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
  ============================
   (∀ 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 H := 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:
change (let _ := CoreTactics.block in T)

Goals:
  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  hd' : A
  tl : list A
  p : P i hd hd'
  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_hd P i hd hd' tl p
                                      |}
                                      {|
                                        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_hd P i hd hd' tl p
        |}
        {|
          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_hd P i hd hd' tl p
           |}
           {|
             pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
             pr2 := 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'
  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:
try simpl in H; DepElim.simplify_equations_in H
DEBUG LTAC Evaluated term: (∀ (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)

Goals:
  
  A : Type
  P : nat → A → A → Type
  i : nat
  hd : A
  hd' : A
  tl : list A
  p : P i hd hd'
  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_hd P i hd hd' tl p
                                      |}
                                      {|
                                        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_hd P i hd hd' tl p
        |}
        {|
          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_hd P i hd hd' tl p
           |}
           {|
             pr1 := {| pr1 := idx3; pr2 := {| pr1 := idx4; pr2 := idx2 |} |};
             pr2 := 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'
  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:
try simpl in H