\documentclass{article}
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\newtheorem{lemma}{Lemma}
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\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\begin{document}
\title{t15\_radix\_2 (TMLPuGT4RfxgG1nbTQdb3NAPTrnsjyFRQ9A)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ r1\_radix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_radix\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_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 $ k10\_radix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ 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.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}((\\
r1\_xxreal\_0~np\_\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}((r1\_radix\_1~\\
X1~X2~X0){\unicdbdjdcd}(X2=k8\_radix\_1~X1~X0~(k10\_radix\_1~X0~X1~X2))))))\end{array}
\label{hyp:ehcdcdpfchbgegjgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v7\_ordinal1~X2){\unicdbdjdcd}(k5\_radix\_2~X2~X1~X0=k10\_radix\_1~X2~X1~X0)))\end{array}
\label{hyp:ehbdedpfchbgegjgihpfcd}
\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}({\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}
\label{hyp:ehbdddpfchbgegjgihpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v7\_ordinal1~X0){\unicdcdcdhd}((v7\_ordinal1~\\
X1){\unicdcdcdhd}(v7\_ordinal1~X2))){\unicdbdjdcd}((v3\_card\_1~(k5\_radix\_2~X0~X1~X2)~X1){\unicdcdcdhd}\\
(m2\_finseq\_1~(k5\_radix\_2~X0~X1~X2)~k5\_numbers))\end{array}
\label{hyp:egehpflgfdpfchbgegjgihpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v7\_ordinal1~X0){\unicdcdcdhd}((v7\_ordinal1~\\
X1){\unicdcdcdhd}(v7\_ordinal1~X2))){\unicdbdjdcd}((v3\_card\_1~(k10\_radix\_1~X0~X1~X2)~X1){\unicdcdcdhd}\\
(m2\_finseq\_1~(k10\_radix\_1~X0~X1~X2)~(k3\_radix\_1~X0)))\end{array}
\label{hyp:egehpflgbdadpfchbgegjgihpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdfdpfchbgegjgihpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((r1\_xxreal\_0~np\_\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}((r1\_radix\_1~\\
X0~X1~X2){\unicdbdjdcd}(X1=k3\_radix\_2~X0~X2~(k5\_radix\_2~X2~X0~X1))))))\end{array}$$
\end{theorem}
\end{document}
