\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=}
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\newcommand\unicdcdbdgd{\setminus}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t12\_radix\_3 (TMQAhS3tkUeuPXz1j8q7qtgRyokc3RjuZ6E)}
\maketitle
Let $ v1\_int\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k5\_radix\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ np\_\_0 : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_radix\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_nat\_d : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{np\_\_0}}\label{hyp:dhahdgadpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{{r1\_xxreal\_0}~{({{k4\_xcmplx\_0}~{np\_\_1}})}}~{({{k4\_xcmplx\_0}~{np\_\_1}})}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchngbdpfchngbd}
\end{equation}
Assume the following.
\begin{equation}
{{{r1\_xxreal\_0}~{({{k4\_xcmplx\_0}~{np\_\_1}})}}~{np\_\_1}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchngbdpfchbd}
\end{equation}
Assume the following.
\begin{equation}
{{{r1\_xxreal\_0}~{({{k4\_xcmplx\_0}~{np\_\_1}})}}~{np\_\_0}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchngbdpfchad}
\end{equation}
Assume the following.
\begin{equation}
{{{r1\_xxreal\_0}~{np\_\_1}}~{np\_\_1}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdpfchbd}
\end{equation}
Assume the following.
\begin{equation}
{{{r1\_xxreal\_0}~{np\_\_0}}~{np\_\_1}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchadpfchbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_int\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}(((r1\_xxreal\_0~\\
(k1\_radix\_1~(k7\_nat\_d~X1~np\_\_1))~X0){\unicdbdjdcd}(k5\_radix\_3~X0~X1=np\_\_1)){\unicdcdcdhd}\\
(((\preoh r1\_xxreal\_0~(k4\_xcmplx\_0~(k1\_radix\_1~(k7\_nat\_d~X1~np\_\_1)))~\\
X0){\unicdbdjdcd}(k5\_radix\_3~X0~X1=k4\_xcmplx\_0~np\_\_1)){\unicdcdcdhd}((r1\_xxreal\_0~(k4\_xcmplx\_0~\\
(k1\_radix\_1~(k7\_nat\_d~X1~np\_\_1)))~X0){\unicdbdjdcd}((r1\_xxreal\_0~(k1\_radix\_1~\\
(k7\_nat\_d~X1~np\_\_1))~X0){\unicdcdcdid}(k5\_radix\_3~X0~X1=k6\_numbers))))))\end{array}
\label{hyp:egddpfchbgegjgihpfdd}
\end{equation}
\begin{theorem}\label{thm:ehbdcdpfchbgegjgihpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_int\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}((r1\_xxreal\_0~\\
(k4\_xcmplx\_0~np\_\_1)~(k5\_radix\_3~X0~X1)){\unicdcdcdhd}(r1\_xxreal\_0~(k5\_radix\_3~\\
X0~X1)~np\_\_1)))\end{array}$$
\end{theorem}
\end{document}
