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
  x : V.t
  y : V.t
  z : V.t
  d : DisjointAdd x s0 s'
  e : EdgeOf Gl x y
  p : SPath Gl s0 y z
  yin : VSet.In z (V G1)
  IHp : VSet.In z (V G1) ->
        exists n : Z,
          lsp G2 y (first_in G1 Gl p) = Some n /\
          sweight p <= n + diff l (first_in G1 Gl p) z
  ============================
   (exists n : Z,
      lsp G2 x (first_in G1 Gl (spath_step Gl s0 s' x y z d e p)) = Some n /\
      sweight (spath_step Gl s0 s' x y z d e p) <=
      n + diff l (first_in G1 Gl (spath_step Gl s0 s' x y z d e p)) z)


DEBUG:Going to execute:
move : e  => [w /= h]; move : (h)  => /edge_map_spec2
            [e0 [+ e0G2]]