\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=}
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\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t3\_int\_3 (TMMKtjgd6Jom9vfi5anCxJLVgYX3ZwsAJfo)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_int\_3 : {\iota}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k8\_group\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_int\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_int\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_int\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~(u1\_struct\_0~k1\_int\_3)){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(u1\_struct\_0~k1\_int\_3))){\unicdbdjdcd}(m1\_subset\_1~(k4\_int\_3~\\
X0~X1)~(u1\_struct\_0~k1\_int\_3))\end{array}
\label{hyp:egehpflgedpfjgogehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~k1\_int\_3)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~k1\_int\_3)){\unicdbdjdcd}((X1{\unicdcdgdad}k4\_struct\_0~k1\_int\_3){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~k1\_int\_3)){\unicdbdjdcd}((X2=k5\_int\_3~\\
X0~X1){\unicdbdjded}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~k1\_int\_3)){\unicdcdcdhd}(\\
(X0=k3\_rlvect\_1~k1\_int\_3~(k8\_group\_1~k1\_int\_3~X3~X1)~X2){\unicdcdcdhd}((r1\_xxreal\_0~\\
(k4\_struct\_0~k1\_int\_3)~X2){\unicdcdcdhd}(\preoh r1\_xxreal\_0~(k2\_int\_3~X1)~X2))))))))\end{array}
\label{hyp:eghdpfjgogehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~k1\_int\_3)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~k1\_int\_3)){\unicdbdjdcd}((X1{\unicdcdgdad}k4\_struct\_0~k1\_int\_3){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~k1\_int\_3)){\unicdbdjdcd}((X2=k4\_int\_3~\\
X0~X1){\unicdbdjded}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~k1\_int\_3)){\unicdcdcdhd}(\\
(X0=k3\_rlvect\_1~k1\_int\_3~(k8\_group\_1~k1\_int\_3~X2~X1)~X3){\unicdcdcdhd}((r1\_xxreal\_0~\\
(k4\_struct\_0~k1\_int\_3)~X3){\unicdcdcdhd}(\preoh r1\_xxreal\_0~(k2\_int\_3~X1)~X3))))))))\end{array}
\label{hyp:eggdpfjgogehpfdd}
\end{equation}
\begin{theorem}\label{thm:ehddpfjgogehpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~k1\_int\_3)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~k1\_int\_3)){\unicdbdjdcd}((X1{\unicdcdgdad}k4\_struct\_0~k1\_int\_3){\unicdbdjdcd}\\
(X0=k3\_rlvect\_1~k1\_int\_3~(k8\_group\_1~k1\_int\_3~(k4\_int\_3~X0~X1)~\\
X1)~(k5\_int\_3~X0~X1))))\end{array}$$
\end{theorem}
\end{document}
