\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{t1\_binarith (TMRPPqhQnxdr82dar2Wed2S7Vcopz14irF5)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ k2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k8\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k12\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\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}(k4\_finseq\_1~\\
X2=k2\_finseq\_1~X0)))\end{array}
\label{hyp:ehbdcdedpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (m2\_finseq\_1~X2~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_finseq\_1~X3~X1){\unicdbdjdcd}\\
((X0 \in k4\_finseq\_1~X2){\unicdbdjdcd}(k7\_partfun1~X1~(k8\_finseq\_1~X1~X2~X3)~X0=\\
k7\_partfun1~X1~X2~X0)))))\end{array}
\label{hyp:mgbdgdpfggjgogdhfgbhpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~X0)){\unicdbdjdcd}\\
(m2\_finseq\_1~(k12\_finseq\_1~X0~X1)~X0)\end{array}
\label{hyp:egehpflgbdcdpfggjgogdhfgbhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdpfcgjgogbgchjgehig}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(\preoh v1\_xboole\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~X2){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
((v3\_card\_1~X4~X1){\unicdcdcdhd}(m2\_finseq\_1~X4~X2)){\unicdbdjdcd}((X0 \in k2\_finseq\_1~X1){\unicdbdjdcd}\\
(k7\_partfun1~X2~(k8\_finseq\_1~X2~X4~(k12\_finseq\_1~X2~X3))~X0=k7\_partfun1~\\
X2~X4~X0))))))\end{array}$$
\end{theorem}
\end{document}
