\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{t12\_radix\_5 (TMWgMueE1g9UTywgwU8dDzbipX2y4K8jX1Z)}
\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 $ v3\_card\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_radix\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_radix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k8\_radix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_numbers : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  ((v3\_card\_1~X2~X0){\unicdcdcdhd}(m2\_finseq\_1~X2~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v3\_card\_1~X3~X0){\unicdcdcdhd}(m2\_finseq\_1~X3~X1)){\unicdbdjdcd}(({\unicdcdadad} X4 .  (v7\_ordinal1~\\
X4){\unicdbdjdcd}((X4 \in k2\_finseq\_1~X0){\unicdbdjdcd}(k1\_funct\_1~X2~X4=k1\_funct\_1~X3~X4))){\unicdbdjdcd}\\
(X2=X3)))))\end{array}
\label{hyp:ehbdbdjdpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k3\_radix\_1~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~(k3\_radix\_1~X0)~(k1\_zfmisc\_1~k4\_numbers)))\end{array}
\label{hyp:egehpflgddpfchbgegjgihpfbd}
\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}({\unicdcdadad} X3 .  ((v3\_card\_1~X3~X2){\unicdcdcdhd}(m2\_finseq\_1~\\
X3~(k3\_radix\_1~X1))){\unicdbdjdcd}(((X0 \in k2\_finseq\_1~X2){\unicdbdjdcd}(k4\_radix\_1~X0~X1~\\
X2~X3=k1\_funct\_1~X3~X0)){\unicdcdcdhd}((X0=k6\_numbers){\unicdbdjdcd}(k4\_radix\_1~X0~X1~X2~\\
X3=k6\_numbers))))))\end{array}
\label{hyp:egddpfchbgegjgihpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdcdpfchbgegjgihpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((r1\_xxreal\_0~np\_\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v3\_card\_1~X2~X0){\unicdcdcdhd}(m2\_finseq\_1~\\
X2~(k3\_radix\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v3\_card\_1~X3~X0){\unicdcdcdhd}(m2\_finseq\_1~\\
X3~(k3\_radix\_1~X1))){\unicdbdjdcd}(({\unicdcdadad} X4 .  (v7\_ordinal1~X4){\unicdbdjdcd}((X4 \in k2\_finseq\_1~\\
X0){\unicdbdjdcd}(k4\_radix\_1~X4~X1~X0~X2=k4\_radix\_1~X4~X1~X0~X3))){\unicdbdjdcd}(k8\_radix\_1~\\
X0~X1~X2=k8\_radix\_1~X0~X1~X3))))))\end{array}$$
\end{theorem}
\end{document}
