\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{t41\_arytm\_3 (TMKWw75ANak1J2czHg3EPp9qAiL4BX51oLY)}
\maketitle
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k8\_arytm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k4\_arytm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X0)){\unicdbdjdcd}((X0{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}\\
(k4\_arytm\_3~X0~X0=np\_\_1))\end{array}
\label{hyp:ehcdhdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v3\_ordinal1~X1){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}(((X1=k1\_xboole\_0){\unicdbdjdcd}(k8\_arytm\_3~\\
X0~X1=k1\_xboole\_0)){\unicdcdcdhd}(((k4\_arytm\_3~X1~X0=np\_\_1){\unicdbdjdcd}(k8\_arytm\_3~\\
X0~X1=k4\_arytm\_3~X0~X1)){\unicdcdcdhd}(\preoh (X1{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}((k4\_arytm\_3~X1~\\
X0{\unicdcdgdad}np\_\_1){\unicdcdcdhd}(k8\_arytm\_3~X0~X1{\unicdcdgdad}k4\_tarski~(k4\_arytm\_3~X0~X1)~(k4\_arytm\_3~\\
X1~X0)))))))\end{array}
\label{hyp:egbdadpfbgchjhehngpfdd}
\end{equation}
\begin{theorem}\label{thm:ehedbdpfbgchjhehngpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X0)){\unicdbdjdcd}((X0{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}\\
(k8\_arytm\_3~X0~X0=np\_\_1))\end{array}$$
\end{theorem}
\end{document}
