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

theorem Th106:
  for G2 for v1, v2 being Vertex of G2, e being object
  for G1 being addEdge of G2,v1,e,v2
  holds the_Vertices_of G1 = the_Vertices_of G2
proof
  let G2;
  let v1, v2 be Vertex of G2, e be object;
  let G1 be addEdge of G2,v1,e,v2;
  per cases;
  suppose not e in the_Edges_of G2;
    hence thesis by Def11;
  end;
  suppose e in the_Edges_of G2;
    then G1 == G2 by Def11;
    hence thesis by GLIB_000:def 34;
  end;
end;
