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

theorem Th67:
  E is irreflexive iff createGraph(V,E) is loopless
proof
  hereby
    assume E is irreflexive;
    then VertexDomRel(createGraph(V,E)) is irreflexive;
    hence createGraph(V,E) is loopless;
  end;
  assume createGraph(V,E) is loopless;
  then VertexDomRel(createGraph(V,E)) is irreflexive;
  hence thesis;
end;
