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
  s'0 : VSet.t
  x0 : V.t
  y0 : V.t
  z0 : V.t
  d : DisjointAdd x0 s1 s'0
  e : EdgeOf G x0 y0
  a0 : SPath G s1 y0 z0
  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 := s1; pr2 := {| pr1 := y0; pr2 := z0 |} |};
             pr2 := a0
           |}
  ============================
   (forall (pr1 : VSet.t) (pr0 pr2 : V.t) (y1 : SPath G pr1 pr0 pr2),
    {|
      pr1 := pr1;
      pr2 :=
        {|
          pr1 := pr0;
          pr2 :=
            {|
              pr1 := pr2;
              pr2 :=
                {|
                  pr1 := s'0;
                  pr2 :=
                    {|
                      pr1 := x0;
                      pr2 :=
                        {|
                          pr1 := z0;
                          pr2 :=
                            {|
                              pr1 := y1;
                              pr2 := spath_step G s1 s'0 x0 y0 z0 d e a0
                            |}
                        |}
                    |}
                |}
            |}
        |}
    |} =
    {|
      pr1 := s0;
      pr2 :=
        {|
          pr1 := y;
          pr2 :=
            {|
              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 (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:
let H := fresh x in
           intro
           H
Level 4: Backtrace:

The first hypothesis in the goal is not an equality.
Level 4: Backtrace:

The first hypothesis in the goal is not an equality.
Level 4: Backtrace:

The first hypothesis in the goal is not an equality.
Level 4: Backtrace:

The first hypothesis in the goal is not an equality.