Goal:
  
  G : t
  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))
  edges_vertices0 : forall e : EdgeSet.elt,
                    EdgeSet.In e (E G) ->
                    VSet.In e..s (V G) /\ VSet.In e..t (V G)
  source_vertex0 : VSet.In (s G) (V G)
  source_pathOf0 : forall x : VSet.elt,
                   VSet.In x (V G) ->
                   ∥ ∑ p : PathOf G (s G) x, ∥ 0 <= weight p ∥ ∥
  ============================
   (VSet.In i (VSet.add x (nodes G p)) \/ i = z0)


DEBUG:Going to execute:
repeat
            match goal with
            | H:context [ ?x = ?y :> ?T ]
              |- _ =>
                  tryif change T with V.t in H then 
                   fail else
                   tryif change T with VSet.t in H then fail else clear H  
            | H:?P
              |- _ =>
                  tryif prop (VSetDecide.MSetDecideAuxiliary.MSet_Prop P)
                   holds by auto  100 with MSet_Prop then 
                   fail else clear H 
            end