Goal:
  
  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
  ============================
   (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 :=
              pr1
                {|
                  pr1 := i;
                  pr2 :=
                    {|
                      pr1 := hd;
                      pr2 :=
                        {| pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |} |}
                    |}
                |};
            pr2 :=
              {|
                pr1 :=
                  pr1
                    (pr2
                       {|
                         pr1 := i;
                         pr2 :=
                           {|
                             pr1 := hd;
                             pr2 :=
                               {|
                                 pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |}
                               |}
                           |}
                       |})
                  :: pr1
                       (pr2
                          (pr2
                             (pr2
                                {|
                                  pr1 := i;
                                  pr2 :=
                                    {|
                                      pr1 := hd;
                                      pr2 :=
                                        {|
                                          pr1 := hd';
                                          pr2 := {| pr1 := tl; pr2 := p |}
                                        |}
                                    |}
                                |})));
                pr2 :=
                  pr1
                    (pr2
                       (pr2
                          {|
                            pr1 := i;
                            pr2 :=
                              {|
                                pr1 := hd;
                                pr2 :=
                                  {|
                                    pr1 := hd';
                                    pr2 := {| pr1 := tl; pr2 := p |}
                                  |}
                              |}
                          |}))
                  :: pr1
                       (pr2
                          (pr2
                             (pr2
                                {|
                                  pr1 := i;
                                  pr2 :=
                                    {|
                                      pr1 := hd;
                                      pr2 :=
                                        {|
                                          pr1 := hd';
                                          pr2 := {| pr1 := tl; pr2 := p |}
                                        |}
                                    |}
                                |})))
              |}
          |};
        pr2 :=
          OnOne2i_hd P
            (pr1
               {|
                 pr1 := i;
                 pr2 :=
                   {|
                     pr1 := hd;
                     pr2 :=
                       {| pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |} |}
                   |}
               |})
            (pr1
               (pr2
                  {|
                    pr1 := i;
                    pr2 :=
                      {|
                        pr1 := hd;
                        pr2 :=
                          {| pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |} |}
                      |}
                  |}))
            (pr1
               (pr2
                  (pr2
                     {|
                       pr1 := i;
                       pr2 :=
                         {|
                           pr1 := hd;
                           pr2 :=
                             {|
                               pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |}
                             |}
                         |}
                     |})))
            (pr1
               (pr2
                  (pr2
                     (pr2
                        {|
                          pr1 := i;
                          pr2 :=
                            {|
                              pr1 := hd;
                              pr2 :=
                                {|
                                  pr1 := hd';
                                  pr2 := {| pr1 := tl; pr2 := p |}
                                |}
                            |}
                        |}))))
            (pr2
               (pr2
                  (pr2
                     (pr2
                        {|
                          pr1 := i;
                          pr2 :=
                            {|
                              pr1 := hd;
                              pr2 :=
                                {|
                                  pr1 := hd';
                                  pr2 := {| pr1 := tl; pr2 := p |}
                                |}
                            |}
                        |}))))
      |}
      (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 :=
                 pr1
                   {|
                     pr1 := i;
                     pr2 :=
                       {|
                         pr1 := hd;
                         pr2 :=
                           {| pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |} |}
                       |}
                   |};
               pr2 :=
                 {|
                   pr1 :=
                     pr1
                       (pr2
                          {|
                            pr1 := i;
                            pr2 :=
                              {|
                                pr1 := hd;
                                pr2 :=
                                  {|
                                    pr1 := hd';
                                    pr2 := {| pr1 := tl; pr2 := p |}
                                  |}
                              |}
                          |})
                     :: pr1
                          (pr2
                             (pr2
                                (pr2
                                   {|
                                     pr1 := i;
                                     pr2 :=
                                       {|
                                         pr1 := hd;
                                         pr2 :=
                                           {|
                                             pr1 := hd';
                                             pr2 := {| pr1 := tl; pr2 := p |}
                                           |}
                                       |}
                                   |})));
                   pr2 :=
                     pr1
                       (pr2
                          (pr2
                             {|
                               pr1 := i;
                               pr2 :=
                                 {|
                                   pr1 := hd;
                                   pr2 :=
                                     {|
                                       pr1 := hd';
                                       pr2 := {| pr1 := tl; pr2 := p |}
                                     |}
                                 |}
                             |}))
                     :: pr1
                          (pr2
                             (pr2
                                (pr2
                                   {|
                                     pr1 := i;
                                     pr2 :=
                                       {|
                                         pr1 := hd;
                                         pr2 :=
                                           {|
                                             pr1 := hd';
                                             pr2 := {| pr1 := tl; pr2 := p |}
                                           |}
                                       |}
                                   |})))
                 |}
             |};
           pr2 :=
             OnOne2i_hd P
               (pr1
                  {|
                    pr1 := i;
                    pr2 :=
                      {|
                        pr1 := hd;
                        pr2 :=
                          {| pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |} |}
                      |}
                  |})
               (pr1
                  (pr2
                     {|
                       pr1 := i;
                       pr2 :=
                         {|
                           pr1 := hd;
                           pr2 :=
                             {|
                               pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |}
                             |}
                         |}
                     |}))
               (pr1
                  (pr2
                     (pr2
                        {|
                          pr1 := i;
                          pr2 :=
                            {|
                              pr1 := hd;
                              pr2 :=
                                {|
                                  pr1 := hd';
                                  pr2 := {| pr1 := tl; pr2 := p |}
                                |}
                            |}
                        |})))
               (pr1
                  (pr2
                     (pr2
                        (pr2
                           {|
                             pr1 := i;
                             pr2 :=
                               {|
                                 pr1 := hd;
                                 pr2 :=
                                   {|
                                     pr1 := hd';
                                     pr2 := {| pr1 := tl; pr2 := p |}
                                   |}
                               |}
                           |}))))
               (pr2
                  (pr2
                     (pr2
                        (pr2
                           {|
                             pr1 := i;
                             pr2 :=
                               {|
                                 pr1 := hd;
                                 pr2 :=
                                   {|
                                     pr1 := hd';
                                     pr2 := {| pr1 := tl; pr2 := p |}
                                   |}
                               |}
                           |}))))
         |} eq_refl) = eq_refl)


DEBUG:Going to execute:
simpl