Goal:
  
  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
  ============================
   (noConfusion_OnOne2_obligation_2 A P
      {|
        pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
        pr2 := OnOne2_hd P hd hd' tl p
      |}
      {|
        pr1 :=
          {|
            pr1 :=
              pr1
                {|
                  pr1 := hd;
                  pr2 := {| pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |} |}
                |}
              :: pr1
                   (pr2
                      (pr2
                         {|
                           pr1 := hd;
                           pr2 :=
                             {|
                               pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |}
                             |}
                         |}));
            pr2 :=
              pr1
                (pr2
                   {|
                     pr1 := hd;
                     pr2 :=
                       {| pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |} |}
                   |})
              :: pr1
                   (pr2
                      (pr2
                         {|
                           pr1 := hd;
                           pr2 :=
                             {|
                               pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |}
                             |}
                         |}))
          |};
        pr2 :=
          OnOne2_hd P
            (pr1
               {|
                 pr1 := hd;
                 pr2 := {| pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |} |}
               |})
            (pr1
               (pr2
                  {|
                    pr1 := hd;
                    pr2 := {| pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |} |}
                  |}))
            (pr1
               (pr2
                  (pr2
                     {|
                       pr1 := hd;
                       pr2 :=
                         {| pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |} |}
                     |})))
            (pr2
               (pr2
                  (pr2
                     {|
                       pr1 := hd;
                       pr2 :=
                         {| pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |} |}
                     |})))
      |}
      (noConfusion_OnOne2_obligation_1 A P
         {|
           pr1 := {| pr1 := hd :: tl; pr2 := hd' :: tl |};
           pr2 := OnOne2_hd P hd hd' tl p
         |}
         {|
           pr1 :=
             {|
               pr1 :=
                 pr1
                   {|
                     pr1 := hd;
                     pr2 :=
                       {| pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |} |}
                   |}
                 :: pr1
                      (pr2
                         (pr2
                            {|
                              pr1 := hd;
                              pr2 :=
                                {|
                                  pr1 := hd';
                                  pr2 := {| pr1 := tl; pr2 := p |}
                                |}
                            |}));
               pr2 :=
                 pr1
                   (pr2
                      {|
                        pr1 := hd;
                        pr2 :=
                          {| pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |} |}
                      |})
                 :: pr1
                      (pr2
                         (pr2
                            {|
                              pr1 := hd;
                              pr2 :=
                                {|
                                  pr1 := hd';
                                  pr2 := {| pr1 := tl; pr2 := p |}
                                |}
                            |}))
             |};
           pr2 :=
             OnOne2_hd P
               (pr1
                  {|
                    pr1 := hd;
                    pr2 := {| pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |} |}
                  |})
               (pr1
                  (pr2
                     {|
                       pr1 := hd;
                       pr2 :=
                         {| pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |} |}
                     |}))
               (pr1
                  (pr2
                     (pr2
                        {|
                          pr1 := hd;
                          pr2 :=
                            {|
                              pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |}
                            |}
                        |})))
               (pr2
                  (pr2
                     (pr2
                        {|
                          pr1 := hd;
                          pr2 :=
                            {|
                              pr1 := hd'; pr2 := {| pr1 := tl; pr2 := p |}
                            |}
                        |})))
         |} eq_refl) = eq_refl)


DEBUG:Going to execute:
simpl