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


DEBUG:Going to execute:
fun => <coq-core.plugins.ltac::split@0>

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  Γ' : list A
  H : #|Γ| = #|Γ'|
  X : All2_fold P ([] ++ Γ) ([] ++ Γ')
  ============================
   (All2_fold P Γ Γ')

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


DEBUG:Going to execute:
<Coq.Init.Tauto.not_dep_intros>

Goals:
  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  Γ' : list A
  H : #|Γ| = #|Γ'|
  X : All2_fold P ([] ++ Γ) ([] ++ Γ')
  ============================
   (All2_fold P Γ Γ')

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


DEBUG:Going to execute:
repeat
            match goal with
            | |- ?X1 → ?X2 => intro
            | |- ¬ _ => unfold not at 1; intro
            end