reserve G for _Graph;

theorem Th8:
  G is edgeless iff VertexDomRel(G) is empty
proof
  thus G is edgeless implies VertexDomRel(G) is empty;
  thus VertexDomRel(G) is empty implies G is edgeless
  proof
    assume A1: VertexDomRel(G) is empty;
    thus G is edgeless
    proof
      assume not G is edgeless;
      then consider e being object such that
        A2: e in the_Edges_of G by XBOOLE_0:def 1;
      e DJoins (the_Source_of G).e,(the_Target_of G).e,G
        by A2, GLIB_000:def 14;
      hence contradiction by A1, Th1;
    end;
  end;
end;
