  Martin-L\"{o}f type theory $\mathbf{MLTT}$ was extended by Setzer with the
so-called Mahlo universe types. This extension is called $\mathbf{MLM}$ and was
introduced to develop a variant of $\mathbf{MLTT}$ equipped with an analogue of
a large cardinal. Another instance of constructive systems extended with an
analogue of a large set was formulated in the context of Aczel's constructive
set theory: $\mathbf{CZF}$. Rathjen, Griffor and Palmgren extended
$\mathbf{CZF}$ with inaccessible sets of all transfinite orders. It is unknown
whether this extension of $\mathbf{CZF}$ is directly interpretable by Mahlo
universes. In particular, how to construct the transfinite hierarchy of
inaccessible sets using the reflection property of the Mahlo universe in
$\mathbf{MLM}$ is not well understood. We extend $\mathbf{MLM}$ further by
adding the accessibility predicate to it and show that the above extension of
$\mathbf{CZF}$ is directly interpretable in $\mathbf{MLM}$ using the
accessibility predicate.
