Just saying we want the new value to be bottom in the order, and a absorbtive value for the monoidal operation.
And that is the default behavior on the order, and the default lifting of a function of two arguments produces the new monoid we want.
(It's unfortunately not the.default monoid on Maybe a. That uses Nothing as an identity. It's not a great default. About as good as having multiply as the default on the reals would be. It is sometimes what you want, but not often enough to be a good default. )