reserve G for _Graph;

theorem Th3:
  G is loopless iff VertexDomRel(G) is irreflexive
proof
  hereby
    assume G is loopless;
    then VertexDomRel(G) misses id the_Vertices_of G by Lm1;
    hence VertexDomRel(G) is irreflexive by GLIBPRE0:11;
  end;
  assume VertexDomRel(G) is irreflexive;
  then VertexDomRel(G) misses id the_Vertices_of G by GLIBPRE0:11;
  hence G is loopless by Lm1;
end;
