Needless to say though that all the results we obtained thus far are still valid.
let us consider a point (ν, µ) on the boundary between I 0 and I + , namely, there exist a line ℓ +i such that, By definition, for any j ∈ I 0 we have q i < q j for all j ∈ I 0 which implies that Summing over j ∈ I 0 we get that and we must be moving "up" from I 0 to I + when the line ℓ 0 hits ℓ i .