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\begin{document}
\title{t10\_nat\_lat (TMJjMkAoydRmo3Sezbnk8bpEpZBuJjpxQSA)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_nat\_lat : {\iota}$ be given.
Let $ k1\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_nat\_lat : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~k3\_nat\_lat)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~k3\_nat\_lat)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~k3\_nat\_lat)){\unicdbdjdcd}(k1\_binop\_1~k1\_nat\_lat~X0~(k1\_binop\_1~\\
k1\_nat\_lat~X1~X2)=k1\_binop\_1~k1\_nat\_lat~(k1\_binop\_1~k1\_nat\_lat~\\
X0~X1)~X2)))\end{array}
\label{hyp:ehjdpfogbgehpfmgbgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~k3\_nat\_lat)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~k3\_nat\_lat)){\unicdbdjdcd}(k1\_binop\_1~k1\_nat\_lat~\\
X0~X1=k1\_binop\_1~k1\_nat\_lat~X1~X0))\end{array}
\label{hyp:ehgdpfogbgehpfmgbgeh}
\end{equation}
\begin{theorem}\label{thm:ehbdadpfogbgehpfmgbgeh}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~k3\_nat\_lat)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~k3\_nat\_lat)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~k3\_nat\_lat)){\unicdbdjdcd}((k1\_binop\_1~k1\_nat\_lat~X0~(k1\_binop\_1~\\
k1\_nat\_lat~X1~X2)=k1\_binop\_1~k1\_nat\_lat~(k1\_binop\_1~k1\_nat\_lat~\\
X1~X0)~X2){\unicdcdcdhd}((k1\_binop\_1~k1\_nat\_lat~X0~(k1\_binop\_1~k1\_nat\_lat~X1~\\
X2)=k1\_binop\_1~k1\_nat\_lat~(k1\_binop\_1~k1\_nat\_lat~X0~X2)~X1){\unicdcdcdhd}(\\
(k1\_binop\_1~k1\_nat\_lat~X0~(k1\_binop\_1~k1\_nat\_lat~X1~X2)=k1\_binop\_1~\\
k1\_nat\_lat~(k1\_binop\_1~k1\_nat\_lat~X2~X1)~X0){\unicdcdcdhd}(k1\_binop\_1~k1\_nat\_lat~\\
X0~(k1\_binop\_1~k1\_nat\_lat~X1~X2)=k1\_binop\_1~k1\_nat\_lat~(k1\_binop\_1~\\
k1\_nat\_lat~X2~X0)~X1))))))\end{array}$$
\end{theorem}
\end{document}
