Am I missing something? Assuming r is real, the only r that can satisfy -Sqrt[r]>=0 is zero.
$Assumptions = {r \[Element] Reals}; FullSimplify[-Sqrt[r] >= 0]
yields Sqrt[r] <= 0
Sqrt[r] <= 0
rather than r==0
r==0
Good, I learned something... Thanks.
