Goal:
  
  A : Type
  P : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  a : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  d0 : A
  d'0 : A
  Γ0 : list A
  Γ'0 : list A
  b : All2_fold P Γ0 Γ'0
  p0 : P Γ0 Γ'0 d0 d'0
  ============================
   (noConfusion_All2_fold_obligation_2 A P
      {|
        pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
        pr2 := All2_fold_cons P a p
      |}
      {|
        pr1 :=
          {|
            pr1 :=
              pr1
                {|
                  pr1 := d;
                  pr2 :=
                    {|
                      pr1 := d';
                      pr2 :=
                        {|
                          pr1 := Γ;
                          pr2 :=
                            {| pr1 := Γ'; pr2 := {| pr1 := a; pr2 := p |} |}
                        |}
                    |}
                |}
              :: pr1
                   (pr2
                      (pr2
                         {|
                           pr1 := d;
                           pr2 :=
                             {|
                               pr1 := d';
                               pr2 :=
                                 {|
                                   pr1 := Γ;
                                   pr2 :=
                                     {|
                                       pr1 := Γ';
                                       pr2 := {| pr1 := a; pr2 := p |}
                                     |}
                                 |}
                             |}
                         |}));
            pr2 :=
              pr1
                (pr2
                   {|
                     pr1 := d;
                     pr2 :=
                       {|
                         pr1 := d';
                         pr2 :=
                           {|
                             pr1 := Γ;
                             pr2 :=
                               {|
                                 pr1 := Γ'; pr2 := {| pr1 := a; pr2 := p |}
                               |}
                           |}
                       |}
                   |})
              :: pr1
                   (pr2
                      (pr2
                         (pr2
                            {|
                              pr1 := d;
                              pr2 :=
                                {|
                                  pr1 := d';
                                  pr2 :=
                                    {|
                                      pr1 := Γ;
                                      pr2 :=
                                        {|
                                          pr1 := Γ';
                                          pr2 := {| pr1 := a; pr2 := p |}
                                        |}
                                    |}
                                |}
                            |})))
          |};
        pr2 :=
          All2_fold_cons P
            (pr1
               (pr2
                  (pr2
                     (pr2
                        (pr2
                           {|
                             pr1 := d;
                             pr2 :=
                               {|
                                 pr1 := d';
                                 pr2 :=
                                   {|
                                     pr1 := Γ;
                                     pr2 :=
                                       {|
                                         pr1 := Γ';
                                         pr2 := {| pr1 := a; pr2 := p |}
                                       |}
                                   |}
                               |}
                           |})))))
            (pr2
               (pr2
                  (pr2
                     (pr2
                        (pr2
                           {|
                             pr1 := d;
                             pr2 :=
                               {|
                                 pr1 := d';
                                 pr2 :=
                                   {|
                                     pr1 := Γ;
                                     pr2 :=
                                       {|
                                         pr1 := Γ';
                                         pr2 := {| pr1 := a; pr2 := p |}
                                       |}
                                   |}
                               |}
                           |})))))
      |}
      (noConfusion_All2_fold_obligation_1 A P
         {|
           pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
           pr2 := All2_fold_cons P a p
         |}
         {|
           pr1 :=
             {|
               pr1 :=
                 pr1
                   {|
                     pr1 := d;
                     pr2 :=
                       {|
                         pr1 := d';
                         pr2 :=
                           {|
                             pr1 := Γ;
                             pr2 :=
                               {|
                                 pr1 := Γ'; pr2 := {| pr1 := a; pr2 := p |}
                               |}
                           |}
                       |}
                   |}
                 :: pr1
                      (pr2
                         (pr2
                            {|
                              pr1 := d;
                              pr2 :=
                                {|
                                  pr1 := d';
                                  pr2 :=
                                    {|
                                      pr1 := Γ;
                                      pr2 :=
                                        {|
                                          pr1 := Γ';
                                          pr2 := {| pr1 := a; pr2 := p |}
                                        |}
                                    |}
                                |}
                            |}));
               pr2 :=
                 pr1
                   (pr2
                      {|
                        pr1 := d;
                        pr2 :=
                          {|
                            pr1 := d';
                            pr2 :=
                              {|
                                pr1 := Γ;
                                pr2 :=
                                  {|
                                    pr1 := Γ';
                                    pr2 := {| pr1 := a; pr2 := p |}
                                  |}
                              |}
                          |}
                      |})
                 :: pr1
                      (pr2
                         (pr2
                            (pr2
                               {|
                                 pr1 := d;
                                 pr2 :=
                                   {|
                                     pr1 := d';
                                     pr2 :=
                                       {|
                                         pr1 := Γ;
                                         pr2 :=
                                           {|
                                             pr1 := Γ';
                                             pr2 := {| pr1 := a; pr2 := p |}
                                           |}
                                       |}
                                   |}
                               |})))
             |};
           pr2 :=
             All2_fold_cons P
               (pr1
                  (pr2
                     (pr2
                        (pr2
                           (pr2
                              {|
                                pr1 := d;
                                pr2 :=
                                  {|
                                    pr1 := d';
                                    pr2 :=
                                      {|
                                        pr1 := Γ;
                                        pr2 :=
                                          {|
                                            pr1 := Γ';
                                            pr2 := {| pr1 := a; pr2 := p |}
                                          |}
                                      |}
                                  |}
                              |})))))
               (pr2
                  (pr2
                     (pr2
                        (pr2
                           (pr2
                              {|
                                pr1 := d;
                                pr2 :=
                                  {|
                                    pr1 := d';
                                    pr2 :=
                                      {|
                                        pr1 := Γ;
                                        pr2 :=
                                          {|
                                            pr1 := Γ';
                                            pr2 := {| pr1 := a; pr2 := p |}
                                          |}
                                      |}
                                  |}
                              |})))))
         |} eq_refl) = eq_refl)


DEBUG:Going to execute:
simpl

Goals:
    A : Type  P : list A → list A → A → A → Type
  ============================
   (noConfusion_All2_fold_obligation_2 A P
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
      {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
      (noConfusion_All2_fold_obligation_1 A P
         {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
         {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |} I) =
    I)

  
  A : Type
  P : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  a : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  d0 : A
  d'0 : A
  Γ0 : list A
  Γ'0 : list A
  b : All2_fold P Γ0 Γ'0
  p0 : P Γ0 Γ'0 d0 d'0
  ============================
   (eq_refl = eq_refl)


DEBUG:Going to execute:
solve [ constructor ]
Level 5: evaluation returns
idtac of type tacvalue

Level 3: evaluation returns
idtac of type tacvalue

Level 3: evaluation returns
idtac of type tacvalue