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
  d : DisjointAdd x s0 s'
  e : EdgeOf G x y
  a0 : SPath G s0 y z
  IHa0 : 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 := z |} |};
             pr2 := a0
           |}
  pr1 : VSet.t
  pr0 : V.t
  pr2 : V.t
  y1 : SPath G pr1 pr0 pr2
  H2 : SPath_direct_subterm G pr1 pr0 pr2 s' x z y1
         (spath_step G s0 s' x y z d e a0)
  ============================
   (Acc
      (fun
         x
          y : sigma
                (fun
                   index : sigma
                             (fun _ : VSet.t => sigma (fun _ : V.t => V.t))
                 =>
                 SPath G (Init.pr1 index) (Init.pr1 (Init.pr2 index))
                   (Init.pr2 (Init.pr2 index))) =>
       SPath_direct_subterm G (Init.pr1 (Init.pr1 x))
         (Init.pr1 (Init.pr2 (Init.pr1 x)))
         (Init.pr2 (Init.pr2 (Init.pr1 x))) (Init.pr1 (Init.pr1 y))
         (Init.pr1 (Init.pr2 (Init.pr1 y)))
         (Init.pr2 (Init.pr2 (Init.pr1 y))) (Init.pr2 x) 
         (Init.pr2 y))
      {|
        pr1 := {| pr1 := pr1; pr2 := {| pr1 := pr0; pr2 := pr2 |} |};
        pr2 := y1
      |})


DEBUG:Going to execute:
try intros until H; intro_block H;
            (try simpl in H; DepElim.simplify_equations_in H);
            DepElim.generalize_by_eqs_vars H; CoreTactics.block_goal; 
            tac H; CoreTactics.intros_until_block; DepElim.simpl_dep_elim
Level 5: evaluation returns
try intros until H; intro_block H;
 (try simpl in H; DepElim.simplify_equations_in H);
 DepElim.generalize_by_eqs_vars H; CoreTactics.block_goal; 
 tac H; CoreTactics.intros_until_block; DepElim.simpl_dep_elim;
 CoreTactics.unblock_goal
where
tac := fun hyp => DepElim.do_ind hyp
       where
       id := H2
       of type
       constr
of type
tacvalue
H := H2
of type
constr of type tacvalue

Level 4: evaluation returns
try intros until H; intro_block H;
 (try simpl in H; DepElim.simplify_equations_in H);
 DepElim.generalize_by_eqs_vars H; CoreTactics.block_goal; 
 tac H; CoreTactics.intros_until_block; DepElim.simpl_dep_elim;
 CoreTactics.unblock_goal
where
tac := fun hyp => DepElim.do_ind hyp
       where
       id := H2
       of type
       constr
of type
tacvalue
H := H2
of type
constr of type tacvalue

Level 3: evaluation returns
try intros until H; intro_block H;
 (try simpl in H; DepElim.simplify_equations_in H);
 DepElim.generalize_by_eqs_vars H; CoreTactics.block_goal; 
 tac H; CoreTactics.intros_until_block; DepElim.simpl_dep_elim;
 CoreTactics.unblock_goal
where
tac := fun hyp => DepElim.do_ind hyp
       where
       id := H2
       of type
       constr
of type
tacvalue
H := H2
of type
constr of type tacvalue