Note I posted this a few days ago on stackexchange. It seems people there can't help me resolve this.
To make the example reproducible I find I need a number of variables.
All my variables are Reals and greater 0. So I use
$Assumptions = Element[lab, Reals] && Element[q, Reals] &&
Element[r, Reals] && Element[s, Reals] && Element[t, Reals] &&
Element[u, Reals] && Element[v, Reals] &&
lab > 0 && q > 0 && r > 0 && s > 0 && t > 0 && u > 0 && v > 0 && q < 1
From an equation system I get lengthy solutions having terms like following and I am interested whether they are smaller 0.
My problem is to weed out the parts that are "obviously" true. So I actually obtain the following expressions as part of a larger expression.
(s (-1 + q - q u)) < 0 // Refine
lab (-1 + q) q u v < 0 // Refine
They instantly evaluate to True
But as things get more complex (here just summing the two expressions) - Simplify (or Refine) fail to find the simplification instantly (in the sense that they immediately give up).
(s (-1 + q - q u)) + lab (-1 + q) q u v < 0 // Refine
I found just if would delete the lab
it would evaluate nicely. But since I have many much longer expressions this is not really an option to weed through the sub expressions manually. Is there some magic limit in Mathematica that an expression may only contain 5 variables - or something similar that I could override?
All this calculations happen instantaneously and I could definitely live with Mathematica spending some minutes searching for this simplifications. So I am very open to any suggestions even if they strain my machine a bit.