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?