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
  z : V.t
  H2 : DisjointAdd x s0 s'
  H3 : EdgeOf G x y
  X : SPath G s0 y z
  s1 : VSet.t
  x0 : V.t
  pr2 : V.t
  y0 : SPath G s0 y pr2
  ============================
   ({|
      pr1 := pr2;
      pr2 :=
        {|
          pr1 := s1;
          pr2 :=
            {|
              pr1 := x0;
              pr2 :=
                {|
                  pr1 := x0;
                  pr2 := {| pr1 := y0; pr2 := spath_refl G s1 x0 |}
                |}
            |}
        |}
    |} =
    {|
      pr1 := z;
      pr2 :=
        {|
          pr1 := s';
          pr2 :=
            {|
              pr1 := x;
              pr2 :=
                {|
                  pr1 := z;
                  pr2 :=
                    {| pr1 := X; pr2 := spath_step G s0 s' x y z H2 H3 X |}
                |}
            |}
        |}
    |} ->
    let H := CoreTactics.block in
    let H0 := CoreTactics.block in
    Acc
      (fun
         x
          y : sigma
                (fun
                   index : sigma
                             (fun _ : VSet.t => sigma (fun _ : V.t => V.t))
                 =>
                 SPath G (pr1 index) (pr1 (Init.pr2 index))
                   (Init.pr2 (Init.pr2 index))) =>
       SPath_direct_subterm G (pr1 (pr1 x)) (pr1 (Init.pr2 (pr1 x)))
         (Init.pr2 (Init.pr2 (pr1 x))) (pr1 (pr1 y)) 
         (pr1 (Init.pr2 (pr1 y))) (Init.pr2 (Init.pr2 (pr1 y))) 
         (Init.pr2 x) (Init.pr2 y))
      {|
        pr1 := {| pr1 := s0; pr2 := {| pr1 := y; pr2 := pr2 |} |}; pr2 := y0
      |})


DEBUG:Going to execute:
match goal with
           | |- context [ eq_rect_r _ _ eq_refl ] => progress simpl eq_rect_r
           | |- context [ eq_rect _ _ _ _ eq_refl ] => progress simpl eq_rect
           | |- context [ Prop.Logic.transport _ eq_refl _ ] =>
                 progress simpl Prop.Logic.transport
           | |- context [ Logic.eq_elim _ _ _ _ _ eq_refl ] =>
                 progress simpl eq_rect
           | |- context [ Logic.eq_elim_r _ _ _ _ eq_refl ] =>
                 progress simpl Logic.eq_elim_r
           | |- context [ noConfusion_inv _ ] =>
                 progress simpl noConfusion_inv
           | |- DepElim.opaque_ind_pack_eq_inv ?G eq_refl =>
                 apply (DepElim.simplify_ind_pack_inv B x p G)
           | |- let _ := CoreTactics.block in _ => fail 1
           | |- _ => simplify * || simplify ?; cbv beta
           | |- _ -> ?B =>
                 let ty := type of B in
                 intro || (let H := fresh in
                           intro
                           H)
           | |- forall x, _ => let H := fresh x in
                               intro
                               H
           | |- _ => intro
           end