Goal:
  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  idx2 : list A
  idx1 : list A
  b : OnOne2 P idx2 idx1
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2 A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd :: tl; pr2 := hd :: tl'
                                          |};
                                        pr2 := OnOne2_tl P hd tl tl' a
                                      |}
                                      {|
                                        pr1 := {| pr1 := idx2; pr2 := idx1 |};
                                        pr2 := b
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2_obligation_2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
          pr2 := OnOne2_tl P hd tl tl' a
        |} {| pr1 := {| pr1 := idx2; pr2 := idx1 |}; pr2 := b |}
        (noConfusion_OnOne2_obligation_1 A P
           {|
             pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
             pr2 := OnOne2_tl P hd tl tl' a
           |} {| pr1 := {| pr1 := idx2; pr2 := idx1 |}; pr2 := b |} e) = e)


DEBUG:Going to execute:
destruct p

Goals:
  
  A : Type
  P : A → A → Type
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  hd0 : A
  hd'0 : A
  tl0 : list A
  p0 : P hd0 hd'0
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2 A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd :: tl; pr2 := hd' :: tl
                                          |};
                                        pr2 := OnOne2_hd P hd hd' tl p
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd0 :: tl0;
                                            pr2 := hd'0 :: tl0
                                          |};
                                        pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2_obligation_2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
          pr2 := OnOne2_hd P hd hd' tl p
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
          pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
        |}
        (noConfusion_OnOne2_obligation_1 A P
           {|
             pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
             pr2 := OnOne2_hd P hd hd' tl p
           |}
           {|
             pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
             pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
           |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  hd0 : A
  tl0 : list A
  tl' : list A
  b : OnOne2 P tl0 tl'
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2 A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd :: tl; pr2 := hd' :: tl
                                          |};
                                        pr2 := OnOne2_hd P hd hd' tl p
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd0 :: tl0;
                                            pr2 := hd0 :: tl'
                                          |};
                                        pr2 := OnOne2_tl P hd0 tl0 tl' b
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2_obligation_2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
          pr2 := OnOne2_hd P hd hd' tl p
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
          pr2 := OnOne2_tl P hd0 tl0 tl' b
        |}
        (noConfusion_OnOne2_obligation_1 A P
           {|
             pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
             pr2 := OnOne2_hd P hd hd' tl p
           |}
           {|
             pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
             pr2 := OnOne2_tl P hd0 tl0 tl' b
           |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  hd' : A
  tl0 : list A
  p : P hd0 hd'
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2 A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd :: tl; pr2 := hd :: tl'
                                          |};
                                        pr2 := OnOne2_tl P hd tl tl' a
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd0 :: tl0;
                                            pr2 := hd' :: tl0
                                          |};
                                        pr2 := OnOne2_hd P hd0 hd' tl0 p
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2_obligation_2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
          pr2 := OnOne2_tl P hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
          pr2 := OnOne2_hd P hd0 hd' tl0 p
        |}
        (noConfusion_OnOne2_obligation_1 A P
           {|
             pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
             pr2 := OnOne2_tl P hd tl tl' a
           |}
           {|
             pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
             pr2 := OnOne2_hd P hd0 hd' tl0 p
           |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  tl0 : list A
  tl'0 : list A
  b : OnOne2 P tl0 tl'0
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2 A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd :: tl; pr2 := hd :: tl'
                                          |};
                                        pr2 := OnOne2_tl P hd tl tl' a
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd0 :: tl0;
                                            pr2 := hd0 :: tl'0
                                          |};
                                        pr2 := OnOne2_tl P hd0 tl0 tl'0 b
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2_obligation_2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
          pr2 := OnOne2_tl P hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
          pr2 := OnOne2_tl P hd0 tl0 tl'0 b
        |}
        (noConfusion_OnOne2_obligation_1 A P
           {|
             pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
             pr2 := OnOne2_tl P hd tl tl' a
           |}
           {|
             pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
             pr2 := OnOne2_tl P hd0 tl0 tl'0 b
           |} e) = e)


DEBUG:Going to execute:
DepElim.simpl_dep_elim

Goals:
  
  A : Type
  P : A → A → Type
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  hd0 : A
  hd'0 : A
  tl0 : list A
  p0 : P hd0 hd'0
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2 A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd :: tl; pr2 := hd' :: tl
                                          |};
                                        pr2 := OnOne2_hd P hd hd' tl p
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd0 :: tl0;
                                            pr2 := hd'0 :: tl0
                                          |};
                                        pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2_obligation_2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
          pr2 := OnOne2_hd P hd hd' tl p
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
          pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
        |}
        (noConfusion_OnOne2_obligation_1 A P
           {|
             pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
             pr2 := OnOne2_hd P hd hd' tl p
           |}
           {|
             pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
             pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
           |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  hd0 : A
  tl0 : list A
  tl' : list A
  b : OnOne2 P tl0 tl'
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2 A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd :: tl; pr2 := hd' :: tl
                                          |};
                                        pr2 := OnOne2_hd P hd hd' tl p
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd0 :: tl0;
                                            pr2 := hd0 :: tl'
                                          |};
                                        pr2 := OnOne2_tl P hd0 tl0 tl' b
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2_obligation_2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
          pr2 := OnOne2_hd P hd hd' tl p
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
          pr2 := OnOne2_tl P hd0 tl0 tl' b
        |}
        (noConfusion_OnOne2_obligation_1 A P
           {|
             pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
             pr2 := OnOne2_hd P hd hd' tl p
           |}
           {|
             pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
             pr2 := OnOne2_tl P hd0 tl0 tl' b
           |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  hd' : A
  tl0 : list A
  p : P hd0 hd'
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2 A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd :: tl; pr2 := hd :: tl'
                                          |};
                                        pr2 := OnOne2_tl P hd tl tl' a
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd0 :: tl0;
                                            pr2 := hd' :: tl0
                                          |};
                                        pr2 := OnOne2_hd P hd0 hd' tl0 p
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2_obligation_2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
          pr2 := OnOne2_tl P hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
          pr2 := OnOne2_hd P hd0 hd' tl0 p
        |}
        (noConfusion_OnOne2_obligation_1 A P
           {|
             pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
             pr2 := OnOne2_tl P hd tl tl' a
           |}
           {|
             pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
             pr2 := OnOne2_hd P hd0 hd' tl0 p
           |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  tl0 : list A
  tl'0 : list A
  b : OnOne2 P tl0 tl'0
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2 A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd :: tl; pr2 := hd :: tl'
                                          |};
                                        pr2 := OnOne2_tl P hd tl tl' a
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd0 :: tl0;
                                            pr2 := hd0 :: tl'0
                                          |};
                                        pr2 := OnOne2_tl P hd0 tl0 tl'0 b
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2_obligation_2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
          pr2 := OnOne2_tl P hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
          pr2 := OnOne2_tl P hd0 tl0 tl'0 b
        |}
        (noConfusion_OnOne2_obligation_1 A P
           {|
             pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
             pr2 := OnOne2_tl P hd tl tl' a
           |}
           {|
             pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
             pr2 := OnOne2_tl P hd0 tl0 tl'0 b
           |} e) = e)


DEBUG:Going to execute:
DepElim.simplify_dep_elim; DepElim.simplify_IH_hyps;
            DepElim.unblock_dep_elim

Goals:
  
  A : Type
  P : A → A → Type
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  hd0 : A
  hd'0 : A
  tl0 : list A
  p0 : P hd0 hd'0
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2 A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd :: tl; pr2 := hd' :: tl
                                          |};
                                        pr2 := OnOne2_hd P hd hd' tl p
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd0 :: tl0;
                                            pr2 := hd'0 :: tl0
                                          |};
                                        pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2_obligation_2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
          pr2 := OnOne2_hd P hd hd' tl p
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
          pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
        |}
        (noConfusion_OnOne2_obligation_1 A P
           {|
             pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
             pr2 := OnOne2_hd P hd hd' tl p
           |}
           {|
             pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
             pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
           |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  hd0 : A
  tl0 : list A
  tl' : list A
  b : OnOne2 P tl0 tl'
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2 A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd :: tl; pr2 := hd' :: tl
                                          |};
                                        pr2 := OnOne2_hd P hd hd' tl p
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd0 :: tl0;
                                            pr2 := hd0 :: tl'
                                          |};
                                        pr2 := OnOne2_tl P hd0 tl0 tl' b
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2_obligation_2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
          pr2 := OnOne2_hd P hd hd' tl p
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
          pr2 := OnOne2_tl P hd0 tl0 tl' b
        |}
        (noConfusion_OnOne2_obligation_1 A P
           {|
             pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
             pr2 := OnOne2_hd P hd hd' tl p
           |}
           {|
             pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
             pr2 := OnOne2_tl P hd0 tl0 tl' b
           |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  hd' : A
  tl0 : list A
  p : P hd0 hd'
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2 A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd :: tl; pr2 := hd :: tl'
                                          |};
                                        pr2 := OnOne2_tl P hd tl tl' a
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd0 :: tl0;
                                            pr2 := hd' :: tl0
                                          |};
                                        pr2 := OnOne2_hd P hd0 hd' tl0 p
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2_obligation_2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
          pr2 := OnOne2_tl P hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
          pr2 := OnOne2_hd P hd0 hd' tl0 p
        |}
        (noConfusion_OnOne2_obligation_1 A P
           {|
             pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
             pr2 := OnOne2_tl P hd tl tl' a
           |}
           {|
             pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
             pr2 := OnOne2_hd P hd0 hd' tl0 p
           |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  tl0 : list A
  tl'0 : list A
  b : OnOne2 P tl0 tl'0
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2 A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd :: tl; pr2 := hd :: tl'
                                          |};
                                        pr2 := OnOne2_tl P hd tl tl' a
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd0 :: tl0;
                                            pr2 := hd0 :: tl'0
                                          |};
                                        pr2 := OnOne2_tl P hd0 tl0 tl'0 b
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2_obligation_2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
          pr2 := OnOne2_tl P hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
          pr2 := OnOne2_tl P hd0 tl0 tl'0 b
        |}
        (noConfusion_OnOne2_obligation_1 A P
           {|
             pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
             pr2 := OnOne2_tl P hd tl tl' a
           |}
           {|
             pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
             pr2 := OnOne2_tl P hd0 tl0 tl'0 b
           |} e) = e)


DEBUG:Going to execute:
DepElim.simplify_dep_elim; DepElim.simplify_IH_hyps

Goals:
  
  A : Type
  P : A → A → Type
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  hd0 : A
  hd'0 : A
  tl0 : list A
  p0 : P hd0 hd'0
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2 A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd :: tl; pr2 := hd' :: tl
                                          |};
                                        pr2 := OnOne2_hd P hd hd' tl p
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd0 :: tl0;
                                            pr2 := hd'0 :: tl0
                                          |};
                                        pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2_obligation_2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
          pr2 := OnOne2_hd P hd hd' tl p
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
          pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
        |}
        (noConfusion_OnOne2_obligation_1 A P
           {|
             pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
             pr2 := OnOne2_hd P hd hd' tl p
           |}
           {|
             pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
             pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
           |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  hd0 : A
  tl0 : list A
  tl' : list A
  b : OnOne2 P tl0 tl'
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2 A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd :: tl; pr2 := hd' :: tl
                                          |};
                                        pr2 := OnOne2_hd P hd hd' tl p
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd0 :: tl0;
                                            pr2 := hd0 :: tl'
                                          |};
                                        pr2 := OnOne2_tl P hd0 tl0 tl' b
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2_obligation_2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
          pr2 := OnOne2_hd P hd hd' tl p
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
          pr2 := OnOne2_tl P hd0 tl0 tl' b
        |}
        (noConfusion_OnOne2_obligation_1 A P
           {|
             pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
             pr2 := OnOne2_hd P hd hd' tl p
           |}
           {|
             pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
             pr2 := OnOne2_tl P hd0 tl0 tl' b
           |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  hd' : A
  tl0 : list A
  p : P hd0 hd'
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2 A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd :: tl; pr2 := hd :: tl'
                                          |};
                                        pr2 := OnOne2_tl P hd tl tl' a
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd0 :: tl0;
                                            pr2 := hd' :: tl0
                                          |};
                                        pr2 := OnOne2_hd P hd0 hd' tl0 p
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2_obligation_2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
          pr2 := OnOne2_tl P hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
          pr2 := OnOne2_hd P hd0 hd' tl0 p
        |}
        (noConfusion_OnOne2_obligation_1 A P
           {|
             pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
             pr2 := OnOne2_tl P hd tl tl' a
           |}
           {|
             pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
             pr2 := OnOne2_hd P hd0 hd' tl0 p
           |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  tl0 : list A
  tl'0 : list A
  b : OnOne2 P tl0 tl'0
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2 A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd :: tl; pr2 := hd :: tl'
                                          |};
                                        pr2 := OnOne2_tl P hd tl tl' a
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd0 :: tl0;
                                            pr2 := hd0 :: tl'0
                                          |};
                                        pr2 := OnOne2_tl P hd0 tl0 tl'0 b
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2_obligation_2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
          pr2 := OnOne2_tl P hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
          pr2 := OnOne2_tl P hd0 tl0 tl'0 b
        |}
        (noConfusion_OnOne2_obligation_1 A P
           {|
             pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
             pr2 := OnOne2_tl P hd tl tl' a
           |}
           {|
             pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
             pr2 := OnOne2_tl P hd0 tl0 tl'0 b
           |} e) = e)


DEBUG:Going to execute:
DepElim.simplify_dep_elim

Goals:
  
  A : Type
  P : A → A → Type
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  hd0 : A
  hd'0 : A
  tl0 : list A
  p0 : P hd0 hd'0
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2 A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd :: tl; pr2 := hd' :: tl
                                          |};
                                        pr2 := OnOne2_hd P hd hd' tl p
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd0 :: tl0;
                                            pr2 := hd'0 :: tl0
                                          |};
                                        pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2_obligation_2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
          pr2 := OnOne2_hd P hd hd' tl p
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
          pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
        |}
        (noConfusion_OnOne2_obligation_1 A P
           {|
             pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
             pr2 := OnOne2_hd P hd hd' tl p
           |}
           {|
             pr1 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |};
             pr2 := OnOne2_hd P hd0 hd'0 tl0 p0
           |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  hd0 : A
  tl0 : list A
  tl' : list A
  b : OnOne2 P tl0 tl'
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2 A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd :: tl; pr2 := hd' :: tl
                                          |};
                                        pr2 := OnOne2_hd P hd hd' tl p
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd0 :: tl0;
                                            pr2 := hd0 :: tl'
                                          |};
                                        pr2 := OnOne2_tl P hd0 tl0 tl' b
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2_obligation_2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
          pr2 := OnOne2_hd P hd hd' tl p
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
          pr2 := OnOne2_tl P hd0 tl0 tl' b
        |}
        (noConfusion_OnOne2_obligation_1 A P
           {|
             pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
             pr2 := OnOne2_hd P hd hd' tl p
           |}
           {|
             pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |};
             pr2 := OnOne2_tl P hd0 tl0 tl' b
           |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  hd' : A
  tl0 : list A
  p : P hd0 hd'
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2 A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd :: tl; pr2 := hd :: tl'
                                          |};
                                        pr2 := OnOne2_tl P hd tl tl' a
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd0 :: tl0;
                                            pr2 := hd' :: tl0
                                          |};
                                        pr2 := OnOne2_hd P hd0 hd' tl0 p
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2_obligation_2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
          pr2 := OnOne2_tl P hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
          pr2 := OnOne2_hd P hd0 hd' tl0 p
        |}
        (noConfusion_OnOne2_obligation_1 A P
           {|
             pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
             pr2 := OnOne2_tl P hd tl tl' a
           |}
           {|
             pr1 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |};
             pr2 := OnOne2_hd P hd0 hd' tl0 p
           |} e) = e)

  
  A : Type
  P : A → A → Type
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2 P tl tl'
  hd0 : A
  tl0 : list A
  tl'0 : list A
  b : OnOne2 P tl0 tl'0
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2 A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd :: tl; pr2 := hd :: tl'
                                          |};
                                        pr2 := OnOne2_tl P hd tl tl' a
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := hd0 :: tl0;
                                            pr2 := hd0 :: tl'0
                                          |};
                                        pr2 := OnOne2_tl P hd0 tl0 tl'0 b
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2_obligation_2 A P
        {|
          pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
          pr2 := OnOne2_tl P hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
          pr2 := OnOne2_tl P hd0 tl0 tl'0 b
        |}
        (noConfusion_OnOne2_obligation_1 A P
           {|
             pr1 := {| pr1 := hd :: tl; pr2 := hd :: tl' |};
             pr2 := OnOne2_tl P hd tl tl' a
           |}
           {|
             pr1 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |};
             pr2 := OnOne2_tl P hd0 tl0 tl'0 b
           |} e) = e)


DEBUG:Going to execute:
repeat DepElim.simplify_one_dep_elim