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
  x : VSet.elt
  y : VSet.elt
  xin : VSet.In x (V G1)
  yin : VSet.In y (V G1)
  n : Z
  p : SPath Gl (V Gl) x y
  ============================
   ((exists n : Z,
       lsp G2 x (first_in G1 Gl p) = Some n /\
       sweight p <= n + diff l (first_in G1 Gl p) y) ->
    sweight p <= diff l x y)


DEBUG:Going to execute:
rewrite first_in_first // lsp_xx => - [?] 
[[=]] <- //
DEBUG LTAC Evaluated term: bound