\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{t19\_partit1 (TMc7CB9uVCwjicDAHntXbANbWbySjEfsKc2)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_eqrel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_partit1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_setfam\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  \\
{\unicdcdadad} X4 .  (m1\_eqrel\_1~X4~X0){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_eqrel\_1~X5~X0){\unicdbdjdcd}\\
(((r1\_setfam\_1~X4~X5){\unicdcdcdhd}((X1 \in X5){\unicdcdcdhd}((X2 \in X4){\unicdcdcdhd}((X3 \in X1){\unicdcdcdhd}(X3 \in X2))))){\unicdbdjdcd}\\
(r1\_tarski~X2~X1))))\end{array}
\label{hyp:ehbdidpfahbgchehjgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_eqrel\_1~X1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_eqrel\_1~X2~X0){\unicdbdjdcd}(r1\_setfam\_1~X1~(k3\_partit1~X0~\\
X1~X2))))\end{array}
\label{hyp:ehbdgdpfahbgchehjgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((m1\_eqrel\_1~\\
X1~X0){\unicdcdcdhd}(m1\_eqrel\_1~X2~X0))){\unicdbdjdcd}(m1\_eqrel\_1~(k3\_partit1~X0~X1~X2)~X0)\end{array}
\label{hyp:egehpflgddpfahbgchehjgehbd}
\end{equation}
\begin{theorem}\label{thm:ehbdjdpfahbgchehjgehbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  \\
{\unicdcdadad} X4 .  (m1\_eqrel\_1~X4~X0){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_eqrel\_1~X5~X0){\unicdbdjdcd}\\
(((X1 \in k3\_partit1~X0~X4~X5){\unicdcdcdhd}((X2 \in X4){\unicdcdcdhd}((X3 \in X1){\unicdcdcdhd}(X3 \in X2)))){\unicdbdjdcd}(r1\_tarski~\\
X2~X1))))\end{array}$$
\end{theorem}
\end{document}
