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

theorem
  for G2 for v1, v2 being Vertex of G2, e being object
  for G1 being addEdge of G2,v1,e,v2
  holds G1.edgesBetween(the_Vertices_of G2) = the_Edges_of G1
proof
  let G2;
  let v1, v2 be Vertex of G2, e be object;
  let G1 be addEdge of G2,v1,e,v2;
  thus G1.edgesBetween(the_Vertices_of G2)
     = G1.edgesBetween(the_Vertices_of G1) by Th106
    .= the_Edges_of G1 by GLIB_000:34;
end;
