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


DEBUG:Going to execute:
destruct p

Goals:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  ============================
   ({| pr1 := Γ; pr2 := [] |} = {| pr1 := []; pr2 := [] |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ' d' × Q Γ Γ' d d') Γ [])

  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  d : A
  d' : A
  Γ0 : list A
  Γ' : list A
  H : All2_fold Q Γ0 Γ'
  q : Q Γ0 Γ' d d'
  ============================
   ({| pr1 := Γ; pr2 := [] |} = {| pr1 := d :: Γ0; pr2 := d' :: Γ' |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ' d' × Q Γ Γ' d d') Γ [])

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

  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  d : A
  Γ0 : list A
  X : All_fold P Γ0
  p : P Γ0 d
  IHX : ∀ Γ : list A,
          All2_fold Q Γ Γ0
          → All2_fold (λ (Γ0 Γ' : list A) (d d' : A), P Γ' d' × Q Γ0 Γ' d d')
              Γ Γ0
  d0 : A
  d' : A
  Γ1 : list A
  Γ' : list A
  H : All2_fold Q Γ1 Γ'
  q : Q Γ1 Γ' d0 d'
  ============================
   ({| pr1 := Γ; pr2 := d :: Γ0 |} = {| pr1 := d0 :: Γ1; pr2 := d' :: Γ' |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ' d' × Q Γ Γ' d d') Γ
        (d :: Γ0))


DEBUG:Going to execute:
DepElim.simpl_dep_elim

Goals:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  ============================
   ({| pr1 := Γ; pr2 := [] |} = {| pr1 := []; pr2 := [] |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ' d' × Q Γ Γ' d d') Γ [])

  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  d : A
  d' : A
  Γ0 : list A
  Γ' : list A
  H : All2_fold Q Γ0 Γ'
  q : Q Γ0 Γ' d d'
  ============================
   ({| pr1 := Γ; pr2 := [] |} = {| pr1 := d :: Γ0; pr2 := d' :: Γ' |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ' d' × Q Γ Γ' d d') Γ [])

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

  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  d : A
  Γ0 : list A
  X : All_fold P Γ0
  p : P Γ0 d
  IHX : ∀ Γ : list A,
          All2_fold Q Γ Γ0
          → All2_fold (λ (Γ0 Γ' : list A) (d d' : A), P Γ' d' × Q Γ0 Γ' d d')
              Γ Γ0
  d0 : A
  d' : A
  Γ1 : list A
  Γ' : list A
  H : All2_fold Q Γ1 Γ'
  q : Q Γ1 Γ' d0 d'
  ============================
   ({| pr1 := Γ; pr2 := d :: Γ0 |} = {| pr1 := d0 :: Γ1; pr2 := d' :: Γ' |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ' d' × Q Γ Γ' d d') Γ
        (d :: Γ0))


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

Goals:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  ============================
   ({| pr1 := Γ; pr2 := [] |} = {| pr1 := []; pr2 := [] |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ' d' × Q Γ Γ' d d') Γ [])

  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  d : A
  d' : A
  Γ0 : list A
  Γ' : list A
  H : All2_fold Q Γ0 Γ'
  q : Q Γ0 Γ' d d'
  ============================
   ({| pr1 := Γ; pr2 := [] |} = {| pr1 := d :: Γ0; pr2 := d' :: Γ' |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ' d' × Q Γ Γ' d d') Γ [])

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

  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  d : A
  Γ0 : list A
  X : All_fold P Γ0
  p : P Γ0 d
  IHX : ∀ Γ : list A,
          All2_fold Q Γ Γ0
          → All2_fold (λ (Γ0 Γ' : list A) (d d' : A), P Γ' d' × Q Γ0 Γ' d d')
              Γ Γ0
  d0 : A
  d' : A
  Γ1 : list A
  Γ' : list A
  H : All2_fold Q Γ1 Γ'
  q : Q Γ1 Γ' d0 d'
  ============================
   ({| pr1 := Γ; pr2 := d :: Γ0 |} = {| pr1 := d0 :: Γ1; pr2 := d' :: Γ' |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ' d' × Q Γ Γ' d d') Γ
        (d :: Γ0))


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

Goals:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  ============================
   ({| pr1 := Γ; pr2 := [] |} = {| pr1 := []; pr2 := [] |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ' d' × Q Γ Γ' d d') Γ [])

  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  d : A
  d' : A
  Γ0 : list A
  Γ' : list A
  H : All2_fold Q Γ0 Γ'
  q : Q Γ0 Γ' d d'
  ============================
   ({| pr1 := Γ; pr2 := [] |} = {| pr1 := d :: Γ0; pr2 := d' :: Γ' |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ' d' × Q Γ Γ' d d') Γ [])

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

  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  d : A
  Γ0 : list A
  X : All_fold P Γ0
  p : P Γ0 d
  IHX : ∀ Γ : list A,
          All2_fold Q Γ Γ0
          → All2_fold (λ (Γ0 Γ' : list A) (d d' : A), P Γ' d' × Q Γ0 Γ' d d')
              Γ Γ0
  d0 : A
  d' : A
  Γ1 : list A
  Γ' : list A
  H : All2_fold Q Γ1 Γ'
  q : Q Γ1 Γ' d0 d'
  ============================
   ({| pr1 := Γ; pr2 := d :: Γ0 |} = {| pr1 := d0 :: Γ1; pr2 := d' :: Γ' |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ' d' × Q Γ Γ' d d') Γ
        (d :: Γ0))


DEBUG:Going to execute:
DepElim.simplify_dep_elim

Goals:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  ============================
   ({| pr1 := Γ; pr2 := [] |} = {| pr1 := []; pr2 := [] |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ' d' × Q Γ Γ' d d') Γ [])

  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  d : A
  d' : A
  Γ0 : list A
  Γ' : list A
  H : All2_fold Q Γ0 Γ'
  q : Q Γ0 Γ' d d'
  ============================
   ({| pr1 := Γ; pr2 := [] |} = {| pr1 := d :: Γ0; pr2 := d' :: Γ' |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ' d' × Q Γ Γ' d d') Γ [])

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

  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  d : A
  Γ0 : list A
  X : All_fold P Γ0
  p : P Γ0 d
  IHX : ∀ Γ : list A,
          All2_fold Q Γ Γ0
          → All2_fold (λ (Γ0 Γ' : list A) (d d' : A), P Γ' d' × Q Γ0 Γ' d d')
              Γ Γ0
  d0 : A
  d' : A
  Γ1 : list A
  Γ' : list A
  H : All2_fold Q Γ1 Γ'
  q : Q Γ1 Γ' d0 d'
  ============================
   ({| pr1 := Γ; pr2 := d :: Γ0 |} = {| pr1 := d0 :: Γ1; pr2 := d' :: Γ' |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ' d' × Q Γ Γ' d d') Γ
        (d :: Γ0))


DEBUG:Going to execute:
repeat DepElim.simplify_one_dep_elim