reserve G for _Graph;
reserve G2 for _Graph, G1 for Supergraph of G2;
reserve V for set;
reserve v for object;

theorem
  for G2, v for G1 being addVertex of G2, v
  holds G1 == G2 iff v in the_Vertices_of G2 by Th82, ZFMISC_1:31;
