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 : forall e : EdgeOf G z0 z,
        VSet.In i (nodes G (PathOf_add_end p e)) ->
        VSet.In i (nodes G p) \/ i = z0
  H : VSet.In i (VSet.add x (nodes G (PathOf_add_end p e)))
  ============================
   (VSet.In i (VSet.add x (nodes G p)) \/ i = z0)


DEBUG:Going to execute:
repeat
            match goal with
            | |- context [ VSet.singleton ?t ] =>
                  VSetDecide.MSetDecideAuxiliary.abstract_term t
            | _:context [ VSet.singleton ?t ]
              |- _ => VSetDecide.MSetDecideAuxiliary.abstract_term t
            | |- context [ VSet.add ?t _ ] =>
                  VSetDecide.MSetDecideAuxiliary.abstract_term t
            | _:context [ VSet.add ?t _ ]
              |- _ => VSetDecide.MSetDecideAuxiliary.abstract_term t
            | |- context [ VSet.remove ?t _ ] =>
                  VSetDecide.MSetDecideAuxiliary.abstract_term t
            | _:context [ VSet.remove ?t _ ]
              |- _ => VSetDecide.MSetDecideAuxiliary.abstract_term t
            | |- context [ VSet.In ?t _ ] =>
                  VSetDecide.MSetDecideAuxiliary.abstract_term t
            | _:context [ VSet.In ?t _ ]
              |- _ => VSetDecide.MSetDecideAuxiliary.abstract_term t
            end