less numerical dimension

LEMMA 4.4 Let .X; / be a divisorially log terminal pair, where X is a Q-factorial projective variety and .KX C / is nef. Let A0 be an ample divisor, and let 0 0 be a divisor such that KX C A0 C 0 is pseudoeffective, with numerical dimension k. Suppose that has a component P which is vertical for the ample model W X Z0 of KX C A0 C 0. Then there are an ample divisor A1 and a divisor 0 1 such that KX C A1 C 1 is pseudoeffective and the numerical dimension of KX C A1 C 1 is less than k. (page) (Brown et al., 2018, p. 952)