Goal:
  
  A : Type
  P : list A → list A → A → A → Type
  Γ : list A
  Γ' : list A
  a : A
  Δ : list A
  H : #|Γ| = #|Γ'|
  IHΔ : ∀ Γ Γ' Δ' : list A,
          #|Γ| = #|Γ'|
          → 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'
  H' : All2_fold P ((a :: Δ) ++ Γ) ([] ++ Γ')
  H0 : S (#|Δ| + #|Γ|) = #|Γ'|
  ============================
   (All2_fold P Γ Γ'
    × All2_fold (λ Δ Δ' : list A, P (Δ ++ Γ) (Δ' ++ Γ')) (a :: Δ) [])


DEBUG:Going to execute:
idtac