Goal:
  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  Γ' : list A
  Δ : list A
  Δ' : list A
  H : #|Δ| = #|Δ'|
  ============================
   (All2_fold P (Δ ++ Γ) (Δ' ++ Γ')
    → All2_fold P Γ Γ'
      × All2_fold (λ Δ Δ' : list A, P (Δ ++ Γ) (Δ' ++ Γ')) Δ Δ')


DEBUG:Going to execute:
induction Δ in H, Δ', Γ, Γ' |- *

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  Γ' : list A
  Δ' : list A
  H : #|[]| = #|Δ'|
  ============================
   (All2_fold P ([] ++ Γ) (Δ' ++ Γ')
    → All2_fold P Γ Γ'
      × All2_fold (λ Δ Δ' : list A, P (Δ ++ Γ) (Δ' ++ Γ')) [] Δ')

  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  Γ' : list A
  a : A
  Δ : list A
  Δ' : list A
  H : #|a :: Δ| = #|Δ'|
  IHΔ : ∀ Γ Γ' Δ' : list A,
          #|Δ| = #|Δ'|
          → All2_fold P (Δ ++ Γ) (Δ' ++ Γ')
            → All2_fold P Γ Γ'
              × All2_fold (λ Δ Δ'0 : list A, P (Δ ++ Γ) (Δ'0 ++ Γ')) Δ Δ'
  ============================
   (All2_fold P ((a :: Δ) ++ Γ) (Δ' ++ Γ')
    → All2_fold P Γ Γ'
      × All2_fold (λ Δ Δ' : list A, P (Δ ++ Γ) (Δ' ++ Γ')) (a :: Δ) Δ')


DEBUG:Going to execute:
destruct Δ'
DEBUG LTAC Evaluated term: Δ

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  Γ' : list A
  H : #|[]| = #|[]|
  ============================
   (All2_fold P ([] ++ Γ) ([] ++ Γ')
    → All2_fold P Γ Γ'
      × All2_fold (λ Δ Δ' : list A, P (Δ ++ Γ) (Δ' ++ Γ')) [] [])

  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  Γ' : list A
  a : A
  Δ' : list A
  H : #|[]| = #|a :: Δ'|
  ============================
   (All2_fold P ([] ++ Γ) ((a :: Δ') ++ Γ')
    → All2_fold P Γ Γ'
      × All2_fold (λ Δ Δ' : list A, P (Δ ++ Γ) (Δ' ++ Γ')) [] (a :: Δ'))

  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  Γ' : list A
  a : A
  Δ : list A
  H : #|a :: Δ| = #|[]|
  IHΔ : ∀ Γ Γ' Δ' : list A,
          #|Δ| = #|Δ'|
          → All2_fold P (Δ ++ Γ) (Δ' ++ Γ')
            → All2_fold P Γ Γ'
              × All2_fold (λ Δ Δ'0 : list A, P (Δ ++ Γ) (Δ'0 ++ Γ')) Δ Δ'
  ============================
   (All2_fold P ((a :: Δ) ++ Γ) ([] ++ Γ')
    → All2_fold P Γ Γ'
      × All2_fold (λ Δ Δ' : list A, P (Δ ++ Γ) (Δ' ++ Γ')) (a :: Δ) [])

  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  Γ' : list A
  a : A
  Δ : list A
  a0 : A
  Δ' : list A
  H : #|a :: Δ| = #|a0 :: Δ'|
  IHΔ : ∀ Γ Γ' Δ' : list A,
          #|Δ| = #|Δ'|
          → All2_fold P (Δ ++ Γ) (Δ' ++ Γ')
            → All2_fold P Γ Γ'
              × All2_fold (λ Δ Δ'0 : list A, P (Δ ++ Γ) (Δ'0 ++ Γ')) Δ Δ'
  ============================
   (All2_fold P ((a :: Δ) ++ Γ) ((a0 :: Δ') ++ Γ')
    → All2_fold P Γ Γ'
      × All2_fold (λ Δ Δ' : list A, P (Δ ++ Γ) (Δ' ++ Γ')) 
          (a :: Δ) (a0 :: Δ'))


DEBUG:Going to execute:
try discriminate
DEBUG LTAC Evaluated term: Δ'
DEBUG LTAC Evaluated term: Δ'