Goal:
  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  X : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  IHX : All_fold Q Γ
        → All_fold Q Γ'
          → All2_fold
              (λ (Γ Γ' : list A) (x y : A), Q Γ x × Q Γ' y × P Γ Γ' x y) Γ Γ'
  l : All_fold Q Γ
  q : Q Γ d
  r1 : list A
  r : All_fold Q r1
  ============================
   (d' :: Γ' = r1
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (x y : A), Q Γ x × Q Γ' y × P Γ Γ' x y)
        (d :: Γ) (d' :: Γ'))


DEBUG:Going to execute:
destruct p

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  X : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  IHX : All_fold Q Γ
        → All_fold Q Γ'
          → All2_fold
              (λ (Γ Γ' : list A) (x y : A), Q Γ x × Q Γ' y × P Γ Γ' x y) Γ Γ'
  l : All_fold Q Γ
  q : Q Γ d
  ============================
   (d' :: Γ' = []
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (x y : A), Q Γ x × Q Γ' y × P Γ Γ' x y)
        (d :: Γ) (d' :: Γ'))

  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  X : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  IHX : All_fold Q Γ
        → All_fold Q Γ'
          → All2_fold
              (λ (Γ Γ' : list A) (x y : A), Q Γ x × Q Γ' y × P Γ Γ' x y) Γ Γ'
  l : All_fold Q Γ
  q : Q Γ d
  d0 : A
  Γ0 : list A
  r : All_fold Q Γ0
  q0 : Q Γ0 d0
  ============================
   (d' :: Γ' = d0 :: Γ0
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (x y : A), Q Γ x × Q Γ' y × P Γ Γ' x y)
        (d :: Γ) (d' :: Γ'))


DEBUG:Going to execute:
DepElim.simpl_dep_elim

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  X : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  IHX : All_fold Q Γ
        → All_fold Q Γ'
          → All2_fold
              (λ (Γ Γ' : list A) (x y : A), Q Γ x × Q Γ' y × P Γ Γ' x y) Γ Γ'
  l : All_fold Q Γ
  q : Q Γ d
  ============================
   (d' :: Γ' = []
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (x y : A), Q Γ x × Q Γ' y × P Γ Γ' x y)
        (d :: Γ) (d' :: Γ'))

  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  X : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  IHX : All_fold Q Γ
        → All_fold Q Γ'
          → All2_fold
              (λ (Γ Γ' : list A) (x y : A), Q Γ x × Q Γ' y × P Γ Γ' x y) Γ Γ'
  l : All_fold Q Γ
  q : Q Γ d
  d0 : A
  Γ0 : list A
  r : All_fold Q Γ0
  q0 : Q Γ0 d0
  ============================
   (d' :: Γ' = d0 :: Γ0
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (x y : A), Q Γ x × Q Γ' y × P Γ Γ' x y)
        (d :: Γ) (d' :: Γ'))


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
  Q : list A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  X : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  IHX : All_fold Q Γ
        → All_fold Q Γ'
          → All2_fold
              (λ (Γ Γ' : list A) (x y : A), Q Γ x × Q Γ' y × P Γ Γ' x y) Γ Γ'
  l : All_fold Q Γ
  q : Q Γ d
  ============================
   (d' :: Γ' = []
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (x y : A), Q Γ x × Q Γ' y × P Γ Γ' x y)
        (d :: Γ) (d' :: Γ'))

  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  X : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  IHX : All_fold Q Γ
        → All_fold Q Γ'
          → All2_fold
              (λ (Γ Γ' : list A) (x y : A), Q Γ x × Q Γ' y × P Γ Γ' x y) Γ Γ'
  l : All_fold Q Γ
  q : Q Γ d
  d0 : A
  Γ0 : list A
  r : All_fold Q Γ0
  q0 : Q Γ0 d0
  ============================
   (d' :: Γ' = d0 :: Γ0
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (x y : A), Q Γ x × Q Γ' y × P Γ Γ' x y)
        (d :: Γ) (d' :: Γ'))


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

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  X : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  IHX : All_fold Q Γ
        → All_fold Q Γ'
          → All2_fold
              (λ (Γ Γ' : list A) (x y : A), Q Γ x × Q Γ' y × P Γ Γ' x y) Γ Γ'
  l : All_fold Q Γ
  q : Q Γ d
  ============================
   (d' :: Γ' = []
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (x y : A), Q Γ x × Q Γ' y × P Γ Γ' x y)
        (d :: Γ) (d' :: Γ'))

  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  X : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  IHX : All_fold Q Γ
        → All_fold Q Γ'
          → All2_fold
              (λ (Γ Γ' : list A) (x y : A), Q Γ x × Q Γ' y × P Γ Γ' x y) Γ Γ'
  l : All_fold Q Γ
  q : Q Γ d
  d0 : A
  Γ0 : list A
  r : All_fold Q Γ0
  q0 : Q Γ0 d0
  ============================
   (d' :: Γ' = d0 :: Γ0
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (x y : A), Q Γ x × Q Γ' y × P Γ Γ' x y)
        (d :: Γ) (d' :: Γ'))


DEBUG:Going to execute:
DepElim.simplify_dep_elim

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  X : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  IHX : All_fold Q Γ
        → All_fold Q Γ'
          → All2_fold
              (λ (Γ Γ' : list A) (x y : A), Q Γ x × Q Γ' y × P Γ Γ' x y) Γ Γ'
  l : All_fold Q Γ
  q : Q Γ d
  ============================
   (d' :: Γ' = []
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (x y : A), Q Γ x × Q Γ' y × P Γ Γ' x y)
        (d :: Γ) (d' :: Γ'))

  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  X : All2_fold P Γ Γ'
  p : P Γ Γ' d d'
  IHX : All_fold Q Γ
        → All_fold Q Γ'
          → All2_fold
              (λ (Γ Γ' : list A) (x y : A), Q Γ x × Q Γ' y × P Γ Γ' x y) Γ Γ'
  l : All_fold Q Γ
  q : Q Γ d
  d0 : A
  Γ0 : list A
  r : All_fold Q Γ0
  q0 : Q Γ0 d0
  ============================
   (d' :: Γ' = d0 :: Γ0
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      All2_fold (λ (Γ Γ' : list A) (x y : A), Q Γ x × Q Γ' y × P Γ Γ' x y)
        (d :: Γ) (d' :: Γ'))


DEBUG:Going to execute:
repeat DepElim.simplify_one_dep_elim