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
  x : V.t
  s1 : VSet.t
  vsub : VSet.Subset s0 s1
  ============================
   (let q := SPath_sub Gl vsub (map_spath from1 (spath_refl G1 s0 x)) in
    sweight q = diff l x x)


DEBUG:Going to execute:
simp map_spath