reconsider E = {} as Subset of KD by XBOOLE_1:2;
( E in the topology of KD & card E c= card (Segm (i + 1)) ) by PRE_TOPC:def 2;
then E in the_subsets_with_limited_card ((Segm (i + 1)), the topology of KD) by Def2;
hence not Skeleton_of (KD,i) is void ; :: thesis: verum