reserve G for _Graph;

theorem Th23:
  for G being non _trivial _Graph, v being Vertex of G
  for H being removeVertex of G, v
  holds VertexDomRel(H) = VertexDomRel(G)
    \ ([: {v}, the_Vertices_of G :] \/ [: the_Vertices_of G, {v} :])
proof
  let G be non _trivial _Graph, v be Vertex of G;
  let H be removeVertex of G, v;
  (the_Vertices_of G) \ {v} is non empty by GLIB_000:20;
  then not (the_Vertices_of G) c= {v} by XBOOLE_1:37;
  hence thesis by Th22, XBOOLE_0:def 8;
end;
