Goal:
  
  A : Type
  B : Type
  P : B → A → A → Type
  idx0 : list B
  idx1 : list A
  idx : list A
  a : OnOne2All P idx0 idx1 idx
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  e : NoConfusion_OnOne2All A B P
        {|
          pr1 := {| pr1 := idx0; pr2 := {| pr1 := idx1; pr2 := idx |} |};
          pr2 := a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 := {| pr1 := idx0; pr2 := {| pr1 := idx1; pr2 := idx |} |};
        pr2 := a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_OnOne2All_obligation_1 A B P
         {|
           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:
  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  hd' : A
  tl : list A
  p : P b0 hd hd'
  e0 : #|bs| = #|tl|
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  e : NoConfusion_OnOne2All A B P
        {|
          pr1 :=
            {|
              pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
            |};
          pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
          |};
        pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_OnOne2All_obligation_1 A B P
         {|
           pr1 :=
             {|
               pr1 := b0 :: bs;
               pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
             |};
           pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)

  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2All P bs tl tl'
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  e : NoConfusion_OnOne2All A B P
        {|
          pr1 :=
            {|
              pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
            |};
          pr2 := OnOne2All_tl P b0 bs hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
          |};
        pr2 := OnOne2All_tl P b0 bs hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_OnOne2All_obligation_1 A B P
         {|
           pr1 :=
             {|
               pr1 := b0 :: bs;
               pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
             |};
           pr2 := OnOne2All_tl P b0 bs hd tl tl' a
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)


DEBUG:Going to execute:
DepElim.depelim b

Goals:
  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  hd' : A
  tl : list A
  p : P b0 hd hd'
  e0 : #|bs| = #|tl|
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  e : NoConfusion_OnOne2All A B P
        {|
          pr1 :=
            {|
              pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
            |};
          pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
          |};
        pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_OnOne2All_obligation_1 A B P
         {|
           pr1 :=
             {|
               pr1 := b0 :: bs;
               pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
             |};
           pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)

  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2All P bs tl tl'
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  e : NoConfusion_OnOne2All A B P
        {|
          pr1 :=
            {|
              pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
            |};
          pr2 := OnOne2All_tl P b0 bs hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
          |};
        pr2 := OnOne2All_tl P b0 bs hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_OnOne2All_obligation_1 A B P
         {|
           pr1 :=
             {|
               pr1 := b0 :: bs;
               pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
             |};
           pr2 := OnOne2All_tl P b0 bs hd tl tl' 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:
  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  hd' : A
  tl : list A
  p : P b0 hd hd'
  e0 : #|bs| = #|tl|
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  e : NoConfusion_OnOne2All A B P
        {|
          pr1 :=
            {|
              pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
            |};
          pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
          |};
        pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_OnOne2All_obligation_1 A B P
         {|
           pr1 :=
             {|
               pr1 := b0 :: bs;
               pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
             |};
           pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)

  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2All P bs tl tl'
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  e : NoConfusion_OnOne2All A B P
        {|
          pr1 :=
            {|
              pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
            |};
          pr2 := OnOne2All_tl P b0 bs hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
          |};
        pr2 := OnOne2All_tl P b0 bs hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_OnOne2All_obligation_1 A B P
         {|
           pr1 :=
             {|
               pr1 := b0 :: bs;
               pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
             |};
           pr2 := OnOne2All_tl P b0 bs hd tl tl' 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:
  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  hd' : A
  tl : list A
  p : P b0 hd hd'
  e0 : #|bs| = #|tl|
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  e : NoConfusion_OnOne2All A B P
        {|
          pr1 :=
            {|
              pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
            |};
          pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
          |};
        pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_OnOne2All_obligation_1 A B P
         {|
           pr1 :=
             {|
               pr1 := b0 :: bs;
               pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
             |};
           pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)

  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2All P bs tl tl'
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  e : NoConfusion_OnOne2All A B P
        {|
          pr1 :=
            {|
              pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
            |};
          pr2 := OnOne2All_tl P b0 bs hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
          |};
        pr2 := OnOne2All_tl P b0 bs hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_OnOne2All_obligation_1 A B P
         {|
           pr1 :=
             {|
               pr1 := b0 :: bs;
               pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
             |};
           pr2 := OnOne2All_tl P b0 bs hd tl tl' 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:
  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  hd' : A
  tl : list A
  p : P b0 hd hd'
  e0 : #|bs| = #|tl|
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  e : NoConfusion_OnOne2All A B P
        {|
          pr1 :=
            {|
              pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
            |};
          pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
          |};
        pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_OnOne2All_obligation_1 A B P
         {|
           pr1 :=
             {|
               pr1 := b0 :: bs;
               pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
             |};
           pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)

  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2All P bs tl tl'
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  e : NoConfusion_OnOne2All A B P
        {|
          pr1 :=
            {|
              pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
            |};
          pr2 := OnOne2All_tl P b0 bs hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
          |};
        pr2 := OnOne2All_tl P b0 bs hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_OnOne2All_obligation_1 A B P
         {|
           pr1 :=
             {|
               pr1 := b0 :: bs;
               pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
             |};
           pr2 := OnOne2All_tl P b0 bs hd tl tl' a
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)


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

Goals:
  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  hd' : A
  tl : list A
  p : P b0 hd hd'
  e0 : #|bs| = #|tl|
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  e : NoConfusion_OnOne2All A B P
        {|
          pr1 :=
            {|
              pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
            |};
          pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
          |};
        pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_OnOne2All_obligation_1 A B P
         {|
           pr1 :=
             {|
               pr1 := b0 :: bs;
               pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
             |};
           pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)

  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2All P bs tl tl'
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  e : NoConfusion_OnOne2All A B P
        {|
          pr1 :=
            {|
              pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
            |};
          pr2 := OnOne2All_tl P b0 bs hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
          |};
        pr2 := OnOne2All_tl P b0 bs hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_OnOne2All_obligation_1 A B P
         {|
           pr1 :=
             {|
               pr1 := b0 :: bs;
               pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
             |};
           pr2 := OnOne2All_tl P b0 bs hd tl tl' 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:
  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  hd' : A
  tl : list A
  p : P b0 hd hd'
  e0 : #|bs| = #|tl|
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  e : NoConfusion_OnOne2All A B P
        {|
          pr1 :=
            {|
              pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
            |};
          pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
          |};
        pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_OnOne2All_obligation_1 A B P
         {|
           pr1 :=
             {|
               pr1 := b0 :: bs;
               pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
             |};
           pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)

  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2All P bs tl tl'
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  e : NoConfusion_OnOne2All A B P
        {|
          pr1 :=
            {|
              pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
            |};
          pr2 := OnOne2All_tl P b0 bs hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
          |};
        pr2 := OnOne2All_tl P b0 bs hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_OnOne2All_obligation_1 A B P
         {|
           pr1 :=
             {|
               pr1 := b0 :: bs;
               pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
             |};
           pr2 := OnOne2All_tl P b0 bs hd tl tl' 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:
  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  hd' : A
  tl : list A
  p : P b0 hd hd'
  e0 : #|bs| = #|tl|
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  e : NoConfusion_OnOne2All A B P
        {|
          pr1 :=
            {|
              pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
            |};
          pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
          |};
        pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_OnOne2All_obligation_1 A B P
         {|
           pr1 :=
             {|
               pr1 := b0 :: bs;
               pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
             |};
           pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)

  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2All P bs tl tl'
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  e : NoConfusion_OnOne2All A B P
        {|
          pr1 :=
            {|
              pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
            |};
          pr2 := OnOne2All_tl P b0 bs hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
          |};
        pr2 := OnOne2All_tl P b0 bs hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_OnOne2All_obligation_1 A B P
         {|
           pr1 :=
             {|
               pr1 := b0 :: bs;
               pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
             |};
           pr2 := OnOne2All_tl P b0 bs hd tl tl' a
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)


DEBUG:Going to execute:
DepElim.do_depelim_nosimpl tac H

Goals:
  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  hd' : A
  tl : list A
  p : P b0 hd hd'
  e0 : #|bs| = #|tl|
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  e : NoConfusion_OnOne2All A B P
        {|
          pr1 :=
            {|
              pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
            |};
          pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
          |};
        pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_OnOne2All_obligation_1 A B P
         {|
           pr1 :=
             {|
               pr1 := b0 :: bs;
               pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
             |};
           pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)

  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2All P bs tl tl'
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  e : NoConfusion_OnOne2All A B P
        {|
          pr1 :=
            {|
              pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
            |};
          pr2 := OnOne2All_tl P b0 bs hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
          |};
        pr2 := OnOne2All_tl P b0 bs hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_OnOne2All_obligation_1 A B P
         {|
           pr1 :=
             {|
               pr1 := b0 :: bs;
               pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
             |};
           pr2 := OnOne2All_tl P b0 bs hd tl tl' 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:
  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  hd' : A
  tl : list A
  p : P b0 hd hd'
  e0 : #|bs| = #|tl|
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  e : NoConfusion_OnOne2All A B P
        {|
          pr1 :=
            {|
              pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
            |};
          pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
          |};
        pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_OnOne2All_obligation_1 A B P
         {|
           pr1 :=
             {|
               pr1 := b0 :: bs;
               pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
             |};
           pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)

  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2All P bs tl tl'
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  e : NoConfusion_OnOne2All A B P
        {|
          pr1 :=
            {|
              pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
            |};
          pr2 := OnOne2All_tl P b0 bs hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
          |};
        pr2 := OnOne2All_tl P b0 bs hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_OnOne2All_obligation_1 A B P
         {|
           pr1 :=
             {|
               pr1 := b0 :: bs;
               pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
             |};
           pr2 := OnOne2All_tl P b0 bs hd tl tl' 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:
  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  hd' : A
  tl : list A
  p : P b0 hd hd'
  e0 : #|bs| = #|tl|
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  e : NoConfusion_OnOne2All A B P
        {|
          pr1 :=
            {|
              pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
            |};
          pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
          |};
        pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_OnOne2All_obligation_1 A B P
         {|
           pr1 :=
             {|
               pr1 := b0 :: bs;
               pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
             |};
           pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)

  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2All P bs tl tl'
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  e : NoConfusion_OnOne2All A B P
        {|
          pr1 :=
            {|
              pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
            |};
          pr2 := OnOne2All_tl P b0 bs hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
          |};
        pr2 := OnOne2All_tl P b0 bs hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_OnOne2All_obligation_1 A B P
         {|
           pr1 :=
             {|
               pr1 := b0 :: bs;
               pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
             |};
           pr2 := OnOne2All_tl P b0 bs hd tl tl' 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:
  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  hd' : A
  tl : list A
  p : P b0 hd hd'
  e0 : #|bs| = #|tl|
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  e : NoConfusion_OnOne2All A B P
        {|
          pr1 :=
            {|
              pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
            |};
          pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
          |};
        pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_OnOne2All_obligation_1 A B P
         {|
           pr1 :=
             {|
               pr1 := b0 :: bs;
               pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
             |};
           pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)

  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2All P bs tl tl'
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  e : NoConfusion_OnOne2All A B P
        {|
          pr1 :=
            {|
              pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
            |};
          pr2 := OnOne2All_tl P b0 bs hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
          |};
        pr2 := OnOne2All_tl P b0 bs hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_OnOne2All_obligation_1 A B P
         {|
           pr1 :=
             {|
               pr1 := b0 :: bs;
               pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
             |};
           pr2 := OnOne2All_tl P b0 bs hd tl tl' a
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)


DEBUG:Going to execute:
DepElim.do_intros H

Goals:
  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  hd' : A
  tl : list A
  p : P b0 hd hd'
  e0 : #|bs| = #|tl|
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  e : NoConfusion_OnOne2All A B P
        {|
          pr1 :=
            {|
              pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
            |};
          pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
          |};
        pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_OnOne2All_obligation_1 A B P
         {|
           pr1 :=
             {|
               pr1 := b0 :: bs;
               pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
             |};
           pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)

  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2All P bs tl tl'
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  e : NoConfusion_OnOne2All A B P
        {|
          pr1 :=
            {|
              pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
            |};
          pr2 := OnOne2All_tl P b0 bs hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
          |};
        pr2 := OnOne2All_tl P b0 bs hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_OnOne2All_obligation_1 A B P
         {|
           pr1 :=
             {|
               pr1 := b0 :: bs;
               pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
             |};
           pr2 := OnOne2All_tl P b0 bs hd tl tl' 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:
  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  hd' : A
  tl : list A
  p : P b0 hd hd'
  e0 : #|bs| = #|tl|
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  e : NoConfusion_OnOne2All A B P
        {|
          pr1 :=
            {|
              pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
            |};
          pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
          |};
        pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_OnOne2All_obligation_1 A B P
         {|
           pr1 :=
             {|
               pr1 := b0 :: bs;
               pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
             |};
           pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)

  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2All P bs tl tl'
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  e : NoConfusion_OnOne2All A B P
        {|
          pr1 :=
            {|
              pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
            |};
          pr2 := OnOne2All_tl P b0 bs hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
          |};
        pr2 := OnOne2All_tl P b0 bs hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_OnOne2All_obligation_1 A B P
         {|
           pr1 :=
             {|
               pr1 := b0 :: bs;
               pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
             |};
           pr2 := OnOne2All_tl P b0 bs hd tl tl' 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:
  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  hd' : A
  tl : list A
  p : P b0 hd hd'
  e0 : #|bs| = #|tl|
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  e : NoConfusion_OnOne2All A B P
        {|
          pr1 :=
            {|
              pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
            |};
          pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
          |};
        pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_OnOne2All_obligation_1 A B P
         {|
           pr1 :=
             {|
               pr1 := b0 :: bs;
               pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
             |};
           pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)

  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2All P bs tl tl'
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  e : NoConfusion_OnOne2All A B P
        {|
          pr1 :=
            {|
              pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
            |};
          pr2 := OnOne2All_tl P b0 bs hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
          |};
        pr2 := OnOne2All_tl P b0 bs hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_OnOne2All_obligation_1 A B P
         {|
           pr1 :=
             {|
               pr1 := b0 :: bs;
               pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
             |};
           pr2 := OnOne2All_tl P b0 bs hd tl tl' 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:
  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  hd' : A
  tl : list A
  p : P b0 hd hd'
  e0 : #|bs| = #|tl|
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  e : NoConfusion_OnOne2All A B P
        {|
          pr1 :=
            {|
              pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
            |};
          pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
          |};
        pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_OnOne2All_obligation_1 A B P
         {|
           pr1 :=
             {|
               pr1 := b0 :: bs;
               pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |}
             |};
           pr2 := OnOne2All_hd P b0 bs hd hd' tl p e0
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)

  
  A : Type
  B : Type
  P : B → A → A → Type
  b0 : B
  bs : list B
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2All P bs tl tl'
  idx3 : list B
  idx4 : list A
  idx2 : list A
  b : OnOne2All P idx3 idx4 idx2
  e : NoConfusion_OnOne2All A B P
        {|
          pr1 :=
            {|
              pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
            |};
          pr2 := OnOne2All_tl P b0 bs hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
  ============================
   (noConfusion_OnOne2All_obligation_2 A B P
      {|
        pr1 :=
          {|
            pr1 := b0 :: bs; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
          |};
        pr2 := OnOne2All_tl P b0 bs hd tl tl' a
      |}
      {|
        pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
        pr2 := b
      |}
      (noConfusion_OnOne2All_obligation_1 A B P
         {|
           pr1 :=
             {|
               pr1 := b0 :: bs;
               pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |}
             |};
           pr2 := OnOne2All_tl P b0 bs hd tl tl' a
         |}
         {|
           pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
           pr2 := b
         |} e) = e)


DEBUG:Going to execute:
try intros until H