A semiring with monus, or m-semiring, is a semiring $(\mathbb{K}, \oplus, \otimes, \mathbb{0}, \mathbb{1})$ with a further binary operation $\ominus$. Here it is axiomatized through the natural order of a canonically ordered semiring, $a \le b$ when $b = a \oplus c$ for some $c$, by the Galois connection $a \ominus b \le c \iff a \le b \oplus c$; the three equations of the paper's definition, $a \oplus (b \ominus a) = b \oplus (a \ominus b)$, $(a \ominus b) \ominus c = a \ominus (b \oplus c)$ and $a \ominus a = \mathbb{0} \ominus a = \mathbb{0}$, follow and are the claims of this module. The class also carries the duplicate-eliminating operator $\delta$ of Amsterdamer, Deutch and Tannen (2011), with $\delta(\mathbb{0}) = \mathbb{0}$, $\delta(\mathbb{1} \oplus \dots \oplus \mathbb{1}) = \mathbb{1}$ and $a \otimes \delta(a \oplus b) = a$, which the paper's rewriting of aggregation uses. An alternative linear order on an annotation type is bundled separately: it is what makes a type of annotations usable as a value type once data and annotations share a column.