Goal:
  
  G1 : t
  G2 : t
  l : labelling
  Gl := relabel_on G1 G2 l : t
  H : invariants G1
  preserves_edges : forall e : EdgeSet.elt,
                    EdgeSet.In e (E G1) -> EdgeSet.In e (E G2)
  HGl : correct_labelling G1 l
  H0 : invariants G2
  H1 : acyclic_no_loop G2
  embed : forall v1 v2 : VSet.elt,
          VSet.In v1 (V G1) ->
          VSet.In v2 (V G1) -> (lsp G2 v1 v2 <= lsp G1 v1 v2)%nbar
  s0 : VSet.t
  s' : VSet.t
  z : V.t
  s : V.t
  w' : Z
  t : V.t
  d : DisjointAdd (s, w', t)..s s0 s'
  p : SPath Gl s0 t z
  disj : Disjoint (VSet.add (s, w', t)..s (snodes Gl p)) (V G1)
  IHp : Disjoint (snodes Gl p) (V G1) ->
        (Some (sweight p) <= lsp G2 t z)%nbar
  sin : VSet.In (s, w', t)..s (V G1)
  _b_ : VSet.In (s, w', t)..t (V G1)
  ============================
   (VSet.In s (VSet.add (s, w', t)..s (snodes Gl p)))


DEBUG:Going to execute:
trivial; hnf; intros; (solve
            [ do
            ![ solve
             [ trivial | apply : eq_sym ; trivial ]
             | discriminate
             | contradiction
             | Ltac.split ]
            | case not_locked_false_eq_true; Ltac.assumption
            | match goal with
              | H:~ _ |- _ => solve [ case H; trivial ]
              end ])