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
  ============================
   (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:
unfold iff in *; fold any not; intros;
            VSetDecide.MSetDecideAuxiliary.abstract_elements;
            VSetDecide.MSetDecideAuxiliary.no_logical_interdep; decompose
            records; VSetDecide.MSetDecideAuxiliary.discard_nonMSet;
            unfold VSet.Empty, VSet.Subset, VSet.Equal in *; 
            intros; VSetDecide.MSetDecideAuxiliary.change_to_E_t;
            VSetDecide.MSetDecideAuxiliary.E_eq_to_Logic_eq; subst ++;
            VSetDecide.MSetDecideAuxiliary.Logic_eq_to_E_eq; pull not using
            MSet_decidability; unfold not in *;
            match goal with
            | H:VSet.In ?x ?r -> False
              |- VSet.In ?x ?s -> False =>
                  contradict H; VSetDecide.MSetDecideAuxiliary.fsetdec_body
            | H:VSet.In ?x ?r -> False
              |- ?x = ?y -> False =>
                  contradict H; VSetDecide.MSetDecideAuxiliary.fsetdec_body
            | H:VSet.In ?x ?r -> False
              |- ?y = ?x -> False =>
                  contradict H; VSetDecide.MSetDecideAuxiliary.fsetdec_body
            | H:?P -> False
              |- ?Q -> False =>
                  tryif prop (VSetDecide.MSetDecideAuxiliary.MSet_elt_Prop P)
                   holds by auto  100 with MSet_Prop then
                   (contradict H; VSetDecide.MSetDecideAuxiliary.fsetdec_body)
                    else VSetDecide.MSetDecideAuxiliary.fsetdec_body 
            | |- _ => VSetDecide.MSetDecideAuxiliary.fsetdec_body
            end