reserve G for _Graph;

theorem Th25:
  for V being set, H being addVertices of G, V
  holds VertexDomRel(H) = VertexDomRel(G)
proof
  let V be set, H be addVertices of G, V;
  G is Subgraph of H by GLIB_006:57;
  then A1: VertexDomRel(G) c= VertexDomRel(H) by Th15;
  now
    let v,w be object;
    assume [v,w] in VertexDomRel(H);
    then consider e being object such that
      A2: e DJoins v,w,H by Th1;
    e DJoins v,w,G by A2, GLIB_006:85;
    hence [v,w] in VertexDomRel(G) by Th1;
  end;
  then VertexDomRel(H) c= VertexDomRel(G) by RELAT_1:def 3;
  hence thesis by A1, XBOOLE_0:def 10;
end;
