We will apply this kind of treatment to inequalities I1 and I2. We will use some of the derived inequalities in the proofs of the properties in the next section. The good "balance" between the strength of an inequality and its "starting point" changes from problem to problem, and we
picked the most suitable inequalities for our purposes from a list that we obtained by gradually weakening the mentioned inequalities. We will supply this list in the Appendix along with the way we obtained them; some of these inequalities might also be useful in other applications.