Goal:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  Γ : list A
  a : All_fold P Γ
  H : ∀ (Γ : list A) (d : A),
        All_fold P Γ → All2_fold Q Γ Γ → P Γ d → Q Γ Γ d d
  ============================
   (All2_fold Q Γ Γ)


DEBUG:Going to execute:
induction a

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

  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  H : ∀ (Γ : list A) (d : A),
        All_fold P Γ → All2_fold Q Γ Γ → P Γ d → Q Γ Γ d d
  IHa : All2_fold Q Γ Γ
  ============================
   (All2_fold Q (d :: Γ) (d :: Γ))


DEBUG:Going to execute:
constructor
DEBUG LTAC Evaluated term: a

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

  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  H : ∀ (Γ : list A) (d : A),
        All_fold P Γ → All2_fold Q Γ Γ → P Γ d → Q Γ Γ d d
  IHa : All2_fold Q Γ Γ
  ============================
   (All2_fold Q (d :: Γ) (d :: Γ))


DEBUG:Going to execute:
<coq-core.plugins.ltac::constructor@0>

Goals:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  H : ∀ (Γ : list A) (d : A),
        All_fold P Γ → All2_fold Q Γ Γ → P Γ d → Q Γ Γ d d
  IHa : All2_fold Q Γ Γ
  ============================
   (All2_fold Q Γ Γ)

  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  H : ∀ (Γ : list A) (d : A),
        All_fold P Γ → All2_fold Q Γ Γ → P Γ d → Q Γ Γ d d
  IHa : All2_fold Q Γ Γ
  ============================
   (Q Γ Γ d d)


DEBUG:Going to execute:
auto

Goals:
  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  H : ∀ (Γ : list A) (d : A),
        All_fold P Γ → All2_fold Q Γ Γ → P Γ d → Q Γ Γ d d
  IHa : All2_fold Q Γ Γ
  ============================
   (All2_fold Q Γ Γ)

  
  A : Type
  P : list A → A → Type
  Q : list A → list A → A → A → Type
  d : A
  Γ : list A
  a : All_fold P Γ
  p : P Γ d
  H : ∀ (Γ : list A) (d : A),
        All_fold P Γ → All2_fold Q Γ Γ → P Γ d → Q Γ Γ d d
  IHa : All2_fold Q Γ Γ
  ============================
   (Q Γ Γ d d)


DEBUG:Going to execute:
<coq-core.plugins.ltac::auto@0> $1 $2 $3