subset\_1~(k4\_arytm\_3~\\
X0~X1)~k4\_ordinal1)\end{array}
\label{hyp:egehpflgedpfbgchjhehngpfdd}
\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~k4\_ordinal1){\unicdbdjdcd}(((X0 \in k4\_ordinal1){\unicdbdjdcd}((X1=k7\_arytm\_3~X0){\unicdbdjded}(X1=\\
np\_\_1))){\unicdcdcdhd}((\preoh X0 \in k4\_ordinal1){\unicdbdjdcd}((X1=k7\_arytm\_3~X0){\unicdbdjded}({\unicdcdaddd} X2 .  \\
((v3\_ordinal1~X2){\unicdcdcdhd}(v7\_ordinal1~X2)){\unicdcdcdhd}(X0=k4\_tarski~X2~X1))))))\end{array}
\label{hyp:egjdpfbgchjhehngpfdd}
\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~k4\_ordinal1){\unicdbdjdcd}(((X0 \in k4\_ordinal1){\unicdbdjdcd}((X1=k6\_arytm\_3~X0){\unicdbdjded}(X1=\\
X0))){\unicdcdcdhd}((\preoh X0 \in k4\_ordinal1){\unicdbdjdcd}((X1=k6\_arytm\_3~X0){\unicdbdjded}({\unicdcdaddd} X2 .  \\
((v3\_ordinal1~X2){\unicdcdcdhd}(v7\_ordinal1~X2)){\unicdcdcdhd}(X0=k4\_tarski~X1~X2))))))\end{array}
\label{hyp:egidpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k4\_tarski~X0~X1=k2\_tarski~(k2\_tarski~X0~\\
X1)~(k1\_tarski~X0)\end{array}
\label{hyp:egfdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v3\_ordinal1~X1){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}(((X1=k1\_xboole\_0){\unicdbdjdcd}(k8\_arytm\_3~\\
X0~X1=k1\_xboole\_0)){\unicdcdcdhd}(((k4\_arytm\_3~X1~X0=np\_\_1){\unicdbdjdcd}(k8\_arytm\_3~\\
X0~X1=k4\_arytm\_3~X0~X1)){\unicdcdcdhd}(\preoh (X1{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}((k4\_arytm\_3~X1~\\
X0{\unicdcdgdad}np\_\_1){\unicdcdcdhd}(k8\_arytm\_3~X0~X1{\unicdcdgdad}k4\_tarski~(k4\_arytm\_3~X0~X1)~(k4\_arytm\_3~\\
X1~X0)))))))\end{array}
\label{hyp:egbdadpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_tarski}~{X0}}~{X1}}={{{k2\_tarski}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{v3\_ordinal1}~{X0}})}}}\label{hyp:dgdggdpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehedcdpfbgchjhehngpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v3\_ordinal1~X1){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}((X0{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}((k6\_arytm\_3~\\
(k8\_arytm\_3~X1~X0)=k4\_arytm\_3~X1~X0){\unicdcdcdhd}(k7\_arytm\_3~(k8\_arytm\_3~\\
X1~X0)=k4\_arytm\_3~X0~X1))))\end{array}$$
\end{theorem}
\end{document}
