
theorem
  for V being non empty set, E being set, S,T being Function of E,V
  st ex v being Element of V st S"{v} is infinite or T"{v} is infinite
  holds createGraph(V,E,S,T) is non locally-finite
proof
  let V be non empty set, E be set, S,T be Function of E,V;
  given v being Element of V such that
    A1: S"{v} is infinite or T"{v} is infinite;
  set G = createGraph(V,E,S,T);
  reconsider v as Vertex of G;
  per cases by A1;
  suppose S"{v} is infinite;
    then (the_Source_of G)"{v} is infinite;
    then v.edgesOut() is infinite by GLIB_000:147;
    hence thesis by Th25;
  end;
  suppose T"{v} is infinite;
    then (the_Target_of G)"{v} is infinite;
    then v.edgesIn() is infinite by GLIB_000:147;
    hence thesis by Th25;
  end;
end;
