
theorem
  for G1 being _trivial Cycle-like _Graph
  for v being Vertex of G1, e being Edge of G1
  ex G2 being _trivial edgeless _Graph st G1 is addEdge of G2,v,e,v
proof
  let G1 be _trivial Cycle-like _Graph;
  let v be Vertex of G1, e be Edge of G1;
  take G2 = the removeEdge of G1,e;
  set u = (the_Source_of G1).e, w = (the_Target_of G1).e;
  u = v & w = v by ZFMISC_1:def 10;
  hence thesis by GLIB_008:37;
end;
