Goal:
  
  A : Type
  P : list A → list A → A → A → Type
  Q : list A → A → Type
  d : A
  d' : A
  Γ : list A
  Γ' : list A
  X : All2_fold (λ (Γ Γ' : list A) (x y : A), Q Γ x × Q Γ' y × P Γ Γ' x y) Γ
        Γ'
  IHX : All2_fold P Γ Γ' × All_fold Q Γ × All_fold Q Γ'
  a : Q Γ d
  b : Q Γ' d' × P Γ Γ' d d'
  ============================
   (All2_fold P Γ Γ'
    → All_fold Q Γ × All_fold Q Γ'
      → All2_fold P (d :: Γ) (d' :: Γ')
        × All_fold Q (d :: Γ) × All_fold Q (d' :: Γ'))


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