reserve G, G1, G2 for _Graph, H for Subgraph of G;

theorem Th7:
  G is edgeless iff G == createGraph([#]the_Vertices_of G)
proof
  set H = the removeEdges of G, the_Edges_of G;
  hereby
    assume G is edgeless;
    then A1: the_Edges_of G = the_Edges_of H;
    A2: the_Vertices_of G = the_Vertices_of H by GLIB_000:def 33;
    G is Subgraph of G by GLIB_000:40;
    then A3: G == H by A1, A2, GLIB_000:86;
    H == createGraph([#]the_Vertices_of G) by Th6;
    hence G == createGraph([#]the_Vertices_of G) by A3, GLIB_000:85;
  end;
  assume G == createGraph([#]the_Vertices_of G);
  hence thesis by GLIB_008:52;
end;
