Goal:
  
  G : t
  idx0 : VSet.t
  idx1 : V.t
  idx : V.t
  a : SPath idx0 idx1 idx
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  e : NoConfusion_SPath
        {|
          pr1 := {| pr1 := idx0; pr2 := {| pr1 := idx1; pr2 := idx |} |};
          pr2 := a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := idx0; pr2 := {| pr1 := idx1; pr2 := idx |} |};
        pr2 := a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := idx0; pr2 := {| pr1 := idx1; pr2 := idx |} |};
           pr2 := a
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)


DEBUG:Going to execute:
destruct a
Level 3: evaluation returns
idtac of type tacvalue


Goals:
  
  G : t
  s0 : VSet.t
  x : V.t
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  e : NoConfusion_SPath
        {|
          pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
          pr2 := spath_refl s0 x
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
        pr2 := spath_refl s0 x
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
           pr2 := spath_refl s0 x
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)

  
  G : t
  s0 : VSet.t
  s' : VSet.t
  x : V.t
  y : V.t
  z : V.t
  d : DisjointAdd x s0 s'
  e0 : EdgeOf x y
  a : SPath s0 y z
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  e : NoConfusion_SPath
        {|
          pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
          pr2 := spath_step d e0 a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
        pr2 := spath_step d e0 a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
           pr2 := spath_step d e0 a
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)


DEBUG:Going to execute:
DepElim.depelim b

Goals:
  
  G : t
  s0 : VSet.t
  x : V.t
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  e : NoConfusion_SPath
        {|
          pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
          pr2 := spath_refl s0 x
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
        pr2 := spath_refl s0 x
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
           pr2 := spath_refl s0 x
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)

  
  G : t
  s0 : VSet.t
  s' : VSet.t
  x : V.t
  y : V.t
  z : V.t
  d : DisjointAdd x s0 s'
  e0 : EdgeOf x y
  a : SPath s0 y z
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  e : NoConfusion_SPath
        {|
          pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
          pr2 := spath_step d e0 a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
        pr2 := spath_step d e0 a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
           pr2 := spath_step d e0 a
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)


DEBUG:Going to execute:
fun id =>
             DepElim.do_depelim ltac:(fun hyp => DepElim.do_case hyp) id

Goals:
  
  G : t
  s0 : VSet.t
  x : V.t
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  e : NoConfusion_SPath
        {|
          pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
          pr2 := spath_refl s0 x
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
        pr2 := spath_refl s0 x
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
           pr2 := spath_refl s0 x
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)

  
  G : t
  s0 : VSet.t
  s' : VSet.t
  x : V.t
  y : V.t
  z : V.t
  d : DisjointAdd x s0 s'
  e0 : EdgeOf x y
  a : SPath s0 y z
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  e : NoConfusion_SPath
        {|
          pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
          pr2 := spath_step d e0 a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
        pr2 := spath_step d e0 a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
           pr2 := spath_step d e0 a
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)


DEBUG:Going to execute:
DepElim.do_depelim ltac:(fun hyp => DepElim.do_case hyp) id

Goals:
  
  G : t
  s0 : VSet.t
  x : V.t
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  e : NoConfusion_SPath
        {|
          pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
          pr2 := spath_refl s0 x
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
        pr2 := spath_refl s0 x
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
           pr2 := spath_refl s0 x
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)

  
  G : t
  s0 : VSet.t
  s' : VSet.t
  x : V.t
  y : V.t
  z : V.t
  d : DisjointAdd x s0 s'
  e0 : EdgeOf x y
  a : SPath s0 y z
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  e : NoConfusion_SPath
        {|
          pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
          pr2 := spath_step d e0 a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
        pr2 := spath_step d e0 a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
           pr2 := spath_step d e0 a
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)


DEBUG:Going to execute:
fun tac H =>
             DepElim.do_depelim_nosimpl tac H; DepElim.simpl_dep_elim;
              CoreTactics.unblock_goal

Goals:
  
  G : t
  s0 : VSet.t
  x : V.t
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  e : NoConfusion_SPath
        {|
          pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
          pr2 := spath_refl s0 x
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
        pr2 := spath_refl s0 x
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
           pr2 := spath_refl s0 x
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)

  
  G : t
  s0 : VSet.t
  s' : VSet.t
  x : V.t
  y : V.t
  z : V.t
  d : DisjointAdd x s0 s'
  e0 : EdgeOf x y
  a : SPath s0 y z
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  e : NoConfusion_SPath
        {|
          pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
          pr2 := spath_step d e0 a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
        pr2 := spath_step d e0 a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
           pr2 := spath_step d e0 a
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)


DEBUG:Going to execute:
fun hyp => DepElim.do_case hyp

Goals:
  
  G : t
  s0 : VSet.t
  x : V.t
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  e : NoConfusion_SPath
        {|
          pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
          pr2 := spath_refl s0 x
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
        pr2 := spath_refl s0 x
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
           pr2 := spath_refl s0 x
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)

  
  G : t
  s0 : VSet.t
  s' : VSet.t
  x : V.t
  y : V.t
  z : V.t
  d : DisjointAdd x s0 s'
  e0 : EdgeOf x y
  a : SPath s0 y z
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  e : NoConfusion_SPath
        {|
          pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
          pr2 := spath_step d e0 a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
        pr2 := spath_step d e0 a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
           pr2 := spath_step d e0 a
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)


DEBUG:Going to execute:
DepElim.do_depelim_nosimpl tac H; DepElim.simpl_dep_elim;
            CoreTactics.unblock_goal

Goals:
  
  G : t
  s0 : VSet.t
  x : V.t
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  e : NoConfusion_SPath
        {|
          pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
          pr2 := spath_refl s0 x
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
        pr2 := spath_refl s0 x
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
           pr2 := spath_refl s0 x
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)

  
  G : t
  s0 : VSet.t
  s' : VSet.t
  x : V.t
  y : V.t
  z : V.t
  d : DisjointAdd x s0 s'
  e0 : EdgeOf x y
  a : SPath s0 y z
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  e : NoConfusion_SPath
        {|
          pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
          pr2 := spath_step d e0 a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
        pr2 := spath_step d e0 a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
           pr2 := spath_step d e0 a
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)


DEBUG:Going to execute:
DepElim.do_depelim_nosimpl tac H; DepElim.simpl_dep_elim
Level 4: evaluation returns
DepElim.do_depelim_nosimpl tac H; DepElim.simpl_dep_elim;
 CoreTactics.unblock_goal
where
tac := fun hyp => DepElim.do_case hyp
       where
       id := b
       of type
       constr
of type
tacvalue
H := b
of type
constr of type tacvalue

Level 4: evaluation returns
DepElim.do_depelim_nosimpl tac H; DepElim.simpl_dep_elim;
 CoreTactics.unblock_goal
where
tac := fun hyp => DepElim.do_case hyp
       where
       id := b
       of type
       constr
of type
tacvalue
H := b
of type
constr of type tacvalue

Level 3: evaluation returns
DepElim.do_depelim_nosimpl tac H; DepElim.simpl_dep_elim;
 CoreTactics.unblock_goal
where
tac := fun hyp => DepElim.do_case hyp
       where
       id := b
       of type
       constr
of type
tacvalue
H := b
of type
constr of type tacvalue

Level 3: evaluation returns
DepElim.do_depelim_nosimpl tac H; DepElim.simpl_dep_elim;
 CoreTactics.unblock_goal
where
tac := fun hyp => DepElim.do_case hyp
       where
       id := b
       of type
       constr
of type
tacvalue
H := b
of type
constr of type tacvalue


Goals:
  
  G : t
  s0 : VSet.t
  x : V.t
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  e : NoConfusion_SPath
        {|
          pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
          pr2 := spath_refl s0 x
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
        pr2 := spath_refl s0 x
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
           pr2 := spath_refl s0 x
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)

  
  G : t
  s0 : VSet.t
  s' : VSet.t
  x : V.t
  y : V.t
  z : V.t
  d : DisjointAdd x s0 s'
  e0 : EdgeOf x y
  a : SPath s0 y z
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  e : NoConfusion_SPath
        {|
          pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
          pr2 := spath_step d e0 a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
        pr2 := spath_step d e0 a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
           pr2 := spath_step d e0 a
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)


DEBUG:Going to execute:
DepElim.do_depelim_nosimpl tac H

Goals:
  
  G : t
  s0 : VSet.t
  x : V.t
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  e : NoConfusion_SPath
        {|
          pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
          pr2 := spath_refl s0 x
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
        pr2 := spath_refl s0 x
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
           pr2 := spath_refl s0 x
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)

  
  G : t
  s0 : VSet.t
  s' : VSet.t
  x : V.t
  y : V.t
  z : V.t
  d : DisjointAdd x s0 s'
  e0 : EdgeOf x y
  a : SPath s0 y z
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  e : NoConfusion_SPath
        {|
          pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
          pr2 := spath_step d e0 a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
        pr2 := spath_step d e0 a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
           pr2 := spath_step d e0 a
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)


DEBUG:Going to execute:
fun tac H =>
             DepElim.do_intros H; DepElim.generalize_by_eqs H; tac H

Goals:
  
  G : t
  s0 : VSet.t
  x : V.t
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  e : NoConfusion_SPath
        {|
          pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
          pr2 := spath_refl s0 x
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
        pr2 := spath_refl s0 x
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
           pr2 := spath_refl s0 x
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)

  
  G : t
  s0 : VSet.t
  s' : VSet.t
  x : V.t
  y : V.t
  z : V.t
  d : DisjointAdd x s0 s'
  e0 : EdgeOf x y
  a : SPath s0 y z
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  e : NoConfusion_SPath
        {|
          pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
          pr2 := spath_step d e0 a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
        pr2 := spath_step d e0 a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
           pr2 := spath_step d e0 a
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)


DEBUG:Going to execute:
DepElim.do_intros H; DepElim.generalize_by_eqs H; tac H

Goals:
  
  G : t
  s0 : VSet.t
  x : V.t
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  e : NoConfusion_SPath
        {|
          pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
          pr2 := spath_refl s0 x
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
        pr2 := spath_refl s0 x
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
           pr2 := spath_refl s0 x
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)

  
  G : t
  s0 : VSet.t
  s' : VSet.t
  x : V.t
  y : V.t
  z : V.t
  d : DisjointAdd x s0 s'
  e0 : EdgeOf x y
  a : SPath s0 y z
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  e : NoConfusion_SPath
        {|
          pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
          pr2 := spath_step d e0 a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
        pr2 := spath_step d e0 a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
           pr2 := spath_step d e0 a
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)


DEBUG:Going to execute:
DepElim.do_intros H; DepElim.generalize_by_eqs H
Level 3: evaluation returns
DepElim.do_intros H; DepElim.generalize_by_eqs H; tac H
where
tac := fun hyp => DepElim.do_case hyp
       where
       id := b
       of type
       constr
of type
tacvalue
H := b
of type
constr of type tacvalue

Level 3: evaluation returns
DepElim.do_intros H; DepElim.generalize_by_eqs H; tac H
where
tac := fun hyp => DepElim.do_case hyp
       where
       id := b
       of type
       constr
of type
tacvalue
H := b
of type
constr of type tacvalue


Goals:
  
  G : t
  s0 : VSet.t
  x : V.t
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  e : NoConfusion_SPath
        {|
          pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
          pr2 := spath_refl s0 x
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
        pr2 := spath_refl s0 x
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
           pr2 := spath_refl s0 x
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)

  
  G : t
  s0 : VSet.t
  s' : VSet.t
  x : V.t
  y : V.t
  z : V.t
  d : DisjointAdd x s0 s'
  e0 : EdgeOf x y
  a : SPath s0 y z
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  e : NoConfusion_SPath
        {|
          pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
          pr2 := spath_step d e0 a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
        pr2 := spath_step d e0 a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
           pr2 := spath_step d e0 a
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)


DEBUG:Going to execute:
DepElim.do_intros H

Goals:
  
  G : t
  s0 : VSet.t
  x : V.t
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  e : NoConfusion_SPath
        {|
          pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
          pr2 := spath_refl s0 x
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
        pr2 := spath_refl s0 x
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
           pr2 := spath_refl s0 x
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)

  
  G : t
  s0 : VSet.t
  s' : VSet.t
  x : V.t
  y : V.t
  z : V.t
  d : DisjointAdd x s0 s'
  e0 : EdgeOf x y
  a : SPath s0 y z
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  e : NoConfusion_SPath
        {|
          pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
          pr2 := spath_step d e0 a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
        pr2 := spath_step d e0 a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
           pr2 := spath_step d e0 a
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)


DEBUG:Going to execute:
fun H =>
             try intros until H; intro_block_id H || intro_block H;
              (try simpl in H; DepElim.simplify_equations_in H)

Goals:
  
  G : t
  s0 : VSet.t
  x : V.t
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  e : NoConfusion_SPath
        {|
          pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
          pr2 := spath_refl s0 x
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
        pr2 := spath_refl s0 x
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
           pr2 := spath_refl s0 x
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)

  
  G : t
  s0 : VSet.t
  s' : VSet.t
  x : V.t
  y : V.t
  z : V.t
  d : DisjointAdd x s0 s'
  e0 : EdgeOf x y
  a : SPath s0 y z
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  e : NoConfusion_SPath
        {|
          pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
          pr2 := spath_step d e0 a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
        pr2 := spath_step d e0 a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
           pr2 := spath_step d e0 a
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)


DEBUG:Going to execute:
try intros until H; intro_block_id H || intro_block H;
            (try simpl in H; DepElim.simplify_equations_in H)

Goals:
  
  G : t
  s0 : VSet.t
  x : V.t
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  e : NoConfusion_SPath
        {|
          pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
          pr2 := spath_refl s0 x
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
        pr2 := spath_refl s0 x
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
           pr2 := spath_refl s0 x
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)

  
  G : t
  s0 : VSet.t
  s' : VSet.t
  x : V.t
  y : V.t
  z : V.t
  d : DisjointAdd x s0 s'
  e0 : EdgeOf x y
  a : SPath s0 y z
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  e : NoConfusion_SPath
        {|
          pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
          pr2 := spath_step d e0 a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
        pr2 := spath_step d e0 a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
           pr2 := spath_step d e0 a
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)


DEBUG:Going to execute:
try intros until H; intro_block_id H || intro_block H
Level 3: evaluation returns
try intros until H; intro_block_id H || intro_block H;
 (try simpl in H; DepElim.simplify_equations_in H)
where
H := b
of type
constr of type tacvalue

Level 3: evaluation returns
try intros until H; intro_block_id H || intro_block H;
 (try simpl in H; DepElim.simplify_equations_in H)
where
H := b
of type
constr of type tacvalue


Goals:
  
  G : t
  s0 : VSet.t
  x : V.t
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  e : NoConfusion_SPath
        {|
          pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
          pr2 := spath_refl s0 x
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
        pr2 := spath_refl s0 x
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s0; pr2 := {| pr1 := x; pr2 := x |} |};
           pr2 := spath_refl s0 x
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)

  
  G : t
  s0 : VSet.t
  s' : VSet.t
  x : V.t
  y : V.t
  z : V.t
  d : DisjointAdd x s0 s'
  e0 : EdgeOf x y
  a : SPath s0 y z
  idx3 : VSet.t
  idx4 : V.t
  idx2 : V.t
  b : SPath idx3 idx4 idx2
  e : NoConfusion_SPath
        {|
          pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
          pr2 := spath_step d e0 a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_SPath_obligation_2
      {|
        pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
        pr2 := spath_step d e0 a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_SPath_obligation_1
         {|
           pr1 := {| pr1 := s'; pr2 := {| pr1 := x; pr2 := z |} |};
           pr2 := spath_step d e0 a
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)


DEBUG:Going to execute:
try intros until H