reserve G for _Graph;
reserve V for non empty set, E for Relation of V;

theorem Th66:
  V is trivial iff createGraph(V,E) is _trivial
proof
  hereby
    assume V is trivial;
    then the_Vertices_of createGraph(V,E) is trivial;
    then consider v being object such that
      A1: the_Vertices_of createGraph(V,E) = {v} by ZFMISC_1:131;
    card the_Vertices_of createGraph(V,E) = 1 by A1, CARD_1:30;
    hence createGraph(V,E) is _trivial;
  end;
  assume createGraph(V,E) is _trivial;
  then the_Vertices_of createGraph(V,E) is trivial;
  hence V is trivial;
end;
