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
  d : DisjointAdd s s0 s'
  t : V.t
  p : SPath Gl s0 t z
  yin : VSet.In z (V G1)
  IHp : VSet.In z (V G1) ->
        exists n : Z,
          lsp G2 t (first_in G1 Gl p) = Some n /\
          sweight p <= n + diff l (first_in G1 Gl p) z
  w0 : Z
  h : EdgeSet.In (s, w0, t) (E Gl)
  e0G2 : EdgeSet.In (s, w0, t) (E G2)
  E : EdgeSet.mem (s, w0, t) (E G1) = false
  w1 : Z
  wpb : sweight p <= w1 + diff l (first_in G1 Gl p) z
  Ex : VSet.mem s (V G1) = false
  n : Z
  E2 : lsp G2 s (first_in G1 Gl p) = Some n
  le : w0 + w1 <= n
  ============================
   (w0 + sweight p <= n + diff l (first_in G1 Gl p) z)


DEBUG:Going to execute:
trivial; hnf; intros