reserve G, G2 for _Graph, V, E for set,
  v for object;

theorem
  for G, v, V for G1 being addAdjVertexToAll of G,v,V
  for G2 being addAdjVertexFromAll of G,v,V, w being object
  holds (w is Vertex of G1 iff w is Vertex of G2) by Th32;
