\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}
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\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t36\_arytm\_3 (TMRArNkeprtasJjPssi5GKVohKipckKrWh6)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_arytm\_3 : {\iota}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_arytm\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_arytm\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ r1\_arytm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_arytm\_3){\unicdbdjdcd}(\preoh (\preoh X0 \in k4\_ordinal1){\unicdcdcdhd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k4\_ordinal1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~k4\_ordinal1){\unicdbdjdcd}(\preoh (X0=k4\_tarski~X1~X2){\unicdcdcdhd}((r1\_arytm\_3~X1~X2){\unicdcdcdhd}(\\
(X2{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}(X2{\unicdcdgdad}np\_\_1)))))))\end{array}
\label{hyp:ehcdjdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (k4\_tarski~X0~X1=\\
k4\_tarski~X2~X3){\unicdbdjdcd}((X0=X2){\unicdcdcdhd}(X1=X3))\end{array}
\label{hyp:ehbdpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_arytm\_3){\unicdbdjdcd}(m1\_subset\_1~(k7\_arytm\_3~\\
X0)~k4\_ordinal1)\end{array}
\label{hyp:egehpflghdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_arytm\_3){\unicdbdjdcd}(m1\_subset\_1~(k6\_arytm\_3~\\
X0)~k4\_ordinal1)\end{array}
\label{hyp:egehpflggdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_arytm\_3){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k4\_ordinal1){\unicdbdjdcd}(((X0 \in k4\_ordinal1){\unicdbdjdcd}((X1=k7\_arytm\_3~X0){\unicdbdjded}(X1=\\
np\_\_1))){\unicdcdcdhd}((\preoh X0 \in k4\_ordinal1){\unicdbdjdcd}((X1=k7\_arytm\_3~X0){\unicdbdjded}({\unicdcdaddd} X2 .  \\
((v3\_ordinal1~X2){\unicdcdcdhd}(v7\_ordinal1~X2)){\unicdcdcdhd}(X0=k4\_tarski~X2~X1))))))\end{array}
\label{hyp:egjdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_arytm\_3){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k4\_ordinal1){\unicdbdjdcd}(((X0 \in k4\_ordinal1){\unicdbdjdcd}((X1=k6\_arytm\_3~X0){\unicdbdjded}(X1=\\
X0))){\unicdcdcdhd}((\preoh X0 \in k4\_ordinal1){\unicdbdjdcd}((X1=k6\_arytm\_3~X0){\unicdbdjded}({\unicdcdaddd} X2 .  \\
((v3\_ordinal1~X2){\unicdcdcdhd}(v7\_ordinal1~X2)){\unicdcdcdhd}(X0=k4\_tarski~X1~X2))))))\end{array}
\label{hyp:egidpfbgchjhehngpfdd}
\end{equation}
\begin{theorem}\label{thm:ehddgdpfbgchjhehngpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_arytm\_3){\unicdbdjdcd}((\preoh X0 \in k4\_ordinal1){\unicdbdjdcd}\\
((X0=k4\_tarski~(k6\_arytm\_3~X0)~(k7\_arytm\_3~X0)){\unicdcdcdhd}(k7\_arytm\_3~\\
X0{\unicdcdgdad}np\_\_1)))\end{array}$$
\end{theorem}
\end{document}
