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


DEBUG:Going to execute:
induction 1; split