Goal:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  Γ' : list A
  ============================
   (All_fold P Γ'
    → All2_fold Q Γ Γ'
      → All2_fold (λ (Γ Γ' : list A) (d d' : A), P Γ' d' × Q Γ Γ' d d') Γ Γ')


DEBUG:Going to execute:
induction 1 in Γ |- *

Goals:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  ============================
   (All2_fold Q Γ []
    → 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
  ============================
   (All2_fold Q Γ (d :: Γ0)
    → 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:
intros H

Goals:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  H : All2_fold Q Γ []
  ============================
   (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
  H : All2_fold Q Γ (d :: Γ0)
  ============================
   (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 H

Goals:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  H : All2_fold Q Γ []
  ============================
   (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
  H : All2_fold Q Γ (d :: Γ0)
  ============================
   (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:
fun H => DepElim.depelim H

Goals:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  H : All2_fold Q Γ []
  ============================
   (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
  H : All2_fold Q Γ (d :: Γ0)
  ============================
   (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.depelim H

Goals:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  H : All2_fold Q Γ []
  ============================
   (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
  H : All2_fold Q Γ (d :: Γ0)
  ============================
   (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:
fun id =>
             DepElim.do_depelim ltac:(fun hyp => DepElim.do_case hyp) id

Goals:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  H : All2_fold Q Γ []
  ============================
   (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
  H : All2_fold Q Γ (d :: Γ0)
  ============================
   (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.do_depelim ltac:(fun hyp => DepElim.do_case hyp) id

Goals:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  H : All2_fold Q Γ []
  ============================
   (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
  H : All2_fold Q Γ (d :: Γ0)
  ============================
   (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:
fun tac H =>
             DepElim.do_depelim_nosimpl tac H; DepElim.simpl_dep_elim;
              CoreTactics.unblock_goal

Goals:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  H : All2_fold Q Γ []
  ============================
   (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
  H : All2_fold Q Γ (d :: Γ0)
  ============================
   (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:
fun hyp => DepElim.do_case hyp

Goals:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  H : All2_fold Q Γ []
  ============================
   (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
  H : All2_fold Q Γ (d :: Γ0)
  ============================
   (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.do_depelim_nosimpl tac H; DepElim.simpl_dep_elim;
            CoreTactics.unblock_goal

Goals:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  H : All2_fold Q Γ []
  ============================
   (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
  H : All2_fold Q Γ (d :: Γ0)
  ============================
   (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.do_depelim_nosimpl tac H; DepElim.simpl_dep_elim
Level 3: evaluation returns
DepElim.do_depelim_nosimpl tac H; DepElim.simpl_dep_elim;
 CoreTactics.unblock_goal
where
tac := fun hyp => DepElim.do_case hyp
       where
       id := H
       of type
       ident
of type
tacvalue
H := H
of type
ident of type tacvalue

Level 3: evaluation returns
DepElim.do_depelim_nosimpl tac H; DepElim.simpl_dep_elim;
 CoreTactics.unblock_goal
where
tac := fun hyp => DepElim.do_case hyp
       where
       id := H
       of type
       ident
of type
tacvalue
H := H
of type
ident of type tacvalue

Level 2: evaluation returns
DepElim.do_depelim_nosimpl tac H; DepElim.simpl_dep_elim;
 CoreTactics.unblock_goal
where
tac := fun hyp => DepElim.do_case hyp
       where
       id := H
       of type
       ident
of type
tacvalue
H := H
of type
ident of type tacvalue

Level 2: evaluation returns
DepElim.do_depelim_nosimpl tac H; DepElim.simpl_dep_elim;
 CoreTactics.unblock_goal
where
tac := fun hyp => DepElim.do_case hyp
       where
       id := H
       of type
       ident
of type
tacvalue
H := H
of type
ident of type tacvalue

Level 1: evaluation returns
DepElim.do_depelim_nosimpl tac H; DepElim.simpl_dep_elim;
 CoreTactics.unblock_goal
where
tac := fun hyp => DepElim.do_case hyp
       where
       id := H
       of type
       ident
of type
tacvalue
H := H
of type
ident of type tacvalue

Level 1: evaluation returns
DepElim.do_depelim_nosimpl tac H; DepElim.simpl_dep_elim;
 CoreTactics.unblock_goal
where
tac := fun hyp => DepElim.do_case hyp
       where
       id := H
       of type
       ident
of type
tacvalue
H := H
of type
ident of type tacvalue


Goals:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  H : All2_fold Q Γ []
  ============================
   (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
  H : All2_fold Q Γ (d :: Γ0)
  ============================
   (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.do_depelim_nosimpl tac H

Goals:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  H : All2_fold Q Γ []
  ============================
   (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
  H : All2_fold Q Γ (d :: Γ0)
  ============================
   (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:
fun tac H =>
             DepElim.do_intros H; DepElim.generalize_by_eqs H; tac H

Goals:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  H : All2_fold Q Γ []
  ============================
   (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
  H : All2_fold Q Γ (d :: Γ0)
  ============================
   (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.do_intros H; DepElim.generalize_by_eqs H; tac H

Goals:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  H : All2_fold Q Γ []
  ============================
   (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
  H : All2_fold Q Γ (d :: Γ0)
  ============================
   (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.do_intros H; DepElim.generalize_by_eqs H
Level 1: evaluation returns
DepElim.do_intros H; DepElim.generalize_by_eqs H; tac H
where
tac := fun hyp => DepElim.do_case hyp
       where
       id := H
       of type
       ident
of type
tacvalue
H := H
of type
ident of type tacvalue

Level 1: evaluation returns
DepElim.do_intros H; DepElim.generalize_by_eqs H; tac H
where
tac := fun hyp => DepElim.do_case hyp
       where
       id := H
       of type
       ident
of type
tacvalue
H := H
of type
ident of type tacvalue


Goals:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  H : All2_fold Q Γ []
  ============================
   (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
  H : All2_fold Q Γ (d :: Γ0)
  ============================
   (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.do_intros H

Goals:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  H : All2_fold Q Γ []
  ============================
   (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
  H : All2_fold Q Γ (d :: Γ0)
  ============================
   (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:
fun H =>
             try intros until H; intro_block_id H || intro_block H;
              (try simpl in H; DepElim.simplify_equations_in H)

Goals:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  H : All2_fold Q Γ []
  ============================
   (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
  H : All2_fold Q Γ (d :: Γ0)
  ============================
   (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:
try intros until H; intro_block_id H || intro_block H;
            (try simpl in H; DepElim.simplify_equations_in H)

Goals:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  H : All2_fold Q Γ []
  ============================
   (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
  H : All2_fold Q Γ (d :: Γ0)
  ============================
   (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:
try intros until H; intro_block_id H || intro_block H
Level 1: evaluation returns
try intros until H; intro_block_id H || intro_block H;
 (try simpl in H; DepElim.simplify_equations_in H)
where
H := H
of type
ident of type tacvalue

Level 1: evaluation returns
try intros until H; intro_block_id H || intro_block H;
 (try simpl in H; DepElim.simplify_equations_in H)
where
H := H
of type
ident of type tacvalue


Goals:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  H : All2_fold Q Γ []
  ============================
   (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
  H : All2_fold Q Γ (d :: Γ0)
  ============================
   (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:
try intros until H