Goal:
  
  G : t
  HI : invariants G
  HG : acyclic_no_loop G
  z : V.t
  x : V.t
  y : V.t
  z0 : V.t
  e0 : EdgeOf G x y
  p : PathOf G y z0
  e : EdgeOf G z0 z
  i : VSet.elt
  IHp : VSet.In i (nodes G p) \/ i = z0
  H : VSet.In i (nodes G (PathOf_add_end p e))
  ============================
   (VSet.In i (VSet.add x (nodes G p)) \/ i = z0)


DEBUG:Going to execute:
match type of P with
           | Prop =>
               match goal with
               | H':context [ H ] |- _ => clear dependent H'
               end
           | _ => fail
           end