\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{t47\_arytm\_3 (TMXY5giiBm5rGpmYyYzEace5Dw66PS8ZNVZ)}
\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 $ k9\_arytm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_arytm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_ordinal3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_ordinal2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_ordinal2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_ordinal3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v3\_ordinal1~X2){\unicdbdjdcd}(k11\_ordinal2~(k10\_ordinal2~X0~X1)~X2=k10\_ordinal2~\\
(k11\_ordinal2~X0~X2)~(k11\_ordinal2~X1~X2))))\end{array}
\label{hyp:ehedgdpfpgchegjgogbgmgdd}
\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}({\unicdcdadad} X2 .  ((v3\_ordinal1~\\
X2){\unicdcdcdhd}(v7\_ordinal1~X2)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v3\_ordinal1~X3){\unicdcdcdhd}(v7\_ordinal1~\\
X3)){\unicdbdjdcd}(\preoh (X1{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}((X0{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}(k9\_arytm\_3~(k8\_arytm\_3~\\
X2~X1)~(k8\_arytm\_3~X3~X0){\unicdcdgdad}k8\_arytm\_3~(k8\_ordinal3~(k9\_ordinal3~\\
X2~X0)~(k9\_ordinal3~X1~X3))~(k9\_ordinal3~X1~X0)))))))\end{array}
\label{hyp:ehedgdpfbgchjhehngpfdd}
\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}({\unicdcdadad} X2 .  ((v3\_ordinal1~\\
X2){\unicdcdcdhd}(v7\_ordinal1~X2)){\unicdbdjdcd}((X0{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}(k8\_arytm\_3~(k9\_ordinal3~\\
X1~X0)~(k9\_ordinal3~X2~X0)=k8\_arytm\_3~X1~X2))))\end{array}
\label{hyp:ehededpfbgchjhehngpfdd}
\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}(k9\_ordinal3~X0~X1=k11\_ordinal2~\\
X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfpgchegjgogbgmgdd}
\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}(k8\_ordinal3~X0~X1=k10\_ordinal2~\\
X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpfpgchegjgogbgmgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}(\\
(v3\_ordinal1~(k10\_ordinal2~X0~X1)){\unicdcdcdhd}(v7\_ordinal1~(k10\_ordinal2~\\
X0~X1)))\end{array}
\label{hyp:ggdgfdpfpgchegjgogbgmgcd}
\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}((v3\_ordinal1~(k11\_ordinal2~\\
X0~X1)){\unicdcdcdhd}(v7\_ordinal1~(k11\_ordinal2~X0~X1)))\end{array}
\label{hyp:ggdgedpfpgchegjgogbgmgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v3\_ordinal1~X0){\unicdcdcdhd}(v3\_ordinal1~X1)){\unicdbdjdcd}(\\
v3\_ordinal1~(k11\_ordinal2~X0~X1))\end{array}
\label{hyp:egehpflgbdbdpfpgchegjgogbgmgcd}
\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}(k9\_ordinal3~X0~X1=k9\_ordinal3~\\
X1~X0)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgjdpfpgchegjgogbgmgdd}
\end{equation}
\begin{theorem}\label{thm:ehedhdpfbgchjhehngpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v3\_ordinal1~X1){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v3\_ordinal1~\\
X2){\unicdcdcdhd}(v7\_ordinal1~X2)){\unicdbdjdcd}((X0{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}(k9\_arytm\_3~(k8\_arytm\_3~\\
X1~X0)~(k8\_arytm\_3~X2~X0)=k8\_arytm\_3~(k8\_ordinal3~X1~X2)~X0))))\end{array}$$
\end{theorem}
\end{document}
