If you evaluate
Reduce[$Assumptions && (s (-1 + q - q u)) + lab (-1 + q) q u v < 0]
you can recognize that it is equivalent to $Assumptions. Mathematica should know, because
Simplify[Equivalent[$Assumptions,
Reduce[$Assumptions && (s (-1 + q - q u)) + lab (-1 + q) q u v <
0]]]
gives True. You can automate this idea:
inequalityCheck[ineq_] :=
Simplify[Equivalent[$Assumptions, Reduce[$Assumptions && ineq]]]
I have not tried it on other inequalities, though.
