Goal:
  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  Δ : list A
  ============================
   (All2_fold P Γ Δ
    → All2_fold Q Γ Δ
      → All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) Γ Δ)


DEBUG:Going to execute:
induction 1

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → A → A → Type
  ============================
   (All2_fold Q [] []
    → All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) [] [])

  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → 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 : All2_fold Q Γ Γ'
        → All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) Γ Γ'
  ============================
   (All2_fold Q (d :: Γ) (d' :: Γ')
    → All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) 
        (d :: Γ) (d' :: Γ'))


DEBUG:Going to execute:
intros h

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → A → A → Type
  h : All2_fold Q [] []
  ============================
   (All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) [] [])

  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → 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 : All2_fold Q Γ Γ'
        → All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) Γ Γ'
  h : All2_fold Q (d :: Γ) (d' :: Γ')
  ============================
   (All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) 
      (d :: Γ) (d' :: Γ'))


DEBUG:Going to execute:
depelim h

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → A → A → Type
  h : All2_fold Q [] []
  ============================
   (All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) [] [])

  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → 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 : All2_fold Q Γ Γ'
        → All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) Γ Γ'
  h : All2_fold Q (d :: Γ) (d' :: Γ')
  ============================
   (All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) 
      (d :: Γ) (d' :: Γ'))


DEBUG:Going to execute:
fun H => DepElim.depelim H

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → A → A → Type
  h : All2_fold Q [] []
  ============================
   (All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) [] [])

  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → 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 : All2_fold Q Γ Γ'
        → All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) Γ Γ'
  h : All2_fold Q (d :: Γ) (d' :: Γ')
  ============================
   (All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) 
      (d :: Γ) (d' :: Γ'))


DEBUG:Going to execute:
DepElim.depelim H

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → A → A → Type
  h : All2_fold Q [] []
  ============================
   (All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) [] [])

  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → 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 : All2_fold Q Γ Γ'
        → All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) Γ Γ'
  h : All2_fold Q (d :: Γ) (d' :: Γ')
  ============================
   (All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) 
      (d :: Γ) (d' :: Γ'))


DEBUG:Going to execute:
fun id =>
             DepElim.do_depelim ltac:(fun hyp => DepElim.do_case hyp) id

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → A → A → Type
  h : All2_fold Q [] []
  ============================
   (All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) [] [])

  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → 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 : All2_fold Q Γ Γ'
        → All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) Γ Γ'
  h : All2_fold Q (d :: Γ) (d' :: Γ')
  ============================
   (All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) 
      (d :: Γ) (d' :: Γ'))


DEBUG:Going to execute:
DepElim.do_depelim ltac:(fun hyp => DepElim.do_case hyp) id

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → A → A → Type
  h : All2_fold Q [] []
  ============================
   (All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) [] [])

  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → 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 : All2_fold Q Γ Γ'
        → All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) Γ Γ'
  h : All2_fold Q (d :: Γ) (d' :: Γ')
  ============================
   (All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) 
      (d :: Γ) (d' :: Γ'))


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 → list A → A → A → Type
  Q : list A → list A → A → A → Type
  h : All2_fold Q [] []
  ============================
   (All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) [] [])

  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → 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 : All2_fold Q Γ Γ'
        → All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) Γ Γ'
  h : All2_fold Q (d :: Γ) (d' :: Γ')
  ============================
   (All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) 
      (d :: Γ) (d' :: Γ'))


DEBUG:Going to execute:
fun hyp => DepElim.do_case hyp

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → A → A → Type
  h : All2_fold Q [] []
  ============================
   (All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) [] [])

  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → 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 : All2_fold Q Γ Γ'
        → All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) Γ Γ'
  h : All2_fold Q (d :: Γ) (d' :: Γ')
  ============================
   (All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) 
      (d :: Γ) (d' :: Γ'))


DEBUG:Going to execute:
DepElim.do_depelim_nosimpl tac H; DepElim.simpl_dep_elim;
            CoreTactics.unblock_goal

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → A → A → Type
  h : All2_fold Q [] []
  ============================
   (All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) [] [])

  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → 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 : All2_fold Q Γ Γ'
        → All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) Γ Γ'
  h : All2_fold Q (d :: Γ) (d' :: Γ')
  ============================
   (All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) 
      (d :: Γ) (d' :: Γ'))


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 → list A → A → A → Type
  Q : list A → list A → A → A → Type
  h : All2_fold Q [] []
  ============================
   (All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) [] [])

  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → 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 : All2_fold Q Γ Γ'
        → All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) Γ Γ'
  h : All2_fold Q (d :: Γ) (d' :: Γ')
  ============================
   (All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) 
      (d :: Γ) (d' :: Γ'))


DEBUG:Going to execute:
DepElim.do_depelim_nosimpl tac H

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → A → A → Type
  h : All2_fold Q [] []
  ============================
   (All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) [] [])

  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → 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 : All2_fold Q Γ Γ'
        → All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) Γ Γ'
  h : All2_fold Q (d :: Γ) (d' :: Γ')
  ============================
   (All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) 
      (d :: Γ) (d' :: Γ'))


DEBUG:Going to execute:
fun tac H =>
             DepElim.do_intros H; DepElim.generalize_by_eqs H; tac H

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → A → A → Type
  h : All2_fold Q [] []
  ============================
   (All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) [] [])

  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → 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 : All2_fold Q Γ Γ'
        → All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) Γ Γ'
  h : All2_fold Q (d :: Γ) (d' :: Γ')
  ============================
   (All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) 
      (d :: Γ) (d' :: Γ'))


DEBUG:Going to execute:
DepElim.do_intros H; DepElim.generalize_by_eqs H; tac H

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → A → A → Type
  h : All2_fold Q [] []
  ============================
   (All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) [] [])

  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → 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 : All2_fold Q Γ Γ'
        → All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) Γ Γ'
  h : All2_fold Q (d :: Γ) (d' :: Γ')
  ============================
   (All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) 
      (d :: Γ) (d' :: Γ'))


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 → list A → A → A → Type
  Q : list A → list A → A → A → Type
  h : All2_fold Q [] []
  ============================
   (All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) [] [])

  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → 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 : All2_fold Q Γ Γ'
        → All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) Γ Γ'
  h : All2_fold Q (d :: Γ) (d' :: Γ')
  ============================
   (All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) 
      (d :: Γ) (d' :: Γ'))


DEBUG:Going to execute:
DepElim.do_intros H

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → A → A → Type
  h : All2_fold Q [] []
  ============================
   (All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) [] [])

  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → 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 : All2_fold Q Γ Γ'
        → All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) Γ Γ'
  h : All2_fold Q (d :: Γ) (d' :: Γ')
  ============================
   (All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) 
      (d :: Γ) (d' :: Γ'))


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 → list A → A → A → Type
  Q : list A → list A → A → A → Type
  h : All2_fold Q [] []
  ============================
   (All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) [] [])

  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → 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 : All2_fold Q Γ Γ'
        → All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) Γ Γ'
  h : All2_fold Q (d :: Γ) (d' :: Γ')
  ============================
   (All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) 
      (d :: Γ) (d' :: Γ'))


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 → list A → A → A → Type
  Q : list A → list A → A → A → Type
  h : All2_fold Q [] []
  ============================
   (All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) [] [])

  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → 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 : All2_fold Q Γ Γ'
        → All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) Γ Γ'
  h : All2_fold Q (d :: Γ) (d' :: Γ')
  ============================
   (All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) 
      (d :: Γ) (d' :: Γ'))


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 → list A → A → A → Type
  Q : list A → list A → A → A → Type
  h : All2_fold Q [] []
  ============================
   (All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) [] [])

  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → list A → 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 : All2_fold Q Γ Γ'
        → All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) Γ Γ'
  h : All2_fold Q (d :: Γ) (d' :: Γ')
  ============================
   (All2_fold (λ (Γ Δ : list A) (x y : A), P Γ Δ x y × Q Γ Δ x y) 
      (d :: Γ) (d' :: Γ'))


DEBUG:Going to execute:
try intros until H