
theorem Th14:
  for G2 being _Graph, v being object, V being Subset of the_Vertices_of G2
  for G1 being addAdjVertexAll of G2,v,V st not v in the_Vertices_of G2
  holds G1 is non loopfull
proof
  let G2 be _Graph, v be object, V be Subset of the_Vertices_of G2;
  let G1 be addAdjVertexAll of G2,v,V;
  assume A1: not v in the_Vertices_of G2;
  then reconsider v as Vertex of G1 by GLIB_007:50;
  for e being object holds not e Joins v,v,G1 by A1, GLIB_007:def 4;
  hence thesis;
end;
