Goal:
  
  G : t
  x : V.t
  y : V.t
  z0 : V.t
  p : PathOf G y z0
  i : V.t
  H : VSet.E.eq i x
  source_vertex0 : VSet.In (s G) (V G)
  ============================
   ((x = i \/ VSet.In i (nodes G p)) \/ i = z0)


DEBUG:Going to execute:
let dec := solve_decidable using db in
           unfold not, iff in * |-;
            repeat
             match goal with
             | H:context [ True -> False ]
               |- _ => rewrite -> Decidable.not_true_iff in H
             | H:context [ False -> False ]
               |- _ => rewrite -> Decidable.not_false_iff in H
             | H:context [ (?P -> False) -> False ]
               |- _ => rewrite -> (Decidable.not_not_iff P) in H by dec
             | H:context [ (?P -> False) -> ?Q -> False ]
               |- _ => rewrite -> (Decidable.contrapositive P Q) in H by dec
             | H:context [ (?P -> False) \/ ?Q ]
               |- _ => VSetDecide.MSetLogicalFacts.or_not_l_iff_in P Q H dec
             | H:context [ ?P \/ (?Q -> False) ]
               |- _ => VSetDecide.MSetLogicalFacts.or_not_r_iff_in P Q H dec
             | H:context [ (?P -> False) -> ?Q ]
               |- _ => rewrite -> (Decidable.imp_not_l P Q) in H by dec
             | H:context [ ?P \/ ?Q -> False ]
               |- _ => rewrite -> (Decidable.not_or_iff P Q) in H
             | H:context [ ?P /\ ?Q -> False ]
               |- _ => rewrite -> (Decidable.not_and_iff P Q) in H
             | H:context [ (?P -> ?Q) -> False ]
               |- _ => rewrite -> (Decidable.not_imp_iff P Q) in H by dec
             end; fold any not