\documentclass{article}
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\newtheorem{lemma}{Lemma}
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\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
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\begin{document}
\title{t11\_arytm\_3 (TMdBYihyuDwnUY9Wc7TCt7QpodAV5LM6okg)}
\maketitle
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r2\_arytm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k8\_ordinal3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_ordinal3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_ordinal2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_ordinal3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_ordinal2 : {{\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}(k5\_ordinal3~(k11\_ordinal2~X0~X1)~(k11\_ordinal2~\\
X2~X1)=k11\_ordinal2~(k5\_ordinal3~X0~X2)~X1)))\end{array}
\label{hyp:ehgdddpfpgchegjgogbgmgdd}
\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}((r2\_arytm\_3~X0~X1){\unicdbdjded}({\unicdcdaddd} X2 .  \\
((v3\_ordinal1~X2){\unicdcdcdhd}(v7\_ordinal1~X2)){\unicdcdcdhd}(X1=k9\_ordinal3~X0~X2))))\end{array}
\label{hyp:ehfdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}(k5\_ordinal3~\\
(k10\_ordinal2~X0~X1)~X0=X1))\end{array}
\label{hyp:ehfdcdpfpgchegjgogbgmgdd}
\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}(v7\_ordinal1~X0)){\unicdcdcdhd}\\
((v3\_ordinal1~X1){\unicdcdcdhd}(v7\_ordinal1~X1))){\unicdbdjdcd}((v3\_ordinal1~(k5\_ordinal3~\\
X0~X1)){\unicdcdcdhd}(v7\_ordinal1~(k5\_ordinal3~X0~X1)))\end{array}
\label{hyp:ggdgddpfpgchegjgogbgmgdd}
\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}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{v3\_ordinal1}~{X0}})}}}\label{hyp:dgdggdpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehbdbdpfbgchjhehngpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v3\_ordinal1~X1){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v3\_ordinal1~\\
X2){\unicdcdcdhd}(v7\_ordinal1~X2)){\unicdbdjdcd}(((r2\_arytm\_3~X0~X1){\unicdcdcdhd}(r2\_arytm\_3~X0~(k8\_ordinal3~\\
X1~X2))){\unicdbdjdcd}(r2\_arytm\_3~X0~X2))))\end{array}$$
\end{theorem}
\end{document}
