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
  G : t
  s0 : VSet.t
  s' : VSet.t
  x : V.t
  y : V.t
  H2 : DisjointAdd x s0 s'
  H3 : EdgeOf G x y
  X : SPath G s0 y x
  H4 : spath_refl G s' x = spath_step G s0 s' x y x H2 H3 X
  ============================
   (Acc
      (fun
         x
          y : sigma
                (fun
                   index : sigma
                             (fun _ : VSet.t => sigma (fun _ : V.t => V.t))
                 => SPath G (pr1 index) (pr1 (pr2 index)) (pr2 (pr2 index)))
       =>
       SPath_direct_subterm G (pr1 (pr1 x)) (pr1 (pr2 (pr1 x)))
         (pr2 (pr2 (pr1 x))) (pr1 (pr1 y)) (pr1 (pr2 (pr1 y)))
         (pr2 (pr2 (pr1 y))) (pr2 x) (pr2 y))
      {| pr1 := {| pr1 := s0; pr2 := {| pr1 := y; pr2 := x |} |}; pr2 := X |})


DEBUG:Going to execute:
intro
Level 2: Backtrace:

The goal is not a product.
Level 2: Backtrace:

The goal is not a product.
Level 2: Backtrace:

The goal is not a product.
Level 2: Backtrace:

The goal is not a product.