
theorem Th54:
  for G2 being _Graph, v1, v2 being Vertex of G2, e being object
  for G1 being addEdge of G2,v1,e,v2 st not e in the_Edges_of G2
  holds G1 is non edgeless
proof
  let G2 be _Graph, v1, v2 be Vertex of G2, e be object;
  let G1 be addEdge of G2, v1, e, v2;
  assume not e in the_Edges_of G2;
  then the_Edges_of G1 = the_Edges_of G2 \/ {e} by GLIB_006:def 11;
  hence thesis;
end;
