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'
  idx2 : list A
  idx1 : list A
  b : All2_fold P idx2 idx1
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_All2_fold A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := d :: Γ; pr2 := d' :: Γ'
                                          |};
                                        pr2 := All2_fold_cons P a p
                                      |}
                                      {|
                                        pr1 := {| pr1 := idx2; pr2 := idx1 |};
                                        pr2 := b
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_All2_fold_obligation_2 A P
        {|
          pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
          pr2 := All2_fold_cons P a p
        |} {| pr1 := {| pr1 := idx2; pr2 := idx1 |}; pr2 := b |}
        (noConfusion_All2_fold_obligation_1 A P
           {|
             pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
             pr2 := All2_fold_cons P a p
           |} {| pr1 := {| pr1 := idx2; pr2 := idx1 |}; pr2 := b |} e) = e)


DEBUG:Going to execute:
destruct p

Goals:
    A : Type  P : list A → list A → A → A → Type
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_All2_fold A P
                                      {|
                                        pr1 := {| pr1 := []; pr2 := [] |};
                                        pr2 := All2_fold_nil P
                                      |}
                                      {|
                                        pr1 := {| pr1 := []; pr2 := [] |};
                                        pr2 := All2_fold_nil P
                                      |}),
      let H0 := CoreTactics.block in
      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 |} e) =
      e)

  
  A : Type
  P : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  b : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_All2_fold A P
                                      {|
                                        pr1 := {| pr1 := []; pr2 := [] |};
                                        pr2 := All2_fold_nil P
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := d :: Γ; pr2 := d' :: Γ'
                                          |};
                                        pr2 := All2_fold_cons P b p
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_All2_fold_obligation_2 A P
        {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
        {|
          pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
          pr2 := All2_fold_cons P b p
        |}
        (noConfusion_All2_fold_obligation_1 A P
           {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
           {|
             pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
             pr2 := All2_fold_cons P b p
           |} e) = e)

  
  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'
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_All2_fold A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := d :: Γ; pr2 := d' :: Γ'
                                          |};
                                        pr2 := All2_fold_cons P a p
                                      |}
                                      {|
                                        pr1 := {| pr1 := []; pr2 := [] |};
                                        pr2 := All2_fold_nil P
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_All2_fold_obligation_2 A P
        {|
          pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
          pr2 := All2_fold_cons P a p
        |} {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
        (noConfusion_All2_fold_obligation_1 A P
           {|
             pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
             pr2 := All2_fold_cons P a p
           |} {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
           e) = e)

  
  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
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_All2_fold A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := d :: Γ; pr2 := d' :: Γ'
                                          |};
                                        pr2 := All2_fold_cons P a p
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := d0 :: Γ0;
                                            pr2 := d'0 :: Γ'0
                                          |};
                                        pr2 := All2_fold_cons P b p0
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_All2_fold_obligation_2 A P
        {|
          pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
          pr2 := All2_fold_cons P a p
        |}
        {|
          pr1 := {| pr1 := d0 :: Γ0; pr2 := d'0 :: Γ'0 |};
          pr2 := All2_fold_cons P b p0
        |}
        (noConfusion_All2_fold_obligation_1 A P
           {|
             pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
             pr2 := All2_fold_cons P a p
           |}
           {|
             pr1 := {| pr1 := d0 :: Γ0; pr2 := d'0 :: Γ'0 |};
             pr2 := All2_fold_cons P b p0
           |} e) = e)


DEBUG:Going to execute:
DepElim.simpl_dep_elim

Goals:
    A : Type  P : list A → list A → A → A → Type
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_All2_fold A P
                                      {|
                                        pr1 := {| pr1 := []; pr2 := [] |};
                                        pr2 := All2_fold_nil P
                                      |}
                                      {|
                                        pr1 := {| pr1 := []; pr2 := [] |};
                                        pr2 := All2_fold_nil P
                                      |}),
      let H0 := CoreTactics.block in
      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 |} e) =
      e)

  
  A : Type
  P : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  b : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_All2_fold A P
                                      {|
                                        pr1 := {| pr1 := []; pr2 := [] |};
                                        pr2 := All2_fold_nil P
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := d :: Γ; pr2 := d' :: Γ'
                                          |};
                                        pr2 := All2_fold_cons P b p
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_All2_fold_obligation_2 A P
        {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
        {|
          pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
          pr2 := All2_fold_cons P b p
        |}
        (noConfusion_All2_fold_obligation_1 A P
           {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
           {|
             pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
             pr2 := All2_fold_cons P b p
           |} e) = e)

  
  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'
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_All2_fold A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := d :: Γ; pr2 := d' :: Γ'
                                          |};
                                        pr2 := All2_fold_cons P a p
                                      |}
                                      {|
                                        pr1 := {| pr1 := []; pr2 := [] |};
                                        pr2 := All2_fold_nil P
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_All2_fold_obligation_2 A P
        {|
          pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
          pr2 := All2_fold_cons P a p
        |} {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
        (noConfusion_All2_fold_obligation_1 A P
           {|
             pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
             pr2 := All2_fold_cons P a p
           |} {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
           e) = e)

  
  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
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_All2_fold A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := d :: Γ; pr2 := d' :: Γ'
                                          |};
                                        pr2 := All2_fold_cons P a p
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := d0 :: Γ0;
                                            pr2 := d'0 :: Γ'0
                                          |};
                                        pr2 := All2_fold_cons P b p0
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_All2_fold_obligation_2 A P
        {|
          pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
          pr2 := All2_fold_cons P a p
        |}
        {|
          pr1 := {| pr1 := d0 :: Γ0; pr2 := d'0 :: Γ'0 |};
          pr2 := All2_fold_cons P b p0
        |}
        (noConfusion_All2_fold_obligation_1 A P
           {|
             pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
             pr2 := All2_fold_cons P a p
           |}
           {|
             pr1 := {| pr1 := d0 :: Γ0; pr2 := d'0 :: Γ'0 |};
             pr2 := All2_fold_cons P b p0
           |} e) = e)


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

Goals:
    A : Type  P : list A → list A → A → A → Type
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_All2_fold A P
                                      {|
                                        pr1 := {| pr1 := []; pr2 := [] |};
                                        pr2 := All2_fold_nil P
                                      |}
                                      {|
                                        pr1 := {| pr1 := []; pr2 := [] |};
                                        pr2 := All2_fold_nil P
                                      |}),
      let H0 := CoreTactics.block in
      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 |} e) =
      e)

  
  A : Type
  P : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  b : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_All2_fold A P
                                      {|
                                        pr1 := {| pr1 := []; pr2 := [] |};
                                        pr2 := All2_fold_nil P
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := d :: Γ; pr2 := d' :: Γ'
                                          |};
                                        pr2 := All2_fold_cons P b p
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_All2_fold_obligation_2 A P
        {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
        {|
          pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
          pr2 := All2_fold_cons P b p
        |}
        (noConfusion_All2_fold_obligation_1 A P
           {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
           {|
             pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
             pr2 := All2_fold_cons P b p
           |} e) = e)

  
  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'
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_All2_fold A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := d :: Γ; pr2 := d' :: Γ'
                                          |};
                                        pr2 := All2_fold_cons P a p
                                      |}
                                      {|
                                        pr1 := {| pr1 := []; pr2 := [] |};
                                        pr2 := All2_fold_nil P
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_All2_fold_obligation_2 A P
        {|
          pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
          pr2 := All2_fold_cons P a p
        |} {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
        (noConfusion_All2_fold_obligation_1 A P
           {|
             pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
             pr2 := All2_fold_cons P a p
           |} {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
           e) = e)

  
  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
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_All2_fold A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := d :: Γ; pr2 := d' :: Γ'
                                          |};
                                        pr2 := All2_fold_cons P a p
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := d0 :: Γ0;
                                            pr2 := d'0 :: Γ'0
                                          |};
                                        pr2 := All2_fold_cons P b p0
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_All2_fold_obligation_2 A P
        {|
          pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
          pr2 := All2_fold_cons P a p
        |}
        {|
          pr1 := {| pr1 := d0 :: Γ0; pr2 := d'0 :: Γ'0 |};
          pr2 := All2_fold_cons P b p0
        |}
        (noConfusion_All2_fold_obligation_1 A P
           {|
             pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
             pr2 := All2_fold_cons P a p
           |}
           {|
             pr1 := {| pr1 := d0 :: Γ0; pr2 := d'0 :: Γ'0 |};
             pr2 := All2_fold_cons P b p0
           |} e) = e)


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

Goals:
    A : Type  P : list A → list A → A → A → Type
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_All2_fold A P
                                      {|
                                        pr1 := {| pr1 := []; pr2 := [] |};
                                        pr2 := All2_fold_nil P
                                      |}
                                      {|
                                        pr1 := {| pr1 := []; pr2 := [] |};
                                        pr2 := All2_fold_nil P
                                      |}),
      let H0 := CoreTactics.block in
      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 |} e) =
      e)

  
  A : Type
  P : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  b : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_All2_fold A P
                                      {|
                                        pr1 := {| pr1 := []; pr2 := [] |};
                                        pr2 := All2_fold_nil P
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := d :: Γ; pr2 := d' :: Γ'
                                          |};
                                        pr2 := All2_fold_cons P b p
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_All2_fold_obligation_2 A P
        {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
        {|
          pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
          pr2 := All2_fold_cons P b p
        |}
        (noConfusion_All2_fold_obligation_1 A P
           {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
           {|
             pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
             pr2 := All2_fold_cons P b p
           |} e) = e)

  
  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'
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_All2_fold A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := d :: Γ; pr2 := d' :: Γ'
                                          |};
                                        pr2 := All2_fold_cons P a p
                                      |}
                                      {|
                                        pr1 := {| pr1 := []; pr2 := [] |};
                                        pr2 := All2_fold_nil P
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_All2_fold_obligation_2 A P
        {|
          pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
          pr2 := All2_fold_cons P a p
        |} {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
        (noConfusion_All2_fold_obligation_1 A P
           {|
             pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
             pr2 := All2_fold_cons P a p
           |} {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
           e) = e)

  
  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
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_All2_fold A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := d :: Γ; pr2 := d' :: Γ'
                                          |};
                                        pr2 := All2_fold_cons P a p
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := d0 :: Γ0;
                                            pr2 := d'0 :: Γ'0
                                          |};
                                        pr2 := All2_fold_cons P b p0
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_All2_fold_obligation_2 A P
        {|
          pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
          pr2 := All2_fold_cons P a p
        |}
        {|
          pr1 := {| pr1 := d0 :: Γ0; pr2 := d'0 :: Γ'0 |};
          pr2 := All2_fold_cons P b p0
        |}
        (noConfusion_All2_fold_obligation_1 A P
           {|
             pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
             pr2 := All2_fold_cons P a p
           |}
           {|
             pr1 := {| pr1 := d0 :: Γ0; pr2 := d'0 :: Γ'0 |};
             pr2 := All2_fold_cons P b p0
           |} e) = e)


DEBUG:Going to execute:
DepElim.simplify_dep_elim

Goals:
    A : Type  P : list A → list A → A → A → Type
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_All2_fold A P
                                      {|
                                        pr1 := {| pr1 := []; pr2 := [] |};
                                        pr2 := All2_fold_nil P
                                      |}
                                      {|
                                        pr1 := {| pr1 := []; pr2 := [] |};
                                        pr2 := All2_fold_nil P
                                      |}),
      let H0 := CoreTactics.block in
      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 |} e) =
      e)

  
  A : Type
  P : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  b : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_All2_fold A P
                                      {|
                                        pr1 := {| pr1 := []; pr2 := [] |};
                                        pr2 := All2_fold_nil P
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := d :: Γ; pr2 := d' :: Γ'
                                          |};
                                        pr2 := All2_fold_cons P b p
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_All2_fold_obligation_2 A P
        {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
        {|
          pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
          pr2 := All2_fold_cons P b p
        |}
        (noConfusion_All2_fold_obligation_1 A P
           {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
           {|
             pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
             pr2 := All2_fold_cons P b p
           |} e) = e)

  
  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'
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_All2_fold A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := d :: Γ; pr2 := d' :: Γ'
                                          |};
                                        pr2 := All2_fold_cons P a p
                                      |}
                                      {|
                                        pr1 := {| pr1 := []; pr2 := [] |};
                                        pr2 := All2_fold_nil P
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_All2_fold_obligation_2 A P
        {|
          pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
          pr2 := All2_fold_cons P a p
        |} {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
        (noConfusion_All2_fold_obligation_1 A P
           {|
             pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
             pr2 := All2_fold_cons P a p
           |} {| pr1 := {| pr1 := []; pr2 := [] |}; pr2 := All2_fold_nil P |}
           e) = e)

  
  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
  ============================
   (∀ (H := CoreTactics.block) (e : NoConfusion_All2_fold A P
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := d :: Γ; pr2 := d' :: Γ'
                                          |};
                                        pr2 := All2_fold_cons P a p
                                      |}
                                      {|
                                        pr1 :=
                                          {|
                                            pr1 := d0 :: Γ0;
                                            pr2 := d'0 :: Γ'0
                                          |};
                                        pr2 := All2_fold_cons P b p0
                                      |}),
      let H0 := CoreTactics.block in
      noConfusion_All2_fold_obligation_2 A P
        {|
          pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
          pr2 := All2_fold_cons P a p
        |}
        {|
          pr1 := {| pr1 := d0 :: Γ0; pr2 := d'0 :: Γ'0 |};
          pr2 := All2_fold_cons P b p0
        |}
        (noConfusion_All2_fold_obligation_1 A P
           {|
             pr1 := {| pr1 := d :: Γ; pr2 := d' :: Γ' |};
             pr2 := All2_fold_cons P a p
           |}
           {|
             pr1 := {| pr1 := d0 :: Γ0; pr2 := d'0 :: Γ'0 |};
             pr2 := All2_fold_cons P b p0
           |} e) = e)


DEBUG:Going to execute:
repeat DepElim.simplify_one_dep_elim