I think that the source is Richard Dedekind's Was sind und was sollen die Zahlen ? (Vieweg: Braunschweig, 1888).
I quote from the English translation : THE NATURE AND MEANING OF NUMBERS, (The Open Court Publishing Co., 1901) :
98. Definition [page 37]. If $n$ is any number, then will we denote by $Z_n$ the system [set] of all numbers that are not greater than $n$ [...].
106. Theorem [page 38]. If $m < n$, then is $Z_m$ proper part of $Z_n$ and conversely.
I've found it through :
- Gregory Moore, Zermelo's Axiom of Choice : Its Origin Development and Influence (1982), page 26.
We can easily generalise it to a poset $M$ whatever, defining the mapping :
$\pi : a \to M_a$, for any $a \in M.$
where $M_a = \{ x \in M : x \le a \}$