\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
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\begin{document}
\title{t13\_radix\_2 (TMYRU4Rk38heXqw7GgSevJiZsUntYoJWtXy)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_card\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k3\_radix\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_radix\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k8\_radix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_radix\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k7\_radix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_wsierp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k16\_rvsum\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_numbers : {\iota}$ be given.
Let $ k1\_gr\_cy\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v3\_card\_1~X2~X0){\unicdcdcdhd}(m2\_finseq\_1~X2~k5\_numbers)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v3\_card\_1~X3~X0){\unicdcdcdhd}(m2\_finseq\_1~X3~(k3\_radix\_1~X1))){\unicdbdjdcd}((X2=X3){\unicdbdjdcd}\\
(k2\_radix\_2~X0~X1~X2=k7\_radix\_1~X0~X1~X3)))))\end{array}
\label{hyp:ehbdcdpfchbgegjgihpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_finseq\_1~X0~k5\_numbers){\unicdbdjdcd}(k2\_wsierp\_1~X0=k16\_rvsum\_1~\\
X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfhhdhjgfgchahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_finseq\_1~X0~k4\_numbers){\unicdbdjdcd}(k1\_gr\_cy\_1~X0=k16\_rvsum\_1~\\
X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfhgchpfdgjhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v7\_ordinal1~X0){\unicdcdcdhd}((v7\_ordinal1~\\
X1){\unicdcdcdhd}((v3\_card\_1~X2~X0){\unicdcdcdhd}(m1\_finseq\_1~X2~(k3\_radix\_1~X1))))){\unicdbdjdcd}(\\
(v3\_card\_1~(k7\_radix\_1~X0~X1~X2)~X0){\unicdcdcdhd}(m2\_finseq\_1~(k7\_radix\_1~\\
X0~X1~X2)~k4\_numbers))\end{array}
\label{hyp:egehpflghdpfchbgegjgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v7\_ordinal1~X0){\unicdcdcdhd}((v7\_ordinal1~\\
X1){\unicdcdcdhd}((v3\_card\_1~X2~X0){\unicdcdcdhd}(m1\_finseq\_1~X2~k5\_numbers)))){\unicdbdjdcd}((v3\_card\_1~\\
(k2\_radix\_2~X0~X1~X2)~X0){\unicdcdcdhd}(m2\_finseq\_1~(k2\_radix\_2~X0~X1~X2)~k5\_numbers))\end{array}
\label{hyp:egehpflgcdpfchbgegjgihpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v3\_card\_1~X2~X0){\unicdcdcdhd}(m2\_finseq\_1~X2~(k3\_radix\_1~X1))){\unicdbdjdcd}(k8\_radix\_1~\\
X0~X1~X2=k1\_gr\_cy\_1~(k7\_radix\_1~X0~X1~X2))))\end{array}
\label{hyp:eghdpfchbgegjgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v3\_card\_1~X2~X0){\unicdcdcdhd}(m2\_finseq\_1~X2~k5\_numbers)){\unicdbdjdcd}(k3\_radix\_2~\\
X0~X1~X2=k2\_wsierp\_1~(k2\_radix\_2~X0~X1~X2))))\end{array}
\label{hyp:egddpfchbgegjgihpfcd}
\end{equation}
\begin{theorem}\label{thm:ehbdddpfchbgegjgihpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v3\_card\_1~X2~X0){\unicdcdcdhd}(m2\_finseq\_1~X2~k5\_numbers)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v3\_card\_1~X3~X0){\unicdcdcdhd}(m2\_finseq\_1~X3~(k3\_radix\_1~X1))){\unicdbdjdcd}((X2=X3){\unicdbdjdcd}\\
(k3\_radix\_2~X0~X1~X2=k8\_radix\_1~X0~X1~X3)))))\end{array}$$
\end{theorem}
\end{document}
