Goal:
  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2i P (S i) tl tl'
  idx3 : nat
  idx4 : list A
  idx2 : list A
  b : OnOne2i P idx3 idx4 idx2
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2i A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i;
                                            pr2 :=
                                              {|
                                                pr1 := hd :: tl;
                                                pr2 := hd :: tl'
                                              |}
                                          |};
                                        pr2 := OnOne2i_tl P i hd tl tl' a
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := idx3;
                                            pr2 :=
                                              {| pr1 := idx4; pr2 := idx2 |}
                                          |};
                                        pr2 := b
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2i_obligation_2 A P
        {|
          pr1 :=
            {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
          pr2 := OnOne2i_tl P i hd tl tl' a
        |}
        {|
          pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
          pr2 := b
        |}
        (noConfusion_OnOne2i_obligation_1 A P
           {|
             pr1 :=
               {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
             pr2 := OnOne2i_tl P i hd tl tl' a
           |}
           {|
             pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
             pr2 := b
           |} e) = e)


DEBUG:Going to execute:
destruct p

Goals:
  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  hd' : A
  tl : list A
  p : P i hd hd'
  i0 : nat
  hd0 : A
  hd'0 : A
  tl0 : list A
  p0 : P i0 hd0 hd'0
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2i A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i;
                                            pr2 :=
                                              {|
                                                pr1 := hd :: tl;
                                                pr2 := hd' :: tl
                                              |}
                                          |};
                                        pr2 := OnOne2i_hd P i hd hd' tl p
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i0;
                                            pr2 :=
                                              {|
                                                pr1 := hd0 :: tl0;
                                                pr2 := hd'0 :: tl0
                                              |}
                                          |};
                                        pr2 :=
                                          OnOne2i_hd P i0 hd0 hd'0 tl0 p0
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2i_obligation_2 A P
        {|
          pr1 :=
            {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
          pr2 := OnOne2i_hd P i hd hd' tl p
        |}
        {|
          pr1 :=
            {|
              pr1 := i0; pr2 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |}
            |};
          pr2 := OnOne2i_hd P i0 hd0 hd'0 tl0 p0
        |}
        (noConfusion_OnOne2i_obligation_1 A P
           {|
             pr1 :=
               {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
             pr2 := OnOne2i_hd P i hd hd' tl p
           |}
           {|
             pr1 :=
               {|
                 pr1 := i0;
                 pr2 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |}
               |};
             pr2 := OnOne2i_hd P i0 hd0 hd'0 tl0 p0
           |} e) = e)

  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  hd' : A
  tl : list A
  p : P i hd hd'
  i0 : nat
  hd0 : A
  tl0 : list A
  tl' : list A
  b : OnOne2i P (S i0) tl0 tl'
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2i A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i;
                                            pr2 :=
                                              {|
                                                pr1 := hd :: tl;
                                                pr2 := hd' :: tl
                                              |}
                                          |};
                                        pr2 := OnOne2i_hd P i hd hd' tl p
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i0;
                                            pr2 :=
                                              {|
                                                pr1 := hd0 :: tl0;
                                                pr2 := hd0 :: tl'
                                              |}
                                          |};
                                        pr2 := OnOne2i_tl P i0 hd0 tl0 tl' b
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2i_obligation_2 A P
        {|
          pr1 :=
            {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
          pr2 := OnOne2i_hd P i hd hd' tl p
        |}
        {|
          pr1 :=
            {|
              pr1 := i0; pr2 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |}
            |};
          pr2 := OnOne2i_tl P i0 hd0 tl0 tl' b
        |}
        (noConfusion_OnOne2i_obligation_1 A P
           {|
             pr1 :=
               {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
             pr2 := OnOne2i_hd P i hd hd' tl p
           |}
           {|
             pr1 :=
               {|
                 pr1 := i0; pr2 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |}
               |};
             pr2 := OnOne2i_tl P i0 hd0 tl0 tl' b
           |} e) = e)

  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2i P (S i) tl tl'
  i0 : nat
  hd0 : A
  hd' : A
  tl0 : list A
  p : P i0 hd0 hd'
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2i A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i;
                                            pr2 :=
                                              {|
                                                pr1 := hd :: tl;
                                                pr2 := hd :: tl'
                                              |}
                                          |};
                                        pr2 := OnOne2i_tl P i hd tl tl' a
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i0;
                                            pr2 :=
                                              {|
                                                pr1 := hd0 :: tl0;
                                                pr2 := hd' :: tl0
                                              |}
                                          |};
                                        pr2 := OnOne2i_hd P i0 hd0 hd' tl0 p
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2i_obligation_2 A P
        {|
          pr1 :=
            {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
          pr2 := OnOne2i_tl P i hd tl tl' a
        |}
        {|
          pr1 :=
            {|
              pr1 := i0; pr2 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |}
            |};
          pr2 := OnOne2i_hd P i0 hd0 hd' tl0 p
        |}
        (noConfusion_OnOne2i_obligation_1 A P
           {|
             pr1 :=
               {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
             pr2 := OnOne2i_tl P i hd tl tl' a
           |}
           {|
             pr1 :=
               {|
                 pr1 := i0; pr2 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |}
               |};
             pr2 := OnOne2i_hd P i0 hd0 hd' tl0 p
           |} e) = e)

  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2i P (S i) tl tl'
  i0 : nat
  hd0 : A
  tl0 : list A
  tl'0 : list A
  b : OnOne2i P (S i0) tl0 tl'0
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2i A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i;
                                            pr2 :=
                                              {|
                                                pr1 := hd :: tl;
                                                pr2 := hd :: tl'
                                              |}
                                          |};
                                        pr2 := OnOne2i_tl P i hd tl tl' a
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i0;
                                            pr2 :=
                                              {|
                                                pr1 := hd0 :: tl0;
                                                pr2 := hd0 :: tl'0
                                              |}
                                          |};
                                        pr2 := OnOne2i_tl P i0 hd0 tl0 tl'0 b
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2i_obligation_2 A P
        {|
          pr1 :=
            {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
          pr2 := OnOne2i_tl P i hd tl tl' a
        |}
        {|
          pr1 :=
            {|
              pr1 := i0; pr2 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |}
            |};
          pr2 := OnOne2i_tl P i0 hd0 tl0 tl'0 b
        |}
        (noConfusion_OnOne2i_obligation_1 A P
           {|
             pr1 :=
               {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
             pr2 := OnOne2i_tl P i hd tl tl' a
           |}
           {|
             pr1 :=
               {|
                 pr1 := i0;
                 pr2 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |}
               |};
             pr2 := OnOne2i_tl P i0 hd0 tl0 tl'0 b
           |} e) = e)


DEBUG:Going to execute:
DepElim.simpl_dep_elim

Goals:
  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  hd' : A
  tl : list A
  p : P i hd hd'
  i0 : nat
  hd0 : A
  hd'0 : A
  tl0 : list A
  p0 : P i0 hd0 hd'0
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2i A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i;
                                            pr2 :=
                                              {|
                                                pr1 := hd :: tl;
                                                pr2 := hd' :: tl
                                              |}
                                          |};
                                        pr2 := OnOne2i_hd P i hd hd' tl p
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i0;
                                            pr2 :=
                                              {|
                                                pr1 := hd0 :: tl0;
                                                pr2 := hd'0 :: tl0
                                              |}
                                          |};
                                        pr2 :=
                                          OnOne2i_hd P i0 hd0 hd'0 tl0 p0
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2i_obligation_2 A P
        {|
          pr1 :=
            {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
          pr2 := OnOne2i_hd P i hd hd' tl p
        |}
        {|
          pr1 :=
            {|
              pr1 := i0; pr2 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |}
            |};
          pr2 := OnOne2i_hd P i0 hd0 hd'0 tl0 p0
        |}
        (noConfusion_OnOne2i_obligation_1 A P
           {|
             pr1 :=
               {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
             pr2 := OnOne2i_hd P i hd hd' tl p
           |}
           {|
             pr1 :=
               {|
                 pr1 := i0;
                 pr2 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |}
               |};
             pr2 := OnOne2i_hd P i0 hd0 hd'0 tl0 p0
           |} e) = e)

  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  hd' : A
  tl : list A
  p : P i hd hd'
  i0 : nat
  hd0 : A
  tl0 : list A
  tl' : list A
  b : OnOne2i P (S i0) tl0 tl'
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2i A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i;
                                            pr2 :=
                                              {|
                                                pr1 := hd :: tl;
                                                pr2 := hd' :: tl
                                              |}
                                          |};
                                        pr2 := OnOne2i_hd P i hd hd' tl p
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i0;
                                            pr2 :=
                                              {|
                                                pr1 := hd0 :: tl0;
                                                pr2 := hd0 :: tl'
                                              |}
                                          |};
                                        pr2 := OnOne2i_tl P i0 hd0 tl0 tl' b
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2i_obligation_2 A P
        {|
          pr1 :=
            {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
          pr2 := OnOne2i_hd P i hd hd' tl p
        |}
        {|
          pr1 :=
            {|
              pr1 := i0; pr2 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |}
            |};
          pr2 := OnOne2i_tl P i0 hd0 tl0 tl' b
        |}
        (noConfusion_OnOne2i_obligation_1 A P
           {|
             pr1 :=
               {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
             pr2 := OnOne2i_hd P i hd hd' tl p
           |}
           {|
             pr1 :=
               {|
                 pr1 := i0; pr2 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |}
               |};
             pr2 := OnOne2i_tl P i0 hd0 tl0 tl' b
           |} e) = e)

  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2i P (S i) tl tl'
  i0 : nat
  hd0 : A
  hd' : A
  tl0 : list A
  p : P i0 hd0 hd'
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2i A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i;
                                            pr2 :=
                                              {|
                                                pr1 := hd :: tl;
                                                pr2 := hd :: tl'
                                              |}
                                          |};
                                        pr2 := OnOne2i_tl P i hd tl tl' a
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i0;
                                            pr2 :=
                                              {|
                                                pr1 := hd0 :: tl0;
                                                pr2 := hd' :: tl0
                                              |}
                                          |};
                                        pr2 := OnOne2i_hd P i0 hd0 hd' tl0 p
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2i_obligation_2 A P
        {|
          pr1 :=
            {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
          pr2 := OnOne2i_tl P i hd tl tl' a
        |}
        {|
          pr1 :=
            {|
              pr1 := i0; pr2 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |}
            |};
          pr2 := OnOne2i_hd P i0 hd0 hd' tl0 p
        |}
        (noConfusion_OnOne2i_obligation_1 A P
           {|
             pr1 :=
               {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
             pr2 := OnOne2i_tl P i hd tl tl' a
           |}
           {|
             pr1 :=
               {|
                 pr1 := i0; pr2 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |}
               |};
             pr2 := OnOne2i_hd P i0 hd0 hd' tl0 p
           |} e) = e)

  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2i P (S i) tl tl'
  i0 : nat
  hd0 : A
  tl0 : list A
  tl'0 : list A
  b : OnOne2i P (S i0) tl0 tl'0
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2i A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i;
                                            pr2 :=
                                              {|
                                                pr1 := hd :: tl;
                                                pr2 := hd :: tl'
                                              |}
                                          |};
                                        pr2 := OnOne2i_tl P i hd tl tl' a
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i0;
                                            pr2 :=
                                              {|
                                                pr1 := hd0 :: tl0;
                                                pr2 := hd0 :: tl'0
                                              |}
                                          |};
                                        pr2 := OnOne2i_tl P i0 hd0 tl0 tl'0 b
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2i_obligation_2 A P
        {|
          pr1 :=
            {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
          pr2 := OnOne2i_tl P i hd tl tl' a
        |}
        {|
          pr1 :=
            {|
              pr1 := i0; pr2 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |}
            |};
          pr2 := OnOne2i_tl P i0 hd0 tl0 tl'0 b
        |}
        (noConfusion_OnOne2i_obligation_1 A P
           {|
             pr1 :=
               {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
             pr2 := OnOne2i_tl P i hd tl tl' a
           |}
           {|
             pr1 :=
               {|
                 pr1 := i0;
                 pr2 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |}
               |};
             pr2 := OnOne2i_tl P i0 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 : nat → A → A → Type
  i : nat
  hd : A
  hd' : A
  tl : list A
  p : P i hd hd'
  i0 : nat
  hd0 : A
  hd'0 : A
  tl0 : list A
  p0 : P i0 hd0 hd'0
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2i A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i;
                                            pr2 :=
                                              {|
                                                pr1 := hd :: tl;
                                                pr2 := hd' :: tl
                                              |}
                                          |};
                                        pr2 := OnOne2i_hd P i hd hd' tl p
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i0;
                                            pr2 :=
                                              {|
                                                pr1 := hd0 :: tl0;
                                                pr2 := hd'0 :: tl0
                                              |}
                                          |};
                                        pr2 :=
                                          OnOne2i_hd P i0 hd0 hd'0 tl0 p0
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2i_obligation_2 A P
        {|
          pr1 :=
            {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
          pr2 := OnOne2i_hd P i hd hd' tl p
        |}
        {|
          pr1 :=
            {|
              pr1 := i0; pr2 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |}
            |};
          pr2 := OnOne2i_hd P i0 hd0 hd'0 tl0 p0
        |}
        (noConfusion_OnOne2i_obligation_1 A P
           {|
             pr1 :=
               {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
             pr2 := OnOne2i_hd P i hd hd' tl p
           |}
           {|
             pr1 :=
               {|
                 pr1 := i0;
                 pr2 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |}
               |};
             pr2 := OnOne2i_hd P i0 hd0 hd'0 tl0 p0
           |} e) = e)

  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  hd' : A
  tl : list A
  p : P i hd hd'
  i0 : nat
  hd0 : A
  tl0 : list A
  tl' : list A
  b : OnOne2i P (S i0) tl0 tl'
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2i A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i;
                                            pr2 :=
                                              {|
                                                pr1 := hd :: tl;
                                                pr2 := hd' :: tl
                                              |}
                                          |};
                                        pr2 := OnOne2i_hd P i hd hd' tl p
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i0;
                                            pr2 :=
                                              {|
                                                pr1 := hd0 :: tl0;
                                                pr2 := hd0 :: tl'
                                              |}
                                          |};
                                        pr2 := OnOne2i_tl P i0 hd0 tl0 tl' b
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2i_obligation_2 A P
        {|
          pr1 :=
            {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
          pr2 := OnOne2i_hd P i hd hd' tl p
        |}
        {|
          pr1 :=
            {|
              pr1 := i0; pr2 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |}
            |};
          pr2 := OnOne2i_tl P i0 hd0 tl0 tl' b
        |}
        (noConfusion_OnOne2i_obligation_1 A P
           {|
             pr1 :=
               {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
             pr2 := OnOne2i_hd P i hd hd' tl p
           |}
           {|
             pr1 :=
               {|
                 pr1 := i0; pr2 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |}
               |};
             pr2 := OnOne2i_tl P i0 hd0 tl0 tl' b
           |} e) = e)

  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2i P (S i) tl tl'
  i0 : nat
  hd0 : A
  hd' : A
  tl0 : list A
  p : P i0 hd0 hd'
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2i A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i;
                                            pr2 :=
                                              {|
                                                pr1 := hd :: tl;
                                                pr2 := hd :: tl'
                                              |}
                                          |};
                                        pr2 := OnOne2i_tl P i hd tl tl' a
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i0;
                                            pr2 :=
                                              {|
                                                pr1 := hd0 :: tl0;
                                                pr2 := hd' :: tl0
                                              |}
                                          |};
                                        pr2 := OnOne2i_hd P i0 hd0 hd' tl0 p
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2i_obligation_2 A P
        {|
          pr1 :=
            {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
          pr2 := OnOne2i_tl P i hd tl tl' a
        |}
        {|
          pr1 :=
            {|
              pr1 := i0; pr2 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |}
            |};
          pr2 := OnOne2i_hd P i0 hd0 hd' tl0 p
        |}
        (noConfusion_OnOne2i_obligation_1 A P
           {|
             pr1 :=
               {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
             pr2 := OnOne2i_tl P i hd tl tl' a
           |}
           {|
             pr1 :=
               {|
                 pr1 := i0; pr2 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |}
               |};
             pr2 := OnOne2i_hd P i0 hd0 hd' tl0 p
           |} e) = e)

  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2i P (S i) tl tl'
  i0 : nat
  hd0 : A
  tl0 : list A
  tl'0 : list A
  b : OnOne2i P (S i0) tl0 tl'0
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2i A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i;
                                            pr2 :=
                                              {|
                                                pr1 := hd :: tl;
                                                pr2 := hd :: tl'
                                              |}
                                          |};
                                        pr2 := OnOne2i_tl P i hd tl tl' a
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i0;
                                            pr2 :=
                                              {|
                                                pr1 := hd0 :: tl0;
                                                pr2 := hd0 :: tl'0
                                              |}
                                          |};
                                        pr2 := OnOne2i_tl P i0 hd0 tl0 tl'0 b
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2i_obligation_2 A P
        {|
          pr1 :=
            {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
          pr2 := OnOne2i_tl P i hd tl tl' a
        |}
        {|
          pr1 :=
            {|
              pr1 := i0; pr2 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |}
            |};
          pr2 := OnOne2i_tl P i0 hd0 tl0 tl'0 b
        |}
        (noConfusion_OnOne2i_obligation_1 A P
           {|
             pr1 :=
               {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
             pr2 := OnOne2i_tl P i hd tl tl' a
           |}
           {|
             pr1 :=
               {|
                 pr1 := i0;
                 pr2 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |}
               |};
             pr2 := OnOne2i_tl P i0 hd0 tl0 tl'0 b
           |} e) = e)


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

Goals:
  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  hd' : A
  tl : list A
  p : P i hd hd'
  i0 : nat
  hd0 : A
  hd'0 : A
  tl0 : list A
  p0 : P i0 hd0 hd'0
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2i A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i;
                                            pr2 :=
                                              {|
                                                pr1 := hd :: tl;
                                                pr2 := hd' :: tl
                                              |}
                                          |};
                                        pr2 := OnOne2i_hd P i hd hd' tl p
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i0;
                                            pr2 :=
                                              {|
                                                pr1 := hd0 :: tl0;
                                                pr2 := hd'0 :: tl0
                                              |}
                                          |};
                                        pr2 :=
                                          OnOne2i_hd P i0 hd0 hd'0 tl0 p0
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2i_obligation_2 A P
        {|
          pr1 :=
            {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
          pr2 := OnOne2i_hd P i hd hd' tl p
        |}
        {|
          pr1 :=
            {|
              pr1 := i0; pr2 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |}
            |};
          pr2 := OnOne2i_hd P i0 hd0 hd'0 tl0 p0
        |}
        (noConfusion_OnOne2i_obligation_1 A P
           {|
             pr1 :=
               {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
             pr2 := OnOne2i_hd P i hd hd' tl p
           |}
           {|
             pr1 :=
               {|
                 pr1 := i0;
                 pr2 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |}
               |};
             pr2 := OnOne2i_hd P i0 hd0 hd'0 tl0 p0
           |} e) = e)

  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  hd' : A
  tl : list A
  p : P i hd hd'
  i0 : nat
  hd0 : A
  tl0 : list A
  tl' : list A
  b : OnOne2i P (S i0) tl0 tl'
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2i A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i;
                                            pr2 :=
                                              {|
                                                pr1 := hd :: tl;
                                                pr2 := hd' :: tl
                                              |}
                                          |};
                                        pr2 := OnOne2i_hd P i hd hd' tl p
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i0;
                                            pr2 :=
                                              {|
                                                pr1 := hd0 :: tl0;
                                                pr2 := hd0 :: tl'
                                              |}
                                          |};
                                        pr2 := OnOne2i_tl P i0 hd0 tl0 tl' b
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2i_obligation_2 A P
        {|
          pr1 :=
            {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
          pr2 := OnOne2i_hd P i hd hd' tl p
        |}
        {|
          pr1 :=
            {|
              pr1 := i0; pr2 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |}
            |};
          pr2 := OnOne2i_tl P i0 hd0 tl0 tl' b
        |}
        (noConfusion_OnOne2i_obligation_1 A P
           {|
             pr1 :=
               {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
             pr2 := OnOne2i_hd P i hd hd' tl p
           |}
           {|
             pr1 :=
               {|
                 pr1 := i0; pr2 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |}
               |};
             pr2 := OnOne2i_tl P i0 hd0 tl0 tl' b
           |} e) = e)

  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2i P (S i) tl tl'
  i0 : nat
  hd0 : A
  hd' : A
  tl0 : list A
  p : P i0 hd0 hd'
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2i A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i;
                                            pr2 :=
                                              {|
                                                pr1 := hd :: tl;
                                                pr2 := hd :: tl'
                                              |}
                                          |};
                                        pr2 := OnOne2i_tl P i hd tl tl' a
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i0;
                                            pr2 :=
                                              {|
                                                pr1 := hd0 :: tl0;
                                                pr2 := hd' :: tl0
                                              |}
                                          |};
                                        pr2 := OnOne2i_hd P i0 hd0 hd' tl0 p
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2i_obligation_2 A P
        {|
          pr1 :=
            {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
          pr2 := OnOne2i_tl P i hd tl tl' a
        |}
        {|
          pr1 :=
            {|
              pr1 := i0; pr2 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |}
            |};
          pr2 := OnOne2i_hd P i0 hd0 hd' tl0 p
        |}
        (noConfusion_OnOne2i_obligation_1 A P
           {|
             pr1 :=
               {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
             pr2 := OnOne2i_tl P i hd tl tl' a
           |}
           {|
             pr1 :=
               {|
                 pr1 := i0; pr2 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |}
               |};
             pr2 := OnOne2i_hd P i0 hd0 hd' tl0 p
           |} e) = e)

  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2i P (S i) tl tl'
  i0 : nat
  hd0 : A
  tl0 : list A
  tl'0 : list A
  b : OnOne2i P (S i0) tl0 tl'0
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2i A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i;
                                            pr2 :=
                                              {|
                                                pr1 := hd :: tl;
                                                pr2 := hd :: tl'
                                              |}
                                          |};
                                        pr2 := OnOne2i_tl P i hd tl tl' a
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i0;
                                            pr2 :=
                                              {|
                                                pr1 := hd0 :: tl0;
                                                pr2 := hd0 :: tl'0
                                              |}
                                          |};
                                        pr2 := OnOne2i_tl P i0 hd0 tl0 tl'0 b
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2i_obligation_2 A P
        {|
          pr1 :=
            {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
          pr2 := OnOne2i_tl P i hd tl tl' a
        |}
        {|
          pr1 :=
            {|
              pr1 := i0; pr2 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |}
            |};
          pr2 := OnOne2i_tl P i0 hd0 tl0 tl'0 b
        |}
        (noConfusion_OnOne2i_obligation_1 A P
           {|
             pr1 :=
               {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
             pr2 := OnOne2i_tl P i hd tl tl' a
           |}
           {|
             pr1 :=
               {|
                 pr1 := i0;
                 pr2 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |}
               |};
             pr2 := OnOne2i_tl P i0 hd0 tl0 tl'0 b
           |} e) = e)


DEBUG:Going to execute:
DepElim.simplify_dep_elim

Goals:
  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  hd' : A
  tl : list A
  p : P i hd hd'
  i0 : nat
  hd0 : A
  hd'0 : A
  tl0 : list A
  p0 : P i0 hd0 hd'0
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2i A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i;
                                            pr2 :=
                                              {|
                                                pr1 := hd :: tl;
                                                pr2 := hd' :: tl
                                              |}
                                          |};
                                        pr2 := OnOne2i_hd P i hd hd' tl p
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i0;
                                            pr2 :=
                                              {|
                                                pr1 := hd0 :: tl0;
                                                pr2 := hd'0 :: tl0
                                              |}
                                          |};
                                        pr2 :=
                                          OnOne2i_hd P i0 hd0 hd'0 tl0 p0
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2i_obligation_2 A P
        {|
          pr1 :=
            {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
          pr2 := OnOne2i_hd P i hd hd' tl p
        |}
        {|
          pr1 :=
            {|
              pr1 := i0; pr2 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |}
            |};
          pr2 := OnOne2i_hd P i0 hd0 hd'0 tl0 p0
        |}
        (noConfusion_OnOne2i_obligation_1 A P
           {|
             pr1 :=
               {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
             pr2 := OnOne2i_hd P i hd hd' tl p
           |}
           {|
             pr1 :=
               {|
                 pr1 := i0;
                 pr2 := {| pr1 := hd0 :: tl0; pr2 := hd'0 :: tl0 |}
               |};
             pr2 := OnOne2i_hd P i0 hd0 hd'0 tl0 p0
           |} e) = e)

  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  hd' : A
  tl : list A
  p : P i hd hd'
  i0 : nat
  hd0 : A
  tl0 : list A
  tl' : list A
  b : OnOne2i P (S i0) tl0 tl'
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2i A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i;
                                            pr2 :=
                                              {|
                                                pr1 := hd :: tl;
                                                pr2 := hd' :: tl
                                              |}
                                          |};
                                        pr2 := OnOne2i_hd P i hd hd' tl p
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i0;
                                            pr2 :=
                                              {|
                                                pr1 := hd0 :: tl0;
                                                pr2 := hd0 :: tl'
                                              |}
                                          |};
                                        pr2 := OnOne2i_tl P i0 hd0 tl0 tl' b
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2i_obligation_2 A P
        {|
          pr1 :=
            {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
          pr2 := OnOne2i_hd P i hd hd' tl p
        |}
        {|
          pr1 :=
            {|
              pr1 := i0; pr2 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |}
            |};
          pr2 := OnOne2i_tl P i0 hd0 tl0 tl' b
        |}
        (noConfusion_OnOne2i_obligation_1 A P
           {|
             pr1 :=
               {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd' :: tl |} |};
             pr2 := OnOne2i_hd P i hd hd' tl p
           |}
           {|
             pr1 :=
               {|
                 pr1 := i0; pr2 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl' |}
               |};
             pr2 := OnOne2i_tl P i0 hd0 tl0 tl' b
           |} e) = e)

  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2i P (S i) tl tl'
  i0 : nat
  hd0 : A
  hd' : A
  tl0 : list A
  p : P i0 hd0 hd'
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2i A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i;
                                            pr2 :=
                                              {|
                                                pr1 := hd :: tl;
                                                pr2 := hd :: tl'
                                              |}
                                          |};
                                        pr2 := OnOne2i_tl P i hd tl tl' a
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i0;
                                            pr2 :=
                                              {|
                                                pr1 := hd0 :: tl0;
                                                pr2 := hd' :: tl0
                                              |}
                                          |};
                                        pr2 := OnOne2i_hd P i0 hd0 hd' tl0 p
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2i_obligation_2 A P
        {|
          pr1 :=
            {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
          pr2 := OnOne2i_tl P i hd tl tl' a
        |}
        {|
          pr1 :=
            {|
              pr1 := i0; pr2 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |}
            |};
          pr2 := OnOne2i_hd P i0 hd0 hd' tl0 p
        |}
        (noConfusion_OnOne2i_obligation_1 A P
           {|
             pr1 :=
               {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
             pr2 := OnOne2i_tl P i hd tl tl' a
           |}
           {|
             pr1 :=
               {|
                 pr1 := i0; pr2 := {| pr1 := hd0 :: tl0; pr2 := hd' :: tl0 |}
               |};
             pr2 := OnOne2i_hd P i0 hd0 hd' tl0 p
           |} e) = e)

  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  tl : list A
  tl' : list A
  a : OnOne2i P (S i) tl tl'
  i0 : nat
  hd0 : A
  tl0 : list A
  tl'0 : list A
  b : OnOne2i P (S i0) tl0 tl'0
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_OnOne2i A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i;
                                            pr2 :=
                                              {|
                                                pr1 := hd :: tl;
                                                pr2 := hd :: tl'
                                              |}
                                          |};
                                        pr2 := OnOne2i_tl P i hd tl tl' a
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := i0;
                                            pr2 :=
                                              {|
                                                pr1 := hd0 :: tl0;
                                                pr2 := hd0 :: tl'0
                                              |}
                                          |};
                                        pr2 := OnOne2i_tl P i0 hd0 tl0 tl'0 b
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_OnOne2i_obligation_2 A P
        {|
          pr1 :=
            {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
          pr2 := OnOne2i_tl P i hd tl tl' a
        |}
        {|
          pr1 :=
            {|
              pr1 := i0; pr2 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |}
            |};
          pr2 := OnOne2i_tl P i0 hd0 tl0 tl'0 b
        |}
        (noConfusion_OnOne2i_obligation_1 A P
           {|
             pr1 :=
               {| pr1 := i; pr2 := {| pr1 := hd :: tl; pr2 := hd :: tl' |} |};
             pr2 := OnOne2i_tl P i hd tl tl' a
           |}
           {|
             pr1 :=
               {|
                 pr1 := i0;
                 pr2 := {| pr1 := hd0 :: tl0; pr2 := hd0 :: tl'0 |}
               |};
             pr2 := OnOne2i_tl P i0 hd0 tl0 tl'0 b
           |} e) = e)


DEBUG:Going to execute:
repeat DepElim.simplify_one_dep_elim