# Concavity: Definition similar to sub-modularity

We know that for $$b \geq a$$, and some $$s \geq 0$$, a concave function $$f$$ satisfies:

$$f(a+s) - f(a) \geq f(b+s) - f(b)$$.

This is not a frequent definition of concavity, but can be found, e.g., here.

My question is, what is the name of this property? Is it easy to prove without Taylor Expansions?