This is a supplement material for a published article by the authors.In the published paper `Determination of Stability with respect to Positive Orthant
for a Class of Positive Nonlinear Systems,' IEEE Trans. on Automatic Control, vol. 53, no. 5, pp. 1329-1334, 2008, by the authors, some proofs are omitted due to the space limitation of the journal. In this note, we present those omitted proofs
