Goal:
  
  A : Type
  P : list A → list A → A → A → Type
  n : nat
  a : A
  Γ : list A
  d' : A
  Γ'0 : list A
  d : A
  IHn : ∀ (Γ Γ' : list A) (d : A),
          All2_fold P Γ Γ'
          → nth_error Γ n = Some d
            → ∑ d' : A,
                nth_error Γ' n = Some d'
                × All2_fold P (skipn (S n) Γ) (skipn (S n) Γ')
                  × P (skipn (S n) Γ) (skipn (S n) Γ') d d'
  Hrel : All2_fold P Γ Γ'0
  p : P Γ Γ'0 a d'
  H : nth_error Γ n = Some d
  x : A
  p0 : nth_error Γ'0 n = Some x
       × All2_fold P (skipn (S n) Γ) (skipn (S n) Γ'0)
         × P (skipn (S n) Γ) (skipn (S n) Γ'0) d x
  ============================
   (nth_error Γ'0 n = Some ?d'
    × All2_fold P (skipn (S (S n)) (a :: Γ)) (skipn (S (S n)) (d' :: Γ'0))
      × P (skipn (S (S n)) (a :: Γ)) (skipn (S (S n)) (d' :: Γ'0)) d ?d')


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