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
  x : V.t
  pr1 : VSet.t
  pr0 : V.t
  pr2 : V.t
  y0 : SPath G pr1 pr0 pr2
  H2 : SPath_direct_subterm G pr1 pr0 pr2 s0 x x y0 (spath_refl G s0 x)
  H3 := {|
          pr1 :=
            {|
              pr1 := pr1;
              pr2 :=
                {|
                  pr1 := pr0;
                  pr2 :=
                    {|
                      pr1 := pr2;
                      pr2 :=
                        {|
                          pr1 := s0;
                          pr2 :=
                            {|
                              pr1 := x;
                              pr2 :=
                                {|
                                  pr1 := x;
                                  pr2 :=
                                    {| pr1 := y0; pr2 := spath_refl G s0 x |}
                                |}
                            |}
                        |}
                    |}
                |}
            |};
          pr2 := H2
        |}
     : sigma
         (fun
            index : sigma
                      (fun H : VSet.t =>
                       sigma
                         (fun H0 : V.t =>
                          sigma
                            (fun H1 : V.t =>
                             sigma
                               (fun H2 : VSet.t =>
                                sigma
                                  (fun H3 : V.t =>
                                   sigma
                                     (fun H4 : V.t =>
                                      sigma
                                        (fun _ : SPath G H H0 H1 =>
                                         SPath G H2 H3 H4))))))) =>
          SPath_direct_subterm G (Init.pr1 index) 
            (Init.pr1 (Init.pr2 index))
            (Init.pr1 (Init.pr2 (Init.pr2 index)))
            (Init.pr1 (Init.pr2 (Init.pr2 (Init.pr2 index))))
            (Init.pr1 (Init.pr2 (Init.pr2 (Init.pr2 (Init.pr2 index)))))
            (Init.pr1
               (Init.pr2 (Init.pr2 (Init.pr2 (Init.pr2 (Init.pr2 index))))))
            (Init.pr1
               (Init.pr2
                  (Init.pr2 (Init.pr2 (Init.pr2 (Init.pr2 (Init.pr2 index)))))))
            (Init.pr2
               (Init.pr2
                  (Init.pr2 (Init.pr2 (Init.pr2 (Init.pr2 (Init.pr2 index))))))))
  H4 := {|
          pr1 := pr1;
          pr2 :=
            {|
              pr1 := pr0;
              pr2 :=
                {|
                  pr1 := pr2;
                  pr2 :=
                    {|
                      pr1 := s0;
                      pr2 :=
                        {|
                          pr1 := x;
                          pr2 :=
                            {|
                              pr1 := x;
                              pr2 :=
                                {| pr1 := y0; pr2 := spath_refl G s0 x |}
                            |}
                        |}
                    |}
                |}
            |}
        |}
     : sigma
         (fun H : VSet.t =>
          sigma
            (fun H0 : V.t =>
             sigma
               (fun H1 : V.t =>
                sigma
                  (fun H2 : VSet.t =>
                   sigma
                     (fun H3 : V.t =>
                      sigma
                        (fun H4 : V.t =>
                         sigma (fun _ : SPath G H H0 H1 => SPath G H2 H3 H4)))))))
  H5 := H2
     : (fun
          index : sigma
                    (fun H : VSet.t =>
                     sigma
                       (fun H0 : V.t =>
                        sigma
                          (fun H1 : V.t =>
                           sigma
                             (fun H2 : VSet.t =>
                              sigma
                                (fun H3 : V.t =>
                                 sigma
                                   (fun H4 : V.t =>
                                    sigma
                                      (fun _ : SPath G H H0 H1 =>
                                       SPath G H2 H3 H4))))))) =>
        SPath_direct_subterm G (Init.pr1 index) (Init.pr1 (Init.pr2 index))
          (Init.pr1 (Init.pr2 (Init.pr2 index)))
          (Init.pr1 (Init.pr2 (Init.pr2 (Init.pr2 index))))
          (Init.pr1 (Init.pr2 (Init.pr2 (Init.pr2 (Init.pr2 index)))))
          (Init.pr1
             (Init.pr2 (Init.pr2 (Init.pr2 (Init.pr2 (Init.pr2 index))))))
          (Init.pr1
             (Init.pr2
                (Init.pr2 (Init.pr2 (Init.pr2 (Init.pr2 (Init.pr2 index)))))))
          (Init.pr2
             (Init.pr2
                (Init.pr2 (Init.pr2 (Init.pr2 (Init.pr2 (Init.pr2 index))))))))
         H4
  ============================
   ({|
      pr1 := pr1;
      pr2 :=
        {|
          pr1 := pr0;
          pr2 :=
            {|
              pr1 := pr2;
              pr2 :=
                {|
                  pr1 := s0;
                  pr2 :=
                    {|
                      pr1 := x;
                      pr2 :=
                        {|
                          pr1 := x;
                          pr2 := {| pr1 := y0; pr2 := spath_refl G s0 x |}
                        |}
                    |}
                |}
            |}
        |}
    |} = H4 ->
    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 (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 := y0
      |})


DEBUG:Going to execute:
<coq-core.plugins.ltac::clearbody@0> $1