Goal:
  
  A : Type
  P : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  H : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  IHAll2_fold : ∀ (H := CoreTactics.block) (Γ0 : list A),
                  {| pr1 := Γ0; pr2 := Γ0 |} = {| pr1 := Γ; pr2 := Γ' |}
                  → let H0 := CoreTactics.block in
                    let H1 := CoreTactics.block in
                    All_fold (λ (Γ : list A) (d : A), P Γ Γ d d) Γ0
  ============================
   (∀ (H := CoreTactics.block) (Γ0 : list A),
      {| pr1 := Γ0; pr2 := Γ0 |} = {| pr1 := d :: Γ; pr2 := d' :: Γ' |}
      → let H0 := CoreTactics.block in
        let H1 := CoreTactics.block in
        All_fold (λ (Γ : list A) (d : A), P Γ Γ d d) Γ0)


DEBUG:Going to execute:
intros _

Goals:
    A : Type  P : list A → list A → A → A → Type
  ============================
   (∀ Γ : list A,
      {| pr1 := Γ; pr2 := Γ |} = {| pr1 := []; pr2 := [] |}
      → let H := CoreTactics.block in
        let H0 := CoreTactics.block in
        All_fold (λ (Γ0 : list A) (d : A), P Γ0 Γ0 d d) Γ)

  
  A : Type
  P : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  H : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  IHAll2_fold : ∀ (H := CoreTactics.block) (Γ0 : list A),
                  {| pr1 := Γ0; pr2 := Γ0 |} = {| pr1 := Γ; pr2 := Γ' |}
                  → let H0 := CoreTactics.block in
                    let H1 := CoreTactics.block in
                    All_fold (λ (Γ : list A) (d : A), P Γ Γ d d) Γ0
  ============================
   (∀ Γ0 : list A,
      {| pr1 := Γ0; pr2 := Γ0 |} = {| pr1 := d :: Γ; pr2 := d' :: Γ' |}
      → let H := CoreTactics.block in
        let H0 := CoreTactics.block in
        All_fold (λ (Γ : list A) (d : A), P Γ Γ d d) Γ0)


DEBUG:Going to execute:
DepElim.simpl_dep_elim

Goals:
    A : Type  P : list A → list A → A → A → Type
  ============================
   (∀ Γ : list A,
      {| pr1 := Γ; pr2 := Γ |} = {| pr1 := []; pr2 := [] |}
      → let H := CoreTactics.block in
        let H0 := CoreTactics.block in
        All_fold (λ (Γ0 : list A) (d : A), P Γ0 Γ0 d d) Γ)

  
  A : Type
  P : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  H : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  IHAll2_fold : ∀ (H := CoreTactics.block) (Γ0 : list A),
                  {| pr1 := Γ0; pr2 := Γ0 |} = {| pr1 := Γ; pr2 := Γ' |}
                  → let H0 := CoreTactics.block in
                    let H1 := CoreTactics.block in
                    All_fold (λ (Γ : list A) (d : A), P Γ Γ d d) Γ0
  ============================
   (∀ Γ0 : list A,
      {| pr1 := Γ0; pr2 := Γ0 |} = {| pr1 := d :: Γ; pr2 := d' :: Γ' |}
      → let H := CoreTactics.block in
        let H0 := CoreTactics.block in
        All_fold (λ (Γ : list A) (d : A), P Γ Γ d d) Γ0)


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
  ============================
   (∀ Γ : list A,
      {| pr1 := Γ; pr2 := Γ |} = {| pr1 := []; pr2 := [] |}
      → let H := CoreTactics.block in
        let H0 := CoreTactics.block in
        All_fold (λ (Γ0 : list A) (d : A), P Γ0 Γ0 d d) Γ)

  
  A : Type
  P : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  H : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  IHAll2_fold : ∀ (H := CoreTactics.block) (Γ0 : list A),
                  {| pr1 := Γ0; pr2 := Γ0 |} = {| pr1 := Γ; pr2 := Γ' |}
                  → let H0 := CoreTactics.block in
                    let H1 := CoreTactics.block in
                    All_fold (λ (Γ : list A) (d : A), P Γ Γ d d) Γ0
  ============================
   (∀ Γ0 : list A,
      {| pr1 := Γ0; pr2 := Γ0 |} = {| pr1 := d :: Γ; pr2 := d' :: Γ' |}
      → let H := CoreTactics.block in
        let H0 := CoreTactics.block in
        All_fold (λ (Γ : list A) (d : A), P Γ Γ d d) Γ0)


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

Goals:
    A : Type  P : list A → list A → A → A → Type
  ============================
   (∀ Γ : list A,
      {| pr1 := Γ; pr2 := Γ |} = {| pr1 := []; pr2 := [] |}
      → let H := CoreTactics.block in
        let H0 := CoreTactics.block in
        All_fold (λ (Γ0 : list A) (d : A), P Γ0 Γ0 d d) Γ)

  
  A : Type
  P : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  H : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  IHAll2_fold : ∀ (H := CoreTactics.block) (Γ0 : list A),
                  {| pr1 := Γ0; pr2 := Γ0 |} = {| pr1 := Γ; pr2 := Γ' |}
                  → let H0 := CoreTactics.block in
                    let H1 := CoreTactics.block in
                    All_fold (λ (Γ : list A) (d : A), P Γ Γ d d) Γ0
  ============================
   (∀ Γ0 : list A,
      {| pr1 := Γ0; pr2 := Γ0 |} = {| pr1 := d :: Γ; pr2 := d' :: Γ' |}
      → let H := CoreTactics.block in
        let H0 := CoreTactics.block in
        All_fold (λ (Γ : list A) (d : A), P Γ Γ d d) Γ0)


DEBUG:Going to execute:
DepElim.simplify_dep_elim

Goals:
    A : Type  P : list A → list A → A → A → Type
  ============================
   (∀ Γ : list A,
      {| pr1 := Γ; pr2 := Γ |} = {| pr1 := []; pr2 := [] |}
      → let H := CoreTactics.block in
        let H0 := CoreTactics.block in
        All_fold (λ (Γ0 : list A) (d : A), P Γ0 Γ0 d d) Γ)

  
  A : Type
  P : list A → list A → A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  H : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  IHAll2_fold : ∀ (H := CoreTactics.block) (Γ0 : list A),
                  {| pr1 := Γ0; pr2 := Γ0 |} = {| pr1 := Γ; pr2 := Γ' |}
                  → let H0 := CoreTactics.block in
                    let H1 := CoreTactics.block in
                    All_fold (λ (Γ : list A) (d : A), P Γ Γ d d) Γ0
  ============================
   (∀ Γ0 : list A,
      {| pr1 := Γ0; pr2 := Γ0 |} = {| pr1 := d :: Γ; pr2 := d' :: Γ' |}
      → let H := CoreTactics.block in
        let H0 := CoreTactics.block in
        All_fold (λ (Γ : list A) (d : A), P Γ Γ d d) Γ0)


DEBUG:Going to execute:
repeat DepElim.simplify_one_dep_elim